1.2 The Scientific Methods

Section learning objectives.

By the end of this section, you will be able to do the following:

  • Explain how the methods of science are used to make scientific discoveries
  • Define a scientific model and describe examples of physical and mathematical models used in physics
  • Compare and contrast hypothesis, theory, and law

Teacher Support

The learning objectives in this section will help your students master the following standards:

  • (A) know the definition of science and understand that it has limitations, as specified in subsection (b)(2) of this section;
  • (B) know that scientific hypotheses are tentative and testable statements that must be capable of being supported or not supported by observational evidence. Hypotheses of durable explanatory power which have been tested over a wide variety of conditions are incorporated into theories;
  • (C) know that scientific theories are based on natural and physical phenomena and are capable of being tested by multiple independent researchers. Unlike hypotheses, scientific theories are well-established and highly-reliable explanations, but may be subject to change as new areas of science and new technologies are developed;
  • (D) distinguish between scientific hypotheses and scientific theories.

Section Key Terms

[OL] Pre-assessment for this section could involve students sharing or writing down an anecdote about when they used the methods of science. Then, students could label their thought processes in their anecdote with the appropriate scientific methods. The class could also discuss their definitions of theory and law, both outside and within the context of science.

[OL] It should be noted and possibly mentioned that a scientist , as mentioned in this section, does not necessarily mean a trained scientist. It could be anyone using methods of science.

Scientific Methods

Scientists often plan and carry out investigations to answer questions about the universe around us. These investigations may lead to natural laws. Such laws are intrinsic to the universe, meaning that humans did not create them and cannot change them. We can only discover and understand them. Their discovery is a very human endeavor, with all the elements of mystery, imagination, struggle, triumph, and disappointment inherent in any creative effort. The cornerstone of discovering natural laws is observation. Science must describe the universe as it is, not as we imagine or wish it to be.

We all are curious to some extent. We look around, make generalizations, and try to understand what we see. For example, we look up and wonder whether one type of cloud signals an oncoming storm. As we become serious about exploring nature, we become more organized and formal in collecting and analyzing data. We attempt greater precision, perform controlled experiments (if we can), and write down ideas about how data may be organized. We then formulate models, theories, and laws based on the data we have collected, and communicate those results with others. This, in a nutshell, describes the scientific method that scientists employ to decide scientific issues on the basis of evidence from observation and experiment.

An investigation often begins with a scientist making an observation . The scientist observes a pattern or trend within the natural world. Observation may generate questions that the scientist wishes to answer. Next, the scientist may perform some research about the topic and devise a hypothesis . A hypothesis is a testable statement that describes how something in the natural world works. In essence, a hypothesis is an educated guess that explains something about an observation.

[OL] An educated guess is used throughout this section in describing a hypothesis to combat the tendency to think of a theory as an educated guess.

Scientists may test the hypothesis by performing an experiment . During an experiment, the scientist collects data that will help them learn about the phenomenon they are studying. Then the scientists analyze the results of the experiment (that is, the data), often using statistical, mathematical, and/or graphical methods. From the data analysis, they draw conclusions. They may conclude that their experiment either supports or rejects their hypothesis. If the hypothesis is supported, the scientist usually goes on to test another hypothesis related to the first. If their hypothesis is rejected, they will often then test a new and different hypothesis in their effort to learn more about whatever they are studying.

Scientific processes can be applied to many situations. Let’s say that you try to turn on your car, but it will not start. You have just made an observation! You ask yourself, "Why won’t my car start?" You can now use scientific processes to answer this question. First, you generate a hypothesis such as, "The car won’t start because it has no gasoline in the gas tank." To test this hypothesis, you put gasoline in the car and try to start it again. If the car starts, then your hypothesis is supported by the experiment. If the car does not start, then your hypothesis is rejected. You will then need to think up a new hypothesis to test such as, "My car won’t start because the fuel pump is broken." Hopefully, your investigations lead you to discover why the car won’t start and enable you to fix it.

A model is a representation of something that is often too difficult (or impossible) to study directly. Models can take the form of physical models, equations, computer programs, or simulations—computer graphics/animations. Models are tools that are especially useful in modern physics because they let us visualize phenomena that we normally cannot observe with our senses, such as very small objects or objects that move at high speeds. For example, we can understand the structure of an atom using models, without seeing an atom with our own eyes. Although images of single atoms are now possible, these images are extremely difficult to achieve and are only possible due to the success of our models. The existence of these images is a consequence rather than a source of our understanding of atoms. Models are always approximate, so they are simpler to consider than the real situation; the more complete a model is, the more complicated it must be. Models put the intangible or the extremely complex into human terms that we can visualize, discuss, and hypothesize about.

Scientific models are constructed based on the results of previous experiments. Even still, models often only describe a phenomenon partially or in a few limited situations. Some phenomena are so complex that they may be impossible to model them in their entirety, even using computers. An example is the electron cloud model of the atom in which electrons are moving around the atom’s center in distinct clouds ( Figure 1.12 ), that represent the likelihood of finding an electron in different places. This model helps us to visualize the structure of an atom. However, it does not show us exactly where an electron will be within its cloud at any one particular time.

As mentioned previously, physicists use a variety of models including equations, physical models, computer simulations, etc. For example, three-dimensional models are often commonly used in chemistry and physics to model molecules. Properties other than appearance or location are usually modelled using mathematics, where functions are used to show how these properties relate to one another. Processes such as the formation of a star or the planets, can also be modelled using computer simulations. Once a simulation is correctly programmed based on actual experimental data, the simulation can allow us to view processes that happened in the past or happen too quickly or slowly for us to observe directly. In addition, scientists can also run virtual experiments using computer-based models. In a model of planet formation, for example, the scientist could alter the amount or type of rocks present in space and see how it affects planet formation.

Scientists use models and experimental results to construct explanations of observations or design solutions to problems. For example, one way to make a car more fuel efficient is to reduce the friction or drag caused by air flowing around the moving car. This can be done by designing the body shape of the car to be more aerodynamic, such as by using rounded corners instead of sharp ones. Engineers can then construct physical models of the car body, place them in a wind tunnel, and examine the flow of air around the model. This can also be done mathematically in a computer simulation. The air flow pattern can be analyzed for regions smooth air flow and for eddies that indicate drag. The model of the car body may have to be altered slightly to produce the smoothest pattern of air flow (i.e., the least drag). The pattern with the least drag may be the solution to increasing fuel efficiency of the car. This solution might then be incorporated into the car design.

Using Models and the Scientific Processes

Be sure to secure loose items before opening the window or door.

In this activity, you will learn about scientific models by making a model of how air flows through your classroom or a room in your house.

  • One room with at least one window or door that can be opened
  • Work with a group of four, as directed by your teacher. Close all of the windows and doors in the room you are working in. Your teacher may assign you a specific window or door to study.
  • Before opening any windows or doors, draw a to-scale diagram of your room. First, measure the length and width of your room using the tape measure. Then, transform the measurement using a scale that could fit on your paper, such as 5 centimeters = 1 meter.
  • Your teacher will assign you a specific window or door to study air flow. On your diagram, add arrows showing your hypothesis (before opening any windows or doors) of how air will flow through the room when your assigned window or door is opened. Use pencil so that you can easily make changes to your diagram.
  • On your diagram, mark four locations where you would like to test air flow in your room. To test for airflow, hold a strip of single ply tissue paper between the thumb and index finger. Note the direction that the paper moves when exposed to the airflow. Then, for each location, predict which way the paper will move if your air flow diagram is correct.
  • Now, each member of your group will stand in one of the four selected areas. Each member will test the airflow Agree upon an approximate height at which everyone will hold their papers.
  • When you teacher tells you to, open your assigned window and/or door. Each person should note the direction that their paper points immediately after the window or door was opened. Record your results on your diagram.
  • Did the airflow test data support or refute the hypothetical model of air flow shown in your diagram? Why or why not? Correct your model based on your experimental evidence.
  • With your group, discuss how accurate your model is. What limitations did it have? Write down the limitations that your group agreed upon.
  • Yes, you could use your model to predict air flow through a new window. The earlier experiment of air flow would help you model the system more accurately.
  • Yes, you could use your model to predict air flow through a new window. The earlier experiment of air flow is not useful for modeling the new system.
  • No, you cannot model a system to predict the air flow through a new window. The earlier experiment of air flow would help you model the system more accurately.
  • No, you cannot model a system to predict the air flow through a new window. The earlier experiment of air flow is not useful for modeling the new system.

This Snap Lab! has students construct a model of how air flows in their classroom. Each group of four students will create a model of air flow in their classroom using a scale drawing of the room. Then, the groups will test the validity of their model by placing weathervanes that they have constructed around the room and opening a window or door. By observing the weather vanes, students will see how air actually flows through the room from a specific window or door. Students will then correct their model based on their experimental evidence. The following material list is given per group:

  • One room with at least one window or door that can be opened (An optimal configuration would be one window or door per group.)
  • Several pieces of construction paper (at least four per group)
  • Strips of single ply tissue paper
  • One tape measure (long enough to measure the dimensions of the room)
  • Group size can vary depending on the number of windows/doors available and the number of students in the class.
  • The room dimensions could be provided by the teacher. Also, students may need a brief introduction in how to make a drawing to scale.
  • This is another opportunity to discuss controlled experiments in terms of why the students should hold the strips of tissue paper at the same height and in the same way. One student could also serve as a control and stand far away from the window/door or in another area that will not receive air flow from the window/door.
  • You will probably need to coordinate this when multiple windows or doors are used. Only one window or door should be opened at a time for best results. Between openings, allow a short period (5 minutes) when all windows and doors are closed, if possible.

Answers to the Grasp Check will vary, but the air flow in the new window or door should be based on what the students observed in their experiment.

Scientific Laws and Theories

A scientific law is a description of a pattern in nature that is true in all circumstances that have been studied. That is, physical laws are meant to be universal , meaning that they apply throughout the known universe. Laws are often also concise, whereas theories are more complicated. A law can be expressed in the form of a single sentence or mathematical equation. For example, Newton’s second law of motion , which relates the motion of an object to the force applied ( F ), the mass of the object ( m ), and the object’s acceleration ( a ), is simply stated using the equation

Scientific ideas and explanations that are true in many, but not all situations in the universe are usually called principles . An example is Pascal’s principle , which explains properties of liquids, but not solids or gases. However, the distinction between laws and principles is sometimes not carefully made in science.

A theory is an explanation for patterns in nature that is supported by much scientific evidence and verified multiple times by multiple researchers. While many people confuse theories with educated guesses or hypotheses, theories have withstood more rigorous testing and verification than hypotheses.

[OL] Explain to students that in informal, everyday English the word theory can be used to describe an idea that is possibly true but that has not been proven to be true. This use of the word theory often leads people to think that scientific theories are nothing more than educated guesses. This is not just a misconception among students, but among the general public as well.

As a closing idea about scientific processes, we want to point out that scientific laws and theories, even those that have been supported by experiments for centuries, can still be changed by new discoveries. This is especially true when new technologies emerge that allow us to observe things that were formerly unobservable. Imagine how viewing previously invisible objects with a microscope or viewing Earth for the first time from space may have instantly changed our scientific theories and laws! What discoveries still await us in the future? The constant retesting and perfecting of our scientific laws and theories allows our knowledge of nature to progress. For this reason, many scientists are reluctant to say that their studies prove anything. By saying support instead of prove , it keeps the door open for future discoveries, even if they won’t occur for centuries or even millennia.

[OL] With regard to scientists avoiding using the word prove , the general public knows that science has proven certain things such as that the heart pumps blood and the Earth is round. However, scientists should shy away from using prove because it is impossible to test every single instance and every set of conditions in a system to absolutely prove anything. Using support or similar terminology leaves the door open for further discovery.

Check Your Understanding

  • Models are simpler to analyze.
  • Models give more accurate results.
  • Models provide more reliable predictions.
  • Models do not require any computer calculations.
  • They are the same.
  • A hypothesis has been thoroughly tested and found to be true.
  • A hypothesis is a tentative assumption based on what is already known.
  • A hypothesis is a broad explanation firmly supported by evidence.
  • A scientific model is a representation of something that can be easily studied directly. It is useful for studying things that can be easily analyzed by humans.
  • A scientific model is a representation of something that is often too difficult to study directly. It is useful for studying a complex system or systems that humans cannot observe directly.
  • A scientific model is a representation of scientific equipment. It is useful for studying working principles of scientific equipment.
  • A scientific model is a representation of a laboratory where experiments are performed. It is useful for studying requirements needed inside the laboratory.
  • The hypothesis must be validated by scientific experiments.
  • The hypothesis must not include any physical quantity.
  • The hypothesis must be a short and concise statement.
  • The hypothesis must apply to all the situations in the universe.
  • A scientific theory is an explanation of natural phenomena that is supported by evidence.
  • A scientific theory is an explanation of natural phenomena without the support of evidence.
  • A scientific theory is an educated guess about the natural phenomena occurring in nature.
  • A scientific theory is an uneducated guess about natural phenomena occurring in nature.
  • A hypothesis is an explanation of the natural world with experimental support, while a scientific theory is an educated guess about a natural phenomenon.
  • A hypothesis is an educated guess about natural phenomenon, while a scientific theory is an explanation of natural world with experimental support.
  • A hypothesis is experimental evidence of a natural phenomenon, while a scientific theory is an explanation of the natural world with experimental support.
  • A hypothesis is an explanation of the natural world with experimental support, while a scientific theory is experimental evidence of a natural phenomenon.

Use the Check Your Understanding questions to assess students’ achievement of the section’s learning objectives. If students are struggling with a specific objective, the Check Your Understanding will help identify which objective and direct students to the relevant content.

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What is Hypothesis?

We have heard of many hypotheses which have led to great inventions in science. Assumptions that are made on the basis of some evidence are known as hypotheses. In this article, let us learn in detail about the hypothesis and the type of hypothesis with examples.

A hypothesis is an assumption that is made based on some evidence. This is the initial point of any investigation that translates the research questions into predictions. It includes components like variables, population and the relation between the variables. A research hypothesis is a hypothesis that is used to test the relationship between two or more variables.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

  • The hypothesis should be clear and precise to consider it to be reliable.
  • If the hypothesis is a relational hypothesis, then it should be stating the relationship between variables.
  • The hypothesis must be specific and should have scope for conducting more tests.
  • The way of explanation of the hypothesis must be very simple and it should also be understood that the simplicity of the hypothesis is not related to its significance.

Sources of Hypothesis

Following are the sources of hypothesis:

  • The resemblance between the phenomenon.
  • Observations from past studies, present-day experiences and from the competitors.
  • Scientific theories.
  • General patterns that influence the thinking process of people.

Types of Hypothesis

There are six forms of hypothesis and they are:

  • Simple hypothesis
  • Complex hypothesis
  • Directional hypothesis
  • Non-directional hypothesis
  • Null hypothesis
  • Associative and casual hypothesis

Simple Hypothesis

It shows a relationship between one dependent variable and a single independent variable. For example – If you eat more vegetables, you will lose weight faster. Here, eating more vegetables is an independent variable, while losing weight is the dependent variable.

Complex Hypothesis

It shows the relationship between two or more dependent variables and two or more independent variables. Eating more vegetables and fruits leads to weight loss, glowing skin, and reduces the risk of many diseases such as heart disease.

Directional Hypothesis

It shows how a researcher is intellectual and committed to a particular outcome. The relationship between the variables can also predict its nature. For example- children aged four years eating proper food over a five-year period are having higher IQ levels than children not having a proper meal. This shows the effect and direction of the effect.

Non-directional Hypothesis

It is used when there is no theory involved. It is a statement that a relationship exists between two variables, without predicting the exact nature (direction) of the relationship.

Null Hypothesis

It provides a statement which is contrary to the hypothesis. It’s a negative statement, and there is no relationship between independent and dependent variables. The symbol is denoted by “H O ”.

Associative and Causal Hypothesis

Associative hypothesis occurs when there is a change in one variable resulting in a change in the other variable. Whereas, the causal hypothesis proposes a cause and effect interaction between two or more variables.

Examples of Hypothesis

Following are the examples of hypotheses based on their types:

  • Consumption of sugary drinks every day leads to obesity is an example of a simple hypothesis.
  • All lilies have the same number of petals is an example of a null hypothesis.
  • If a person gets 7 hours of sleep, then he will feel less fatigue than if he sleeps less. It is an example of a directional hypothesis.

Functions of Hypothesis

Following are the functions performed by the hypothesis:

  • Hypothesis helps in making an observation and experiments possible.
  • It becomes the start point for the investigation.
  • Hypothesis helps in verifying the observations.
  • It helps in directing the inquiries in the right direction.

How will Hypothesis help in the Scientific Method?

Researchers use hypotheses to put down their thoughts directing how the experiment would take place. Following are the steps that are involved in the scientific method:

  • Formation of question
  • Doing background research
  • Creation of hypothesis
  • Designing an experiment
  • Collection of data
  • Result analysis
  • Summarizing the experiment
  • Communicating the results

Frequently Asked Questions – FAQs

What is hypothesis.

A hypothesis is an assumption made based on some evidence.

Give an example of simple hypothesis?

What are the types of hypothesis.

Types of hypothesis are:

  • Associative and Casual hypothesis

State true or false: Hypothesis is the initial point of any investigation that translates the research questions into a prediction.

Define complex hypothesis..

A complex hypothesis shows the relationship between two or more dependent variables and two or more independent variables.

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What is a scientific hypothesis?

It's the initial building block in the scientific method.

A girl looks at plants in a test tube for a science experiment. What's her scientific hypothesis?

Hypothesis basics

What makes a hypothesis testable.

  • Types of hypotheses
  • Hypothesis versus theory

Additional resources


A scientific hypothesis is a tentative, testable explanation for a phenomenon in the natural world. It's the initial building block in the scientific method . Many describe it as an "educated guess" based on prior knowledge and observation. While this is true, a hypothesis is more informed than a guess. While an "educated guess" suggests a random prediction based on a person's expertise, developing a hypothesis requires active observation and background research. 

The basic idea of a hypothesis is that there is no predetermined outcome. For a solution to be termed a scientific hypothesis, it has to be an idea that can be supported or refuted through carefully crafted experimentation or observation. This concept, called falsifiability and testability, was advanced in the mid-20th century by Austrian-British philosopher Karl Popper in his famous book "The Logic of Scientific Discovery" (Routledge, 1959).

A key function of a hypothesis is to derive predictions about the results of future experiments and then perform those experiments to see whether they support the predictions.

A hypothesis is usually written in the form of an if-then statement, which gives a possibility (if) and explains what may happen because of the possibility (then). The statement could also include "may," according to California State University, Bakersfield .

Here are some examples of hypothesis statements:

  • If garlic repels fleas, then a dog that is given garlic every day will not get fleas.
  • If sugar causes cavities, then people who eat a lot of candy may be more prone to cavities.
  • If ultraviolet light can damage the eyes, then maybe this light can cause blindness.

A useful hypothesis should be testable and falsifiable. That means that it should be possible to prove it wrong. A theory that can't be proved wrong is nonscientific, according to Karl Popper's 1963 book " Conjectures and Refutations ."

An example of an untestable statement is, "Dogs are better than cats." That's because the definition of "better" is vague and subjective. However, an untestable statement can be reworded to make it testable. For example, the previous statement could be changed to this: "Owning a dog is associated with higher levels of physical fitness than owning a cat." With this statement, the researcher can take measures of physical fitness from dog and cat owners and compare the two.

Types of scientific hypotheses

Elementary-age students study alternative energy using homemade windmills during public school science class.

In an experiment, researchers generally state their hypotheses in two ways. The null hypothesis predicts that there will be no relationship between the variables tested, or no difference between the experimental groups. The alternative hypothesis predicts the opposite: that there will be a difference between the experimental groups. This is usually the hypothesis scientists are most interested in, according to the University of Miami .

For example, a null hypothesis might state, "There will be no difference in the rate of muscle growth between people who take a protein supplement and people who don't." The alternative hypothesis would state, "There will be a difference in the rate of muscle growth between people who take a protein supplement and people who don't."

If the results of the experiment show a relationship between the variables, then the null hypothesis has been rejected in favor of the alternative hypothesis, according to the book " Research Methods in Psychology " (​​BCcampus, 2015). 

There are other ways to describe an alternative hypothesis. The alternative hypothesis above does not specify a direction of the effect, only that there will be a difference between the two groups. That type of prediction is called a two-tailed hypothesis. If a hypothesis specifies a certain direction — for example, that people who take a protein supplement will gain more muscle than people who don't — it is called a one-tailed hypothesis, according to William M. K. Trochim , a professor of Policy Analysis and Management at Cornell University.

Sometimes, errors take place during an experiment. These errors can happen in one of two ways. A type I error is when the null hypothesis is rejected when it is true. This is also known as a false positive. A type II error occurs when the null hypothesis is not rejected when it is false. This is also known as a false negative, according to the University of California, Berkeley . 

A hypothesis can be rejected or modified, but it can never be proved correct 100% of the time. For example, a scientist can form a hypothesis stating that if a certain type of tomato has a gene for red pigment, that type of tomato will be red. During research, the scientist then finds that each tomato of this type is red. Though the findings confirm the hypothesis, there may be a tomato of that type somewhere in the world that isn't red. Thus, the hypothesis is true, but it may not be true 100% of the time.

Scientific theory vs. scientific hypothesis

The best hypotheses are simple. They deal with a relatively narrow set of phenomena. But theories are broader; they generally combine multiple hypotheses into a general explanation for a wide range of phenomena, according to the University of California, Berkeley . For example, a hypothesis might state, "If animals adapt to suit their environments, then birds that live on islands with lots of seeds to eat will have differently shaped beaks than birds that live on islands with lots of insects to eat." After testing many hypotheses like these, Charles Darwin formulated an overarching theory: the theory of evolution by natural selection.

"Theories are the ways that we make sense of what we observe in the natural world," Tanner said. "Theories are structures of ideas that explain and interpret facts." 

  • Read more about writing a hypothesis, from the American Medical Writers Association.
  • Find out why a hypothesis isn't always necessary in science, from The American Biology Teacher.
  • Learn about null and alternative hypotheses, from Prof. Essa on YouTube .

Encyclopedia Britannica. Scientific Hypothesis. Jan. 13, 2022. https://www.britannica.com/science/scientific-hypothesis

Karl Popper, "The Logic of Scientific Discovery," Routledge, 1959.

California State University, Bakersfield, "Formatting a testable hypothesis." https://www.csub.edu/~ddodenhoff/Bio100/Bio100sp04/formattingahypothesis.htm  

Karl Popper, "Conjectures and Refutations," Routledge, 1963.

Price, P., Jhangiani, R., & Chiang, I., "Research Methods of Psychology — 2nd Canadian Edition," BCcampus, 2015.‌

University of Miami, "The Scientific Method" http://www.bio.miami.edu/dana/161/evolution/161app1_scimethod.pdf  

William M.K. Trochim, "Research Methods Knowledge Base," https://conjointly.com/kb/hypotheses-explained/  

University of California, Berkeley, "Multiple Hypothesis Testing and False Discovery Rate" https://www.stat.berkeley.edu/~hhuang/STAT141/Lecture-FDR.pdf  

University of California, Berkeley, "Science at multiple levels" https://undsci.berkeley.edu/article/0_0_0/howscienceworks_19

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Mechanics (Essentials) - Class 11th

Course: mechanics (essentials) - class 11th   >   unit 2.

  • Introduction to physics
  • What is physics?

The scientific method

  • Models and Approximations in Physics


  • Make an observation.
  • Ask a question.
  • Form a hypothesis , or testable explanation.
  • Make a prediction based on the hypothesis.
  • Test the prediction.
  • Iterate: use the results to make new hypotheses or predictions.

Scientific method example: Failure to toast

1. make an observation..

  • Observation: the toaster won't toast.

2. Ask a question.

  • Question: Why won't my toaster toast?

3. Propose a hypothesis.

  • Hypothesis: Maybe the outlet is broken.

4. Make predictions.

  • Prediction: If I plug the toaster into a different outlet, then it will toast the bread.

5. Test the predictions.

  • Test of prediction: Plug the toaster into a different outlet and try again.
  • If the toaster does toast, then the hypothesis is supported—likely correct.
  • If the toaster doesn't toast, then the hypothesis is not supported—likely wrong.

Logical possibility

Practical possibility, building a body of evidence, 6. iterate..

  • Iteration time!
  • If the hypothesis was supported, we might do additional tests to confirm it, or revise it to be more specific. For instance, we might investigate why the outlet is broken.
  • If the hypothesis was not supported, we would come up with a new hypothesis. For instance, the next hypothesis might be that there's a broken wire in the toaster.

Want to join the conversation?

Hypothesis, Model, Theory, and Law

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  • Important Physicists
  • Thermodynamics
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what is a hypothesis physics

  • M.S., Mathematics Education, Indiana University
  • B.A., Physics, Wabash College

In common usage, the words hypothesis, model, theory, and law have different interpretations and are at times used without precision, but in science they have very exact meanings.

Perhaps the most difficult and intriguing step is the development of a specific, testable hypothesis. A useful hypothesis enables predictions by applying deductive reasoning, often in the form of mathematical analysis. It is a limited statement regarding the cause and effect in a specific situation, which can be tested by experimentation and observation or by statistical analysis of the probabilities from the data obtained. The outcome of the test hypothesis should be currently unknown, so that the results can provide useful data regarding the validity of the hypothesis.

Sometimes a hypothesis is developed that must wait for new knowledge or technology to be testable. The concept of atoms was proposed by the ancient Greeks , who had no means of testing it. Centuries later, when more knowledge became available, the hypothesis gained support and was eventually accepted by the scientific community, though it has had to be amended many times over the year. Atoms are not indivisible, as the Greeks supposed.

A model is used for situations when it is known that the hypothesis has a limitation on its validity. The Bohr model of the atom , for example, depicts electrons circling the atomic nucleus in a fashion similar to planets in the solar system. This model is useful in determining the energies of the quantum states of the electron in the simple hydrogen atom, but it is by no means represents the true nature of the atom. Scientists (and science students) often use such idealized models  to get an initial grasp on analyzing complex situations.

Theory and Law

A scientific theory or law represents a hypothesis (or group of related hypotheses) which has been confirmed through repeated testing, almost always conducted over a span of many years. Generally, a theory is an explanation for a set of related phenomena, like the theory of evolution or the big bang theory . 

The word "law" is often invoked in reference to a specific mathematical equation that relates the different elements within a theory. Pascal's Law refers an equation that describes differences in pressure based on height. In the overall theory of universal gravitation developed by Sir Isaac Newton , the key equation that describes the gravitational attraction between two objects is called the law of gravity .

These days, physicists rarely apply the word "law" to their ideas. In part, this is because so many of the previous "laws of nature" were found to be not so much laws as guidelines, that work well within certain parameters but not within others.

Scientific Paradigms

Once a scientific theory is established, it is very hard to get the scientific community to discard it. In physics, the concept of ether as a medium for light wave transmission ran into serious opposition in the late 1800s, but it was not disregarded until the early 1900s, when Albert Einstein proposed alternate explanations for the wave nature of light that did not rely upon a medium for transmission.

The science philosopher Thomas Kuhn developed the term scientific paradigm to explain the working set of theories under which science operates. He did extensive work on the scientific revolutions that take place when one paradigm is overturned in favor of a new set of theories. His work suggests that the very nature of science changes when these paradigms are significantly different. The nature of physics prior to relativity and quantum mechanics is fundamentally different from that after their discovery, just as biology prior to Darwin’s Theory of Evolution is fundamentally different from the biology that followed it. The very nature of the inquiry changes.

One consequence of the scientific method is to try to maintain consistency in the inquiry when these revolutions occur and to avoid attempts to overthrow existing paradigms on ideological grounds.

Occam’s Razor

One principle of note in regards to the scientific method is Occam’s Razor (alternately spelled Ockham's Razor), which is named after the 14th century English logician and Franciscan friar William of Ockham. Occam did not create the concept—the work of Thomas Aquinas and even Aristotle referred to some form of it. The name was first attributed to him (to our knowledge) in the 1800s, indicating that he must have espoused the philosophy enough that his name became associated with it.

The Razor is often stated in Latin as:

entia non sunt multiplicanda praeter necessitatem
or, translated to English:
entities should not be multiplied beyond necessity

Occam's Razor indicates that the most simple explanation that fits the available data is the one which is preferable. Assuming that two hypotheses presented have equal predictive power, the one which makes the fewest assumptions and hypothetical entities takes precedence. This appeal to simplicity has been adopted by most of science, and is invoked in this popular quote by Albert Einstein:

Everything should be made as simple as possible, but not simpler.

It is significant to note that Occam's Razor does not prove that the simpler hypothesis is, indeed, the true explanation of how nature behaves. Scientific principles should be as simple as possible, but that's no proof that nature itself is simple.

However, it is generally the case that when a more complex system is at work there is some element of the evidence which doesn't fit the simpler hypothesis, so Occam's Razor is rarely wrong as it deals only with hypotheses of purely equal predictive power. The predictive power is more important than the simplicity.

Edited by Anne Marie Helmenstine, Ph.D.

  • Scientific Hypothesis, Model, Theory, and Law
  • Theory Definition in Science
  • The Basics of Physics in Scientific Study
  • A Brief History of Atomic Theory
  • Einstein's Theory of Relativity
  • What Is a Paradigm Shift?
  • Wave Particle Duality and How It Works
  • Scientific Method
  • Oversimplification and Exaggeration Fallacies
  • Hypothesis Definition (Science)
  • Kinetic Molecular Theory of Gases
  • Understanding Cosmology and Its Impact
  • The History of Gravity
  • Tips on Winning the Debate on Evolution
  • The Copenhagen Interpretation of Quantum Mechanics
  • Geological Thinking: Method of Multiple Working Hypotheses


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1 Atoms in Motion 1

what is a hypothesis physics

1–1 Introduction

This two-year course in physics is presented from the point of view that you, the reader, are going to be a physicist. This is not necessarily the case of course, but that is what every professor in every subject assumes! If you are going to be a physicist, you will have a lot to study: two hundred years of the most rapidly developing field of knowledge that there is. So much knowledge, in fact, that you might think that you cannot learn all of it in four years, and truly you cannot; you will have to go to graduate school too!

Surprisingly enough, in spite of the tremendous amount of work that has been done for all this time it is possible to condense the enormous mass of results to a large extent—that is, to find laws which summarize all our knowledge. Even so, the laws are so hard to grasp that it is unfair to you to start exploring this tremendous subject without some kind of map or outline of the relationship of one part of the subject of science to another. Following these preliminary remarks, the first three chapters will therefore outline the relation of physics to the rest of the sciences, the relations of the sciences to each other, and the meaning of science, to help us develop a “feel” for the subject.

You might ask why we cannot teach physics by just giving the basic laws on page one and then showing how they work in all possible circumstances, as we do in Euclidean geometry, where we state the axioms and then make all sorts of deductions. (So, not satisfied to learn physics in four years, you want to learn it in four minutes?) We cannot do it in this way for two reasons. First, we do not yet know all the basic laws: there is an expanding frontier of ignorance. Second, the correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean. No, it is not possible to do it that way. We can only do it piece by piece.

Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected.

The principle of science, the definition, almost, is the following: The test of all knowledge is experiment . Experiment is the sole judge of scientific “truth.” But what is the source of knowledge? Where do the laws that are to be tested come from? Experiment, itself, helps to produce these laws, in the sense that it gives us hints. But also needed is imagination to create from these hints the great generalizations—to guess at the wonderful, simple, but very strange patterns beneath them all, and then to experiment to check again whether we have made the right guess. This imagining process is so difficult that there is a division of labor in physics: there are theoretical physicists who imagine, deduce, and guess at new laws, but do not experiment; and then there are experimental physicists who experiment, imagine, deduce, and guess.

We said that the laws of nature are approximate: that we first find the “wrong” ones, and then we find the “right” ones. Now, how can an experiment be “wrong”? First, in a trivial way: if something is wrong with the apparatus that you did not notice. But these things are easily fixed, and checked back and forth. So without snatching at such minor things, how can the results of an experiment be wrong? Only by being inaccurate. For example, the mass of an object never seems to change: a spinning top has the same weight as a still one. So a “law” was invented: mass is constant, independent of speed. That “law” is now found to be incorrect. Mass is found to increase with velocity, but appreciable increases require velocities near that of light. A true law is: if an object moves with a speed of less than one hundred miles a second the mass is constant to within one part in a million. In some such approximate form this is a correct law. So in practice one might think that the new law makes no significant difference. Well, yes and no. For ordinary speeds we can certainly forget it and use the simple constant-mass law as a good approximation. But for high speeds we are wrong, and the higher the speed, the more wrong we are.

Finally, and most interesting, philosophically we are completely wrong with the approximate law. Our entire picture of the world has to be altered even though the mass changes only by a little bit. This is a very peculiar thing about the philosophy, or the ideas, behind the laws. Even a very small effect sometimes requires profound changes in our ideas.

Now, what should we teach first? Should we teach the correct but unfamiliar law with its strange and difficult conceptual ideas, for example the theory of relativity, four-dimensional space-time, and so on? Or should we first teach the simple “constant-mass” law, which is only approximate, but does not involve such difficult ideas? The first is more exciting, more wonderful, and more fun, but the second is easier to get at first, and is a first step to a real understanding of the first idea. This point arises again and again in teaching physics. At different times we shall have to resolve it in different ways, but at each stage it is worth learning what is now known, how accurate it is, how it fits into everything else, and how it may be changed when we learn more.

Let us now proceed with our outline, or general map, of our understanding of science today (in particular, physics, but also of other sciences on the periphery), so that when we later concentrate on some particular point we will have some idea of the background, why that particular point is interesting, and how it fits into the big structure. So, what is our overall picture of the world?

1–2 Matter is made of atoms

If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact , or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another . In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied.

To illustrate the power of the atomic idea, suppose that we have a drop of water a quarter of an inch on the side. If we look at it very closely we see nothing but water—smooth, continuous water. Even if we magnify it with the best optical microscope available—roughly two thousand times—then the water drop will be roughly forty feet across, about as big as a large room, and if we looked rather closely, we would still see relatively smooth water—but here and there small football-shaped things swimming back and forth. Very interesting. These are paramecia. You may stop at this point and get so curious about the paramecia with their wiggling cilia and twisting bodies that you go no further, except perhaps to magnify the paramecia still more and see inside. This, of course, is a subject for biology, but for the present we pass on and look still more closely at the water material itself, magnifying it two thousand times again. Now the drop of water extends about fifteen miles across, and if we look very closely at it we see a kind of teeming, something which no longer has a smooth appearance—it looks something like a crowd at a football game as seen from a very great distance. In order to see what this teeming is about, we will magnify it another two hundred and fifty times and we will see something similar to what is shown in Fig.  1–1 . This is a picture of water magnified a billion times, but idealized in several ways. In the first place, the particles are drawn in a simple manner with sharp edges, which is inaccurate. Secondly, for simplicity, they are sketched almost schematically in a two-dimensional arrangement, but of course they are moving around in three dimensions. Notice that there are two kinds of “blobs” or circles to represent the atoms of oxygen (black) and hydrogen (white), and that each oxygen has two hydrogens tied to it. (Each little group of an oxygen with its two hydrogens is called a molecule.) The picture is idealized further in that the real particles in nature are continually jiggling and bouncing, turning and twisting around one another. You will have to imagine this as a dynamic rather than a static picture. Another thing that cannot be illustrated in a drawing is the fact that the particles are “stuck together”—that they attract each other, this one pulled by that one, etc. The whole group is “glued together,” so to speak. On the other hand, the particles do not squeeze through each other. If you try to squeeze two of them too close together, they repel.

The atoms are $1$ or $2\times10^{-8}$ cm in radius. Now $10^{-8}$ cm is called an angstrom (just as another name), so we say they are 1 or 2 angstroms (Å) in radius. Another way to remember their size is this: if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple.

Now imagine this great drop of water with all of these jiggling particles stuck together and tagging along with each other. The water keeps its volume; it does not fall apart, because of the attraction of the molecules for each other. If the drop is on a slope, where it can move from one place to another, the water will flow, but it does not just disappear—things do not just fly apart—because of the molecular attraction. Now the jiggling motion is what we represent as heat : when we increase the temperature, we increase the motion. If we heat the water, the jiggling increases and the volume between the atoms increases, and if the heating continues there comes a time when the pull between the molecules is not enough to hold them together and they do fly apart and become separated from one another. Of course, this is how we manufacture steam out of water—by increasing the temperature; the particles fly apart because of the increased motion.

In Fig.  1–2 we have a picture of steam. This picture of steam fails in one respect: at ordinary atmospheric pressure there certainly would not be as many as three water molecules in this figure. Most squares this size would contain none—but we accidentally have two and a half or three in the picture (just so it would not be completely blank). Now in the case of steam we see the characteristic molecules more clearly than in the case of water. For simplicity, the molecules are drawn so that there is a $120^\circ$ angle between the hydrogen atoms. In actual fact the angle is $105^\circ3'$, and the distance between the center of a hydrogen and the center of the oxygen is 0.957 Å, so we know this molecule very well.

Let us see what some of the properties of steam vapor or any other gas are. The molecules, being separated from one another, will bounce against the walls. Imagine a room with a number of tennis balls (a hundred or so) bouncing around in perpetual motion. When they bombard the wall, this pushes the wall away. (Of course we would have to push the wall back.) This means that the gas exerts a jittery force which our coarse senses (not being ourselves magnified a billion times) feel only as an average push . In order to confine a gas we must apply a pressure. Figure  1–3 shows a standard vessel for holding gases (used in all textbooks), a cylinder with a piston in it. Now, it makes no difference what the shapes of water molecules are, so for simplicity we shall draw them as tennis balls or little dots. These things are in perpetual motion in all directions. So many of them are hitting the top piston all the time that to keep it from being patiently knocked out of the tank by this continuous banging, we shall have to hold the piston down by a certain force, which we call the pressure (really, the pressure times the area is the force). Clearly, the force is proportional to the area, for if we increase the area but keep the number of molecules per cubic centimeter the same, we increase the number of collisions with the piston in the same proportion as the area was increased.

Now let us put twice as many molecules in this tank, so as to double the density, and let them have the same speed, i.e., the same temperature. Then, to a close approximation, the number of collisions will be doubled, and since each will be just as “energetic” as before, the pressure is proportional to the density. If we consider the true nature of the forces between the atoms, we would expect a slight decrease in pressure because of the attraction between the atoms, and a slight increase because of the finite volume they occupy. Nevertheless, to an excellent approximation, if the density is low enough that there are not many atoms, the pressure is proportional to the density .

We can also see something else: If we increase the temperature without changing the density of the gas, i.e., if we increase the speed of the atoms, what is going to happen to the pressure? Well, the atoms hit harder because they are moving faster, and in addition they hit more often, so the pressure increases. You see how simple the ideas of atomic theory are.

Let us consider another situation. Suppose that the piston moves inward, so that the atoms are slowly compressed into a smaller space. What happens when an atom hits the moving piston? Evidently it picks up speed from the collision. You can try it by bouncing a ping-pong ball from a forward-moving paddle, for example, and you will find that it comes off with more speed than that with which it struck. (Special example: if an atom happens to be standing still and the piston hits it, it will certainly move.) So the atoms are “hotter” when they come away from the piston than they were before they struck it. Therefore all the atoms which are in the vessel will have picked up speed. This means that when we compress a gas slowly, the temperature of the gas increases . So, under slow compression , a gas will increase in temperature, and under slow expansion it will decrease in temperature.

We now return to our drop of water and look in another direction. Suppose that we decrease the temperature of our drop of water. Suppose that the jiggling of the molecules of the atoms in the water is steadily decreasing. We know that there are forces of attraction between the atoms, so that after a while they will not be able to jiggle so well. What will happen at very low temperatures is indicated in Fig.  1–4 : the molecules lock into a new pattern which is ice . This particular schematic diagram of ice is wrong because it is in two dimensions, but it is right qualitatively. The interesting point is that the material has a definite place for every atom , and you can easily appreciate that if somehow or other we were to hold all the atoms at one end of the drop in a certain arrangement, each atom in a certain place, then because of the structure of interconnections, which is rigid, the other end miles away (at our magnified scale) will have a definite location. So if we hold a needle of ice at one end, the other end resists our pushing it aside, unlike the case of water, in which the structure is broken down because of the increased jiggling so that the atoms all move around in different ways. The difference between solids and liquids is, then, that in a solid the atoms are arranged in some kind of an array, called a crystalline array , and they do not have a random position at long distances; the position of the atoms on one side of the crystal is determined by that of other atoms millions of atoms away on the other side of the crystal. Figure  1–4 is an invented arrangement for ice, and although it contains many of the correct features of ice, it is not the true arrangement. One of the correct features is that there is a part of the symmetry that is hexagonal. You can see that if we turn the picture around an axis by $60^\circ$, the picture returns to itself. So there is a symmetry in the ice which accounts for the six-sided appearance of snowflakes. Another thing we can see from Fig.  1–4 is why ice shrinks when it melts. The particular crystal pattern of ice shown here has many “holes” in it, as does the true ice structure. When the organization breaks down, these holes can be occupied by molecules. Most simple substances, with the exception of water and type metal, expand upon melting, because the atoms are closely packed in the solid crystal and upon melting need more room to jiggle around, but an open structure collapses, as in the case of water.

Now although ice has a “rigid” crystalline form, its temperature can change—ice has heat. If we wish, we can change the amount of heat. What is the heat in the case of ice? The atoms are not standing still. They are jiggling and vibrating. So even though there is a definite order to the crystal—a definite structure—all of the atoms are vibrating “in place.” As we increase the temperature, they vibrate with greater and greater amplitude, until they shake themselves out of place. We call this melting . As we decrease the temperature, the vibration decreases and decreases until, at absolute zero, there is a minimum amount of vibration that the atoms can have, but not zero . This minimum amount of motion that atoms can have is not enough to melt a substance, with one exception: helium. Helium merely decreases the atomic motions as much as it can, but even at absolute zero there is still enough motion to keep it from freezing. Helium, even at absolute zero, does not freeze, unless the pressure is made so great as to make the atoms squash together. If we increase the pressure, we can make it solidify.

1–3 Atomic processes

So much for the description of solids, liquids, and gases from the atomic point of view. However, the atomic hypothesis also describes processes , and so we shall now look at a number of processes from an atomic standpoint. The first process that we shall look at is associated with the surface of the water. What happens at the surface of the water? We shall now make the picture more complicated—and more realistic—by imagining that the surface is in air. Figure  1–5 shows the surface of water in air. We see the water molecules as before, forming a body of liquid water, but now we also see the surface of the water. Above the surface we find a number of things: First of all there are water molecules, as in steam. This is water vapor , which is always found above liquid water. (There is an equilibrium between the steam vapor and the water which will be described later.) In addition we find some other molecules—here two oxygen atoms stuck together by themselves, forming an oxygen molecule , there two nitrogen atoms also stuck together to make a nitrogen molecule. Air consists almost entirely of nitrogen, oxygen, some water vapor, and lesser amounts of carbon dioxide, argon, and other things. So above the water surface is the air, a gas, containing some water vapor. Now what is happening in this picture? The molecules in the water are always jiggling around. From time to time, one on the surface happens to be hit a little harder than usual, and gets knocked away. It is hard to see that happening in the picture because it is a still picture. But we can imagine that one molecule near the surface has just been hit and is flying out, or perhaps another one has been hit and is flying out. Thus, molecule by molecule, the water disappears—it evaporates. But if we close the vessel above, after a while we shall find a large number of molecules of water amongst the air molecules. From time to time, one of these vapor molecules comes flying down to the water and gets stuck again. So we see that what looks like a dead, uninteresting thing—a glass of water with a cover, that has been sitting there for perhaps twenty years—really contains a dynamic and interesting phenomenon which is going on all the time. To our eyes, our crude eyes, nothing is changing, but if we could see it a billion times magnified, we would see that from its own point of view it is always changing: molecules are leaving the surface, molecules are coming back.

Why do we see no change ? Because just as many molecules are leaving as are coming back! In the long run “nothing happens.” If we then take the top of the vessel off and blow the moist air away, replacing it with dry air, then the number of molecules leaving is just the same as it was before, because this depends on the jiggling of the water, but the number coming back is greatly reduced because there are so many fewer water molecules above the water. Therefore there are more going out than coming in, and the water evaporates. Hence, if you wish to evaporate water turn on the fan!

Here is something else: Which molecules leave? When a molecule leaves it is due to an accidental, extra accumulation of a little bit more than ordinary energy, which it needs if it is to break away from the attractions of its neighbors. Therefore, since those that leave have more energy than the average, the ones that are left have less average motion than they had before. So the liquid gradually cools if it evaporates. Of course, when a molecule of vapor comes from the air to the water below there is a sudden great attraction as the molecule approaches the surface. This speeds up the incoming molecule and results in generation of heat. So when they leave they take away heat; when they come back they generate heat. Of course when there is no net evaporation the result is nothing—the water is not changing temperature. If we blow on the water so as to maintain a continuous preponderance in the number evaporating, then the water is cooled. Hence, blow on soup to cool it!

Of course you should realize that the processes just described are more complicated than we have indicated. Not only does the water go into the air, but also, from time to time, one of the oxygen or nitrogen molecules will come in and “get lost” in the mass of water molecules, and work its way into the water. Thus the air dissolves in the water; oxygen and nitrogen molecules will work their way into the water and the water will contain air. If we suddenly take the air away from the vessel, then the air molecules will leave more rapidly than they come in, and in doing so will make bubbles. This is very bad for divers, as you may know.

Now we go on to another process. In Fig.  1–6 we see, from an atomic point of view, a solid dissolving in water. If we put a crystal of salt in the water, what will happen? Salt is a solid, a crystal, an organized arrangement of “salt atoms.” Figure  1–7 is an illustration of the three-dimensional structure of common salt, sodium chloride. Strictly speaking, the crystal is not made of atoms, but of what we call ions . An ion is an atom which either has a few extra electrons or has lost a few electrons. In a salt crystal we find chlorine ions (chlorine atoms with an extra electron) and sodium ions (sodium atoms with one electron missing). The ions all stick together by electrical attraction in the solid salt, but when we put them in the water we find, because of the attractions of the negative oxygen and positive hydrogen for the ions, that some of the ions jiggle loose. In Fig.  1–6 we see a chlorine ion getting loose, and other atoms floating in the water in the form of ions. This picture was made with some care. Notice, for example, that the hydrogen ends of the water molecules are more likely to be near the chlorine ion, while near the sodium ion we are more likely to find the oxygen end, because the sodium is positive and the oxygen end of the water is negative, and they attract electrically. Can we tell from this picture whether the salt is dissolving in water or crystallizing out of water? Of course we cannot tell, because while some of the atoms are leaving the crystal other atoms are rejoining it. The process is a dynamic one, just as in the case of evaporation, and it depends on whether there is more or less salt in the water than the amount needed for equilibrium. By equilibrium we mean that situation in which the rate at which atoms are leaving just matches the rate at which they are coming back. If there is almost no salt in the water, more atoms leave than return, and the salt dissolves. If, on the other hand, there are too many “salt atoms,” more return than leave, and the salt is crystallizing.

In passing, we mention that the concept of a molecule of a substance is only approximate and exists only for a certain class of substances. It is clear in the case of water that the three atoms are actually stuck together. It is not so clear in the case of sodium chloride in the solid. There is just an arrangement of sodium and chlorine ions in a cubic pattern. There is no natural way to group them as “molecules of salt.”

Returning to our discussion of solution and precipitation, if we increase the temperature of the salt solution, then the rate at which atoms are taken away is increased, and so is the rate at which atoms are brought back. It turns out to be very difficult, in general, to predict which way it is going to go, whether more or less of the solid will dissolve. Most substances dissolve more, but some substances dissolve less, as the temperature increases.

1–4 Chemical reactions

In all of the processes which have been described so far, the atoms and the ions have not changed partners, but of course there are circumstances in which the atoms do change combinations, forming new molecules. This is illustrated in Fig.  1–8 . A process in which the rearrangement of the atomic partners occurs is what we call a chemical reaction . The other processes so far described are called physical processes, but there is no sharp distinction between the two. (Nature does not care what we call it, she just keeps on doing it.) This figure is supposed to represent carbon burning in oxygen. In the case of oxygen, two oxygen atoms stick together very strongly. (Why do not three or even four stick together? That is one of the very peculiar characteristics of such atomic processes. Atoms are very special: they like certain particular partners, certain particular directions, and so on. It is the job of physics to analyze why each one wants what it wants. At any rate, two oxygen atoms form, saturated and happy, a molecule.)

The carbon atoms are supposed to be in a solid crystal (which could be graphite or diamond 2 ). Now, for example, one of the oxygen molecules can come over to the carbon, and each atom can pick up a carbon atom and go flying off in a new combination—“carbon-oxygen”—which is a molecule of the gas called carbon monoxide. It is given the chemical name CO. It is very simple: the letters “CO” are practically a picture of that molecule. But carbon attracts oxygen much more than oxygen attracts oxygen or carbon attracts carbon. Therefore in this process the oxygen may arrive with only a little energy, but the oxygen and carbon will snap together with a tremendous vengeance and commotion, and everything near them will pick up the energy. A large amount of motion energy, kinetic energy, is thus generated. This of course is burning ; we are getting heat from the combination of oxygen and carbon. The heat is ordinarily in the form of the molecular motion of the hot gas, but in certain circumstances it can be so enormous that it generates light . That is how one gets flames .

In addition, the carbon monoxide is not quite satisfied. It is possible for it to attach another oxygen, so that we might have a much more complicated reaction in which the oxygen is combining with the carbon, while at the same time there happens to be a collision with a carbon monoxide molecule. One oxygen atom could attach itself to the CO and ultimately form a molecule, composed of one carbon and two oxygens, which is designated CO$_2$ and called carbon dioxide. If we burn the carbon with very little oxygen in a very rapid reaction (for example, in an automobile engine, where the explosion is so fast that there is not time for it to make carbon dioxide) a considerable amount of carbon monoxide is formed. In many such rearrangements, a very large amount of energy is released, forming explosions, flames, etc., depending on the reactions. Chemists have studied these arrangements of the atoms, and found that every substance is some type of arrangement of atoms .

To illustrate this idea, let us consider another example. If we go into a field of small violets, we know what “that smell” is. It is some kind of molecule , or arrangement of atoms, that has worked its way into our noses. First of all, how did it work its way in? That is rather easy. If the smell is some kind of molecule in the air, jiggling around and being knocked every which way, it might have accidentally worked its way into the nose. Certainly it has no particular desire to get into our nose. It is merely one helpless part of a jostling crowd of molecules, and in its aimless wanderings this particular chunk of matter happens to find itself in the nose.

Now chemists can take special molecules like the odor of violets, and analyze them and tell us the exact arrangement of the atoms in space. We know that the carbon dioxide molecule is straight and symmetrical: O—C—O. (That can be determined easily, too, by physical methods.) However, even for the vastly more complicated arrangements of atoms that there are in chemistry, one can, by a long, remarkable process of detective work, find the arrangements of the atoms. Figure  1–9 is a picture of the air in the neighborhood of a violet; again we find nitrogen and oxygen in the air, and water vapor. (Why is there water vapor? Because the violet is wet . All plants transpire.) However, we also see a “monster” composed of carbon atoms, hydrogen atoms, and oxygen atoms, which have picked a certain particular pattern in which to be arranged. It is a much more complicated arrangement than that of carbon dioxide; in fact, it is an enormously complicated arrangement. Unfortunately, we cannot picture all that is really known about it chemically, because the precise arrangement of all the atoms is actually known in three dimensions, while our picture is in only two dimensions. The six carbons which form a ring do not form a flat ring, but a kind of “puckered” ring. All of the angles and distances are known. So a chemical formula is merely a picture of such a molecule. When the chemist writes such a thing on the blackboard, he is trying to “draw,” roughly speaking, in two dimensions. For example, we see a “ring” of six carbons, and a “chain” of carbons hanging on the end, with an oxygen second from the end, three hydrogens tied to that carbon, two carbons and three hydrogens sticking up here, etc.

How does the chemist find what the arrangement is? He mixes bottles full of stuff together, and if it turns red, it tells him that it consists of one hydrogen and two carbons tied on here; if it turns blue, on the other hand, that is not the way it is at all. This is one of the most fantastic pieces of detective work that has ever been done—organic chemistry. To discover the arrangement of the atoms in these enormously complicated arrays the chemist looks at what happens when he mixes two different substances together. The physicist could never quite believe that the chemist knew what he was talking about when he described the arrangement of the atoms. For about twenty years it has been possible, in some cases, to look at such molecules (not quite as complicated as this one, but some which contain parts of it) by a physical method, and it has been possible to locate every atom, not by looking at colors, but by measuring where they are . And lo and behold!, the chemists are almost always correct.

It turns out, in fact, that in the odor of violets there are three slightly different molecules, which differ only in the arrangement of the hydrogen atoms.

One problem of chemistry is to name a substance, so that we will know what it is. Find a name for this shape! Not only must the name tell the shape, but it must also tell that here is an oxygen atom, there a hydrogen—exactly what and where each atom is. So we can appreciate that the chemical names must be complex in order to be complete. You see that the name of this thing in the more complete form that will tell you the structure of it is 4-(2, 2, 3, 6 tetramethyl-5-cyclohexenyl)-3-buten-2-one, and that tells you that this is the arrangement. We can appreciate the difficulties that the chemists have, and also appreciate the reason for such long names. It is not that they wish to be obscure, but they have an extremely difficult problem in trying to describe the molecules in words!

How do we know that there are atoms? By one of the tricks mentioned earlier: we make the hypothesis that there are atoms, and one after the other results come out the way we predict, as they ought to if things are made of atoms. There is also somewhat more direct evidence, a good example of which is the following: The atoms are so small that you cannot see them with a light microscope—in fact, not even with an electron microscope. (With a light microscope you can only see things which are much bigger.) Now if the atoms are always in motion, say in water, and we put a big ball of something in the water, a ball much bigger than the atoms, the ball will jiggle around—much as in a push ball game, where a great big ball is pushed around by a lot of people. The people are pushing in various directions, and the ball moves around the field in an irregular fashion. So, in the same way, the “large ball” will move because of the inequalities of the collisions on one side to the other, from one moment to the next. Therefore, if we look at very tiny particles (colloids) in water through an excellent microscope, we see a perpetual jiggling of the particles, which is the result of the bombardment of the atoms. This is called the Brownian motion .

We can see further evidence for atoms in the structure of crystals. In many cases the structures deduced by x-ray analysis agree in their spatial “shapes” with the forms actually exhibited by crystals as they occur in nature. The angles between the various “faces” of a crystal agree, within seconds of arc, with angles deduced on the assumption that a crystal is made of many “layers” of atoms.

Everything is made of atoms . That is the key hypothesis. The most important hypothesis in all of biology, for example, is that everything that animals do, atoms do . In other words, there is nothing that living things do that cannot be understood from the point of view that they are made of atoms acting according to the laws of physics . This was not known from the beginning: it took some experimenting and theorizing to suggest this hypothesis, but now it is accepted, and it is the most useful theory for producing new ideas in the field of biology.

If a piece of steel or a piece of salt, consisting of atoms one next to the other, can have such interesting properties; if water—which is nothing but these little blobs, mile upon mile of the same thing over the earth—can form waves and foam, and make rushing noises and strange patterns as it runs over cement; if all of this, all the life of a stream of water, can be nothing but a pile of atoms, how much more is possible ? If instead of arranging the atoms in some definite pattern, again and again repeated, on and on, or even forming little lumps of complexity like the odor of violets, we make an arrangement which is always different from place to place, with different kinds of atoms arranged in many ways, continually changing, not repeating, how much more marvelously is it possible that this thing might behave? Is it possible that that “thing” walking back and forth in front of you, talking to you, is a great glob of these atoms in a very complex arrangement, such that the sheer complexity of it staggers the imagination as to what it can do? When we say we are a pile of atoms, we do not mean we are merely a pile of atoms, because a pile of atoms which is not repeated from one to the other might well have the possibilities which you see before you in the mirror.

  • The original tape recording of this lecture suffered some damage in the making, so it sounds 'clipped' in many places, particularly when Feynman speaks loudly. (This is the only recording in the collection that is damaged.) An illustrated transcript of the lecture can be found here . ↩
  • One can burn a diamond in air. ↩

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6.6: De Broglie’s Matter Waves

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Learning Objectives

By the end of this section, you will be able to:

  • Describe de Broglie’s hypothesis of matter waves
  • Explain how the de Broglie’s hypothesis gives the rationale for the quantization of angular momentum in Bohr’s quantum theory of the hydrogen atom
  • Describe the Davisson–Germer experiment
  • Interpret de Broglie’s idea of matter waves and how they account for electron diffraction phenomena

Compton’s formula established that an electromagnetic wave can behave like a particle of light when interacting with matter. In 1924, Louis de Broglie proposed a new speculative hypothesis that electrons and other particles of matter can behave like waves. Today, this idea is known as de Broglie’s hypothesis of matter waves . In 1926, De Broglie’s hypothesis, together with Bohr’s early quantum theory, led to the development of a new theory of wave quantum mechanics to describe the physics of atoms and subatomic particles. Quantum mechanics has paved the way for new engineering inventions and technologies, such as the laser and magnetic resonance imaging (MRI). These new technologies drive discoveries in other sciences such as biology and chemistry.

According to de Broglie’s hypothesis, massless photons as well as massive particles must satisfy one common set of relations that connect the energy \(E\) with the frequency \(f\), and the linear momentum \(p\) with the wavelength \(λ\). We have discussed these relations for photons in the context of Compton’s effect. We are recalling them now in a more general context. Any particle that has energy and momentum is a de Broglie wave of frequency \(f\) and wavelength \(\lambda\):

\[ E = h f \label{6.53} \]

\[ \lambda = \frac{h}{p} \label{6.54} \]

Here, \(E\) and \(p\) are, respectively, the relativistic energy and the momentum of a particle. De Broglie’s relations are usually expressed in terms of the wave vector \(\vec{k}\), \(k = 2 \pi / \lambda\), and the wave frequency \(\omega = 2 \pi f\), as we usually do for waves:

\begin{aligned} &E=\hbar \omega \label{6.55}\\ &\vec{p}=\hbar \vec{k} \label{6.56} \end{aligned}

Wave theory tells us that a wave carries its energy with the group velocity . For matter waves, this group velocity is the velocity \(u\) of the particle. Identifying the energy E and momentum p of a particle with its relativistic energy \(mc^2\) and its relativistic momentum \(mu\), respectively, it follows from de Broglie relations that matter waves satisfy the following relation:

\[ \lambda f =\frac{\omega}{k}=\frac{E / \hbar}{p / \hbar}=\frac{E}{p} = \frac{m c^{2}}{m u}=\frac{c^{2}}{u}=\frac{c}{\beta} \label{6.57} \]

where \(\beta = u/c\). When a particle is massless we have \(u=c\) and Equation \ref{6.57} becomes \(\lambda f = c\).

Example \(\PageIndex{1}\): How Long are de Broglie Matter Waves?

Calculate the de Broglie wavelength of:

  • a 0.65-kg basketball thrown at a speed of 10 m/s,
  • a nonrelativistic electron with a kinetic energy of 1.0 eV, and
  • a relativistic electron with a kinetic energy of 108 keV.

We use Equation \ref{6.57} to find the de Broglie wavelength. When the problem involves a nonrelativistic object moving with a nonrelativistic speed u , such as in (a) when \(\beta=u / c \ll 1\), we use nonrelativistic momentum p . When the nonrelativistic approximation cannot be used, such as in (c), we must use the relativistic momentum \(p=m u=m_{0} \gamma u=E_{0} \gamma \beta/c\), where the rest mass energy of a particle is \(E_0 = m c^2 \) and \(\gamma\) is the Lorentz factor \(\gamma=1 / \sqrt{1-\beta^{2}}\). The total energy \(E\) of a particle is given by Equation \ref{6.53} and the kinetic energy is \(K=E-E_{0}=(\gamma-1) E_{0}\). When the kinetic energy is known, we can invert Equation 6.4.2 to find the momentum

\[ p=\sqrt{\left(E^{2}-E_{0}^{2}\right) / c^{2}}=\sqrt{K\left(K+2 E_{0}\right)} / c \nonumber \]

and substitute into Equation \ref{6.57} to obtain

\[ \lambda=\frac{h}{p}=\frac{h c}{\sqrt{K\left(K+2 E_{0}\right)}} \label{6.58} \]

Depending on the problem at hand, in this equation we can use the following values for hc :

\[ h c=\left(6.626 \times 10^{-34} \: \mathrm{J} \cdot \mathrm{s}\right)\left(2.998 \times 10^{8} \: \mathrm{m} / \mathrm{s}\right)=1.986 \times 10^{-25} \: \mathrm{J} \cdot \mathrm{m}=1.241 \: \mathrm{eV} \cdot \mu \mathrm{m} \nonumber \]

  • For the basketball, the kinetic energy is \[ K=m u^{2} / 2=(0.65 \: \mathrm{kg})(10 \: \mathrm{m} / \mathrm{s})^{2} / 2=32.5 \: \mathrm{J} \nonumber \] and the rest mass energy is \[ E_{0}=m c^{2}=(0.65 \: \mathrm{kg})\left(2.998 \times 10^{8} \: \mathrm{m} / \mathrm{s}\right)^{2}=5.84 \times 10^{16} \: \mathrm{J} \nonumber \] We see that \(K /\left(K+E_{0}\right) \ll 1\) and use \(p=m u=(0.65 \: \mathrm{kg})(10 \: \mathrm{m} / \mathrm{s})=6.5 \: \mathrm{J} \cdot \mathrm{s} / \mathrm{m} \): \[ \lambda=\frac{h}{p}=\frac{6.626 \times 10^{-34} \: \mathrm{J} \cdot \mathrm{s}}{6.5 \: \mathrm{J} \cdot \mathrm{s} / \mathrm{m}}=1.02 \times 10^{-34} \: \mathrm{m} \nonumber \]
  • For the nonrelativistic electron, \[ E_{0}=mc^{2}=\left(9.109 \times 10^{-31} \mathrm{kg}\right)\left(2.998 \times 10^{8} \mathrm{m} / \mathrm{s}\right)^{2}=511 \mathrm{keV} \nonumber \] and when \(K = 1.0 \: eV\), we have \(K/(K+E_0) = (1/512) \times 10^{-3} \ll 1\), so we can use the nonrelativistic formula. However, it is simpler here to use Equation \ref{6.58}: \[ \lambda=\frac{h}{p}=\frac{h c}{\sqrt{K\left(K+2 E_{0}\right)}}=\frac{1.241 \: \mathrm{eV} \cdot \mu \mathrm{m}}{\sqrt{(1.0 \: \mathrm{eV})[1.0 \: \mathrm{eV}+2(511 \: \mathrm{keV})]}}=1.23 \: \mathrm{nm} \nonumber \] If we use nonrelativistic momentum, we obtain the same result because 1 eV is much smaller than the rest mass of the electron.
  • For a fast electron with \(K=108 \: keV\), relativistic effects cannot be neglected because its total energy is \(E = K = E_0 = 108 \: keV + 511 \: keV = 619 \: keV\) and \(K/E = 108/619\) is not negligible: \[ \lambda=\frac{h}{p}=\frac{h c}{\sqrt{K\left(K+2 E_{0}\right)}}=\frac{1.241 \: \mathrm{eV} \cdot \mu \mathrm{m}}{\sqrt{108 \: \mathrm{keV}[108 \: \mathrm{keV}+2(511 \: \mathrm{keV})]}}=3.55 \: \mathrm{pm} \nonumber \].


We see from these estimates that De Broglie’s wavelengths of macroscopic objects such as a ball are immeasurably small. Therefore, even if they exist, they are not detectable and do not affect the motion of macroscopic objects.

Exercise \(\PageIndex{1}\)

What is de Broglie’s wavelength of a nonrelativistic proton with a kinetic energy of 1.0 eV?

Using the concept of the electron matter wave, de Broglie provided a rationale for the quantization of the electron’s angular momentum in the hydrogen atom, which was postulated in Bohr’s quantum theory. The physical explanation for the first Bohr quantization condition comes naturally when we assume that an electron in a hydrogen atom behaves not like a particle but like a wave. To see it clearly, imagine a stretched guitar string that is clamped at both ends and vibrates in one of its normal modes. If the length of the string is l (Figure \(\PageIndex{1}\)), the wavelengths of these vibrations cannot be arbitrary but must be such that an integer k number of half-wavelengths \(\lambda/2\) fit exactly on the distance l between the ends. This is the condition \(l=k \lambda /2\) for a standing wave on a string. Now suppose that instead of having the string clamped at the walls, we bend its length into a circle and fasten its ends to each other. This produces a circular string that vibrates in normal modes, satisfying the same standing-wave condition, but the number of half-wavelengths must now be an even number \(k\), \(k=2n\), and the length l is now connected to the radius \(r_n\) of the circle. This means that the radii are not arbitrary but must satisfy the following standing-wave condition:

\[ 2 \pi r_{n}=2 n \frac{\lambda}{2} \label{6.59}. \]

If an electron in the n th Bohr orbit moves as a wave, by Equation \ref{6.59} its wavelength must be equal to \(\lambda = 2 \pi r_n / n\). Assuming that Equation \ref{6.58} is valid, the electron wave of this wavelength corresponds to the electron’s linear momentum, \(p = h/\lambda = nh / (2 \pi r_n) = n \hbar /r_n\). In a circular orbit, therefore, the electron’s angular momentum must be

\[ L_{n}=r_{n} p=r_{n} \frac{n \hbar}{r_{n}}=n \hbar \label{6.60} . \]

This equation is the first of Bohr’s quantization conditions, given by Equation 6.5.6 . Providing a physical explanation for Bohr’s quantization condition is a convincing theoretical argument for the existence of matter waves.

Figure A is the standing-wave pattern for a string clamped in the wall. The distance between each node corresponds to the half gamma. Figure B is the standing-wave pattern for an electron wave trapped in the third Bohr orbit in the hydrogen atom. The wave has a circular shape with six nodes. The distance between each two node corresponds to the gamma.

Example \(\PageIndex{2}\): The Electron Wave in the Ground State of Hydrogen

Find the de Broglie wavelength of an electron in the ground state of hydrogen.

We combine the first quantization condition in Equation \ref{6.60} with Equation 6.5.6 and use Equation 6.5.9 for the first Bohr radius with \(n = 1\).

When \(n=1\) and \(r_n = a_0 = 0.529 \: Å\), the Bohr quantization condition gives \(a_{0} p=1 \cdot \hbar \Rightarrow p=\hbar / a_{0}\). The electron wavelength is:

\[ \lambda=h / p = h / \hbar / a_{0} = 2 \pi a_{0} = 2 \pi(0.529 \: Å)=3.324 \: Å .\nonumber \]

We obtain the same result when we use Equation \ref{6.58} directly.

Exercise \(\PageIndex{2}\)

Find the de Broglie wavelength of an electron in the third excited state of hydrogen.

\(\lambda = 2 \pi n a_0 = 2 (3.324 \: Å) = 6.648 \: Å\)

Experimental confirmation of matter waves came in 1927 when C. Davisson and L. Germer performed a series of electron-scattering experiments that clearly showed that electrons do behave like waves. Davisson and Germer did not set up their experiment to confirm de Broglie’s hypothesis: The confirmation came as a byproduct of their routine experimental studies of metal surfaces under electron bombardment.

In the particular experiment that provided the very first evidence of electron waves (known today as the Davisson–Germer experiment ), they studied a surface of nickel. Their nickel sample was specially prepared in a high-temperature oven to change its usual polycrystalline structure to a form in which large single-crystal domains occupy the volume. Figure \(\PageIndex{2}\) shows the experimental setup. Thermal electrons are released from a heated element (usually made of tungsten) in the electron gun and accelerated through a potential difference ΔV, becoming a well-collimated beam of electrons produced by an electron gun. The kinetic energy \(K\) of the electrons is adjusted by selecting a value of the potential difference in the electron gun. This produces a beam of electrons with a set value of linear momentum, in accordance with the conservation of energy:

\[ e \Delta V=K=\frac{p^{2}}{2 m} \Rightarrow p=\sqrt{2 m e \Delta V} \label{6.61} \]

The electron beam is incident on the nickel sample in the direction normal to its surface. At the surface, it scatters in various directions. The intensity of the beam scattered in a selected direction φφ is measured by a highly sensitive detector. The detector’s angular position with respect to the direction of the incident beam can be varied from φ=0° to φ=90°. The entire setup is enclosed in a vacuum chamber to prevent electron collisions with air molecules, as such thermal collisions would change the electrons’ kinetic energy and are not desirable.

Figure shows the schematics of the experimental setup of the Davisson–Germer diffraction experiment. A beam of electrons is emitted by the electron gun, passes through the collimator, and hits Nickel target. Diffracted beam forms an angle phi with the incident beam and is detected by a moving detector. All of this is shown happening in a vacuum

When the nickel target has a polycrystalline form with many randomly oriented microscopic crystals, the incident electrons scatter off its surface in various random directions. As a result, the intensity of the scattered electron beam is much the same in any direction, resembling a diffuse reflection of light from a porous surface. However, when the nickel target has a regular crystalline structure, the intensity of the scattered electron beam shows a clear maximum at a specific angle and the results show a clear diffraction pattern (see Figure \(\PageIndex{3}\)). Similar diffraction patterns formed by X-rays scattered by various crystalline solids were studied in 1912 by father-and-son physicists William H. Bragg and William L. Bragg. The Bragg law in X-ray crystallography provides a connection between the wavelength \(\lambda\) of the radiation incident on a crystalline lattice, the lattice spacing, and the position of the interference maximum in the diffracted radiation (see Diffraction ).

The graph shows the dependence of the intensity of the scattering beam on the scattering angle in degrees. The intensity degrees from 10 to 30 degrees, followed by a sharp increase and maximum at 50 degrees, and then reaches zero at 80 degrees.

The lattice spacing of the Davisson–Germer target, determined with X-ray crystallography, was measured to be \(a=2.15 \: Å\). Unlike X-ray crystallography in which X-rays penetrate the sample, in the original Davisson–Germer experiment, only the surface atoms interact with the incident electron beam. For the surface diffraction, the maximum intensity of the reflected electron beam is observed for scattering angles that satisfy the condition nλ = a sin φ (see Figure \(\PageIndex{4}\)). The first-order maximum (for n=1) is measured at a scattering angle of φ≈50° at ΔV≈54 V, which gives the wavelength of the incident radiation as λ=(2.15 Å) sin 50° = 1.64 Å. On the other hand, a 54-V potential accelerates the incident electrons to kinetic energies of K = 54 eV. Their momentum, calculated from Equation \ref{6.61}, is \(p = 2.478 \times 10^{−5} \: eV \cdot s/m\). When we substitute this result in Equation \ref{6.58}, the de Broglie wavelength is obtained as

\[ \lambda=\frac{h}{p}=\frac{4.136 \times 10^{-15} \mathrm{eV} \cdot \mathrm{s}}{2.478 \times 10^{-5} \mathrm{eV} \cdot \mathrm{s} / \mathrm{m}}=1.67 \mathrm{Å} \label{6.62}. \]

The same result is obtained when we use K = 54eV in Equation \ref{6.61}. The proximity of this theoretical result to the Davisson–Germer experimental value of λ = 1.64 Å is a convincing argument for the existence of de Broglie matter waves.

Figure shows the surface diffraction of a monochromatic electromagnetic wave on a crystalline lattice structure. The in-phase incident beams are reflected from atoms on the surface. Phi is the angle between the incident and the reflected beam, the in-plane distance between the atoms is a.

Diffraction lines measured with low-energy electrons, such as those used in the Davisson–Germer experiment, are quite broad (Figure \(\PageIndex{3}\)) because the incident electrons are scattered only from the surface. The resolution of diffraction images greatly improves when a higher-energy electron beam passes through a thin metal foil. This occurs because the diffraction image is created by scattering off many crystalline planes inside the volume, and the maxima produced in scattering at Bragg angles are sharp (Figure \(\PageIndex{5}\)).

Picture A is a photograph of the diffraction pattern obtained in scattering on a crystalline solid with X-rays. Picture B is a photograph of the diffraction pattern obtained in scattering on a crystalline solid with electrons. Both pictures demonstrate diffracted spots symmetrically arranged around the central beam.

Since the work of Davisson and Germer, de Broglie’s hypothesis has been extensively tested with various experimental techniques, and the existence of de Broglie waves has been confirmed for numerous elementary particles. Neutrons have been used in scattering experiments to determine crystalline structures of solids from interference patterns formed by neutron matter waves. The neutron has zero charge and its mass is comparable with the mass of a positively charged proton. Both neutrons and protons can be seen as matter waves. Therefore, the property of being a matter wave is not specific to electrically charged particles but is true of all particles in motion. Matter waves of molecules as large as carbon \(C_{60}\) have been measured. All physical objects, small or large, have an associated matter wave as long as they remain in motion. The universal character of de Broglie matter waves is firmly established.

Example \(\PageIndex{3A}\): Neutron Scattering

Suppose that a neutron beam is used in a diffraction experiment on a typical crystalline solid. Estimate the kinetic energy of a neutron (in eV) in the neutron beam and compare it with kinetic energy of an ideal gas in equilibrium at room temperature.

We assume that a typical crystal spacing a is of the order of 1.0 Å. To observe a diffraction pattern on such a lattice, the neutron wavelength λ must be on the same order of magnitude as the lattice spacing. We use Equation \ref{6.61} to find the momentum p and kinetic energy K . To compare this energy with the energy \(E_T\) of ideal gas in equilibrium at room temperature \(T = 300 \, K\), we use the relation \(K = 3/2 k_BT\), where \(k_B = 8.62 \times 10^{-5}eV/K\) is the Boltzmann constant.

We evaluate pc to compare it with the neutron’s rest mass energy \(E_0 = 940 \, MeV\):

\[p = \frac{h}{\lambda} \Rightarrow pc = \frac{hc}{\lambda} = \frac{1.241 \times 10^{-6}eV \cdot m}{10^{-10}m} = 12.41 \, keV. \nonumber \]

We see that \(p^2c^2 << E_0^2\) and we can use the nonrelativistic kinetic energy:

\[K = \frac{p^2}{2m_n} = \frac{h^2}{2\lambda^2 m_n} = \frac{(6.63\times 10^{−34}J \cdot s)^2}{(2\times 10^{−20}m^2)(1.66 \times 10^{−27} kg)} = 1.32 \times 10^{−20} J = 82.7 \, meV. \nonumber \]

Kinetic energy of ideal gas in equilibrium at 300 K is:

\[K_T = \frac{3}{2}k_BT = \frac{3}{2} (8.62 \times 10^{-5}eV/K)(300 \, K) = 38.8 \, MeV. \nonumber \]

We see that these energies are of the same order of magnitude.

Neutrons with energies in this range, which is typical for an ideal gas at room temperature, are called “thermal neutrons.”

Example \(\PageIndex{3B}\): Wavelength of a Relativistic Proton

In a supercollider at CERN, protons can be accelerated to velocities of 0.75 c . What are their de Broglie wavelengths at this speed? What are their kinetic energies?

The rest mass energy of a proton is \(E_0 = m_0c^2 = (1.672 \times 10^{−27} kg)(2.998 \times 10^8m/s)^2 = 938 \, MeV\). When the proton’s velocity is known, we have β = 0.75 and \(\beta \gamma = 0.75 / \sqrt{1 - 0.75^2} = 1.714\). We obtain the wavelength λλ and kinetic energy K from relativistic relations.

\[\lambda = \frac{h}{p} = \frac{hc}{\beta \gamma E_0} = \frac{1.241 \, eV \cdot \mu m}{1.714 (938 \, MeV)} = 0.77 \, fm \nonumber \]

\[K = E_0(\gamma - 1) = 938 \, MeV (1 /\sqrt{1 - 0.75^2} - 1) = 480.1\, MeV \nonumber \]

Notice that because a proton is 1835 times more massive than an electron, if this experiment were performed with electrons, a simple rescaling of these results would give us the electron’s wavelength of (1835)0.77 fm = 1.4 pm and its kinetic energy of 480.1 MeV /1835 = 261.6 keV.

Exercise \(\PageIndex{3}\)

Find the de Broglie wavelength and kinetic energy of a free electron that travels at a speed of 0.75 c .

\(\lambda = 1.417 \, pm; \, K = 261.56 \, keV\)

what is a hypothesis physics


Three Famous Hypotheses and How They Were Tested

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Art Hasler

Key Takeaways

  • Ivan Pavlov's experiment demonstrated conditioned responses in dogs.
  • Pavlov's work exemplifies the scientific method, starting with a hypothesis about conditioned responses and testing it through controlled experiments.
  • Pavlov's findings not only advanced an understanding of animal physiology but also laid foundational principles for behaviorism, a major school of thought in psychology that emphasizes the study of observable behaviors.

Coho salmon ( Oncorhynchus kisutch ) are amazing fish. Indigenous to the Pacific Northwest, they begin their lives in freshwater streams and then relocate to the open ocean. But when a Coho salmon reaches breeding age, it'll return to the waterway of its birth , sometimes traveling 400 miles (644 kilometers) to get there.

Enter the late Arthur Davis Hasler. While an ecologist and biologist at the University of Wisconsin, he was intrigued by the question of how these creatures find their home streams. And in 1960, he used a Hypothesis-Presentation.pdf">basic tenet of science — the hypothesis — to find out.

So what is a hypothesis? A hypothesis is a tentative, testable explanation for an observed phenomenon in nature. Hypotheses are narrow in scope — unlike theories , which cover a broad range of observable phenomena and draw from many different lines of evidence. Meanwhile, a prediction is a result you'd expect to get if your hypothesis or theory is accurate.

So back to 1960 and Hasler and those salmon. One unverified idea was that Coho salmon used eyesight to locate their home streams. Hasler set out to test this notion (or hypothesis). First, he rounded up several fish who'd already returned to their native streams. Next, he blindfolded some of the captives — but not all of them — before dumping his salmon into a faraway stretch of water. If the eyesight hypothesis was correct, then Hasler could expect fewer of the blindfolded fish to return to their home streams.

Things didn't work out that way. The fish without blindfolds came back at the same rate as their blindfolded counterparts. (Other experiments demonstrated that smell, and not sight, is the key to the species' homing ability.)

Although Hasler's blindfold hypothesis was disproven, others have fared better. Today, we're looking at three of the best-known experiments in history — and the hypotheses they tested.

Ivan Pavlov and His Dogs (1903-1935)

Isaac newton's radiant prisms (1665), robert paine's revealing starfish (1963-1969).

The Hypothesis : If dogs are susceptible to conditioned responses (drooling), then a dog who is regularly exposed to the same neutral stimulus (metronome/bell) before it receives food will associate this neutral stimulus with the act of eating. Eventually, the dog should begin to drool at a predictable rate when it encounters said stimulus — even before any actual food is offered.

The Experiment : A Nobel Prize-winner and outspoken critic of Soviet communism, Ivan Pavlov is synonymous with man's best friend . In 1903, the Russian-born scientist kicked off a decades-long series of experiments involving dogs and conditioned responses .

Offer a plate of food to a hungry dog and it'll salivate. In this context, the stimulus (the food) will automatically trigger a particular response (the drooling). The latter is an innate, unlearned reaction to the former.

By contrast, the rhythmic sound of a metronome or bell is a neutral stimulus. To a dog, the noise has no inherent meaning and if the animal has never heard it before, the sound won't provoke an instinctive reaction. But the sight of food sure will .

So when Pavlov and his lab assistants played the sound of the metronome/bell before feeding sessions, the researchers conditioned test dogs to mentally link metronomes/bells with mealtime. Due to repeated exposure, the noise alone started to make the dogs' mouths water before they were given food.

According to " Ivan Pavlov: A Russian Life in Science " by biographer Daniel P. Todes, Pavlov's big innovation here was his discovery that he could quantify the reaction of each pooch by measuring the amount of saliva it generated. Every canine predictably drooled at its own consistent rate when he or she encountered a personalized (and artificial) food-related cue.

Pavlov and his assistants used conditioned responses to look at other hypotheses about animal physiology, as well. In one notable experiment, a dog was tested on its ability to tell time . This particular pooch always received food when it heard a metronome click at the rate of 60 strokes per minute. But it never got any food after listening to a slower, 40-strokes-per-minute beat. Lo and behold, Pavlov's animal began to salivate in response to the faster rhythm — but not the slower one . So clearly, it could tell the two rhythmic beats apart.

The Verdict : With the right conditioning — and lots of patience — you can make a hungry dog respond to neutral stimuli by salivating on cue in a way that's both predictable and scientifically quantifiable.

Pavlov's dog

The Hypothesis : If white sunlight is a mixture of all the colors in the visible spectrum — and these travel at varying wavelengths — then each color will refract at a different angle when a beam of sunlight passes through a glass prism.

The Experiments : Color was a scientific mystery before Isaac Newton came along. During the summer of 1665, he started experimenting with glass prisms from the safety of a darkened room in Cambridge, England.

He cut a quarter-inch (0.63-centimeter) circular hole into one of the window shutters, allowing a single beam of sunlight to enter the place. When Newton held up a prism to this ray, an oblong patch of multicolored light was projected onto the opposite wall.

This contained segregated layers of red, orange, yellow, green, blue, indigo and violet light. From top to bottom, this patch measured 13.5 inches (33.65 centimeters) tall, yet it was only 2.6 inches (6.6 centimeters) across.

Newton deduced that these vibrant colors had been hiding within the sunlight itself, but the prism bent (or "refracted") them at different angles, which separated the colors out.

Still, he wasn't 100 percent sure. So Newton replicated the experiment with one small change. This time, he took a second prism and had it intercept the rainbow-like patch of light. Once the refracted colors entered the new prism, they recombined into a circular white sunbeam. In other words, Newton took a ray of white light, broke it apart into a bunch of different colors and then reassembled it. What a neat party trick!

The Verdict : Sunlight really is a blend of all the colors in the rainbow — and yes, these can be individually separated via light refraction.

Isaac Newton

The Hypothesis : If predators limit the populations of the organisms they attack, then we'd expect the prey species to become more common after the eradication of a major predator.

The Experiment : Meet Pisaster ochraceus , also known as the purple sea star (or the purple starfish if you prefer).

Using an extendable stomach , the creature feeds on mussels, limpets, barnacles, snails and other hapless victims. On some seaside rocks (and tidal pools) along the coast of Washington state, this starfish is the apex predator.

The animal made Robert Paine a scientific celebrity. An ecologist by trade, Paine was fascinated by the environmental roles of top predators. In June 1963, he kicked off an ambitious experiment along Washington state's Mukkaw Bay. For years on end, Paine kept a rocky section of this shoreline completely starfish-free.

It was hard work. Paine had to regularly pry wayward sea stars off "his" outcrop — sometimes with a crowbar. Then he'd chuck them into the ocean.

Before the experiment, Paine observed 15 different species of animals and algae inhabiting the area he decided to test. By June 1964 — one year after his starfish purge started — that number had dropped to eight .

Unchecked by purple sea stars, the barnacle population skyrocketed. Subsequently, these were replaced by California mussels , which came to dominate the terrain. By anchoring themselves to rocks in great numbers, the mussels edged out other life-forms. That made the outcrop uninhabitable to most former residents: Even sponges, anemones and algae — organisms that Pisaster ochraceus doesn't eat — were largely evicted.

All those species continued to thrive on another piece of shoreline that Paine left untouched. Later experiments convinced him that Pisaster ochraceus is a " keystone species ," a creature who exerts disproportionate influence over its environment. Eliminate the keystone and the whole system gets disheveled.

The Verdict : Apex predators don't just affect the animals that they hunt. Removing a top predator sets off a chain reaction that can fundamentally transform an entire ecosystem.

purple sea stars

Contrary to popular belief, Pavlov almost never used bells in his dog experiments. Instead, he preferred metronomes, buzzers, harmoniums and electric shocks.

Frequently Asked Questions

How can a hypothesis become a theory, what's the difference between a hypothesis and a prediction.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

A hypothesis (plural hypothesis) is a proposed clarification for a phenomenon. For a hypothesis to be logical speculation. These are the logical strategy necessitate that one can test it. Researchers for the most part base logical hypothesis on past perceptions that can’t sufficiently be clarified with the accessible logical hypothesis.

Despite the fact that the word “hypothesis” is regularly in use. Equivalently, a logical hypothesis isn’t equivalent to a scientific hypothesis. A working hypothesis is a temporarily acknowledged hypothesis proposed for additional exploration, in a cycle starting with an informed estimate or thought.



In its antiquated utilization, hypothesis alluded to an outline of the plot of an old-style dramatization. The English word hypothesis comes from the antiquated Greek word hypothesis. Its exacting or etymological sense is “putting or setting under”. Henceforth in broad use has numerous different implications including “assumption”.

In Common Utilization

In common utilization, a hypothesis alludes to a temporary thought whose legitimacy requires assessment. For legitimate assessment, the composer of a hypothesis needs to characterize particulars in operational terms. A hypothesis requires more work by the scientist to either affirm or negate it. At the appointed time, an affirmed hypothesis may turn out to be important for a hypothesis. At times may develop to turn into a hypothesis itself.

Regularly, a logical hypothesis has the type of numerical model. Sometimes, however not generally, one can likewise plan them as existential proclamations. Expressing that some specific case of the phenomenon under assessment has some trademark and causal clarifications. This has the overall type of explanations, expressing that each case of the specific trademark.

In Innovative Science

In innovative science, a hypothesis is useful to define temporary thoughts inside a business setting. The figured hypothesis is then assessed where either the hypothesis is demonstrated to be “valid” or “bogus”. It is through an undeniable nature or falsifiability-arranged test.

Any valuable hypothesis will empower forecasts by thinking (counting deductive thinking). It may foresee the result of an analysis in a research centre setting or the perception of wonder in nature. The forecast may likewise conjure measurements and just discussion about probabilities. Karl Popper, following others, has contended that a hypothesis must be falsifiable. One can’t view a suggestion or hypothesis as logical on the off chance that it doesn’t concede the chance of being indicated bogus. Different thinkers of science have dismissed the model of falsifiability or enhanced it with other measures.

For example, undeniable nature for e.g., verificationism or soundness like affirmation comprehensive quality. The logical technique includes experimentation, to test the capacity of some hypothesis to satisfactorily address the inquiry under scrutiny. Conversely, liberated perception isn’t as liable to bring up unexplained issues or open issues in science. As it would the plan of a pivotal trial to test the hypothesis. A psychological test may likewise be utilized to test the hypothesis too.

In outlining a hypothesis, the examiner must not right now know the result of a test. It remains sensibly under proceeding with examination. Just in such cases does the analysis, test or study conceivably increment the likelihood of indicating the reality of a hypothesis.

If the specialist definitely knows the result, it considers an “outcome”. The scientist ought to have just thought about this while detailing the hypothesis. On the off chance that one can’t survey the expectations by perception or by experience. The hypothesis should be tried by others giving perceptions. For instance, another innovation or hypothesis may make the essential trials practical.

Characteristics of Hypothesis

Following are the characteristics of the hypothesis:

  • The theory ought to be clear and exact to believe it to be solid.
  • If the hypothesis is a social theory, at that point it ought to express the connection between factors.
  • The theory must be explicit and ought to have scope for leading more tests.
  • The method of clarification of the theory must be basic and it should likewise be perceived that the straightforwardness of the hypothesis isn’t identified with its essentialness.

Sources of Hypothesis

Following are the sources of the hypothesis:

  • The likeness between the wonder.
  • Observations from past investigations, present-day encounters and from the contenders.
  • Scientific hypothesis.
  • General designs that impact the considering cycle individuals.

Types of Hypothesis

There are six forms of the hypothesis and they are:

  • Simple hypothesis
  • Complex hypothesis
  • Directional hypothesis
  • Non-directional hypothesis
  • Null hypothesis
  • Associative and casual hypothesis

Simple Hypothesis

It shows a connection between one ward variable and a solitary autonomous variable. For instance, If you eat more vegetables, you will get in shape quicker. Here, eating more vegetables is a free factor, while getting more fit is the needy variable.

Complex Hypothesis

It shows the connection between at least two ward factors and at least two autonomous factors. Eating more vegetables and natural products prompts weight reduction. May be sparkling skin, diminishes the danger of numerous infections, for example, coronary illness, hypertension and a few diseases.

Directional Hypothesis

It shows how an analyst is scholarly and focused on a specific result. The connection between the factors can likewise foresee its inclination. For instance, kids matured four years eating appropriate food over a five-year time frame are having higher IQ levels than youngsters not having a legitimate dinner. This shows the impact and course of impact.

Non-directional Hypothesis

It is utilized when there is no theory included. It is an explanation that a relationship exists between two factors, without foreseeing the specific nature (course) of the relationship.

Null Hypothesis

It gives the explanation which is in opposition to the theory. It’s a negative assertion, and there is no connection between autonomous and subordinate factors. The image is indicated by “HO”.

Associative and Causal Hypothesis

Acquainted hypothesis happens when there is an adjustment in one variable bringing about an adjustment in the other variable. Though, the causal hypothesis proposes a circumstances and logical results connection between at least two factors.

Examples of Hypothesis

Following are the examples of the hypothesis according to their types:

  • Consumption of sweet beverages consistently prompts weight is a case of a straightforward theory.
  • All lilies have a similar number of petals is a case of an invalid hypothesis.
  • If an individual gets 7 hours of rest, at that point he will feel less weakness than if he dozens less.

FAQs about Hypothesis

Q.1. Write a short note on the term hypothesis.

Answer: A hypothesis (plural hypothesis) is a proposed clarification for a phenomenon. For a hypothesis to be logical speculation. The logical strategy necessitates that one can test it. Researchers for the most part base logical hypothesis on past perceptions that can’t sufficiently be clarified with the accessible logical hypotheses. Despite the fact that the words “hypothesis” and “hypothesis” are regularly utilized equivalently, a logical hypothesis isn’t equivalent to a scientific hypothesis.

Q.2. What are the functions of the Hypothesis?

Answer: Following are the functions performed by the hypothesis:

  • Hypothesis helps in mentioning an objective fact and tests conceivable.
  • It turns into the beginning point for the formal examination.
  • Hypothesis helps in checking the perceptions.
  • It helps in coordinating the requests in the correct ways.

Q.3. How will Hypothesis help in Scientific Method?

Answer: Scientists use theory to put down their considerations coordinating how the test would happen. Following are the means that are engaged with the logical strategy:

  • Formation of inquiry
  • Doing foundation research
  • Creation of hypothesis
  • Designing an investigation
  • Collection of information
  • Result examination
  • Summarizing the trial
  • Communicating the outcomes

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what is a hypothesis physics

Newton didn’t frame hypotheses. Why should we?

The success of a grant proposal shouldn’t hinge on whether the research is driven by a hypothesis, especially in the physical sciences.


“Not hypothesis driven.” With those words and a fatal grade of “Very Good,” a fellow reviewer on a funding agency panel consigned the proposal we were discussing to the wastebasket. I listened in dismay. Certainly the proposal had hypotheses, though it didn’t have boldface sentences beginning “We hypothesize . . .” as signposts for inattentive readers. Then I remembered the famous words from Isaac Newton’s Principia : Hypotheses non fingo . “I do not frame hypotheses.” If that approach worked for Newton, why do we have such a mania for hypothesis-driven research today?

The emphasis on hypothesis-driven research in proposals is strangely embedded in the scientific community, with no obvious origin in funding agencies. The word hypothesis appears nowhere in the NSF guide to writing and reviewing proposals, and only once in the National Institutes of Health proposal guide. Yet grant-writing experts universally stress that proposals should be built around hypotheses and warn that those not written this way risk rejection as “fishing expeditions.”

In recent years, a few voices in the biosciences community have questioned this exclusive focus on hypothesis-driven research, even as the mania spreads to the physical sciences. Allow me to add my voice. Evaluating grant proposals is hard, but shoehorning every proposal into the language of hypothesis testing benefits neither the prospective grantee nor the evaluator. It can also hinder scientific progress.

Hypothesis history

Isaac Newton

Today many high school teachers present the scientific method as synonymous with hypothesis testing. Yet hypotheses are just ideas about how nature works, or what 19th-century scientist and philosopher William Whewell called “happy guesses.” Hypotheses organize our thinking about what might be true, based on what we’ve observed so far. If we have a guess about how nature works, we do experiments to test the guess. In quantitative sciences, the role of theory is to work out consequences of the guess in conjunction with things we know.

Perhaps the most famous hypothesis in all of science is that new species arise from the action of natural selection on random mutations. Charles Darwin based his hypothesis on observations of a few species during his famous voyage to the Galápagos. Charged with predictive power, Darwin’s hypothesis applies to all life, everywhere, at all times. Generations of biologists have tested and built on Darwin’s hypothesis with a vast array of new discoveries. The theory of evolution is now firmly established as the central pillar of biology, as well supported by evidence as any theory in science.

But what would Darwin have written had he been obliged to write a proposal to fund his voyage on HMS Beagle ? He didn’t have the hypothesis of natural selection yet—it grew out of the very observations he was setting out to make. If he wrote, truthfully, that “the isolated islands we will visit are excellent natural laboratories to observe what becomes of species introduced to a new locale,” it would be judged by today’s standards as a fishing expedition without a strong hypothesis.

What did Newton hypothesize, despite his protests to the contrary? He identified the right variables for the problem of planetary motion: force and momentum. Newton’s grant proposal might have read: “I hypothesize that momenta and forces are the right variables to describe the motion of the planets. I propose to develop mathematical methods to predict their orbits, which I will compare with existing observations.” That’s not quite a guess about how nature works, but rather the best way to describe motion mathematically, which by its widespread success grew into intuitive concepts of force, momentum, and energy.

Newton wrote hypotheses non fingo because of what he didn’t hypothesize. He wrote in reaction to vortex theories of gravity originated by René Descartes and Christiaan Huygens. They imagined that so-called empty space was actually filled with swirling vortices of invisible particles that swept the planets along in their orbits. The vortex idea is certainly a guess about how gravity works; it’s just not a very helpful guess. The idea of invisible particles that only reveal themselves by effects on unreachably distant planets is too elastic a notion. It’s not specific enough to make testable predictions. In the language of 20th-century philosopher of science Karl Popper, it’s not readily falsifiable.

Newton didn’t provide a just-so story, a fanciful mechanism for why momentum was conserved or how gravity arose. Instead he formulated simple rules that describe how the planets move—and as it turns out, how nearly everything else moves under ordinary circumstances. Powerful as Newton’s insight was, his description of gravity had the unsettling feature of “spooky action at a distance” of the Sun on the planets, and indeed every mass on every other mass. It took another 250 years for an explanation of the physical origin of gravity.

Albert Einstein’s hypothesis about gravity, unlike Newton’s, was mechanistic: Mass curves space, which is slightly elastic; as a result, straight lines bend near massive objects, including the path of light from distant stars passing near the Sun on its way to our telescopes. It took years for Einstein to develop the math to show that Newton’s description, which was consistent with so many observations, was only an approximation—and to make astounding predictions of things that happen to huge masses (collapse into black holes) or when big masses move really fast (gravitational waves).

Setting physical science apart

So why is present-day funding so focused on hypothesis-driven research? A clue is that hypothesis-driven experimental design is best suited to certain influential fields, especially molecular biology and medicine. Researchers in those fields study complicated, irreducible systems (living organisms), have limited experimental probes, and are often forced to work with small data sets. Unavoidably, the most common experimental protocol in these fields is to poke at a complex living system by giving it a drug or chemical and then measuring some indirectly related response. Those experiments live and die by the statistical test. When a scatter plot of stimulus versus response looks like a cloud of angry bees, the formal discipline of testing the null hypothesis is essential.

HMS Beagle

That is an overly narrow paradigm for what experiments can be. In the physical sciences, we are more able to manipulate and simplify the system of interest. We also enjoy more powerful experimental techniques, in many ways extensions of human senses, allowing us to see into a material, to listen to how it rings in response to being pinged with electromagnetic fields, to feel how it responds to a gentle push on the nanoscale. When you can do those things, experiments can be so much more than testing whether changing X influences Y with statistical significance. In fact, the history of science can be viewed as the development of new ways to probe nature. The Hubble Space Telescope was not driven by a hypothesis but rather by a desire to see deeper into the universe. Observations from Hubble and other modern telescopes enable new hypotheses about the early universe to be formulated and tested.

Progress in science often depends on advances in how to measure something important. A century after Einstein, ultrasensitive detectors brilliantly confirmed his prediction of gravitational waves. Those detectors rely on clever ideas for using lasers and interferometry to measure extremely tiny changes in the distance between two points on Earth. That work was not hypothesis driven, except in the obvious sense that general relativity predicts gravitational waves. Likewise, progress in quantitative sciences often relies on advances in our ability to compute the consequences of hypotheses that already exist.

Hypotheses are all well and good. But in evaluating research proposals, the key criterion should be: Will the proposed work help us answer an important question or reveal an important new question we should have been asking all along?

Scott Milner is William H. Joyce Chair and Professor of Chemical Engineering at the Pennsylvania State University.

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De Broglie Hypothesis

Team Physics - Examples.com

The De Broglie Hypothesis is a fundamental concept in proposed by the French physicist Louis de Broglie in 1924. This groundbreaking idea introduced the wave-particle duality of matter, suggesting that not only light (previously understood to exhibit both wave-like and particle-like properties) but all forms of matter have wave-like characteristics.

De Broglie Equation Derivation

Louis de Broglie hypothesized that if light can display dual characteristics (both wave-like and particle-like properties), then particles, such as electrons, might also exhibit similar dual characteristics. His derivation was based on the parallels between the equations for energy and momentum in both light and material particles.

Step 1: Relating Energy and Momentum for Light

For photons (light particles), the energy (𝐸 E ) and momentum (𝑝 p ) are related by the equations:

Here, ℎ h is Planck’s constant, 𝑓 f is the frequency of the photon, and 𝑐 c is the speed of light. By substituting the energy equation into the momentum equation, we get:

Since the wavelength ( λ ) of a photon is related to its frequency by 𝑐 = 𝜆𝑓, we can rewrite 𝑓 as:

Substituting back, the momentum of a photon can be expressed as:

Step 2: Applying the Concept to Material Particles

De Broglie proposed that if light (which was known to have wave-like properties) has a wavelength given 𝜆 = ℎ/𝑝​, then particles, such as electrons, should also have a wavelength describable by a similar relationship, even though they have mass. Thus, he extended the equation to all matter, proposing that:

where p is now the momentum of the particle, which for a non-relativistic particle is given by:

Here, m is the mass of the particle and v is its velocity.

Step 3: De Broglie Wavelength of Particles

Combining the expressions, the de Broglie wavelength for any particle is thus given by:

This equation implies that every moving particle has a wave associated with it, and the wavelength of that wave is inversely proportional to the particle’s momentum. This groundbreaking idea led to the development of wave mechanics and has been fundamental in many areas of quantum physics, such as the theory behind quantum fields and elementary particles.

De Broglie Wavelength for an Electron

To calculate the De Broglie wavelength of an electron, we use the formula derived by Louis de Broglie which relates a particle’s wavelength to its momentum. The formula is:

  • 𝜆 is the wavelength,
  • ℎ is Planck’s constant, approximately 6.626×10⁻³⁴ Joule seconds,
  • 𝑝 is the momentum of the electron.

Calculating Momentum

The momentum 𝑝 p of an electron can be calculated using the formula: 𝑝=𝑚𝑣 p = m v where:

  • 𝑚 is the mass of the electron, approximately 9.109×10⁻³¹ kg,
  • 𝑣 is the velocity of the electron.

Significance of the De Broglie Equation

The De Broglie equation , 𝜆 = ℎ/𝑝 ​, is a cornerstone in quantum mechanics, providing a profound understanding of the wave-particle duality of matter. Its implications extend far beyond theoretical physics, impacting various scientific fields and technologies.

Fundamental to Quantum Mechanics

The equation integrates wave-like behavior into the description of elementary particles, bridging a gap between classical and quantum physics. This wave-particle duality is essential for the development of quantum mechanics, influencing the theoretical framework that describes how subatomic particles behave.

Basis for Modern Physics Theories

De Broglie’s insights laid the groundwork for Schrödinger to formulate his wave equation, which uses the concept of wavefunctions to describe the statistical behavior of systems. The wave-particle duality concept is integral to quantum field theory, which extends quantum mechanics to more complex systems including fields and forces.

Experimental Validation and Applications

The equation has been empirically validated through experiments such as electron diffraction and neutron diffraction, which demonstrate that particles exhibit wave-like behavior under certain conditions. These experiments are pivotal for technologies such as electron microscopes, which rely on electron waves to achieve high-resolution imaging beyond the capability of traditional optical microscopes.

Technological Impact

Understanding the wave properties of particles enables the exploitation of phenomena such as quantum tunneling, utilized in devices like tunnel diodes and the scanning tunneling microscope. These applications are crucial in electronics and materials science, where quantum effects are significant.

Educational and Conceptual Influence

The De Broglie equation has also profoundly impacted educational approaches in physics, providing a fundamental concept that challenges and expands our understanding of the natural world. It encourages a more nuanced view of matter, essential for students and researchers delving into quantum physics.

Relation between De Broglie Equation and Bohr’s Hypothesis of Atom

De broglie’s equation.

Louis de Broglie introduced his theory of electron waves in 1924, which proposed that particles could exhibit properties of waves. His famous equation relates the wavelength of a particle to its momentum: 𝜆 = ℎ/𝑝 where 𝜆is the wavelength, ℎ is Planck’s constant, and 𝑝 p is the momentum of the particle.

Bohr’s Hypothesis of the Atom

Niels Bohr proposed his model of the atom in 1913. His key hypothesis was that electrons orbit the nucleus in distinct orbits without radiating energy, contrary to what classical electromagnetism would predict. To explain the stability of these orbits, Bohr introduced the concept of quantization:

  • Electrons can only occupy certain allowed orbits.
  • The angular momentum of electrons in these orbits is quantized, specifically, it is an integer multiple of the reduced Planck constant
  • (ℏ): 𝐿 = 𝑛×ℎ/2𝜋 = 𝑛ℏ
  • where 𝐿 L is the angular momentum, n is a positive integer (quantum number), and h is Planck’s constant.

Integrating De Broglie’s Equation with Bohr’s Model

De Broglie’s theory was revolutionary because it provided a theoretical justification for Bohr’s quantization condition by interpreting the electron not just as a particle, but as a wave that must form a standing wave pattern around the nucleus. For the electron wave to be stable and not interfere destructively with itself, the circumference of the electron’s orbit must be an integer multiple of its wavelength:

where 𝑟 is the radius of the electron’s orbit, and n is an integer. This condition ensures that the wave ‘fits’ perfectly into its orbital path around the nucleus.

Substituting De Broglie’s Equation

By substituting De Broglie’s expression for the wavelength into the condition for a stable orbit, we get:

Using the expression for momentum 𝑝=𝑚𝑣 p = mv and the definition of angular momentum 𝐿=𝑚𝑣𝑟 L = mvr , we can relate this to Bohr’s quantization of angular momentum:

Thus, De Broglie’s hypothesis not only supported Bohr’s model but also suggested a deeper wave nature of the electron. It bridged the gap between the quantized orbits of Bohr’s atom model and the wave-like behavior of particles, paving the way for modern quantum mechanics, which would further refine and expand these ideas in the Schrodinger equation and beyond.

Examples of De Broglie Hypothesis


Electron Diffraction

One of the first confirmations of De Broglie’s hypothesis was the observation of electron diffraction patterns. When electrons are passed through thin metal foils or across a crystal, they produce diffraction patterns similar to those produced by light waves, confirming that electrons behave as waves under certain conditions.

Scanning Tunneling Microscope (STM)

The scanning tunneling microscope, which can image surfaces at the atomic level, operates based on the quantum tunneling of electrons between the microscope’s tip and the surface. The wave nature of electrons, as predicted by De Broglie, is fundamental to the operation of this instrument.

Bohr Model of the Atom

De Broglie’s ideas extended the Bohr model by providing a theoretical basis for the quantization of electron orbits in atoms. His hypothesis suggested that electrons form standing wave patterns around the nucleus, which only occur at certain discrete (quantized) orbits.

Matter Waves

The concept of matter waves is essential in fields like quantum mechanics and has led to further developments in wave mechanics. This includes the use of neutrons, atoms, and molecules in wave-like applications, similar to how light and electrons are used.

Neutron Interferometry

Neutron beams, used in neutron interferometry, exhibit wave-like interference effects. These experiments have provided precise measurements of neutron properties and fundamental quantum phenomena, supporting De Broglie’s hypothesis at larger scales.

Atomic Force Microscopy (AFM)

AFM, like STM, uses the principles of quantum mechanics and the wave-like properties of atoms on a surface to achieve high-resolution imaging. The forces between the tip’s atoms and the sample’s atoms are influenced by their wave functions.

How was the De Broglie Equation derived?

Louis de Broglie proposed that particles of matter, like electrons, could exhibit wave-like properties similar to light. Combining Einstein’s equation relating energy and mass (𝐸 = 𝑚𝑐²) with Planck’s equation relating energy and frequency (𝐸 = ℎ𝑓), and considering the wave equation (𝑐 = 𝑓𝜆), De Broglie derived his hypothesis that matter behaves as waves.

Why is the De Broglie Equation important?

The De Broglie Equation is crucial for understanding quantum mechanics as it introduces the concept of wave-particle duality. This concept states that every particle or quantum entity can exhibit both particle-like and wave-like behavior. It forms the basis for the development of quantum theory, particularly in the formulation of wave mechanics.

Can the De Broglie Equation be applied to all objects?

While theoretically applicable to all matter, in practice, the wave-like properties described by the De Broglie Equation are significant only for very small objects, like subatomic particles. For larger objects, the wavelengths calculated by the equation become so small that they are not detectable with current technology.

What is wave-particle duality?

Wave-particle duality is a fundamental concept of quantum mechanics that suggests that every particle or quantum entity may be partly described in terms not only of particles, but also of waves. It means that elementary particles such as electrons and photons exhibit both particle-like and wave-like properties, depending on the experimental setup.


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Definition of hypothesis

Did you know.

The Difference Between Hypothesis and Theory

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

In the scientific method, the hypothesis is constructed before any applicable research has been done, apart from a basic background review. You ask a question, read up on what has been studied before, and then form a hypothesis.

A hypothesis is usually tentative; it's an assumption or suggestion made strictly for the objective of being tested.

A theory , in contrast, is a principle that has been formed as an attempt to explain things that have already been substantiated by data. It is used in the names of a number of principles accepted in the scientific community, such as the Big Bang Theory . Because of the rigors of experimentation and control, it is understood to be more likely to be true than a hypothesis is.

In non-scientific use, however, hypothesis and theory are often used interchangeably to mean simply an idea, speculation, or hunch, with theory being the more common choice.

Since this casual use does away with the distinctions upheld by the scientific community, hypothesis and theory are prone to being wrongly interpreted even when they are encountered in scientific contexts—or at least, contexts that allude to scientific study without making the critical distinction that scientists employ when weighing hypotheses and theories.

The most common occurrence is when theory is interpreted—and sometimes even gleefully seized upon—to mean something having less truth value than other scientific principles. (The word law applies to principles so firmly established that they are almost never questioned, such as the law of gravity.)

This mistake is one of projection: since we use theory in general to mean something lightly speculated, then it's implied that scientists must be talking about the same level of uncertainty when they use theory to refer to their well-tested and reasoned principles.

The distinction has come to the forefront particularly on occasions when the content of science curricula in schools has been challenged—notably, when a school board in Georgia put stickers on textbooks stating that evolution was "a theory, not a fact, regarding the origin of living things." As Kenneth R. Miller, a cell biologist at Brown University, has said , a theory "doesn’t mean a hunch or a guess. A theory is a system of explanations that ties together a whole bunch of facts. It not only explains those facts, but predicts what you ought to find from other observations and experiments.”

While theories are never completely infallible, they form the basis of scientific reasoning because, as Miller said "to the best of our ability, we’ve tested them, and they’ve held up."

  • proposition
  • supposition

hypothesis , theory , law mean a formula derived by inference from scientific data that explains a principle operating in nature.

hypothesis implies insufficient evidence to provide more than a tentative explanation.

theory implies a greater range of evidence and greater likelihood of truth.

law implies a statement of order and relation in nature that has been found to be invariable under the same conditions.

Examples of hypothesis in a Sentence

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Word History

Greek, from hypotithenai to put under, suppose, from hypo- + tithenai to put — more at do

1641, in the meaning defined at sense 1a

Phrases Containing hypothesis

  • counter - hypothesis
  • nebular hypothesis
  • null hypothesis
  • planetesimal hypothesis
  • Whorfian hypothesis

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This is the Difference Between a Hypothesis and a Theory

In scientific reasoning, they're two completely different things

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“Hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/hypothesis. Accessed 1 May. 2024.

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Kids definition of hypothesis, medical definition, medical definition of hypothesis, more from merriam-webster on hypothesis.

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Machine learning and theory

Theoretical physicists use machine-learning algorithms to speed up difficult calculations and eliminate untenable theories—but could they transform what it means to make discoveries?

Theoretical physicists employ their imaginations and their deep understanding of mathematics to decipher the underlying laws of the universe that govern particles, forces and everything in between. More and more often, theorists are doing that work with the help of machine learning.

As might be expected, the group of theorists using machine learning includes people classified as “computational” theorists. But it also includes “formal” theorists, the people interested in the self-consistency of theoretical frameworks, like string theory or quantum gravity. And it includes “phenomenologists,” the theorists who sit next to experimentalists, hypothesizing about new particles or interactions that could be tested by experiments; analyzing the data the experiments collect; and using results to construct new models and dream up how to test them experimentally.

In all areas of theory, machine-learning algorithms are speeding up processes, performing previously impossible calculations, and even causing theorists to rethink the way theoretical physics research is done.

“We’re near the very beginning of something that, to me, is an obvious revolution: the use of computers in scientific discovery,” says Jim Halverson, a professor of physics at Northeastern University. “It’s like being within 50 years of Galileo pointing his telescope at the sky for the first time. Much of the current progress utilizes machine learning.”

David Shih, a professor in the Department of Physics & Astronomy at Rutgers University, thinks of machine learning similarly. “Instead of looking into the sky, you’re looking into the data,” he says. “So it’s allowing us to see much further into the data. It’s opening up new frontiers.”

Machine learning for theoretical physics

“In the types of theory calculations I perform, there is no dataset, and machine learning is used to accelerate a first-principles theory calculation in a mathematically exact way,” says Phiala Shanahan, an associate professor of physics at MIT who does research in theoretical nuclear and particle physics.

Shanahan uses lattice field theory to calculate the structure of protons, neutrons and nuclei from our underlying understanding of particle physics. She says she uses machine learning to do calculations “much faster than you can do it any other way—or perhaps that you couldn’t have done any other way—and with guaranteed exactness.”

Lattice field theory calculations are computationally intense and take a very long time on traditional computers, leading to what Shanahan calls the “massive computational program” in her field. Machine-learning algorithms speed up the calculations and make them feasible—though theorists still have to use supercomputers to run them.

Shanahan and collaborators recently demonstrated that machine learning could generate samples from an underlying probability distribution relevant for lattice field theory—without using “training data” at all.

The hope is that machine-learning algorithms will enable physicists like Shanahan to directly calculate the properties of nuclei too large to be studied with conventional approaches, such as argon or xenon. This work will be helpful for future experiments like the Deep Underground Neutrino Experiment and various dark matter searches, which will use such nuclei as targets in their experimental apparatuses.

As Shanahan shows, physicists don’t necessarily need to have data to use machine-learning algorithms. But if you do have data, especially if you have a lot of it, machine learning is an extremely powerful tool for processing it.

Halverson incorporates machine learning into his string theory work. The equations that undergird string theory have many possible solutions that theorists must sort, “but the number is so astronomical that brute force scans are simply impossible.”

For example, Halverson has worked on a theoretical dataset that has more than 10^755 elements—well beyond the number of particles in the universe. “In this enormous dataset, you might imagine performing some sort of search problem, with well-defined rules of the game,” he says. “You’re looking for something specific, but you also have to satisfy certain constraints.”

In this way, doing theoretical research in string theory can be similar to playing games like chess or Go. So, Halverson and his colleagues use a machine-learning approach called reinforcement learning, which is often used in gameplay settings, to create an algorithm that can explore an astronomically large system and pinpoint data of interest.

Theorists also use machine learning for so-called discovery applications: searching for hidden correlations in structures and for hidden relationships in raw information. For example, theorists working with data from particle colliders deal with complicated mathematical expressions that must be simplified before physicists can calculate how the particles scatter. Machine learning helps accelerate this process by proposing possible solutions. It is much easier for theorists to take the suggestions and test them than it is to come up with the suggestions in the first place.

Shih also uses machine learning to sort through data in his phenomenological research. He works with the European Space Agency’s Gaia telescope, which is cataloging the positions and velocities of all the stars in the Milky Way.

Recently, Shih and his colleagues combined theory with Gaia data to generate a three-dimensional map of the density of dark matter in our galaxy. “That all is enabled by relatively new machine-learning techniques that weren’t available five years ago,” he says. “You couldn’t imagine doing this kind of data analysis until recently.”

Shih used a different machine-learning technique called simulation-based inference in a collaboration with NANOGrav scientists working on pulsar timing arrays. NANOGrav must make calculations by inverting enormous matrices, a process that has traditionally taken about a week. Machine learning can make these calculations using samples of simulated data, a process that takes closer to 24 hours and creates a database that astrophysicists can sample from in a matter of seconds.

Some phenomenologists are even using machine learning to re-define the way physicists search for new physics.

Traditionally a theorist will come up with a hypothesis, define what it would look like for experimentalists to find evidence that the hypothesis is correct, then ask experimentalists to look for that evidence. But machine learning allows a theorist to come up with a hypothesis, define what it would look like to deviate from that hypothesis, then use an algorithm to look for evidence that the hypothesis is not correct.

“It gets very controversial because normally what we do in science is hypothesis testing: A versus B,” says Jesse Thaler, a professor of physics at MIT and the inaugural director of the National Science Foundation’s Institute for Artificial Intelligence and Fundamental Interactions, IAIFI. “The idea that now you might say, ‘Let’s look for anomalous features’ without actually specifying what you’re looking for specifically—that’s a different way of doing science.”

Benefits and challenges

For many theorists, machine learning has already proven to be a promising tool to further their research. “More classical or conventional approaches typically have to bend the data, reduce them down to fewer dimensions or fit them to a very simple model with just a few parameters,” says Shih. “That of course builds in a lot of biases and assumptions or loses information along the way.

“Using these modern machine-learning techniques, you don’t have to do any of that. You could use all the data with the minimum amount of assumptions.”

But, as Thaler mentions, physicists continue to express concerns about using machine learning for theoretical physics. One issue is that some algorithms give predictions without uncertainties. And physicists have worried that machine learning is too much of a “black box”—that it arrives at decisions without showing its work.

That’s why Halverson and others are working to show that machine-learning algorithms can produce understandable results. “Both in string theory and in broader contexts … we are establishing legitimately rigorous results that would pass a mathematician's sniff test,” Halverson says.

This effort is helping physicists establish new standards for machine learning, and not just in physics. “We in particle physics have such a high standard for what it means to discover something or what it means to have a rigorous analysis that we are, in some ways, leading the charge in transforming machine learning,” Thaler says.

“We’re going from off-the-shelf tools that might not incorporate all of our physics best practices to tools that not only incorporate physics best practices but that we can export to other areas.”

The future of machine learning and theory

Machine learning used in both experiment and theory has led to a blurring of the lines between the two traditionally disparate camps. In fact, some posit that a new type of physicist is emerging: the data physicist . Shih coined the term at a Snowmass US high-energy physics community planning meeting in 2022 to describe scientists at the confluence of experiment, theory and data science. While the title of data physicist is not yet commonly used, the demand is growing for physicists who know how to analyze large amounts of data. And machine-learning is already deeply ingrained in this type of work.

Shih advocates for recruiting and retaining more young people who know how to work with machine learning in physics. “We lose a lot of people to industry,” he says. “Creating robust pipelines that keep talented people in the field—that requires jobs.

“I think we do okay at the postdoc level, and certainly at the graduate student level, but we need to create more faculty jobs that are in this interdisciplinary machine learning–data science space in physics and astronomy.”

Theorists say they believe these jobs are here to stay. And they are not afraid of machine learning taking their place.

Thaler acknowledges that machine learning may eventually be able to do what theoretical physicists do, but he says that will only happen when physicists understand their own science so deeply as to be able to explain all of it to a computer.

“To actually phrase some of the aspects of the scientific process in rigorous, algorithmic terms such that a computer could do it—that itself is a rich scientific endeavor, and one that has a chance of really accelerating the way that we do scientific discovery,” he says.

Ultimately, theorists see machine learning as a tool, “like a hammer,” says Shih. “You have a general tool, and you can apply it to many different places.”

“It’s just a class of algorithms,” says Shanahan, who serves as research coordinator for theoretical physics for IAIFI. “Just like any algorithm, hopefully the benefit is that machine learning enables you to do something that you wouldn’t have been able to do any other way.”

If used well, machine learning could make physicists’ lives a little easier. It might even return time currently spent running calculations and analyzing data.

“We have monstrously huge datasets that could be hiding fascinating phenomena—whether it’s new phenomena that’s beyond the Standard Model or even just phenomena within the Standard Model that we haven’t seen yet,” says Thaler. “If you have to have an entire PhD thesis devoted to studying each little possibility, we just won’t be able to explore the vast space of possibilities fast enough, given the deluge of data that’s coming in.

“Just from the fact that we have limited time, each of us, on this planet, and the limited number of people whose eyeballs are on the data, you want to maximize our ability to find new phenomena,” he says. “Collaborating with computers seems to be one way of doing that.”

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Quantum Physics

Title: performance advantage of quantum hypothesis testing for partially coherent optical sources.

Abstract: Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing. The previous studies assume that the potential source is completely incoherent. In this paper, this problem is generalized to the scenario with partially coherent sources and any prior probabilities. We compare the error probability limit given by the quantum Helstrom bound with the error probability given by direct decision based on the prior probability. On this basis, the quantum-optimal detection advantage and detection-useless region are analyzed. For practical purposes, we propose a specific detection strategy using binary spatial-mode demultiplexing, which can be used in the scenarios without any prior information. This strategy shows superior detection performance and the results hold prospects for achieving super-resolved microscopic and astronomical imaging.

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An illustrative image of small peptide helices.

Researchers reveal a new approach for treating degenerative diseases

Proteins are the workhorses of life. Organisms use them as building blocks, receptors, processors, couriers and catalysts. A protein’s structure is critical to its function. Malformed proteins not only fail to carry out their tasks, they can accumulate and eventually gum up the inner workings of cells. As a result, misfolded proteins cause a variety of degenerative diseases, from Alzheimer’s and Parkinson’s to the blinding disease retinitis pigmentosa. These disorders are currently incurable.

A paper out of UC Santa Barbara reveals a new connection between a particular ion transport protein and the cell’s garbage disposal, which grinds up misfolded proteins to stave off their toxic accumulation. The results, published in Developmental Cell , identify a target for treating these debilitating conditions.

“By studying basic cell biology in fruit fly ovaries, we stumbled upon a way to prevent neurodegeneration, and we think this has potential applications in the treatment of some human diseases,” said senior author Denise Montell , Duggan Professor and Distinguished Professor in the Department of Molecular, Cellular, and Developmental Biology.

For 35 years, Montell’s lab has studied the movement of cells in fruit fly ovaries. It might seem esoteric, she is the first to admit, but it provides a fantastic model for cell mobility. “And cell movement underlies embryonic development, drives wound healing and contributes to tumor metastasis,” she explained. “So it’s a really fundamental cell behavior that we care to understand deeply.”

The setting and characters

The star of this paper is a gene called ZIP7 , which encodes a protein of the same name. In previous work, Montell’s team came across a mutation in this gene that impaired cell mobility, piquing their interest.

The ZIP7 protein ferries zinc ions within a cell. These ions are exceedingly rare within the cytoplasm but abundant in proteins where they often form part of the architecture and catalyze chemical reactions. “ZIP7 is conserved in evolution from plants to yeast to flies to humans,” Montell said. “So it’s doing something really fundamental, because it’s been around for a really long time.”

ZIP7 is also the only zinc transporter found in the endoplasmic reticulum, a membranous structure where a cell makes proteins destined for the outer membrane of the cell or for secretion out of the cell. About a third of our proteins are made here.

Denise Montell wearing a blouse and a jacket

Denise Montell

Denise Montell seeks to identify under-appreciated cell behaviors and tease apart the underlying molecular mechanisms as well as the physiological significance.

If ZIP7 is our protagonist, then misfolded proteins and their disposal are the theme of the study. For proteins, function follows form. It’s not enough to have the right ingredients, a protein must fold correctly to function properly. Misfolded proteins are responsible for a host of diseases and disorders.

But proteins will sometimes misfold even in a healthy cell. Fortunately, cells have a quality control system to deal with this eventuality. If the error is small, the cell can try folding it again. Otherwise, it will tag the misfolded molecule with a small protein called ubiquitin and send it out of the endoplasmic reticulum (ER) for recycling.

Waiting in the cytoplasm are structures called proteasomes, the “garbage disposals” of the cell. “It literally chews up the protein into little pieces that can then be recycled,” Montell said.

“But if the garbage disposal gets overwhelmed — somebody puts too many potato peels in there — then the cell experiences ER stress.” This triggers a response that slows down protein synthesis (pauses our potato prep) and produces more proteasomes so that the system can clear the backlog of waste. If all this fails, the cell undergoes programmed death.

The plot thickens

Co-lead author Xiaoran Guo, Montell’s former Ph.D. student, saw that loss of ZIP7 caused ER stress in the fruit fly’s ovary. So she set out to determine if this stress was the reason the cells lost their mobility. Indeed, inducing ER stress with a different misfolded protein also impaired cell migration.

When Guo over-expressed ZIP7 in these cells, the backlog of misfolded proteins disappeared, the ER stress vanished, and the cells regained their mobility. “I was so surprised that I had to question myself if I had done everything correctly,” Guo said. “If this was real, just ZIP7 alone must be very potent in resolving ER stress.”

What’s more, the misfolded protein she used, called rhodopsin, contains no zinc in its structure. This led Guo to suspect that ZIP7 must be involved somewhere in the degradation pathway. Co-lead author, and fellow doctoral student, Morgan Mutch used a drug to block the proteasome from degrading misfolded rhodopsin and observed that this negated the beneficial effect of ZIP7. She concluded that ZIP7 must be acting somewhere before the proteasome munches up the misfolded protein.

The authors created four modified ZIP7 genes: two mutations disrupted the protein’s ability to carry zinc, while the other two left this unchanged. They discovered that zinc transport was critical in reducing ER stress.

At this point, a new character enters our story: the enzyme Rpn11, which forms part of the proteasome. Much like trying to stuff a large head of broccoli down the disposal, misfolded proteins with ubiquitin tags don’t fit into the proteasome. Rpn11 snips off these tags, enabling the misfolded protein to slip into the proteasome core for disassembly. Zinc is essential forRpn11 to catalyze the removal of ubiquitin.

Diagram of a proteasome processing a tagged, misfolded protein.

“I was very surprised, and then excited, when I saw that increasing ZIP7 expression almost completely prevented the buildup of those ubiquitin-tagged proteins,” Mutch said. “We were expecting the opposite result.”

Mutch determined that ZIP7 was critical in supplying zinc to Rpn11, enabling it to trim the tags that label defective proteins so that they fit into the structure that actually breaks them down. Blocking the Rpn11 enzyme confirmed this hypothesis.

“That feeling when you discover something new, something no one has figured out before, is the best feeling for a scientist,” Mutch added.

A potential therapy

The results suggest that overexpressing ZIP7 could form the basis for treating a variety of diseases. For instance, misfolded rhodopsin causes retinitis pigmentosa, a congenital blinding disease that is currently untreatable. Scientists already have a strain of fruit flies with the mutation that causes a similar disease, so the team overexpressed the ZIP7 gene in these flies to see what would happen.

“We found that it prevents retinal degeneration and blindness,” Montell said. Every single one of the flies with mutant rhodopsin usually develops retinitis pigmentosa, but a full 65% of those with overactive ZIP7 formed eyes that respond normally to light.

Montell’s lab is now collaborating with Professor Dennis Clegg, also at UC Santa Barbara, to further investigate the effect of ZIP7 in human retinal organoids, tissue cultures that bear a mutation that causes retinitis pigmentosa. This project was originally funded by the National Institute for General Medical Sciences. For the next three years it will be supported by a $900,000 grant from the Foundation Fighting Blindness so Montell, Clegg and their colleagues can test the hypothesis that ZIP7 gene therapy will prevent blindness in retinitis pigmentosa patients.

What’s more, proteasome capacity declines as we get older, contributing to many classic signs of aging and increasing the probability of age-related degenerative diseases. Therapies targeting ZIP7 could potentially slow the development or progression of these ailments, as well. They’ve already yielded promising results extending fruit fly lifespan.

“This is a poster child for fundamental, curiosity-driven research,” Montell said. “You’re just studying something because it’s cool, and you follow the data and end up discovering something you never set out to study, possibly even a cure for multiple diseases.”

Harrison Tasoff Science Writer (805) 893-7220 [email protected]

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The University of California, Santa Barbara is a leading research institution that also provides a comprehensive liberal arts learning experience. Our academic community of faculty, students, and staff is characterized by a culture of interdisciplinary collaboration that is responsive to the needs of our multicultural and global society. All of this takes place within a living and learning environment like no other, as we draw inspiration from the beauty and resources of our extraordinary location at the edge of the Pacific Ocean.

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  1. 1.2: Theories, Hypotheses and Models

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  2. 1.2 The Scientific Methods

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  22. Quantum mechanics

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  24. [2404.18120] Performance advantage of quantum hypothesis testing for

    View a PDF of the paper titled Performance advantage of quantum hypothesis testing for partially coherent optical sources, by Jian-Dong Zhang and 3 other authors View PDF Abstract: Determining the presence of a potential optical source in the interest region is important for an imaging system and can be achieved by using hypothesis testing.

  25. The Impact of the Linear No-threshold Hypothesis on... : Health Physics

    As the basis of radiation safety practice and regulations worldwide, the linear no-threshold (LNT) hypothesis exerts enormous influence throughout society. This includes our judicial system, where frivolous lawsuits are filed alleging radiation-induced health effects caused by negligent companies who subject unwitting victims to enormous ...

  26. Researchers reveal a new approach for treating degenerative diseases

    The authors created four modified ZIP7 genes: two mutations disrupted the protein's ability to carry zinc, while the other two left this unchanged. They discovered that zinc transport was critical in reducing ER stress. At this point, a new character enters our story: the enzyme Rpn11, which forms part of the proteasome.