VSJ – October 2005 – Work in Progress

Terry Longhurst, FIAP continues his celebration of the centenary of Einstein’s seminal paper on Special Relativity. This month he examines how much we really know about the nature of electromagnetic radiation.

Albert Einstein’s original theory of relativity was based on two ideas: the concept and principle of relativity. However these proved to be incompatible. Einstein retained his principle of relativity in the general theory and replaced his original concept with the idea that the gravitational field is a material medium. I have suggested that Einstein’s use of Minkowski’s concept of a four-dimensional space-time continuum in his general theory is flawed. This leads us to a fundamental question: is Einstein’s general theory consistent with the known behaviour of light?

We’ll use a thought experiment to examine the question. Einstein himself did this in his original paper but his logic was rather difficult to follow. The example below is more straightforward. It is sufficient to note that, in his general theory, Einstein concluded that the passage of time in the different frames of reference actually is different.

First, what precisely does a ‘fixed and finite velocity of light’ mean? Well, if I am five light seconds distant from an object when it emits some light, then I will perceive that light in five seconds time, irrespective of my motion. If the velocity of light was not fixed and if I were moving towards the source of the light, then the velocities would add and I would perceive the light in less than five seconds. Similarly, if I were moving away, it would take more than five seconds for me to perceive the light.

But if the velocity of light is fixed, then I will perceive the light in five seconds time, irrespective of my subsequent motion. This is difficult to grasp, but it is what Albert Michelson’s results suggest. Furthermore, this velocity applies to all electromagnetic emissions – from gamma rays to radio waves. Let’s apply it to our imaginary experiment.

Transmitter                                                                                                           Alice                      ßBetty

0 sec                       1 sec                       2 sec                       3 sec                       4 sec                       5 sec

In a region of space far away from other material objects there is a radio transmitter and two girls, Alice and Betty, arranged as above. The transmitter emits time signals at one-second intervals. Each girl has a receiver that displays the time signals as they are received. At 10:00:00am the transmitter sends the time ‘10:00:00’. Alice is at rest with respect to the transmitter and 4 light seconds distant from it. So at 10:00:04 her receiver displays ‘10:00:00’, at 10:00:05 it displays ‘10:00:01’ and so on.

Betty is travelling towards Alice and the transmitter at 1/5 of the velocity of light. At 10:00:00am Betty is 5 light seconds distant from the transmitter and thus will receive the time signal ‘10:00:00’ at 10:00:05. However, over the 5-second period she will have moved 1 light second nearer to the transmitter, so at 10:00:05 the girls are adjacent to each other. At that moment Alice will see her receiver displaying ‘10:00:01’ whilst Betty will see hers displaying ‘10:00:00’. Furthermore, if they immediately look at each other’s receiver, Betty sees Alice’s receiver displaying ‘10:00:01’ and Alice sees Betty’s receiver displaying ‘10:00:00’. So both girls observe the disparity. Also for both of them, five seconds have passed since the time signal ‘10:00:00’ was transmitted. So there is no discrepancy in how much time has actually passed for Alice and Betty, it’s just the time signals that are out of sync.

There is a potential flaw in this thought experiment. I said that Betty is moving at one fifth the velocity of light. This is an unimaginably huge velocity and the period of time for which Alice and Betty will be adjacent is very small. Therefore they would have great difficulty in practice in making the observations I have suggested. Furthermore, even at a tiny fraction of that velocity, they would, in fact, need much more sophisticated equipment to enable the observations to be made. But the practical difficulties in actually observing these relationships are irrelevant. The purpose of this thought experiment is to describe the relationships that will arise, not a practical method of observing them.

So, back at the experiment, we now re-run it with a small change. Moments before 10:00:05, a small lateral velocity is applied in opposite directions to the two girls such that at 10:00:05 they have swapped places. Despite this, Alice’s receiver will still show ‘10:00:01’ whilst Betty’s will show ‘10:00:00’. We have placed each girl at exactly the position formerly occupied by the other, yet each still receives the time signals according to her own relationship to the transmitter.

This has to be wrong, doesn’t it? Surely, if each girl occupies the position formerly occupied by the other, she would at that moment receive the transmission that the other would have received? If you picture a ray of light as a photon, or a radio signal as a wave, where they arrive at any specific time must be independent of the observer that happens to be there or even whether there is an observer at all. And that is the problem. We are so used to thinking of light as photons and radio signals as waves, we forget that both descriptions are only abstract models of something that we don’t really understand.

All models have a context in which they can be used, in which they mimic the behaviour of the phenomena they describe. The corollary of this is that such models tend to fail outside that context. And this is where the models of light as photons and radio signals as waves fail.

The reason they fail is that they assume the existence of a material space through which the light or radio wave passes. The imaginary experiment shows that light and radio waves don’t actually behave like that. The time signal that will arrive at any ‘place’ at a given time is dependent upon the relative velocity of the object occupying that ‘place’ and its distance from the transmitter. Without an object at that ‘place’ it is impossible to say when a specific time signal will arrive there.

To put it another way, you may have heard the philosophic question “If a tree falls in a forest and there is no one there to hear it, does it make a noise?” Well, I’m quite sure that a tree, being a material object, does make exactly the same noise whether there is anyone there to hear it or not. But light and radio waves are different. If there is no material object at a particular ‘place’ then the question of when an electromagnetic phenomenon will arrive there is meaningless. So far as they are concerned, there is no ‘there’ to arrive at.

The difference between the behaviour of electromagnetic phenomena and material objects really is that big, that fundamental. It’s as if there are two different universes, the material universe and the electromagnetic universe. These are two very different universes but they can interact and it’s in their interaction that these strange effects arise. So where do we go to from here?

In his final article, Terry asks whether the term ‘velocity of light’ is meaningful at all. You can contact Terry at tlonghurst@iap.org.uk.

[Interesting project or development? Let us know at eo@iap.org.uk!]

Comments are closed.