The similarity in the propagation of the electromagnetic and gravitational forces is well known to physicists. Both operate proportionally to the inverse square of the distance between particles and to their 'charge' on the first case and 'mass' in the second. Recently we have come to understand more about the nature of the basic particles of matter, their charge, and the exchange of photons as the mediating particles of the electromagnetic force. The operation of quantum electrodynamics (QED) has been proved experimentally to a high degree of accuracy. The attempts over the past decades to prove an equivalent theory of quantum gravity, with the graviton taking the equivalent function of the photon, have remained unsolved.
There remains a dichotomy between the need for a definite time in quantum mechanics and the denial of a definite time in general relativity, as set out in Ch. 16 of 'The End of Time' by Julian Barbour. In this book he questions the existence of time. Sir Roger Penrose has expressed his view that gravitation will only be fully understood when we have a better understanding of time.
The writer of this piece has spent many hours puzzling about time and how it could link with gravity. To remind readers of the relation between the two, the following picture is offered. Imagine an astronaut travelling in a spaceship with his window closed. The engine is working to maintain his position at a safe distance from a nearby black hole. He wishes to know whether he is affected by a gravitational field, by how much, and in which direction this lies. In his space suit are fitted four super-accurate clocks, set apart at points on an equilateral pyramid and measuring time to a far more accurate degree than is possible today.
In any gravitational field, the clocks will run at different rates. They will run faster at a higher altitude where 'time differentials' are generated by the influence of masses. These differences in rates of time are proportional to the quality known as 'weight', which we feel when attached to our planet. Correspondingly the 'inertia' felt in the astronaut's spaceship, when it accelerates or slows, is indistinguishable and clocks will run faster at the front of the spaceship when accelerating and at the rear when braking, creating the same differentials.
The greater the gravitational field, the greater the difference in rates of time. A computer would be able to resolve the rates of time from the clocks and calculate the direction and rate of fall. Note that it need not calculate any force, as the mass and density of the astronaut and everything else, is irrelevant. Everything, including light itself, falls at the same rate in the gravitational field.
The falling of star light as it passed the Sun was confirmed, in accordance with the prediction of Albert Einstein in 1915. As light passes, time slows and the speed of light slows correspondingly. This effect also causes the warping of space and the lengthening of the path of light, doubling the deflection as observed from the Earth.
Of course, there is another way the astronaut could find out the direction and rate of fall. He could hold a specially calibrated spring balance or he could drop a ball and calculate its acceleration. If he were to turn off his engine, and allow the spacecraft to orbit the black hole or, in other words, enter 'free fall ', the clocks would start to run at the same rate and he would become weightless. This maximum rate would be the same anywhere in the universe when travelling at uniform velocity and in free fall, from the point of view of the traveller.
Imagine the astronaut arriving at a rotating space station, similar to the one in the film '2001 A Space Odyssey'. The station uses centrifugal force to create 'artificial' gravity. According to Albert Einstein the gravity is no more artificial than that on Earth. In his book 'Relativity' written in 1916 he explains the principle of slowing of clocks and shrinking of distances applied to a rotating disc.
At the centre, or hub, time runs fastest and it slows towards the outer rim. In his words 'the field disappears at the centre of the disc and increases proportionally to the distance from the centre as we proceed outwards'. The astronaut may dock his craft at the centre. As he floats to the top of the ladder at the end of one of the spokes of the station, he had better be careful. As he decends, the gravitational field will increase and he will fall 'down' to the outer wall, unless he holds tight. His clock meter, however, will quickly warn him as the differences in time increase. Einstein makes the point that this will happen anywhere or in any frame of reference, providing the disc is in free fall.
Richard Feynman explained a feature of time in his famous lectures. To adapt his point: If a clock has to be carried up from the ground across a distance A to B and back it will experience two effects. As it reaches a higher altitude, it will speed up. As it moves sideways or upwards it will slow down. How would one calculate, given the equations of special and general relativity, how to make the moving clock register the longest time compared with a clock staying at A? Answer:
Use the equation involving 42.18 dt = a minimum. φ = gravitational potential v = velocity m = mass t = time to a minimum.
Alternatively, throw the clock across from A to B and back and look at it. The clock will automatically find the 'laziest' path in which maximum time is its guide. Both methods will produce a parabolic curve. (Assuming no air resistance).
So, time is linked inextricably with gravity. If we understood what time is, would we understand gravity? Many readers, by now, are probably thinking that they have known what time is for ages. What is this crackpot going on about and what was that about this Barbour chap saying that time does not exist! If so please do not stop reading. The following are some simple thoughts on time.
Firstly, let us agree that there is such a thing as 'psychological time'. We record information, received through our senses, in our brains and in other systems, such as books or computers. There is the 'arrow of time' which points time in a certain direction owing to the quality of entropy. Even if we lost our clocked records relating to happenings at macro scale, we would be able to place them in order.
However many equations in physics are independent of time and run equally well in either direction, future or past. Go down to the scale of quantum physics and we find that time sometimes runs backwards! Richard Feynman explains this and more in his book 'QED, The Strange History of Light and Matter'. Light has an 'amplitude' to travel faster or slower than the speed of light (c) in free space. This is always the same according to Einstein’s laws, but at the extremely small scale of particle interactions, the rule no longer holds.
Imagine going down to the microscopic size of a particle, such as an electron interacting with photons. The electron bumps into a photon. Some 'time' passes and it bumps into [or exchanges with] another photon. How does the electron, or alternatively the photon, 'know' how much time has elapsed between the two events?
It can't because time itself depends upon and is measured by interactions between particles. Perhaps after a number of interactions have occurred the electron could tally up the number of interactions coming from three directions at right angles. It could then say that more was happening in one direction than another. Then a sense of comparison of rate of interaction would build up in three dimensions and it would be possible to develop the quality that physicists refer to as spacetime. Of course, a single particle could not record a count of events. To build the simplest clock, a large number of particles would have to be assembled. Time is only meaningful as a complex pattern of events.
When we say that clocks run slow or fast in relativity, what we now accept is that everything runs slow or fast. Every particle in the clock and its surroundings runs fast. You are ageing at the same rate as your watch. According to Einstein's equations and verified by experiments, if you wave your hand around, it will be ageing extremely slightly less quickly than your body and, because of its height, your head will be a little older than your feet! What we can say about time is that the rate of time is a measure of the rate of interaction of particles of matter and energy, as applied to three dimensional space, and that this changes space itself. This is why physicists talk about spacetime as an entity. It involves the shortening of distances and the curvature of space.
However, we also have to understand that there is no exact count or certainty about this rate of exchange of particles. The laws of quantum mechanics are weird and wonderful, even leaving out the mystifying puzzles involving 'spooky action at a distance'. Most photons involved in the mediation of the electromagnetic force are undetectable 'virtual' photons. Virtual particles of all varieties exist and are undetectable individually. Yet we know that they exist by their effects. By limiting the variety of wavelengths of virtual photons between metal plates, a physical force is detectable, known as the Casimir effect. An excess of virtual photons, with a greater range of wavelengths outside the plates, causes a very small electrostatic force to push the plates together.