The trouble with gravity

The Well Balanced Universe

 

The trouble with gravity

by Edmund Wood

Just like everybody else, the Ancient Greek philosopher, Aristotle, believed that heavy things drop faster than light things. Well, it's true, isn't it? A stone falls faster than a leaf?

The trouble that Aristotle initiated came from the fact that he believed this was always true and furthermore that the rate of fall was proportional to weight. In other words, he thought that a ten pound stone would fall ten times faster than a one pound stone.

Aristotle never did any experiments to test these beliefs; he just wrote his ideas down, along with a load of other statements about nature that he thought were valid, and published them. His standing was such that a lot of people accepted his word as gospel, and his beliefs about gravity went unchallenged for a very long time.

It was virtually 2000 years before the Italian mathematician and physicist, Galileo, demonstrated conclusively that Aristotle was wrong.

Galileo dropped balls of different weights together from the tops of towers, and they landed at the same time. He then had the idea of rolling the balls down an inclined plane instead. This slowed down the process of falling and made it easier to make measurements of what was going on. A water timepiece of his own making gauged the time for the balls to travel over various distances. (This was before the invention of pendulum or spring-balance clocks.) His experiments showed that, for a particular slope, there was the same steady acceleration whatever the weight of the ball. (Also, the final speed was always the same as that of a ball dropped vertically through the same height.)

Natural motion

The trouble came for Galileo when he attempted to understand the motions of planets and moons in the light of his investigations. Galileo was a Copernican: he believed that the planets travelled in circles around the Sun, and that the Moon circled the Earth. With the aid of his self-made telescope he was the first person to see moons orbiting the planet Jupiter; and he believed that they too traced a circular path.

He also stated that if a ball could roll horizontally without any hindrance from air resistance or friction, it would travel in a circle around the Earth forever, at a constant speed. Galileo had decided therefore that natural horizontal motion was constant and circular, while natural vertical motion was acceleration in a straight line.

When the German astronomer, Johannes Kepler, published his finding that orbits were elliptical and not circular, Galileo wouldn't accept it, presumably because it messed up his neat system.

Some time later, the Dutch physicist, Christiaan Huygens, pointed out that in fact circular motion, such as a ball twirled round horizontally on a string, is not a “natural” (unforced) motion but it is a combination of constant speed in a straight line and an acceleration at right angles to the motion caused by a force.

However, Huygens failed to take the next step of applying this to the orbits of celestial objects, because he did not believe that a force could be transmitted across empty space. Instead, he tried to explain the trajectories of the planets by saying that there were vortices (whirlpools) in a substance called the ether which filled all space (following an idea of the philosopher, René Descartes).

Consequently, when the English mathematician, Isaac Newton, published a theory that said there was a force of gravity acting between all matter over any distance, Huygens was one of the leading objectors.

Powerful equations

Newton had come to his conclusions when he had worked out that, if there was such a force, and if its strength reduced by the square of the distance, then objects in space such as planets and moons would follow an elliptical path — just as Kepler had discovered.

Newton was never able to explain how gravity could act across empty space — “action at a distance”, as it was called — but he simply relied on the predictive power of his equations to confirm that his theory was right. The equations proved to be astonishingly accurate, and this silenced all criticism.

The trouble with gravity that worried Newton most was of his own making. It began when he tried to apply his theory to the universe as a whole and discovered that his equations predicted that everything would be unstable. This meant that, regardless of their initial configuration, all particles of matter would gravitate together until they formed a single great mass in an otherwise empty universe.

Such a tendency and fate for the universe was clearly unacceptable. In a letter to his friend, Richard Bentley, Newton graphically illustrated the impossibility of creating a cosmos that was stable under his law of gravity: “I reckon this is as hard as to make not one needle only but an infinite number of them (so many as there are particles in an infinite space) stand accurately poised upon their point.”

The difficulty haunted Newton all his life and he was never able to figure out a satisfactory solution. After his death, the problem was ignored by other scientists, partly because no one had an answer, but mainly because Newton's theory was incredibly successful in virtually every other way. In fact, it was two whole centuries before someone came along who was prepared to bring the problems with gravity out into the open. That person was Albert Einstein.

New concept

Einstein realised that he had to do something to sort out gravity as soon as he had conceived his special theory of relativity.

In this theory, the main assertions were that nothing could travel faster than light and that the measurement of the speed of light would be the same for all observers, regardless of their relative velocity. To make everything work out, measurements of mass, distance and time had to vary instead, according to the relative motion of the observer. The differences would be negligible at low relative velocities but large at speeds close to that of light.

Since, according to Newton, the force of gravity acted instantaneously and depended on the mass of objects and their distance of separation, Newton's equations had to be altered somehow to take the assertions of special relativity into account.

This was not straightforward. Einstein had called his theory “special” because it dealt with the specialised situations where objects had constant velocities. To apply it to gravity, he had to broaden the scope of the theory to include accelerated motion.

The result, ten years later, was the general theory of relativity. In order to produce this masterwork, Einstein had found that he needed to change the whole concept of gravitation. Instead of a force, gravity was now a “curvature in the geometry of spacetime” caused by the presence of mass.

This change of concept removed the need to explain how a force could act across empty space. However, there was no explanation for how mass actually produced such a curvature in the fabric of space and time over any distance — this was just stated as a fact. So whether the problem of action at a distance had actually been resolved was still a matter of debate.

Explained anomaly

Einstein had an immediate success with his new theory which caused him much joy. Although Newton's equations had been extremely successful in describing the motions of objects in the Solar System, astronomers had discovered one small, niggling anomaly that had thwarted all explanations.

The problem concerned the planet Mercury — the nearest to the Sun. It had been found that Mercury's orbit was not quite elliptical. While a large part of the deviation could be accounted for by the influence of the other planets, there was still a tiny remainder that couldn't be explained. Suggestions had been put forward, such as a non-spherical Sun or an undiscovered planet even closer in than Mercury, but all investigations had proved fruitless.

Since Mercury is so close to the Sun, it travels much faster than the other planets. Einstein realised that there should be an effect of relativity on its orbit small, but greater than for any other planet. When he did the calculation of the predicted effect it came out as the same as the unexplained deviation, within the observational error margin.

Disappointment

Buoyed by his success, Einstein decided to try using his new theory of gravity on the whole universe. In order to simplify the task, he first assumed that matter was evenly distributed and that the universe should look the same from any point in spacetime (any place, at any time). Unfortunately, when he applied the equations to such a universe, he found that it would be unstable, just like Newton's: everything would gravitate into one single mass, surrounded by empty space.

This was extremely disappointing and it was not clear what could be wrong — whether the simplifying assumptions or the equations of general relativity. He decided to add an extra factor into the equations, equivalent to a very weak repulsive force that would counteract gravity over large distances. This stabilised the universe but at the cost of creating a new force for which there was no evidence.

Another possible solution was presented by the physicist, George Lemaître. Lemaître suggested that the total collapse under gravity could also be prevented if the universe were expanding. At first, Einstein called this idea “abominable”. However, the astronomer, Edwin Hubble, made the discovery soon afterwards that all the galaxies appeared to be moving away from each other. In the light of this evidence, Einstein abandoned his own less-than-satisfactory solution and accepted Lemaître's expanding universe. This was far preferable to him than the other alternative ― that there was something wrong with general relativity itself.

Problems remain

But why had Einstein originally called Lemaître's solution abominable? One reason was that, if the universe was expanding, then it would not appear the same to observers at different times. Furthermore, it begged the question of what could have caused such a motion. And then, even more seriously, if the equations were worked backwards in time, they predicted that the universe must have started out from a point with infinite density and infinite gravity. This, he knew, was impossible.

Although he conceded that it was not absolutely essential to know the cause of the expansion or to have a universe constant in time, he could not reconcile himself to the presence of the impossible infinities. Regrettably, he was never able to resolve this difficulty in a satisfactory way. In fact, nobody has been able to, and it remains a problem to this day.

A further, similar, complication arose out of the work of the astrophysicist, Karl Schwarzschild, who solved the equations of general relativity to obtain the curvature of spacetime around a spherical body, such as a planet or a star. The equations predicted that if such a body contracted, there would be a point at which the curvature would be so great that the contraction would become unstoppable; all the mass would then disappear into a dimensionless spot with infinite density and infinite gravity. Not even light could escape from such an entity, and so they have become known as “black holes”.

The prediction of even more infinities was not comforting, and, again, neither Einstein nor anyone else could find any way of avoiding them.

(In recent years, black holes have been talked about so much that it tends to be forgotten that they are made up with infinite quantities and that, in the real world, such things are impossible. Astronomers and physicists who do remember this fact tend to believe or hope that only a small amendment to Einstein's theory is necessary in order to resolve the difficulty, if only someone can work it out.)

Predictions confirmed

Einstein had another success with his theory, which had the effect of pushing the problems to the back of people's minds. The astrophysicist, Arthur Eddington, confirmed a prediction of general relativity that the path of a light beam should be bent when passing a massive object. He achieved this by measuring the apparent shift in the positions of stars near the Sun in the sky during a total eclipse.

Many years later, when the cosmic microwave background radiation was discovered, the infinities at the beginning of the universe were brushed even further under the carpet. This was because the discovery appeared to confirm the suggestion of the physicist, George Gamow, that the universe had exploded out of nothing in an immense fireball and that there would be a relic radiation, still detectable but cooled by the expansion, from the moment when the first atoms had condensed.

The fact that, in Gamow's picture, the temperature would also be infinite at time zero did not cause too much heartache. After all, what was one more infinity when the background microwave radiation could be explained, as well as the origin of the first elements and the apparent motions of the galaxies?

All then seemed well enough for a while, but eventually some new cracks started to appear.

At small scales

First to surface was the realisation that general relativity was not compatible with the new and extremely successful quantum mechanics, which describes how the world works on the microscopic level. In Einstein's theory, spacetime is continuous at all scales, whereas in the quantum world everything has to be made up of discrete entities.

Many attempts were made to combine the two approaches using an invented new particle called a graviton, but all have encountered major problems, most commonly involving the appearance of even more infinities in the equations. Physicists have found ways of getting around these infinities using a method they call “renormalization”, but, as the Nobel-prize physicist, Richard Feynman, says in his book, QED: The Strange Theory of Light and Matter: “No matter how clever the word, it is what I call a dippy process!”.

Speedy orbits

The next worry came with the discovery of unexpected velocities of stars in other galaxies. Studies showed that stars further out from the centres were orbiting much too fast for the estimated amount of mass in the galaxies, according to the equations of gravity. The problem was compounded when it was found that galaxies themselves were also orbiting too fast inside galaxy clusters, when the pull from the quantity of estimated matter present was calculated.

What this meant was that either there was extra matter in the galaxies and in the clusters that was going undetected, or else there was something wrong with the equations of gravity. Since a fault in the equations would undermine most of the current astrophysics and cosmology, the theorists chose the first possibility.

The trouble with this solution was that the amount of missing matter that would have to be accounted for was so huge it could not be explained by errors in the observations. The quantity needed was not just a small fraction of what was visible, it was of the order of 100 times the total matter detectable at all wavelengths. Consequently, the theorists had to invent the concept of a completely new substance that we cannot perceive with any kind of telescope and yet which completely dominates the mass of the universe. They called their mysterious material “dark matter”.

Even darker

One of the predictions of the big bang theory was that the gravity of all the galaxies would be gradually slowing down the expansion of the universe. This expectation was significantly enhanced when the pull of all the dark matter was added to the picture. Imagine then the surprise when results from new surveys implied that galaxies have not slowed down but are moving apart faster now than in the past — in other words, the expansion appears to be accelerating.

Rather than find fault with the theory it was decided that there must be yet another unknown and undetectable substance lurking out there in the universe. Dark matter had been added because there wasn't enough gravity; now there was way too much. Consequently, theorists had to put in something extra that was opposing gravity — pushing matter apart rather than pulling it together. And again it had to be something that we cannot detect with any of our instruments.

The name decided upon this time was “dark energy”.

The amount of the extra material necessary was, once more, not small; indeed, even the quantity of dark matter would be dwarfed by the presence of this new, alien substance. In this latest picture, all the objects composed of recognised substances — the Earth, the Sun, the planets, and all the stars, dust and gas in all the galaxies — are made of rare types of matter and energy that in total add up to only a few per cent of the universe. All the rest is supposed to have a strange and unknown nature.

Scientists happy

Having found ways out of most of the difficulties and contradictions, astronomers and physicists are generally very pleased with the present understanding. They have used computer graphics to produce beautiful images of the universe evolving over time, with different colours depicting the presence of normal matter, dark matter and dark energy.

Their programs can tweak the relative proportions of these three basic substances to agree with new observations of the fluctuations in the cosmic microwave background radiation.

Every day, it seems, another black hole or clump of dark matter is “discovered”. (Stars or clumps of gas and dust are found to be moving faster than can be accounted for by the gravity of the detectable matter present, so it is believed that either a black hole or some dark matter must be causing the effect. Of course, you cannot actually see or detect either a black hole or dark matter.)

Everything has been made to fit together into one complete picture, and all the observations can be accounted for. There is no other accepted theory that can achieve this.

Added to all this is the stated belief of theorists that they are close to finding a “theory of everything” — a quantum theory that includes all the fundamental forces and gravity . Superstring theory, loop quantum gravity, supersymmetry, supergravity and M-theory are some of the latest efforts of physicists in their quest to produce a model of the universe that unites general relativity and quantum theory.

In order to develop these new ideas the theorists have had to add more and more hypothetical dimensions to spacetime. At the latest count, they think that we are really living in an eleven-D universe. But this has not put them off. To quote the brilliant physicist, Stephen Hawking, in his award-winning book, The Universe in a Nutshell: “What has convinced many people, including myself, that one should take models with extra dimensions seriously is that there is a web of unexpected relationships, called dualities, between the models... Not to take this web of dualities seriously would be like believing that God put fossils into the rocks in order to mislead Darwin about the evolution of life.”

Incalculable amounts of working hours, effort and money have been and continue to be put into creating these models of the cosmos. So remember, if you ever have a conversation about any of this with a professional physicist, mathematician or astronomer, whatever you do, don't mention the infinities.

© Edmund F Wood, January 2009

 

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