How does gravity work?

by Marianne Freiberger

29/09/2009


 Bangalore Sathyaprakash

B.S. Sathyaprakash

This article was part of a project we ran to celebrate the International Year of Astronomy 2009. The project asked you to nominate the questions about the Universe you'd most like to have answered, and this is one of them. We took it to Professor Bangalore Sathyaprakash of the School of Physics and Astronomy at Cardiff University, and here is his answer. This interview is also available as a podcast.

Gravity according to Newton

"According to Newton's relatively simply picture, gravity is a force that works between two objects," says Sathyaprakash. "So if you have the Earth and the Sun, for example, then the Earth feels a force that is exerted by the Sun, and in turn the Sun feels the same force, exerted by the Earth." The magnitude $F$ of this force is given by the familar inverse square law

  \[ F=G\frac{m_1 m_2}{r^2}, \]    
where $G$ is the gravitational constant, $r$ is the distance between the centres of the Earth and the Sun, and $m_1$ and $m_2$ are their respective masses.

Newtonian gravity diagram

The gravitational interaction of two spherical bodies according to Newton. Image: Dennis Nilsson.

The forces experienced by Earth and Sun may be equal in magnitude, but the resulting motion is not the same for the two bodies. According to Newton's second law of motion, the magnitude of the acceleration a body experiences when it is subjected to a force is equal to the magnitude of the force divided by the body's mass. Since the Sun's mass is large, the acceleration it experiences due to the Earth's gravitational pull is negligible compared to that experienced by the much less massive Earth. That's why the Sun remains more or less stationary, while the Earth is forced on an orbit around it.

Newton's theory of gravity, published in 1687, is remarkably accurate when it comes to most practical purposes, and went unchallenged for over 300 years. Problems arose, however, when Einstein developed his special theory of relativity in 1905. "According to Newton's theory, gravitational interaction is instantaneous. Suppose the Sun were to vanish from the horizon today. We would not notice its disappearance immediately just by looking at the Sun, because light takes some time to travel. But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in a tangential direction to its original path." Einstein's special theory of relativity, however, states that nothing, not even information, can travel faster than the speed of light. "It's possible to use the vanishing Sun analogy to construct [theoretical] gravitational telegraphs which would transmit information instantaneously — and that, according to Einstein, is impossible. That's the reason why Einstein had to reformulate the theory of gravity." Einstein published his reformulation in 1916, under the name of general relativity.

Gravity according to Einstein

"Einstein's theory of general relativity doesn't really look at gravity as a force anymore, rather it replaces the concept of force by that of geometry," says Sathyaprakash. According to general relativity, massive objects curve the geometry of space, and the paths that moving objects take through space are a result of this curvature. An analogy often used is that of a bowling ball placed on a trampoline: the ball will create a dip in the trampoline, curving its surface, so a marble placed nearby will roll into the dip towards the ball. The marble's motion isn't a result of some attractive force exerted by the ball, but a result of the curvature of the surface it's moving on. The analogy is slightly wonky, since it is the Earth's gravity, and not that of the bowling ball, which creates the dip in the trampoline as the bowling ball is drawn to the floor. "We should really move out of this analogy and try and picture the full three-dimensional space, as well as time, as being curved," says Sathyaprakash. "It's because of this curvature that planets move along curved orbits, rather than straight lines."

Einstein's gravity

According to Einstein's general theory of relativity, massive objects curve spacetime. Image courtesy NASA.

In our own solar system the curvature of space, or rather of spacetime, as the two are inextricably linked, is mainly due to the Sun and to a small extent to Jupiter, which is next in line in terms of mass. And since these two bodies themselves move around, albeit only very slightly in the case of the Sun, the result is a dynamic system in which curvature varies continually as massive objects move around spacetime. "There is a famous phrase coined by John Archibald Wheeler: mass tells spacetime how to curve and spacetime tells mass how to move. The dynamics of Einstein's equations, the way these equations work, are encapsulated in this famous phrase."


Black holes and spacetime ripples

So far, Einstein's theory of gravity has proved amazingly accurate, and it's passed every test it's been submitted to. But two of its most important predictions still have not been completely verified. The first is the existence of the infamous black holes. These, so the theory goes, are formed when a lot of mass is concentrated in a tiny region of space. Densely packed mass exerts an immense gravitational pull, as we can easily see by momentarily reverting to Newton's inverse square law. Suppose that you are sitting on the surface of an extremely dense spherical body with a very large mass $M$ and a very small radius $r$. The gravitational force holding you to the body's surface, according to Newton, has magnitude

  \[ F= G\frac{M m}{r^2}, \]    
where $m$ is your own mass. Now since $M$ is very large and $r$ is very small, $F$ in turn is very large. The body exterts a huge gravitational pull, and to escape its clutches you'd need to accelerate away from it very hard indeed. Now if the body is so dense that escape becomes impossible for everything including light, then the resulting object is called a black hole. (To be precise, it's the compactness of a body, the ratio between its gravitational radius and its physical radius, which determines whether it is a black hole.)

A black hole

An artist's concept of a black hole gobbeling up a star. The star approaches (yellow blob on the left), then stretches apart (middle yellow blob), and eventually breaks into stellar crumbs, some of which swirl into the black hole (cloudy ring at right). Image courtesy NASA Jet Propulsion Laboratory.

The idea of black holes has been around since long before Einstein, but they also find a natural incarnation in his geometrical description of gravity. In Einstein's theory, a black hole is a region of space which, due to the presence of some immensely dense mass, has been curved so violently that ordinary physics breaks down in its vicinity. According to the mathematical equations describing the geometry of spacetime, the curvature at the centre of a black hole is infinite. No-one has ever observed a black hole directly, but there is much indirect evidence that these monsters do exist, and physicists believe that one resides at the centre of most galaxies.

The idea of dense objects like black holes shunting their mass around a constantly warping and bending spacetime leads to the second major prediction of Einstein's theory: gravitational waves. "Near black holes the curvature of spacetime is extremely high," explains Sathyaprakash. "Now imagine two black holes moving around each other: the curvature is large but also changing. It's a bit like taking a stick and moving it around in a pond. That's going to generate ripples in the water. Only in the case of black holes, we're talking about ripples in the very fabric of spacetime." Einstein's theory predicts that these ripples, the gravitational waves, should arise whenever massive bodies move about, just as a trampoline experiences tremours when you move a heavy object on its surface. As with black holes, there is indirect evidence that gravitational waves exist, but no-one has ever detected one directly.

Why catch waves?

Gravitational waves from colliding stars

An artist's impression of gravitational waves caused by a pair of massive stars spiralling towards each other and finally colliding. Click here to see an animation of this process on the NASA website. Image: NASA/Dana Berry, Sky Works Digital.

Few things would give a more pleasing confirmation of Einstein's theory of gravity than the direct observation of black holes or gravitational waves, because both epitomise the idea of a flexing and bending spacetime. Sathyaprakash specialises in gravitational waves and believes that they in fact hold the key to both puzzles. "Black holes are black in an electromagnetic sense: they emit no light, no radio waves, and so on. But they could be emitting gravitational waves, the best example being the black hole binary system described above. By observing gravitational waves we might be able to measure the structure of spacetime geometry around black holes in a way that will never be possible in any other experiment. Most galaxies are believed to contain a massive black hole at its centre, and these black holes are not just sitting there idly. They are eating up other material and other black holes in their vicinity all the time. Now when a smaller black hole falls into a bigger one, it takes a very complicated orbit. As it goes around, the small black hole samples the geometry of spacetime in the region, and the gravitational wave signals that are emitted encode that geometry."

What's more, Einstein's equations predict that when two black holes collide, the resulting gravitational waves come with an immense amount of energy in a very short duration. Translated into brightness, this amount of energy would far exceed the light from all the stars in all the galaxies of the Universe. "So even though black holes are black electromagnetically, they could be outshining the entire Universe [in terms of gravitational waves], though only for a very short while. And this is where the interest in gravitational waves comes from."

Detecting gravitational waves

Existing evidence for gravitational waves is indirect. It comes from an astronomical system discovered in 1974 by Joseph Taylor and Russell Hulse, which contains two extremely dense neutron stars. "These stars are only about 10km in radius, but they have the same mass as the Sun" says Sathyaprakash. "Even a spoonful of the neutron star material weighs several billion tons." As with black holes, the motion of these dense stars should cause gravitational waves. Now it turns out that one of these two stars happens to be what's called a pulsar: it emits radio signals at regular intervals, which can be detected on Earth. Using these signals, Hulse and Taylor were able to establish that the two stars were spiralling towards each other. According to Einstein's theory, this can only happen if the system is losing energy in the form of gravitational waves — and the rate at which the two stars drew nearer to each other did indeed match the theory's predictions exactly.

But how can we detect gravitational waves directly? How do they manifest themselves? "Gravitational waves interact with any particle, indeed with any mass," says Sathyaprakash. "In fact, that's the trouble, they interact with everything so democratically that it's very hard to detect them, so we have to construct very sensitive instruments. Basically the tiny distortions in spacetime caused by gravitational waves move masses around. The instruments that currently exist to detect these movements are called laser interferometer gravitational wave detectors." These detectors contain mirrors, and the goal is to detect the tiny movements of these mirrors due to gravitational waves using laser interferometry (see the Plus article Catching waves with Kip Thorne for more information on this technique).

"Currently there are five gravitational wave detectors that are operating," says Sathyaprakash. "There are three instruments in the USA, called Ligo, and two in Europe, called Virgo and GEO 600. One more is being planned in Japan. These detectors are expected to make the first observations around 2014. The goal is to construct a global array of detectors, which can see sources from almost anywhere in the Universe."

LISA

An artist's impression of LISA. Click here to see an animation of LISA in orbit. Image: NASA/Dana Berry, Sky Works Digital.

Two ambitious projects are the laser inteferometer space antenna (LISA), a space-based detector scheduled to take flight some time around 2020, and the Einstein telescope, which could be built around 2025 or 2030. Both will be able to detect gravitational waves from black hole collisions far away in the Universe. Binary black holes and neutron stars will also provide astronomers with an improved way of overcoming the notoriously difficult problem of measuring cosmic distances. Comparing the observed intensity of a gravitational wave from a black hole merger with its intrinsic intensity (which can be calculated theoretically), it is possible to calculate how far the source of the wave is away from us. Thus, observations of waves from many black hole mergers will provide a cosmic distance ladder, distance markers in space and time against which other distances can be measured. This helps to determine some crucial features of the Universe, for example how fast it is expanding. Currently astronomers use other phenomena, for example supernovae, to construct the cosmic distance ladder, but Sathyaprakash says that gravitational waves will greatly increase accuracy (see the Plus article Hubble's top five achievements to find out more about how distances are currently determined).

One exciting possibility is the detection of waves that emanate all the way from the Big Bang. "A tiny fraction of a second after the Big Bang gravitational waves might have been produced. These are travelling to us unscathed without any corruption. By detecting them, we'll be able to deduce the conditions in the very early Universe. In a paper in Nature last month we have already set limits on how strong these gravitational waves could be."

But what if none of the sophisticated detectors that will come into action over the next twenty years will detect any waves? Will that throw doubt on their existence, or even Einstein's theory of gravity as a whole? "We know that gravitational waves exist — I don't think that anybody in their right mind would doubt [Hulse and Taylor's neutron star evidence]," says Sathyaprakash, "In fact, Hulse and Taylor were awarded the 1993 Nobel Prize in Physics for their discovery. What might very well happen, though, is that the sources of gravitational waves turn out not to be very common. The next generation of detectors will be sensitive to a distance of 600 million light years, and the question is whether that's good enough. But current predictions based on the Hulse-Taylor binary pulsar say that we will see events within about 600 or 700 million light years, and that's the distance that advanced detectors are aiming to achieve."

And if we do detect gravitational waves, will we be able to put them to some use here on Earth? "It's not impossible, but it's currently implausible. But when Hertz conducted his first experiments with radio waves he was of the same opinion — so who knows?"

To find out more about black holes and gravitational waves, play this online game developed by Sathyaprakash and his team, have a look at this online tutorial, or the Einstein online website. And don't forget that this interview is also available as a podcast.

Comments

acceleration of light?

article states :

"The body exterts a huge gravitational pull, and to escape its clutches you'd need to accelerate away from it very hard indeed. Now if the body is so dense that escape becomes impossible for everything including light, then the resulting object is called a black hole."

The speed of light is a universal constant, and it does not accelerate. But according to this article, acceleration is needed to escape the body's gravitational pull. Am I missing something here?

but it doesn't escape

but it doesn't escape

Escape velocity

To escape an object's gravitational pull you just need to have enough kinetic energy to balance the gravitational potential energy — that is you have to be able to achieve the escape velocity. The acceleration in the article refers to something stationary on the surface of the object accelerating to this escape velocity. As you say the speed of light is constant, it does not accelerate. Therefore if the escape velocity at the surface of a body is greater than the speed of light (so the radius of the body is smaller than the Schwarzschild radius), then nothing, not even light will be able to escape from the gravitational field.

how gravity works / unified field theory

After observing the results of all the experiments scientists have conducted I have come up with a unified field theory and it includes the mechanism of gravity.
Einstien
was so very close, but had no way of knowing how close he was.

Suppose that you lived in a world where nothing was longer than 60 feet long, and you had a tape measure that was 60 feet long, and it was impossible to make a tape measure longer than 60 feet long. In this world, nothing was larger in dimension than 60 feet. Around this world are millions of galaxies and worlds, all no farther away than 60 feet.
This puzzled all the great minds and scientists of this world as it seemed impossible for so many things to exist in such a small space. Furthermore, it seemed very strange to them that when they sent their rocket ships to explore these worlds and galaxies that their rocket ships could not reach these stars only 60 feet away. The rocket ship would seemingly accelerate to enormous speeds yet never could reach the stars.
It was then theorized that time must speed up the farther from the center of the earth you got making it impossible to travel a journey of 60 feet from the center of the earth. It was also theorized that perhaps gravity became so powerful at 60 feet that the rocket ships came to a stop. It seemed that they could send things on a trip of 99.999999% of 60 feet, but no further. This made sense to them all since the maximum length width or height of anything was 60 feet and this was an accepted constant in their world of physics.
So the scientists got 2- 60’ rods and placed them end to end and measured them and found they only measure 60’. This they theorized meant that each rod had shrunk to 50% of their length, so they tried with 3 rods and found that they were still 60’ long overall combined, so had shrunk to 33.3333% of their length, and so a fourth was added and all with the same result. So the real puzzle was that when they measured the mass of all the rods, they could account for each rod by weight, so 4 rods were four times as heavy as one rod, but when they measured the density of the rods they found the density had not changed. They were puzzled; the size of the object remained the same, yet the weight had quadrupled , while the density remained the same.
Scientists came up with all kinds of theories that all seemed sound except when dimensions began to reach near to 60 feet, and then they all broke down. The pondered all kinds of impossible shapes that might describe the universe to explain this phenomenon but as soon as one scientist seemed to have a brilliant theory of this, another scientist would propose another theory that seemed to disprove the latter. So round and round they went.
What they did not know, and could not know is that the laws of physics had limited the length of the measuring device of their world. Often people would go for a walk and it seemed longer than on other days when they had taken the same distance of a walk, but that’s just the way people are, sometimes it seems farther than other days. What they could not know is if it really was a longer walk or not, they did not know that their measuring capabilities were limited. They all knew that 60 feet plus 60 feet should equal 120 feet, but since the one constant in there universe seemed to be nothing could be longer than 60 feet, and that was accepted fact, unquestionable.
However the truth was that the measuring tape was the problem, it would never measure anything longer than 60 feet, and all measuring devices shared the same characteristic. When the tape was stretched out over the four 60 foot rods, it still read 60 feet, this was because it was actually a very flexible tape measure and literally stretched like a rubber band the entire 240 feet and still only recorded 60 feet.
Another thing the scientists found was that when they stretched the tape out to measure the 240 feet of rod, and it only recorded them to be 60 feet, (not knowing the tape stretched as I just explained) they found it took four times as long to travel each inch of the rod, this seemed to prove to them that time had sped up for the rod, but not for them, and they called this all part of some distance time continuum.
But had they known that their tape measure had the limitations, not the actual length of anything they may have come up with the right answers.
Sounds silly right? To live in a world where they have a maximum length width or height that these dimensions are limited and this is the world they are boxed in to? Well we live in a world where we do the same thing. We have given a maximum to one of our dimensions, and that is speed, we have determined that 183000 miles per second is as fast as anything can go, nothing can go faster. But what if that is not true?
If you were in an empty universe, only you, nothing else existed; how fast are you going? Are you stopped? Or if you constantly accelerated forever would you not exceed the speed of light, and if you did; relative to what? And in this world, our universe and all the universes, how fast are they going? And relative to what? Is there a point in space that is stopped? Is anything going 0 miles per hour? And in what direction? These are the questions that are created in this world because we have a maximum velocity.
But suppose there was no maximum velocity? Suppose things could travel trillions of miles per second and beyond, why can’t we see that in our universe, well in some things we can, quarks and photons seem to be able to travel instantaneously between 2 points, and so scientists are baffled. But what if they knew what I believe to be true, that their measuring device is flawed!
Time must have a limit; it seems to not be able to measure anything traveling faster than 183000 miles per second before it begins to stretch and distort to give us the same reading just like the tape measure in the other world. Light speed is unknown then, since it seems to exceed the speed of time.
God is without beginning or end, so time cannot measure his life span, so God exists before time and after time has ended. Therefore time being a created thing, must have limitations. If time had no speed limit, it would race from beginning to end and be over as fast as it was created, so obviously God put a speed limit on time, and light, being the fastest thing we know of has allowed us to measure its speed, the speed of time is 183000 miles per second.
If what I said is true, it also explains very simply how gravity works, but I will reveal that later
By Dave Morrison
Part 2
If you have been following my two previous papers you will know that I have proposed that light speed is not the velocity limit of all things, however the speed of time is. That is to say that time can not measure anything going faster than 183000 miles per second. So time stretches and flexes when using it to measure the speed of light. Knowing this we can understand how gravity works.
Gravity is nothing more than acceleration, and acceleration is the change in velocity over TIME. Therefore, if time was affected by the simple presence of matter, then acceleration could be simulated. If there was a particle contained within the building blocks of matter that traveled or moved faster than the speed of time, then time would necessarily ripple at this sub atomic level. This would continuously ripple time making stationary objects feel like they are accelerating.
Picture a dragster at a drag strip, and it takes 4 seconds to travel the ¼ mile, the acceleration felt by the driver would be enormous, that is called G-Force. Now take this same dragster and chain it down and lay a sheet of elastic cloth out over the length of the track and chain the dragster down. The elastic is affixed to the finish line so it won’t move at that end.
Now when the dragster takes off it can’t move, but it stretches and bunches up the elastic cloth behind the back tires of the dragster. After the dragster stops it is observed that the dragster tires rotated enough revolutions to travel the entire ¼ mile, however when looking at the elastic it was still attached at the finish line stretched microscopically thin over the quarter mile was 0 inches of elastic. This is impossible with things made from materials of any kind, but not for time.
So time is stretched the same way inside sub atomic particles. A luxon is a sub atomic particle that travels at the speed of light and has no rest mass, which it would not have if it was what was creating the gravitational force that measures mass. A tachyon is a hypothetical (mythical) particle that ravels faster than the speed of light and has an imaginary rest mass, it was invented by scientists to try to make their theories work, My theory does not need it, and even if it was that fast we still could see it and find it, as the speed of time would slow down its appearance to us.
It is claimed that a luxon travels at the speed of light, however since we can not measure anything faster than the speed of light, how do we know? For time changes to make things appear as if they are not able to travel faster than light. This Luxon is in every atom, and rippling time, and thus mimicking acceleration and we call it gravity.
If this is true the larger an object is in mass, the more gravity it would have, oh wait, it does. If this were true, then time would be distorted less and less the farther from a massive body and so gravity would be less and less, and it is.

There, last week I decided it was time to come up with a unifying theory of everything and there you have it.
By Dave Morrison

Speed of Light

Isn't the speed of light 186,000 miles per second not 183,000?

Light speed: 186 282.397 miles per second...

Light speed: 186 282.397 miles per second. Kind of discredits the whole post, no?

no and no

speed of light is 299 792 458 m / s

No. The logic is sound even

No. The logic is sound even if the number is a tad off.

Jan said...

Thanks for this interesting article - but I do find the paragraph below confusing. My first problem is the sentence: "But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in an tangential direction to its original path." Does this vanishing refer to sight? If so, this has nothing to do with gravity.

"According to Newton's theory, gravitational interaction is instantaneous. Suppose the Sun were to vanish from the horizon today. We would not notice its disappearance immediately just by looking at the Sun, because light takes some time to travel. But according to Newton's gravity, the effect of the Sun's vanishing would be felt immediately, as the Earth would fly away in an tangential direction to its original path." Einstein's special theory of relativity, however, states that nothing, not even information, can travel faster than the speed of light. "It's possible to use the vanishing Sun analogy to construct [theoretical] gravitational telegraphs which would transmit information instantaneously — and that, according to Einstein, is impossible. That's the reason why Einstein had to reformulate the theory of gravity." Einstein published his reformulation in 1916, under the name of general relativity.

Jan

The Plus team said...

To clarify: no, here "vanishing" doesn't refer to sight. It refers to the Sun being actually removed, and with it its gravitational pull.

how gravity works / unified field theory

how gravity works / unified field theory
Submitted by Anonymous (not verified) on September 25, 2010.

All objects with mass have been generating a field [gravity] since they came into existance in the universe.

The field's speed of radiation is unknown, but probably light speed. So warped space extends around each mass in a sphere with a gradient of warping as far as light could travel since the mass came into existence.

If another mass and the field that it has generated since it came into existence approaches the first mass then their fields overlap like cell-phone tower signals overlap. At this overlap, space is warped by both masses such that it produces a warped space shape like a sand egg-timer.

The two masses fall towards each other by default and from zero point pressure effect. ie Quantum jitters on a big scale.
There need not be attraction...

How space is warped and by what is another story.