examples of gravitational hypothesis

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High school physics - NGSS

Course: high school physics - ngss   >   unit 2.

• Introduction to gravity
• Viewing g as the value of Earth's gravitational field near the surface

Newton’s law of universal gravitation

• Understand: Newton’s law of universal gravitation
• Apply: Newton’s law of universal gravitation

How to find gravitational field strength

What else should i know about newton’s law of universal gravitation.

• Gravity causes attraction between all objects. Every mass attracts every other mass. That means you are gravitationally attracted to your friend, your pet, and even your pizza.
• The variable r ‍   is the distance between the centers of mass. We measure the distance between the objects from their centers, not their surfaces.

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7.2 Newton's Law of Universal Gravitation and Einstein's Theory of General Relativity

Section learning objectives.

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

• Explain Newton’s law of universal gravitation and compare it to Einstein’s theory of general relativity
• Perform calculations using Newton’s law of universal gravitation

Teacher Support

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

• (D) calculate the effect of forces on objects, including the law of inertia, the relationship between force and acceleration, and the nature of force pairs between objects;
• (A) research and describe the historical development of the concepts of gravitational, electromagnetic, weak nuclear, and strong nuclear forces;
• (B) describe and calculate how the magnitude of the gravitational force between two objects depends on their masses and the distance between their centers.

Section Key Terms

In this section, students will apply Newton’s law of universal gravitation to objects close at hand and far off in the depths of the solar system.

[BL] [OL] Compare the contributions of Kepler, Newton, and Einstein. Place them historically with dates.

[AL] Ask if anyone knows the difference between special relativity and general relativity. Special relativity is a theory of spacetime and applies to observers moving at constant velocity. General relativity is a theory of gravity and applies to observers that are accelerating. General relativity is broader and includes special relativity, which was published first.

Concepts Related to Newton’s Law of Universal Gravitation

Sir Isaac Newton was the first scientist to precisely define the gravitational force, and to show that it could explain both falling bodies and astronomical motions. See Figure 7.7 . But Newton was not the first to suspect that the same force caused both our weight and the motion of planets. His forerunner, Galileo Galilei, had contended that falling bodies and planetary motions had the same cause. Some of Newton’s contemporaries, such as Robert Hooke, Christopher Wren, and Edmund Halley, had also made some progress toward understanding gravitation. But Newton was the first to propose an exact mathematical form and to use that form to show that the motion of heavenly bodies should be conic sections—circles, ellipses, parabolas, and hyperbolas. This theoretical prediction was a major triumph. It had been known for some time that moons, planets, and comets follow such paths, but no one had been able to propose an explanation of the mechanism that caused them to follow these paths and not others.

[BL] [OL] Ask students if it really is obvious why all things fall straight down. Ask them to back up their reasons. Ask if the name Halley rings a bell.

[OL] [AL] Ask if anyone thinks it is strange or even mysterious that a force can act at a distance across empty space. Ask the students to compare and contrast gravitational force with magnetic and electrostatic forces. Note how much force at a distance is like magic or having superpowers.

The gravitational force is relatively simple. It is always attractive, and it depends only on the masses involved and the distance between them. Expressed in modern language, Newton’s universal law of gravitation states that every object in the universe attracts every other object with a force that is directed along a line joining them. The force is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This attraction is illustrated by Figure 7.8 .

For two bodies having masses m and M with a distance r between their centers of mass, the equation for Newton’s universal law of gravitation is

where F is the magnitude of the gravitational force and G is a proportionality factor called the gravitational constant . G is a universal constant, meaning that it is thought to be the same everywhere in the universe. It has been measured experimentally to be G = 6.673 × 10 − 11 N ⋅ m 2 /kg 2 G = 6.673 × 10 − 11 N ⋅ m 2 /kg 2 .

If a person has a mass of 60.0 kg, what would be the force of gravitational attraction on him at Earth’s surface? G is given above, Earth’s mass M is 5.97 × 10 24 kg, and the radius r of Earth is 6.38 × 10 6 m. Putting these values into Newton’s universal law of gravitation gives

We can check this result with the relationship: F = m g = ( 60 kg ) ( 9.8 m/s 2 ) = 588 N F = m g = ( 60 kg ) ( 9.8 m/s 2 ) = 588 N

You may remember that g , the acceleration due to gravity, is another important constant related to gravity. By substituting g for a in the equation for Newton’s second law of motion we get F = m g F = m g . Combining this with the equation for universal gravitation gives

Cancelling the mass m on both sides of the equation and filling in the values for the gravitational constant and mass and radius of the Earth, gives the value of g, which may look familiar.

This is a good point to recall the difference between mass and weight. Mass is the amount of matter in an object; weight is the force of attraction between the mass within two objects. Weight can change because g is different on every moon and planet. An object’s mass m does not change but its weight m g can.

[BL] [OL] Be sure no one is confusing G with g .

[AL] Ask if anyone can explain why G is a universal constant that applies anywhere in the universe. Have them discuss the idea that the laws of physics are the same everywhere and that, at one time, people were not so sure about this. Emphasize that g is not a universal constant.

Virtual Physics

Gravity and orbits.

Move the sun, Earth, moon and space station in this simulation to see how it affects their gravitational forces and orbital paths. Visualize the sizes and distances between different heavenly bodies. Turn off gravity to see what would happen without it!

• The Moon is not affected by the gravitational field of the Sun.
• The Moon is not affected by the gravitational field of the Earth.
• The Moon is affected by the gravitational fields of both the Earth and the Sun, which are always additive.
• The moon is affected by the gravitational fields of both the Earth and the Sun, which are sometimes additive and sometimes opposite.

This is a good animation of the Earth-Moon-Sun system. Have the students try all of the buttons. This will show the paths of the Earth and the moon separately and together. Explain the gravitational force and velocity vectors. Point out the interesting shape of the moon’s path around the sun. Explain that the velocity vector of the moon changes because sometimes the moon is traveling in the direction of Earth’s orbit and sometimes it is traveling in the opposite direction.

Take-Home Experiment: Falling Objects

In this activity you will study the effects of mass and air resistance on the acceleration of falling objects. Make predictions (hypotheses) about the outcome of this experiment. Write them down to compare later with results.

• Four sheets of 8 - 1 / 2 × 11 8 - 1 / 2 × 11 -inch paper
• Crumple one up into a small ball.
• Leave one uncrumpled.
• Take the other two and crumple them up together, so that they make a ball of exactly twice the mass of the other crumpled ball.
• Compare crumpled one-paper ball with crumpled two-paper ball.
• Compare crumpled one-paper ball with uncrumpled paper.
• Some objects fall faster because of air resistance, which acts in the direction of the motion of the object and exerts more force on objects with less surface area.
• Some objects fall faster because of air resistance, which acts in the direction opposite the motion of the object and exerts more force on objects with less surface area.
• Some objects fall faster because of air resistance, which acts in the direction of motion of the object and exerts more force on objects with more surface area.
• Some objects fall faster because of air resistance, which acts in the direction opposite the motion of the object and exerts more force on objects with more surface area.

Ask for predictions (hypotheses) about the outcome of this experiment. Have the students write them down to compare later with results.

It is possible to derive Kepler’s third law from Newton’s law of universal gravitation. Applying Newton’s second law of motion to angular motion gives an expression for centripetal force, which can be equated to the expression for force in the universal gravitation equation. This expression can be manipulated to produce the equation for Kepler’s third law. We saw earlier that the expression r 3 /T 2 is a constant for satellites orbiting the same massive object. The derivation of Kepler’s third law from Newton’s law of universal gravitation and Newton’s second law of motion yields that constant:

where M is the mass of the central body about which the satellites orbit (for example, the sun in our solar system). The usefulness of this equation will be seen later.

[OL] This equation illustrates the difference between Kepler’s and Newton’s work. Ask the students to explain why this is so.

[AL] Ask the students what the attraction would be between two 10 kg balls separated by a distance of 1.0 m. Could they feel it? Later, ask them to calculate it after they have done some similar calculations. Solution:

The universal gravitational constant G is determined experimentally. This determination was first done accurately in 1798 by English scientist Henry Cavendish (1731–1810), more than 100 years after Newton published his universal law of gravitation. The measurement of G is very basic and important because it determines the strength of one of the four forces in nature. Cavendish’s experiment was very difficult because he measured the tiny gravitational attraction between two ordinary-sized masses (tens of kilograms at most) by using an apparatus like that in Figure 7.9 . Remarkably, his value for G differs by less than 1% from the modern value.

Einstein’s Theory of General Relativity

Einstein’s theory of general relativity explained some interesting properties of gravity not covered by Newton’s theory. Einstein based his theory on the postulate that acceleration and gravity have the same effect and cannot be distinguished from each other. He concluded that light must fall in both a gravitational field and in an accelerating reference frame. Figure 7.10 shows this effect (greatly exaggerated) in an accelerating elevator. In Figure 7.10 (a) , the elevator accelerates upward in zero gravity. In Figure 7.10 (b) , the room is not accelerating but is subject to gravity. The effect on light is the same: it “falls” downward in both situations. The person in the elevator cannot tell whether the elevator is accelerating in zero gravity or is stationary and subject to gravity. Thus, gravity affects the path of light, even though we think of gravity as acting between masses, while photons are massless.

[BL] [OL] Ask the students to discuss the postulate. Can they relate the identity of gravity and acceleration to experience?

Einstein’s theory of general relativity got its first verification in 1919 when starlight passing near the sun was observed during a solar eclipse. (See Figure 7.11 .) During an eclipse, the sky is darkened and we can briefly see stars. Those on a line of sight nearest the sun should have a shift in their apparent positions. Not only was this shift observed, but it agreed with Einstein’s predictions well within experimental uncertainties. This discovery created a scientific and public sensation. Einstein was now a folk hero as well as a very great scientist. The bending of light by matter is equivalent to a bending of space itself, with light following the curve. This is another radical change in our concept of space and time. It is also another connection that any particle with mass or energy (e.g., massless photons) is affected by gravity.

To summarize the two views of gravity, Newton envisioned gravity as a tug of war along the line connecting any two objects in the universe. In contrast, Einstein envisioned gravity as a bending of space-time by mass.

Boundless Physics

Nasa gravity probe b.

NASA’s Gravity Probe B (GP-B) mission has confirmed two key predictions derived from Albert Einstein’s general theory of relativity. The probe, shown in Figure 7.12 was launched in 2004. It carried four ultra-precise gyroscopes designed to measure two effects hypothesized by Einstein’s theory:

• The geodetic effect , which is the warping of space and time by the gravitational field of a massive body (in this case, Earth)
• The frame-dragging effect , which is the amount by which a spinning object pulls space and time with it as it rotates

Both effects were measured with unprecedented precision. This was done by pointing the gyroscopes at a single star while orbiting Earth in a polar orbit. As predicted by relativity theory, the gyroscopes experienced very small, but measureable, changes in the direction of their spin caused by the pull of Earth’s gravity.

The principle investigator suggested imagining Earth spinning in honey. As Earth rotates it drags space and time with it as it would a surrounding sea of honey.

• Gravity has no effect on the space-time continuum, and gravity only affects the motion of light.
• The space-time continuum is distorted by gravity, and gravity has no effect on the motion of light.
• Gravity has no effect on either the space-time continuum or on the motion of light.
• The space-time continuum is distorted by gravity, and gravity affects the motion of light.

Explain that it is very exciting when a prediction of relativity theory is tested successfully. Some of the predictions were in doubt because they sounded so bizarre.

Calculations Based on Newton’s Law of Universal Gravitation

Tips for success.

When performing calculations using the equations in this chapter, use units of kilograms for mass, meters for distances, newtons for force, and seconds for time.

The mass of an object is constant, but its weight varies with the strength of the gravitational field. This means the value of g varies from place to place in the universe. The relationship between force, mass, and acceleration from the second law of motion can be written in terms of g .

In this case, the force is the weight of the object, which is caused by the gravitational attraction of the planet or moon on which the object is located. We can use this expression to compare weights of an object on different moons and planets.

[BL] Check to make sure students are clear about the distinction between mass and weight.

[OL] Recall the antics of astronauts of on the moon performed to illustrate the effect of a different value for g .

Watch Physics

Mass and weight clarification.

This video shows the mathematical basis of the relationship between mass and weight. The distinction between mass and weight are clearly explained. The mathematical relationship between mass and weight are shown mathematically in terms of the equation for Newton’s law of universal gravitation and in terms of his second law of motion.

Grasp Check

Would you have the same mass on the moon as you do on Earth? Would you have the same weight?

• You would weigh more on the moon than on Earth because gravity on the moon is stronger than gravity on Earth.
• You would weigh less on the moon than on Earth because gravity on the moon is weaker than gravity on Earth.
• You would weigh less on the moon than on Earth because gravity on the moon is stronger than gravity on Earth.
• You would weigh more on the moon than on Earth because gravity on the moon is weaker than gravity on Earth.

This may be a rather long-winded explanation of the mass-weight distinction, but it should drive home the point.

Two equations involving the gravitational constant, G , are often useful. The first is Newton’s equation, F = G m M r 2 F = G m M r 2 . Several of the values in this equation are either constants or easily obtainable. F is often the weight of an object on the surface of a large object with mass M , which is usually known. The mass of the smaller object, m , is often known, and G is a universal constant with the same value anywhere in the universe. This equation can be used to solve problems involving an object on or orbiting Earth or other massive celestial object. Sometimes it is helpful to equate the right-hand side of the equation to m g and cancel the m on both sides.

The equation r 3 T 2 = G M 4 π 2 r 3 T 2 = G M 4 π 2 is also useful for problems involving objects in orbit. Note that there is no need to know the mass of the object. Often, we know the radius r or the period T and want to find the other. If these are both known, we can use the equation to calculate the mass of a planet or star.

This video demonstrates calculations involving Newton’s universal law of gravitation.

• g and G are both unchanging constants but have different units.
• G is a universal constant that relates force with a pair of masses at a distance, while g relates force with mass and varies with location.
• g describes acceleration while G describes gravitational force.
• g describes gravitational force while G describes acceleration.

This video is a thorough demonstration of many of the calculations to be learned in this subsection.

Worked Example

Change in g.

The value of g on the planet Mars is 3.71 m/s 2 . If you have a mass of 60.0 kg on Earth, what would be your mass on Mars? What would be your weight on Mars?

Weight equals acceleration due to gravity times mass: W = m g W = m g . An object’s mass is constant. Call acceleration due to gravity on Mars g M and weight on Mars W M .

Mass on Mars would be the same, 60 kg.

The value of g on any planet depends on the mass of the planet and the distance from its center. If the material below the surface varies from point to point, the value of g will also vary slightly.

This is a typical mass-weight calculation.

Earth’s g at the Moon

Find the acceleration due to Earth’s gravity at the distance of the moon.

Express the force of gravity in terms of g .

Combine with the equation for universal gravitation.

Cancel m and substitute.

The value of g for the moon is 1.62 m/s 2 . Comparing this value to the answer, we see that Earth’s gravitational influence on an object on the moon’s surface would be insignificant.

[BL] [OL] Review the meanings of all the symbols in these equations: F , G , m , M , r , T , and π π .

[OL] [AL] Have the students memorize the values of G , g , and π to three significant figures.

Practice Problems

• 5.94 × 10 17 kg
• 5.94 × 10 24 kg
• 9.36 × 10 17 kg
• 9.36 × 10 24 kg

Check Your Understanding

• He gave an exact mathematical form for the theory.
• He added a correction term to a previously existing formula.
• Newton found the value of the universal gravitational constant.
• Newton showed that gravitational force is always attractive.
• Gravitational force between two objects is directly proportional to the sum of the squares of their masses and inversely proportional to the square of the distance between them.
• Gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Gravitational force between two objects is directly proportional to the sum of the squares of their masses and inversely proportional to the distance between them.
• Gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the distance between them.

Newton’s law of universal gravitation explains the paths of what?

• A charged particle
• A ball rolling on a plane surface
• A planet moving around the sun
• A stone tied to a string and whirled at constant speed in a horizontal circle

Use the Check Your Answers questions to assess whether students master the learning objectives for this section. If students are struggling with a specific objective, the Check Your Answers will help identify which objective is causing the problem and direct students to the relevant content.

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13: Gravitation

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In this section, we study the nature of the gravitational force for objects as small as ourselves and for systems as massive as entire galaxies. We show how the gravitational force affects objects on Earth and the motion of the Universe itself. Gravity is the first force to be postulated as an action-at-a-distance force, that is, objects exert a gravitational force on one another without physical contact and that force falls to zero only at an infinite distance. Earth exerts a gravitational force on you, but so do our Sun, the Milky Way galaxy, and the billions of galaxies, like those shown above, which are so distant that we cannot see them with the naked eye.

• 13.1: Prelude to Gravitation Our visible Universe contains billions of galaxies, whose very existence is due to the force of gravity. Gravity is ultimately responsible for the energy output of all stars—initiating thermonuclear reactions in stars, allowing the Sun to heat Earth, and making galaxies visible from unfathomable distances.
• 13.2: Newton's Law of Universal Gravitation All masses attract one another with a gravitational force proportional to their masses and inversely proportional to the square of the distance between them. Spherically symmetrical masses can be treated as if all their mass were located at the center. Nonsymmetrical objects can be treated as if their mass were concentrated at their center of mass, provided their distance from other masses is large compared to their size.
• 13.3: Gravitation Near Earth's Surface The weight of an object is the gravitational attraction between Earth and the object. The gravitational field is represented as lines that indicate the direction of the gravitational force; the line spacing indicates the strength of the field. Apparent weight differs from actual weight due to the acceleration of the object.
• 13.4: Gravitational Potential Energy and Total Energy The acceleration due to gravity changes as we move away from Earth, and the expression for gravitational potential energy must reflect this change. The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion. Objects with total energy less than zero are bound; those with zero or greater are unbounded.
• 13.5: Satellite Orbits and Energy Orbital velocities are determined by the mass of the body being orbited and the distance from the center of that body, and not by the mass of a much smaller orbiting object. The period of the orbit is likewise independent of the orbiting object’s mass. Bodies of comparable masses orbit about their common center of mass and their velocities and periods should be determined from Newton’s second law and law of gravitation.
• 13.6: Kepler's Laws of Planetary Motion Johannes Kepler carefully analyzed the positions in the sky of all the known planets and the Moon, plotting their positions at regular intervals of time. From this analysis, he formulated three laws: Kepler’s first law states that every planet moves along an ellipse. Kepler’s second law states that a planet sweeps out equal areas in equal times. Kepler’s third law states that the square of the period is proportional to the cube of the semi-major axis of the orbit.
• 13.7: Tidal Forces Earth’s tides are caused by the difference in gravitational forces from the Moon and the Sun on the different sides of Earth. Spring or neap (high) tides occur when Earth, the Moon, and the Sun are aligned, and neap or (low) tides occur when they form a right triangle. Tidal forces can create internal heating, changes in orbital motion, and even destruction of orbiting bodies.
• 13.8: Einstein's Theory of Gravity According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. The principle of equivalence states that that both mass and acceleration distort space-time and are indistinguishable in comparable circumstances. Black holes, the result of gravitational collapse, are singularities with an event horizon that is proportional to their mass.
• 13.E: Gravitation (Exercises)
• 13.S: Gravitation (Summary)

Thumbnail: Our visible Universe contains billions of galaxies, whose very existence is due to the force of gravity. Gravity is ultimately responsible for the energy output of all stars—initiating thermonuclear reactions in stars, allowing the Sun to heat Earth, and making galaxies visible from unfathomable distances. Most of the dots you see in this image are not stars, but galaxies. (credit: modification of work by NASA).

Gravitational Dynamics

The force of gravity holds Earth and other planets in predictable orbits around the Sun. Gravity also produces more complicated and even chaotic behaviors, particularly where three or more bodies interact. The mutual attraction between planets and moons creates orbital resonances, moving bodies around inside a star system. In many cases, these interactions can even eject a planet from a solar system — or kick a star out from a galaxy. Gravitational dynamics is the study of the interplay of multiple astronomical objects, revealing how stable or not a system can be.

Center for Astrophysics | Harvard & Smithsonian scientists use gravitational dynamics to understand many different phenomena:

Identifying resonant orbits in exoplanet systems. Like Jupiter’s moons, these planets have orbit lengths that are ratios of each other. In particular, in several systems with two known planets, one planet orbits with a period twice the length of the other. The most likely reason for that is gravitational dynamics, with each planet speeding and slowing the other until they match. A New Set of Solar Systems

Locating and observing hypervelocity stars in our galaxy and others. These stars were likely ejected from their host galaxy through a close encounter with the supermassive black hole at the galaxy’s center. The number and type of these stars tells us something about the populations of stars in galactic centers, and how frequently they encounter the supermassive black holes there. Hyperfast Star Was Booted From Milky Way

Looking for “rogue planets” and other interstellar vagabonds. These worlds probably were kicked out of their original star system. Since planets emit no visible light and very little infrared light on their own, these rogues are hard to spot unless astronomers are very lucky. However, a possible vagabond astronomers nicknamed ‘Oumumua visited the Solar System in 2017, and researchers expect to see more once the Large Synoptic Survey Telescope (LSST) is operating. Small Asteroid or Comet 'Visits' from Beyond the Solar System

NASA's Chandra X-ray Observatory and Hubble Space Telescope captured a runaway black hole, which can be seen here as a bright spot in X-ray light. Researchers think the complex gravitational interactions during the collision of two galaxies kicked one of the supermassive black holes out.

Pulled in Several Directions

Starting hundreds of years ago, astronomers have observed interesting patterns in the moons of Jupiter, the rings of Saturn, and the asteroid belt. These patterns include gaps — places where few or no bodies orbit — and orbit lengths that occur in distinct ratios. Astronomers realized these patterns came about from gravitational interactions between more than two objects together. Gaps in the asteroid belt rose from the tug of both the Sun and Jupiter on asteroids; the orbits of Jupiter’s moons were the result of each moon tugging on the others.

Today, multi-body gravitational interactions are an essential concept in understanding the Solar System, exoplanet systems , star clusters , and other environments. Researchers apply gravitational dynamics to models of planet formation and the long-term stability of star systems.

Astronomers also use gravitational effects to look for small exoplanets and even exomoons: moons orbiting planets in other star systems. If the exoplanet transits its host star — passing between the star and us — it blocks the star’s light briefly. Measuring this transit over several orbits, astronomers can measure the effect of another object tugging on it, either slowing or speeding its eclipse. This is a very tiny and hard to measure effect, but it can reveal the existence of exoplanets too small to create their own measurable transits.

Rogue Planets and Runaway Stars

The orbits of the eight planets in the Solar System seem to be very stable. However, that may not always be true: each planet nudges every other one slightly every time they pass each other. Those nudges could potentially add up to change planets’ orbits, or even knock one of the worlds out of the Solar System entirely. It’s even possible the early Solar System had one or more extra planets that got kicked out billions of years ago.

Our own star system aside, astronomers have discovered a small number of “rogue planets”: planets that don’t orbit a star, but drift through interstellar space. Similarly, in the fall of 2017, a small asteroid or comet passed by Earth that may have originated outside the Solar System. These likely formed in other star systems and were ejected thanks to gravitational dynamics.

An even more dramatic example of gravitational ejection involves “hypervelocity stars”. Astronomers have identified a number of stars moving away from the center of the Milky Way at an astounding 3 million kilometers per hour, or 2 million miles per hour. The most likely hypothesis: hypervelocity stars were once part of binary systems, when they drifted too close to the supermassive black hole at the center of the Milky Way. Gravitational dynamics made the binaries unstable, with the black hole pulling one star in and kicking the other one out of the galaxy at those phenomenal speeds.

• How can astronomy improve life on earth?
• How do stars and planets form and evolve?
• Solar & Heliospheric Physics
• The Energetic Universe
• Stellar Astronomy
• The Milky Way Galaxy
• Theoretical Astrophysics
• Computational Astrophysics

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Astronomers observe a new type of binary star long predicted to exist, a dark matter deficient galaxy, abacussummit, telescopes and instruments, spitzer space telescope.

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• Published: 12 December 2022

A roadmap of gravitational wave data analysis

• Lorenzo Speri   ORCID: orcid.org/0000-0002-5442-7267 1   na1 ,
• Nikolaos Karnesis 2   na1 ,
• Arianna I. Renzini 3 , 4   na1 &
• Jonathan R. Gair 1   na1  

Nature Astronomy volume  6 ,  pages 1356–1363 ( 2022 ) Cite this article

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• Astronomical instrumentation
• Compact astrophysical objects
• General relativity and gravity
• Transient astrophysical phenomena

As gravitational wave detectors improve, the rate at which sources are observed is steadily increasing. Scientific exploitation of these sources relies on careful analysis of the data, and so gravitational wave data analysis is also a rapidly growing and evolving field. In this Perspective, we provide an introduction to the basic concepts of gravitational wave data analysis with reference to current pipelines. We describe some of the computational advancements and machine learning techniques that have recently been introduced to reduce the computational burden of the analysis. We conclude by discussing some of the challenges that will be encountered in the analysis of data from future detectors.

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These authors contributed equally: Lorenzo Speri, Nikolaos Karnesis, Arianna I. Renzini, Jonathan R. Gair.

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Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam, Germany

Lorenzo Speri & Jonathan R. Gair

Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, Greece

Nikolaos Karnesis

LIGO Laboratory, California Institute of Technology, Pasadena, CA, USA

Arianna I. Renzini

Department of Physics, California Institute of Technology, Pasadena, CA, USA

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Speri, L., Karnesis, N., Renzini, A.I. et al. A roadmap of gravitational wave data analysis. Nat Astron 6 , 1356–1363 (2022). https://doi.org/10.1038/s41550-022-01849-y

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What is the theory of general relativity?

Here we explore what the theory of general relativity is and how it affects space-time.

• How it works

General relativity FAQs answered by an expert

Gravitational lensing.

• Mercury's orbit
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General relativity is physicist Albert Einstein's understanding of how gravity affects the fabric of space-time.

The theory, which Einstein published in 1915, expanded the theory of special relativity that he had published 10 years earlier. Special relativity argued that space and time are inextricably connected, but that theory didn't acknowledge the existence of gravity .

Einstein spent the decade between the two publications determining that particularly massive objects warp the fabric of space-time , a distortion that manifests as gravity, according to NASA .

Related: The hunt for wormholes: How scientists look for space-time tunnels

How does general relativity work?

To understand general relativity, first, let's start with gravity, the force of attraction that two objects exert on one another. Sir Isaac Newton quantified gravity in the same text in which he formulated his three laws of motion, the " Principia ."

The gravitational force tugging between two bodies depends on how massive each one is and how far apart the two lie, according to NASA Glenn Research Center . Even as the center of the Earth is pulling you toward it (keeping you firmly lodged on the ground), your center of mass is pulling back at the Earth. But the more massive body barely feels the tug from you, while with your much smaller mass, you find yourself firmly rooted thanks to that same force. Yet Newton's laws assume that gravity is an innate force of an object that can act over a distance.

Albert Einstein, in his theory of special relativity, determined that the laws of physics are the same for all non-accelerating observers, and he showed that the speed of light within a vacuum is the same no matter the speed at which an observer travels, according to Wired . 

As a result, he found that space and time were interwoven into a single continuum known as space-time. And events that occur at the same time for one observer could occur at different times for another.

Related: What would happen if the speed of light was much lower?

As he worked out the equations for his general theory of relativity, Einstein realized that massive objects caused a distortion in space-time. Imagine setting a large object in the center of a trampoline. The object would press down into the fabric, causing it to dimple. If you then attempt to roll a marble around the edge of the trampoline, the marble would spiral inward toward the body, pulled in much the same way that the gravity of a planet pulls at rocks in space. 

In the decades since Einstein published his theories, scientists have observed countless of phenomena matching the predictions of relativity.

We asked Elena Giorgi, an assistant professor of mathematics at Columbia University a few commonly asked questions about general relativity.  

Elena Giorgi is an assistant professor of mathematics at Columbia University.

What is general relativity?

General relativity is a physical theory about space and time and it has a beautiful mathematical description. According to general relativity, the spacetime is a 4-dimensional object that has to obey an equation, called the Einstein equation, which explains how the matter curves the spacetime. 

What force is explained by general relativity?

General relativity explains gravity, and in this theory, it is not really a "force" anymore. The gravitational field comes out of the description of general relativity as a result of the curved spacetime. 

When was the theory of general relativity established?

General Relativity was established in 1915 by Albert Einstein and the first solutions to the Einstein equation were found already in early 1916. 

Is general relativity proven?

General relativity has passed all the experimental tests so far, but its applicability is expected to break down when [the] effects of quantum mechanics (the theory of the very small particles) should become dominant. 

Light bends around a massive object, such as a black hole, causing it to act as a lens for the things that lie behind it. Astronomers routinely use this method to study stars and galaxies behind massive objects.

The Einstein Cross, a quasar in the Pegasus constellation , according to the European Space Agency (ESA), and is an excellent example of gravitational lensing. The quasar is seen as it was about 11 billion years ago; the galaxy that it sits behind is about 10 times closer to Earth. Because the two objects align so precisely, four images of the quasar appear around the galaxy because the intense gravity of the galaxy bends the light coming from the quasar.

Related: What Is Quantum Gravity?

In cases like Einstein's cross, the different images of the gravitationally lensed object appear simultaneously, but that isn't always the case. Scientists have also managed to observe lensing examples where, because the light traveling around the lens takes different paths of different lengths, different images arrive at different times, as in the case of one particularly interesting supernova .

Changes in Mercury's orbit

The orbit of Mercury is shifting very gradually over time due to the curvature of space-time around the massive sun, according to NASA . 

As the closest planet to the sun, Mercury’s perihelion (the point along its orbit that it’s closest to the sun) is predicted to follow a slightly different direction over time. Under Newton’s predictions, gravitational forces in the solar system should advance Mercury's precession ( change in its orbital orientation) is measured to be 5,600 arcseconds per century (1 arcsecond is equal to 1/3600 of a degree). However, there is a discrepancy of 43 arcseconds per century, something Einstein's theory of general relativity accounts for. Using Einstein’s theory of curved space-time, the precession of Mercury’s perihelion should advance slightly more than under the predictions of Newton, since planets don’t orbit the sun in a static elliptical orbit. 

Sure enough, several research papers published since the mid 20th century have confirmed Einstein's calculations of Mercury’s perihelion precession to be accurate.  

In a few billion years, this wobble could even cause the innermost planet to collide with the sun or a planet .

Frame-dragging of space-time around rotating bodies

The spin of a heavy object, such as Earth, should twist and distort the space-time around it. In 2004, NASA launched the Gravity Probe B (GP-B). The axes of the satellite's precisely calibrated gyroscopes drifted very slightly over time, according to NASA , a result that matched Einstein's theory.

"Imagine the Earth as if it were immersed in honey," Gravity Probe-B principal investigator Francis Everitt, of Stanford University, said in a NASA statement about the mission.

"As the planet rotates, the honey around it would swirl, and it's the same with space and time. GP-B confirmed two of the most profound predictions of Einstein's universe, having far-reaching implications across astrophysics research."

Gravitational redshift

The electromagnetic radiation of an object is stretched out slightly inside a gravitational field . Think of the sound waves that emanate from a siren on an emergency vehicle; as the vehicle moves toward an observer, sound waves are compressed, but as it moves away, they are stretched out, or redshifted . Known as the Doppler Effect, the same phenomena occurs with waves of light at all frequencies.

In the 1960s, according to the American Physical Society , physicists Robert Pound and Glen Rebka shot gamma-rays first down, then up the side of a tower at Harvard University. Pound and Rebka found that the gamma-rays slightly changed frequency due to distortions caused by gravity.

Einstein predicted that violent events, such as the collision of two black holes, create ripples in space-time known as gravitational waves . And in 2016, the Laser Interferometer Gravitational Wave Observatory ( LIGO ) announced that it had detected such a signal for the first time.

That detection came on Sept. 14, 2015 . LIGO, made up of twin facilities in Louisiana and Washington, had recently been upgraded, and were in the process of being calibrated before they went online. The first detection was so large that, according to then-LIGO spokesperson Gabriela Gonzalez, it took the team several months of analysis to convince themselves that it was a real signal and not a glitch.

Related: Phantom energy and dark gravity: Explaining the dark side of the universe  

"We were very lucky on the first detection that it was so obvious," she said during the 228 American Astronomical Society meeting in June 2016.

Since then, scientists have begun quickly catching gravitational waves. All told LIGO and its European counterpart Virgo have detected a total of 50 gravitational-wave events, according to program officials, according to the Laser Interferometer Gravitational-wave Observatory.

Those collisions have included unusual events like a collision with an object that scientists can't definitively identify as a black hole or neutron star, merging neutron stars accompanied by a bright explosion, mismatched black holes colliding and more.

Observing neutron stars

In 2021 research published in the journal Physical Review X , challenged several of Einstein's predictions by observing a double-pulsar system around 2,400 light-years from Earth. Each of the seven predictions of general relativity was confirmed by the study.  

Pulsars are a type of neutron star that appears to pulse due to beams of electromagnetic radiation and that are emitting from their magnetic poles. 

The pulsar test subjects spin very fast - around 44 times a second - and are 30% more massive than the sun but are only 15 miles (around 24 kilometers) in diameter, making them incredibly dense. This means that their gravitational pull is immense, for example, on the surface of a neutron star gravity is around 1 billion times stronger than its pull on Earth. This makes neutron stars a great test subject to challenge predictions in Einstein's theories, such as the ability of gravity to bend light. 

"We follow the propagation of radio photons emitted from a cosmic lighthouse, a pulsar, and track their movements in the strong gravitational field of a companion pulsar," Professor Ingrid Stairs from the University of British Columbia at Vancouver said in a statement. 

"We see for the first time how the light is not only delayed due to a strong curvature of spacetime around the companion but also that the light is deflected by a small angle of 0.04 degrees that we can detect. Never before has such an experiment been conducted at such a high spacetime curvature" Stairs adds. 

Read more about general relativity in the book Relativity: The Special and the General Theory - 100th Anniversary Edition . Explore the Nature of Space and Time (Isaac Newton Institute Series of Lectures, 3) and The Physics Book: Big Ideas Simply Explained .

Join our Space Forums to keep talking space on the latest missions, night sky and more! And if you have a news tip, correction or comment, let us know at: [email protected].

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Scott is a staff writer for  How It Works  magazine and has previously written for other science and knowledge outlets, including BBC Wildlife magazine, World of Animals magazine,  Space.com  and  All About History magazine . Scott has a masters in science and environmental journalism and a bachelor's degree in conservation biology degree from the University of Lincoln in the U.K. During his academic and professional career, Scott has participated in several animal conservation projects, including English bird surveys, wolf monitoring in Germany and leopard tracking in South Africa. 

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Modified theories of gravity: Why, how and what?

• Review Article
• Published: 05 May 2022
• Volume 54 , article number  44 , ( 2022 )

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• S. Shankaranarayanan 1 &
• Joseph P. Johnson   ORCID: orcid.org/0000-0003-4618-2092 1  

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General relativity (GR) was proven via the direct detection of gravitational waves from the mergers of the binary black holes and binary neutron stars by the advanced LIGO and advanced virgo detectors. These detections confirmed the prediction of GR and provided the first direct evidence of the existence of stellar-mass black holes (BHs). However, the occurrence of singularities at the centers of BHs suggests that GR is inapplicable because of the breakdown of the equivalence principle at the singularities. The fact that these singularities exist indicates that GR cannot be a universal theory of space–time. In the low-energy limit, the theoretical and observational challenges faced by the \(\Lambda \) CDM model also indicate that we might have to look beyond GR as the underlying theory of gravity. Unlike GR, whose field equations contain only up to second-order derivatives, the modified theories with higher derivative Ricci/Riemann tensor gravity models include higher derivatives. Therefore, one expects significant differences between GR and modified theories. Since there are many ways of modifying GR in the strong-gravity and cosmological distances, each model has unique features. This leads to the following crucial question: Are there a set of unique signatures that distinguish GR from modified gravity (MG) theories? This review discusses three aspects of MG theories: (1) Why do we need to consider MG theories? (2) How to modify GR? and (3) What are the observational consequences? The review is written in a pedagogical style with the expectation that it will serve as a useful reference for theorists and observers and those interested in bridging the divide between theory and observations.

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Acknowledgements

The authors fondly remember Prof. Thanu Padmanabhan, who always encouraged his students to create their own paths . The authors thank S. M. Chandran, A. Kushwaha, and Urjit Yajnik for their comments on the earlier draft. JPJ is supported by the CSIR fellowship. This work is supported by SERB-MATRICS and ISRO Respond grants.

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Shankaranarayanan, S., Johnson, J.P. Modified theories of gravity: Why, how and what?. Gen Relativ Gravit 54 , 44 (2022). https://doi.org/10.1007/s10714-022-02927-2

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10 discoveries that prove Einstein was right about the universe — and 1 that proves him wrong

Albert Einstein's theories of relativity have been proven to be true time and again in the more than 100 years following their publication.

Legendary physicist Albert Einstein was a thinker ahead of his time. Born March 14, 1879, Einstein entered a world where the dwarf planet Pluto had yet to be discovered, and the idea of spaceflight was a distant dream. Despite the technical limitations of his time, Einstein published his famous theory of general relativity in 1915, which made predictions about the nature of the universe that would be proven accurate time and again for more than 100 years to come.

Here are 10 recent observations that proved Einstein was right about the nature of the cosmos a century ago — and one that proved him wrong.

1. The first image of a black hole

Einstein's theory of general relativity describes gravity as a consequence of the warping of space-time ; basically, the more massive an object is, the more it will curve space-time and cause smaller objects to fall toward it. The theory also predicts the existence of black holes — massive objects that warp space-time so much that not even light can escape them.

When researchers using the Event Horizon Telescope (EHT) captured the first-ever image of a black hole , they proved Einstein was right about some very specific things — namely, that each black hole has a point of no return called an event horizon , which should be roughly circular and of a predictable size based on the mass of the black hole. The EHT's groundbreaking black hole image showed this prediction was exactly right.

2. Black hole 'echoes'

Astronomers proved Einstein's black hole theories correct yet again when they discovered a strange pattern of X-rays being emitted near a black hole 800 million light-years from Earth. In addition to the expected X-ray emissions flashing from the front of the black hole, the team also detected the predicted "luminous echoes" of X-ray light , which were emitted behind the black hole but still visible from Earth due to the way the black hole bent space-time around it.

3. Gravitational waves

Einstein's theory of relativity also describes enormous ripples in the fabric of space-time called gravitational waves. These waves result from mergers between the most massive objects in the universe, such as black holes and neutron stars. Using a special detector called the Laser Interferometer Gravitational-Wave Observatory (LIGO), physicists confirmed the existence of gravitational waves in 2015 , and have continued to detect dozens of other examples of gravitational waves in the years since, proving Einstein right yet again.

4. Wobbly black hole partners

Studying gravitational waves can reveal the secrets of the massive, distant objects that released them. By studying the gravitational waves emitted by a pair of slowly colliding binary black holes in 2022, physicists confirmed that the massive objects wobbled — or precessed — in their orbits as they swirled ever closer to one another, just as Einstein predicted they should.

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5. A 'dancing' spirograph star

Scientists saw Einstein's theory of precession in action yet again after studying a star orbiting a supermassive black hole for 27 years. After completing two full orbits of the black hole, the star's orbit was seen to "dance" forward in a rosette pattern rather than moving in a fixed elliptical orbit. This movement confirmed Einstein's predictions about how an extremely small object should orbit around a comparatively gargantuan one.

6. A 'frame dragging' neutron star

It's not just black holes that bend space-time around them; the ultra-dense husks of dead stars can do it too. In 2020, physicists studied how a neutron star orbited around a white dwarf (two types of collapsed, dead stars) for the previous 20 years, finding a long-term drift in the way the two objects orbited each other. According to the researchers, this drift was likely caused by an effect called frame dragging; essentially, the white dwarf had tugged on space-time enough to slightly alter the neutron star's orbit over time. This, again, confirms predictions from Einstein's theory of relativity.

7. A gravitational magnifying glass

According to Einstein, if an object is sufficiently massive, it should bend space-time in such a way that distant light emitted behind the object will appear magnified (as seen from Earth). This effect is called gravitational lensing, and has been used extensively to hold a magnifying glass up to objects in the deep universe. Famously, the James Webb Space Telescope's first deep field image used the gravitational lensing effect of a galaxy cluster 4.6 billion light-years away to significantly magnify the light from galaxies more than 13 billion light-years away.

8. Put an Einstein ring on it

One form of gravitational lensing is so vivid that physicists couldn't help but put Einstein's name on it. When the light from a distant object is magnified into a perfect halo around a massive foreground object, scientists call it an "Einstein ring." These stunning objects exist all throughout space, and have been imaged by astronomers and citizen scientists alike.

9. The shifting universe

As light travels across the universe, its wavelength shifts and stretches in several different ways, known as redshift. The most famous type of redshift is due to the expansion of the universe. (Einstein proposed a number called the cosmological constant to account for this apparent expansion in his other equations). However, Einstein also predicted a type of "gravitational redshift," which occurs when light loses energy on its way out of a depression in space-time created by massive objects, such as galaxies. In 2011, a study of the light from hundreds of thousands of distant galaxies proved that gravitational redshift truly does exist , as Einstein suggested.

10. Atoms on the move

Einstein's theories also hold true in the quantum realm, it seems. Relativity suggests that the speed of light is constant in a vacuum, meaning that space should look the same from every direction. In 2015, researchers proved this effect is true even on the smallest scale , when they measured the energy of two electrons moving in different directions around an atom's nucleus. The energy difference between the electrons remained constant, no matter which direction they moved, confirming that piece of Einstein's theory.

11. Wrong about 'spooky action-at-a-distance?'

In a phenomenon called quantum entanglement, linked particles can seemingly communicate with each other across vast distances faster than the speed of light, and only "choose" a state to inhabit once they are measured. Einstein hated this phenomenon, famously deriding it as "spooky action-at-a-distance," and insisted that no influence can travel faster than light, and that objects have a state whether we measure them or not. 

But in a massive, global experiment in which millions of entangled particles were measured around the world, researchers found that the particles seemed to only pick a state the moment they were measured, and no sooner.

"We showed that Einstein's world-view… in which things have properties whether or not you observe them, and no influence travels faster than light, cannot be true — at least one of those things must be false," study co-author Morgan Mitchell , a professor of quantum optics at the Institute of Photonic Sciences in Spain, told Live Science in 2018.

Brandon is the space/physics editor at Live Science. His writing has appeared in The Washington Post, Reader's Digest, CBS.com, the Richard Dawkins Foundation website and other outlets. He holds a bachelor's degree in creative writing from the University of Arizona, with minors in journalism and media arts. He enjoys writing most about space, geoscience and the mysteries of the universe.

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• Russ51 Perhaps "we" are not reading Einstein's objection closely enough. He rejected, specifically, ACTION at a distance. Entanglement does not show this. It shows the measurements at a distance are correlated, and that is very different. This specifically does NOT allow you to alter the spin of one, thereby altering the spin of the distant entangled particle. Ergo communication using entangled particles is NOT possible, and there is indeed no spooky action at a distance. Please correct me if I am wrong, because this is key to the whole concept and it also debunks the key point in the article (not that it matters too much) because it does not disprove Einstein's statement. Reply
• Pentcho Valev The texts below imply that, if the speed of light is VARIABLE (it is!), modern physics, predicated on Einstein's 1905 constant-speed-of-light falsehood, is long dead (exists in a zombie state): "He opened by explaining how Einstein's theory of relativity is the foundation of every other theory in modern physics and that the assumption that the speed of light is constant is the foundation of that theory. Thus a constant speed of light is embedded in all of modern physics and to propose a varying speed of light (VSL) is worse than swearing! It is like proposing a language without vowels." http://www.thegreatdebate.org.uk/VSLRevPrnt.html "If there's one thing every schoolboy knows about Einstein and his theory of relativity, it is that the speed of light in vacuum is constant. No matter what the circumstances, light in vacuum travels at the same speed...The speed of light is the very keystone of physics, the seemingly sure foundation upon which every modern cosmological theory is built, the yardstick by which everything in the universe is measured...The constancy of the speed of light has been woven into the very fabric of physics, into the way physics equations are written, even into the notation used. Nowadays, to "vary" the speed of light is not even a swear word: It is simply not present in the vocabulary of physics." https://www.amazon.com/Faster-Than-Speed-Light-Speculation/dp/0738205257 "The whole of physics is predicated on the constancy of the speed of light...So we had to find ways to change the speed of light without wrecking the whole thing too much." https://motherboard.vice.com/en_us/article/8q87gk/light-speed-slowed Assume that a light source emits equidistant pulses and an observer starts moving towards the source: bg7O4rtlwEE View: https://youtube.com/watch?v=bg7O4rtlwEE The speed of the light pulses relative to the stationary observer is c = df where d is the distance between subsequent pulses and f is the frequency at the stationary observer. The speed of the pulses relative to the moving observer is c'= df' > c where f' > f is the frequency at the moving observer. That is, the speed of light relative to the observer VARIES with the speed of the observer. Reply

Pentcho Valev said: The texts below imply that, if the speed of light is VARIABLE (it is!), modern physics, predicated on Einstein's 1905 constant-speed-of-light falsehood, is long dead (exists in a zombie state): "He opened by explaining how Einstein's theory of relativity is the foundation of every other theory in modern physics and that the assumption that the speed of light is constant is the foundation of that theory. Thus a constant speed of light is embedded in all of modern physics and to propose a varying speed of light (VSL) is worse than swearing! It is like proposing a language without vowels." http://www.thegreatdebate.org.uk/VSLRevPrnt.html "If there's one thing every schoolboy knows about Einstein and his theory of relativity, it is that the speed of light in vacuum is constant. No matter what the circumstances, light in vacuum travels at the same speed...The speed of light is the very keystone of physics, the seemingly sure foundation upon which every modern cosmological theory is built, the yardstick by which everything in the universe is measured...The constancy of the speed of light has been woven into the very fabric of physics, into the way physics equations are written, even into the notation used. Nowadays, to "vary" the speed of light is not even a swear word: It is simply not present in the vocabulary of physics." https://www.amazon.com/Faster-Than-Speed-Light-Speculation/dp/0738205257 "The whole of physics is predicated on the constancy of the speed of light...So we had to find ways to change the speed of light without wrecking the whole thing too much." https://motherboard.vice.com/en_us/article/8q87gk/light-speed-slowed Assume that a light source emits equidistant pulses and an observer starts moving towards the source: bg7O4rtlwEE View: https://youtube.com/watch?v=bg7O4rtlwEE The speed of the light pulses relative to the stationary observer is c = df where d is the distance between subsequent pulses and f is the frequency at the stationary observer. The speed of the pulses relative to the moving observer is c'= df' > c " where f' > f is the frequency at the moving observer. That is, the speed of light relative to the observer VARIES with the speed of the observer.

retired scientist said: You didn't take into account that d changes relative to the moving observer, too.

• Pearlman YeC On the big picture Einstein WAS also right prior to 'premature capitulation to Hubble' right about the universe in equilibrium (expansion vs contraction). His biggest blunder was throwing in the towel too early. reference 'Einstein's Doubt' and biggest regret in Pearlman YeC for the alignment of Torah testimony, science and ancient civ. volume II SPIRAL cosmological redshift hypothesis and model. Reply
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IResearchNet

Gravitational Hypothesis

The gravitational hypothesis is a theory that suggests that workers will gravitate, or move, to jobs that match their cognitive ability. Cognitive ability, generally speaking, is a person’s cognitive capacity or general mental capability that determines how quickly that person can process and understand concepts and ideas. It is believed to be stable once a person reaches adulthood. According to the gravitational hypothesis, one driver of workers’ movement across jobs is their general cognitive ability such that high-ability workers gravitate toward jobs with high cognitive demands and low-ability workers gravitate toward jobs with low cognitive demands. Said another way, workers gravitate to work that they can adequately perform.

Clearly, there are many potential drivers of worker mobility across jobs, but this theory focuses on general cognitive ability in particular. Because cognitive ability is unchanging, workers must move to jobs where they can achieve the best match between their abilities and the cognitive demands of the job. Thus cognitive ability, mobility, and person-job match are all dimensions of the theory.

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Get 10% off with 24start discount code, cognitive ability, mobility, and person-job match.

Although the context within which workers are moving, the labor market or the market where workers find work and organizations find employees, was a focus of mobility researchers for years, the gravitational hypothesis placed a lens specifically on workers’ characteristics. The state of the labor market, such as whether jobs were plentiful or not, was a key contextual factor for the frequency and type of worker mobility. Frequency is the rate or speed with which workers move across jobs in the labor market. Type of mobility is the direction of movement: upward, downward, or lateral. In some research, type of mobility is determined by the change in the salary of the work. An upward move denotes a move to a job with a higher salary than the job held previously, a downward move denotes a move to a job with a lower salary than the job held previously, and a lateral move denotes a move to a job with the same salary as that held previously. In a labor market where jobs are plentiful, workers are expected to move more frequently and have greater opportunities to move to work with higher wages. The worker’s characteristics played a decidedly backseat role in the mobility process.

The gravitational hypothesis suggested that worker characteristics, specifically general cognitive ability, should play a more central role in understanding the mobility of workers in the labor market. Moreover, type of mobility should relate directly to whether or not workers gravitate to work that matches their cognitive ability level. Upward moves suggest a move to work of greater cognitive demands than the work held previously. Downward moves would suggest a move to work of lesser cognitive demands and lateral moves would suggest a move to work of the same cognitive demands compared with the job held previously. Although higher salaries were always preferred over lower ones, this conceptualization of mobility type requires a more complicated calculus to determine whether one move would be preferred to another. Both worker cognitive ability and job cognitive demands need to be considered and the match between them evaluated. Sometimes improving the match requires a move down in job demands and sometimes it requires a move up.

Sorting workers both up and down in terms of cognitive demands runs counter to many views of mobility as generally upward. Further, there are some theories, such as the Peter Principle, that suggest that workers will be promoted to the point above their competencies. The gravitational hypothesis argues that when workers find themselves in work beyond their capabilities, they are more likely to gravitate to work with lower cognitive demands than to either stay in the job or move further upward. That is, over employment, work beyond worker capability, is more likely to lead to a shift downward in an effort to create greater parity between worker capability and job demands. Likewise, underemployment, work that is beneath worker capability, is believed to more likely lead to a shift upward to work that has higher cognitive demands. Whether the worker or the organization is the catalyst for change, such as if the worker quits or is fired, is not differentiated in the theory. Regardless of the direction of movement or the catalyst for the change (e.g., worker or organization), moves that improve the match between workers’ cognitive ability and the work’s cognitive demands are preferred according to this theory.

Thus the gravitational hypothesis suggests a dynamic model of person-job match. Person-job match, the match between person characteristics or desires and the demands or characteristics of the job, can be measured on a variety of dimensions. If a person desires a flexible schedule, finding a job that provides flexibility is considered a good match on this dimension. If a person has a preference for a certain type of workplace culture, finding an organization with such a culture would be a good match on this dimension. The gravitational hypothesis focuses on one dimension of person-job match, the match between worker cognitive ability and work cognitive demands. It is important to note that a person may be seeking match on a variety of these dimensions simultaneously, making fully explicating the matching process difficult. Indeed, matching is a process, one that the gravitation hypothesis acknowledges directly. Gravitation is about movement or change, and the gravitational hypothesis is about movement that leads to improved match between worker ability and the cognitive demands of the work.

Originally, the gravitational hypothesis was developed by job analysis researchers who observed that workers with long job tenures were more likely to have the capability to meet the demands of the work, suggesting that match encouraged stability. Workers still seeking match were more likely to leave jobs and organizations. Indeed, research has found a common outcome of mismatch between workers and their work turnover. Other outcomes of mismatch are low satisfaction and performance. Thus achieving match between workers and their jobs is beneficial to both organizations and workers. A matched employee is more likely to be satisfied, to perform better, and to have long job tenure. The probability of match may be increased through careful recruiting and selection practices that allow both applicants and prospective employers the opportunity to share information that allows for assessment of match quality.

References:

• McCormick, E. J., DeNisi, A. S., & Staw, J. B. (1979). Use of the Position Analysis Questionnaire for establishing the job component validity of tests. Journal of Applied Psychology, 64, 51-56.
• Peter, L. (1969). The Peter Principle. New York: Morrow.
• Wilk, S. L., Demarais, L. B., & Sackett, P. R. (1995). Gravitation to jobs commensurate with ability: Longitudinal and cross-sectional tests. Journal of Applied Psychology, 80, 79-85.
• Wilk, S. L., & Sackett, P. R. (1996). Longitudinal analysis of ability-job complexity fit and job change. Personnel Psychology, 49, 937-967.
• Individual Differences
• Industrial-Organizational Psychology

15 Hypothesis Examples

A hypothesis is defined as a testable prediction , and is used primarily in scientific experiments as a potential or predicted outcome that scientists attempt to prove or disprove (Atkinson et al., 2021; Tan, 2022).

In my types of hypothesis article, I outlined 13 different hypotheses, including the directional hypothesis (which makes a prediction about an effect of a treatment will be positive or negative) and the associative hypothesis (which makes a prediction about the association between two variables).

This article will dive into some interesting examples of hypotheses and examine potential ways you might test each one.

Hypothesis Examples

1. “inadequate sleep decreases memory retention”.

Field: Psychology

Type: Causal Hypothesis A causal hypothesis explores the effect of one variable on another. This example posits that a lack of adequate sleep causes decreased memory retention. In other words, if you are not getting enough sleep, your ability to remember and recall information may suffer.

How to Test:

To test this hypothesis, you might devise an experiment whereby your participants are divided into two groups: one receives an average of 8 hours of sleep per night for a week, while the other gets less than the recommended sleep amount.

During this time, all participants would daily study and recall new, specific information. You’d then measure memory retention of this information for both groups using standard memory tests and compare the results.

Should the group with less sleep have statistically significant poorer memory scores, the hypothesis would be supported.

Ensuring the integrity of the experiment requires taking into account factors such as individual health differences, stress levels, and daily nutrition.

Relevant Study: Sleep loss, learning capacity and academic performance (Curcio, Ferrara & De Gennaro, 2006)

2. “Increase in Temperature Leads to Increase in Kinetic Energy”

Field: Physics

Type: Deductive Hypothesis The deductive hypothesis applies the logic of deductive reasoning – it moves from a general premise to a more specific conclusion. This specific hypothesis assumes that as temperature increases, the kinetic energy of particles also increases – that is, when you heat something up, its particles move around more rapidly.

This hypothesis could be examined by heating a gas in a controlled environment and capturing the movement of its particles as a function of temperature.

You’d gradually increase the temperature and measure the kinetic energy of the gas particles with each increment. If the kinetic energy consistently rises with the temperature, your hypothesis gets supporting evidence.

Variables such as pressure and volume of the gas would need to be held constant to ensure validity of results.

3. “Children Raised in Bilingual Homes Develop Better Cognitive Skills”

Field: Psychology/Linguistics

Type: Comparative Hypothesis The comparative hypothesis posits a difference between two or more groups based on certain variables. In this context, you might propose that children raised in bilingual homes have superior cognitive skills compared to those raised in monolingual homes.

Testing this hypothesis could involve identifying two groups of children: those raised in bilingual homes, and those raised in monolingual homes.

Cognitive skills in both groups would be evaluated using a standard cognitive ability test at different stages of development. The examination would be repeated over a significant time period for consistency.

If the group raised in bilingual homes persistently scores higher than the other, the hypothesis would thereby be supported.

The challenge for the researcher would be controlling for other variables that could impact cognitive development, such as socio-economic status, education level of parents, and parenting styles.

Relevant Study: The cognitive benefits of being bilingual (Marian & Shook, 2012)

4. “High-Fiber Diet Leads to Lower Incidences of Cardiovascular Diseases”

Field: Medicine/Nutrition

Type: Alternative Hypothesis The alternative hypothesis suggests an alternative to a null hypothesis. In this context, the implied null hypothesis could be that diet has no effect on cardiovascular health, which the alternative hypothesis contradicts by suggesting that a high-fiber diet leads to fewer instances of cardiovascular diseases.

To test this hypothesis, a longitudinal study could be conducted on two groups of participants; one adheres to a high-fiber diet, while the other follows a diet low in fiber.

After a fixed period, the cardiovascular health of participants in both groups could be analyzed and compared. If the group following a high-fiber diet has a lower number of recorded cases of cardiovascular diseases, it would provide evidence supporting the hypothesis.

Control measures should be implemented to exclude the influence of other lifestyle and genetic factors that contribute to cardiovascular health.

Relevant Study: Dietary fiber, inflammation, and cardiovascular disease (King, 2005)

5. “Gravity Influences the Directional Growth of Plants”

Field: Agronomy / Botany

Type: Explanatory Hypothesis An explanatory hypothesis attempts to explain a phenomenon. In this case, the hypothesis proposes that gravity affects how plants direct their growth – both above-ground (toward sunlight) and below-ground (towards water and other resources).

The testing could be conducted by growing plants in a rotating cylinder to create artificial gravity.

Observations on the direction of growth, over a specified period, can provide insights into the influencing factors. If plants consistently direct their growth in a manner that indicates the influence of gravitational pull, the hypothesis is substantiated.

It is crucial to ensure that other growth-influencing factors, such as light and water, are uniformly distributed so that only gravity influences the directional growth.

6. “The Implementation of Gamified Learning Improves Students’ Motivation”

Field: Education

Type: Relational Hypothesis The relational hypothesis describes the relation between two variables. Here, the hypothesis is that the implementation of gamified learning has a positive effect on the motivation of students.

To validate this proposition, two sets of classes could be compared: one that implements a learning approach with game-based elements, and another that follows a traditional learning approach.

The students’ motivation levels could be gauged by monitoring their engagement, performance, and feedback over a considerable timeframe.

If the students engaged in the gamified learning context present higher levels of motivation and achievement, the hypothesis would be supported.

Control measures ought to be put into place to account for individual differences, including prior knowledge and attitudes towards learning.

Relevant Study: Does educational gamification improve students’ motivation? (Chapman & Rich, 2018)

7. “Mathematics Anxiety Negatively Affects Performance”

Field: Educational Psychology

Type: Research Hypothesis The research hypothesis involves making a prediction that will be tested. In this case, the hypothesis proposes that a student’s anxiety about math can negatively influence their performance in math-related tasks.

To assess this hypothesis, researchers must first measure the mathematics anxiety levels of a sample of students using a validated instrument, such as the Mathematics Anxiety Rating Scale.

Then, the students’ performance in mathematics would be evaluated through standard testing. If there’s a negative correlation between the levels of math anxiety and math performance (meaning as anxiety increases, performance decreases), the hypothesis would be supported.

It would be crucial to control for relevant factors such as overall academic performance and previous mathematical achievement.

8. “Disruption of Natural Sleep Cycle Impairs Worker Productivity”

Field: Organizational Psychology

Type: Operational Hypothesis The operational hypothesis involves defining the variables in measurable terms. In this example, the hypothesis posits that disrupting the natural sleep cycle, for instance through shift work or irregular working hours, can lessen productivity among workers.

To test this hypothesis, you could collect data from workers who maintain regular working hours and those with irregular schedules.

Measuring productivity could involve examining the worker’s ability to complete tasks, the quality of their work, and their efficiency.

If workers with interrupted sleep cycles demonstrate lower productivity compared to those with regular sleep patterns, it would lend support to the hypothesis.

Consideration should be given to potential confounding variables such as job type, worker age, and overall health.

9. “Regular Physical Activity Reduces the Risk of Depression”

Field: Health Psychology

Type: Predictive Hypothesis A predictive hypothesis involves making a prediction about the outcome of a study based on the observed relationship between variables. In this case, it is hypothesized that individuals who engage in regular physical activity are less likely to suffer from depression.

Longitudinal studies would suit to test this hypothesis, tracking participants’ levels of physical activity and their mental health status over time.

The level of physical activity could be self-reported or monitored, while mental health status could be assessed using standard diagnostic tools or surveys.

If data analysis shows that participants maintaining regular physical activity have a lower incidence of depression, this would endorse the hypothesis.

However, care should be taken to control other lifestyle and behavioral factors that could intervene with the results.

Relevant Study: Regular physical exercise and its association with depression (Kim, 2022)

10. “Regular Meditation Enhances Emotional Stability”

Type: Empirical Hypothesis In the empirical hypothesis, predictions are based on amassed empirical evidence . This particular hypothesis theorizes that frequent meditation leads to improved emotional stability, resonating with numerous studies linking meditation to a variety of psychological benefits.

Earlier studies reported some correlations, but to test this hypothesis directly, you’d organize an experiment where one group meditates regularly over a set period while a control group doesn’t.

Both groups’ emotional stability levels would be measured at the start and end of the experiment using a validated emotional stability assessment.

If regular meditators display noticeable improvements in emotional stability compared to the control group, the hypothesis gains credit.

You’d have to ensure a similar emotional baseline for all participants at the start to avoid skewed results.

11. “Children Exposed to Reading at an Early Age Show Superior Academic Progress”

Type: Directional Hypothesis The directional hypothesis predicts the direction of an expected relationship between variables. Here, the hypothesis anticipates that early exposure to reading positively affects a child’s academic advancement.

A longitudinal study tracking children’s reading habits from an early age and their consequent academic performance could validate this hypothesis.

Parents could report their children’s exposure to reading at home, while standardized school exam results would provide a measure of academic achievement.

If the children exposed to early reading consistently perform better acadically, it gives weight to the hypothesis.

However, it would be important to control for variables that might impact academic performance, such as socioeconomic background, parental education level, and school quality.

12. “Adopting Energy-efficient Technologies Reduces Carbon Footprint of Industries”

Field: Environmental Science

Type: Descriptive Hypothesis A descriptive hypothesis predicts the existence of an association or pattern related to variables. In this scenario, the hypothesis suggests that industries adopting energy-efficient technologies will resultantly show a reduced carbon footprint.

Global industries making use of energy-efficient technologies could track their carbon emissions over time. At the same time, others not implementing such technologies continue their regular tracking.

After a defined time, the carbon emission data of both groups could be compared. If industries that adopted energy-efficient technologies demonstrate a notable reduction in their carbon footprints, the hypothesis would hold strong.

In the experiment, you would exclude variations brought by factors such as industry type, size, and location.

13. “Reduced Screen Time Improves Sleep Quality”

Type: Simple Hypothesis The simple hypothesis is a prediction about the relationship between two variables, excluding any other variables from consideration. This example posits that by reducing time spent on devices like smartphones and computers, an individual should experience improved sleep quality.

A sample group would need to reduce their daily screen time for a pre-determined period. Sleep quality before and after the reduction could be measured using self-report sleep diaries and objective measures like actigraphy, monitoring movement and wakefulness during sleep.

If the data shows that sleep quality improved post the screen time reduction, the hypothesis would be validated.

Other aspects affecting sleep quality, like caffeine intake, should be controlled during the experiment.

Relevant Study: Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep (Waller et al., 2021)

14. Engaging in Brain-Training Games Improves Cognitive Functioning in Elderly

Field: Gerontology

Type: Inductive Hypothesis Inductive hypotheses are based on observations leading to broader generalizations and theories. In this context, the hypothesis deduces from observed instances that engaging in brain-training games can help improve cognitive functioning in the elderly.

A longitudinal study could be conducted where an experimental group of elderly people partakes in regular brain-training games.

Their cognitive functioning could be assessed at the start of the study and at regular intervals using standard neuropsychological tests.

If the group engaging in brain-training games shows better cognitive functioning scores over time compared to a control group not playing these games, the hypothesis would be supported.

15. Farming Practices Influence Soil Erosion Rates

Type: Null Hypothesis A null hypothesis is a negative statement assuming no relationship or difference between variables. The hypothesis in this context asserts there’s no effect of different farming practices on the rates of soil erosion.

Comparing soil erosion rates in areas with different farming practices over a considerable timeframe could help test this hypothesis.

If, statistically, the farming practices do not lead to differences in soil erosion rates, the null hypothesis is accepted.

However, if marked variation appears, the null hypothesis is rejected, meaning farming practices do influence soil erosion rates. It would be crucial to control for external factors like weather, soil type, and natural vegetation.

The variety of hypotheses mentioned above underscores the diversity of research constructs inherent in different fields, each with its unique purpose and way of testing.

While researchers may develop hypotheses primarily as tools to define and narrow the focus of the study, these hypotheses also serve as valuable guiding forces for the data collection and analysis procedures, making the research process more efficient and direction-focused.

Hypotheses serve as a compass for any form of academic research. The diverse examples provided, from Psychology to Educational Studies, Environmental Science to Gerontology, clearly demonstrate how certain hypotheses suit specific fields more aptly than others.

It is important to underline that although these varied hypotheses differ in their structure and methods of testing, each endorses the fundamental value of empiricism in research. Evidence-based decision making remains at the heart of scholarly inquiry, regardless of the research field, thus aligning all hypotheses to the core purpose of scientific investigation.

Testing hypotheses is an essential part of the scientific method . By doing so, researchers can either confirm their predictions, giving further validity to an existing theory, or they might uncover new insights that could potentially shift the field’s understanding of a particular phenomenon. In either case, hypotheses serve as the stepping stones for scientific exploration and discovery.

Atkinson, P., Delamont, S., Cernat, A., Sakshaug, J. W., & Williams, R. A. (2021).  SAGE research methods foundations . SAGE Publications Ltd.

Curcio, G., Ferrara, M., & De Gennaro, L. (2006). Sleep loss, learning capacity and academic performance.  Sleep medicine reviews ,  10 (5), 323-337.

Kim, J. H. (2022). Regular physical exercise and its association with depression: A population-based study short title: Exercise and depression.  Psychiatry Research ,  309 , 114406.

King, D. E. (2005). Dietary fiber, inflammation, and cardiovascular disease.  Molecular nutrition & food research ,  49 (6), 594-600.

Marian, V., & Shook, A. (2012, September). The cognitive benefits of being bilingual. In Cerebrum: the Dana forum on brain science (Vol. 2012). Dana Foundation.

Tan, W. C. K. (2022). Research Methods: A Practical Guide For Students And Researchers (Second Edition) . World Scientific Publishing Company.

Waller, N. A., Zhang, N., Cocci, A. H., D’Agostino, C., Wesolek‐Greenson, S., Wheelock, K., … & Resnicow, K. (2021). Screen time use impacts low‐income preschool children’s sleep quality, tiredness, and ability to fall asleep. Child: care, health and development, 47 (5), 618-626.

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Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

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• Theoretical Astrophysics

Understanding the cosmos involves both observation and theory. Observation provides real-world data about how stars, galaxies, and other objects in space behave. Theory connects that data together into a full understanding, and makes predictions about phenomena we haven’t observed yet. Theoretical astrophysics includes mathematical models for astronomical systems, along with templates to fit to new results when they arise.

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Center for Astrophysics | Harvard & Smithsonian theoretical astrophysicists study a wide range of phenomena:

Building models of star-formation based on observation and theory. Using the data from star-forming regions and theoretical calculations of gas and dust under the action of gravity, astrophysicists have concluded stars tend to be born in pairs. Those binaries may be disrupted later, as happened with our Sun, but the theory suggests there’s a twin Sun somewhere out there. New Evidence That All Stars Are Born in Pairs

Calculating the potential conditions on exoplanets orbiting a variety of stars. Astronomers have discovered a number of planets orbiting red dwarf stars, which are much lower temperature than the Sun. That means potentially habitable worlds in these systems are very close to the star, possibly too close. Calculations show that these exoplanets may be uninhabitable based on magnetic activity and solar wind. More to Life Than the Habitable Zone

Determining the nature of inflation, the extraordinarily rapid expansion of the cosmos that many cosmologists think occurred when the universe was just a split-second old. Inflation explains many aspects of the universe we see today, but we have no direct evidence for it. Early-universe researchers examine the different possible ways inflation could have worked, including potential observable effects. Theorists Propose a New Method to Probe the Beginning of the Universe

Modelling the Cosmos

Theory is the way scientists connect facts into a coherent system of thinking, which they can use to understand the natural world. The most powerful theories both explain what we observe in a coherent way and predict new phenomena, providing us with deep insights into how the universe works.

Science needs both theory and data collected through observation or experiment. Theory produces a mathematical description or model of certain systems, which generalizes data taken from particular observations to explain them and others. In that way, observations are the test of theory, and theory is the explanation for observations. Sometimes theory predicts new phenomena that are later observed, such as gravitational waves, which were first described in 1916, but only detected a century later. In other instances, astronomers observe phenomena for which theorists don’t have an explanation, such as the accelerating expansion of the universe.

Theoretical astrophysics covers as wide a range of topics as observational astronomy.

Star - and planet-formation  models indicate that stars and planets are born from dense, cold clouds of gas and dust, which we describe by modeling the way matter collapses under its own gravity when compressed. Today, researchers model star and planet formation using computers, to understand the details of the magnetic fields of the newborn stars, the way planets migrate within the protoplanetary environment, and other details. [ link to “star” and “planet formation” pages ]

We only know of one planet where life exists, but with thousands of known exoplanets and billions more likely in the Milky Way alone, researchers want to know how possible life is elsewhere. Theoretical models help constrain the possibilities, based on the environments for exoplanets we observe.

Calculating gravitational interactions between three or more objects is still a challenging problem. Astrophysicists use advanced mathematics and computer simulations to model star clusters, multi-planet or -moon systems, and many more.

Theory is necessary for cosmology — the study of the whole universe — for two major reasons. First, there are hundreds of billions of galaxies and countless stars, but only one universe, so we don’t have any way to compare the possibilities if things are slightly different. Second, matter in the early universe was dense and opaque, so it is inaccessible to observations. Theory fills in those gaps, testing ways the universe could have evolved differently, and finding the physical conditions that produce the cosmos we observe. These models help us understand dark matter, dark energy, and other phenomena we observe, but which we don’t have a good explanation for yet.

For much of astrophysics, Newton’s theory of gravity is perfectly adequate to predict how things behave. However, in instances of strong gravity or very large scales, astrophysicists use Albert Einstein’s theory of general relativity. Those cases include black holes, neutron stars, gravitational waves, and the structure of the universe as a whole.

Simulation using the Illustris program of the dark matter governing the distribution of galaxies. Such simulations connect astronomical observations of galaxies to the theory describing how the universe evolves.

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April 9, 2024

Could Gravitational-Wave ‘Memories’ Prove Einstein Wrong?

According to Albert Einstein’s general theory of relativity, the universe remembers every gravitational wave—and scientists could soon test these cosmic recollections

By Paul M. Sutter

Sakkmesterke/Getty Images

Decades ago physicists realized that gravitational waves are no mere passing phenomenon. Instead those ripples in space should leave behind permanent marks: a fixed distortion in their wake. So far this “memory” effect has remained undetected, but the next generation of gravitational-wave detectors should be able to find them. And if they do, it will open up a new avenue to testing our understanding of gravity.

Memories of Einstein

In 1916 Albert Einstein himself predicted the existence of gravitational waves as a consequence of his general theory of relativity. These vibrations in space itself would ripple out from masses experiencing any kind of asymmetrical acceleration. Examples for gravitational-wave sources include stars exploding, black holes merging and even a person spinning around in their office chair! But gravity is by far the weakest of the forces, and gravitational waves are just tiny wrinkles on top of that. Einstein ultimately concluded that although they existed, they were unlikely to ever be detected.

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Almost a century later a team of enterprising physicists finally proved Einstein wrong—by proving him right . Researchers built and used the Laser Interferometer Gravitational-Wave Observatory (LIGO) to detect the signature vibration pattern of two merging black holes .

Around the same time that LIGO was first being conceived about a half-century ago, other theorists discovered something remarkable: gravitational waves can permanently alter space after passing through a region . At first this result seems impossible, like the idea of ocean waves permanently distorting the ever-changing surface of the sea. Waves are by definition transient phenomena. If you stand in one place, a wave washes over you by starting from nothing, rising to a peak and then ebbing back to nothingness. Once the wave is gone, it’s gone.

To understand this effect, known as gravitational-wave memory, we have to remember Einstein’s original insight: any asymmetrical action or motion or event leads to the creation of gravitational waves. It turns out that gravitational waves themselves exhibit such asymmetries.

A passing gravitational wave distorts space, bringing objects closer together before returning them to their original position. That distortion of space is itself an asymmetrical event that creates a new round of gravitational waves that emanate in the wake of the first. Those new waves do the same thing: distort space and bring objects together. That second wave then generates a third, which repeats into a fourth, and on and on. Each round of waves is weaker than the last, but careful calculations reveal that by adding up the ever-diminishing contributions from the infinitudes of generated waves leads to a permanent distortion: once the initial waves pass, two freely floating objects will remain closer to each other forever.

Of course, the real world is complicated. Planets orbit the sun, chunks of rock crash into each other, and so on. This means that the memory effect is usually washed away by the vagaries of everyday life. Hence the calculations and predictions rely on an idealized scenario where we imagine two objects free of any other influence. If you were to stand on one object and measure the distance to the other, after a wave passed, you would find that measurement to be smaller than before.

Thankfully this idealized scenario is exactly what we’ve designed our gravitational-wave detectors to replicate, which means we have the potential to measure the memory effect.

Memories of LISA

Perhaps most surprising of all, this memory effect is roughly as strong as the gravitational influence of the initial wave (which is, to be clear, not big at all: even the strongest gravitational waves washing over Earth cause displacements of less than the width of an atomic nucleus). Despite this strength, however, the effect is as yet undetected. For now, the gravitational-wave-memory effect remains a purely hypothetical, untested prediction of general relativity.

But theorists strongly suspect this memory effect exists. After all, general relativity has (annoyingly) so far withstood every single test that could invalidate its predictions—or at least find a crack in its calculations. The same math that Einstein used to predict the existence of gravitational waves in the first place leads directly to a memory effect.

So why haven’t we measured this memory effect? Simply put, nobody’s gone looking for it yet. To detect gravitational wave memory, you need two things. One, your instrument needs to be freely floating to “remember” the imprint of the gravitational waves. Two, you need to measure gravitational-wave effects over long timescales because it takes a while for the memory effect to build up after the initial wave passes.

Our current gravitational-wave detectors fail on both counts. LIGO uses masses attached to pendulums, which mechanically restore their position after a wave passes, obfuscating any memory measurement. And the design of LIGO is tuned to short-term, high-frequency bursts of gravitational waves.

All that’s about to change, however, with the recent announcement that LISA— the Laser Interferometer Space Antenna —has been green-lit by the European Space Agency for an anticipated launch in 2035. LISA will feature a trio of co-orbiting satellites, meaning that the individual elements will be free-floating, and with its stations set 2.5 million kilometers apart, LISA will specifically hunt for low-frequency gravitational waves—check and check.

LISA should be able to detect gravitational-wave memory by measuring the permanent distortion of space within the solar system after the waves pass through. Again, despite the enormity of their source (LISA will target the waves generated by colliding supermassive black holes), these memory-effect distortions will be incredibly tiny, no bigger than an atomic nucleus.

Memories of the Future

When theorists devise new experimental tests, they want two simultaneous, contradictory outcomes. LISA finding the memory effect is no exception. On one hand, this serves as yet another test of general relativity, and a confirmed detection of wave memory will cement Einstein’s theory as even more robust and capable.

On the other hand, we could really use a way to move past Einstein. We know that his theory is incomplete. It does not describe what happens at the centers of black holes or in the earliest moments of the universe. It does not get along with quantum mechanics. It does not explain dark matter and dark energy, the twin mysteries that together comprise 95 percent of the contents of the universe.

If we fail to see a memory effect—or find one with a different strength than what’s predicted—then we may have found a chink in relativity’s nigh-impervious armor, one that we might leverage and pry open to expose this cherished theory’s deeper flaws and put us on firmer ground for devising a better theory of gravity.

But even if we don’t find a flaw and the memory effect measured by LISA comes out to be exactly in line with predictions, this would still be useful in other ways. For example, when two giant objects collide somewhere in the cosmos, they can do so at any angle from our point of view—and we don’t have a great way of determining that angle, which makes it harder for us to know just how far away such mergers occurred. Observations of the memory effect can break this confusion because the memory effect has a different dependence on distance and viewing angle, so the combined measurement gives a more detailed picture of the scenario.

In another proposal, the next generation of stellar surveys should be able to see the combined effect of the entire past history of gravitational waves imprinted in positions of the stars themselves. After all, gravitational waves have been sloshing around the universe for billions of years, leading to countless memory-effect distortions in their wake. The stars in every galaxy will simply move relative to each other in tiny, subtle ways—but ways that we could measure over time.

The ultimate lesson from this work is that our mundane conceptions of fixed space are incorrect and incomplete. Not only do gravitational waves temporarily change and alter the very fabric of reality but they also leave permanent marks in their wake. The distance between any two points constantly shifts, and in doing so one of the most fundamental aspects of our universe changes.

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Hypothesis that proposes that athletes have different personality traits from non-athletes because of a process of natural selection: individuals who are stable extroverts tend to gravitate towards sport and competition causes all, but the keenest competitors to withdraw so that those who adhere to sport tend to have the greatest levels of extroversion and stability.

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