Tuesday, 23 November, 2004
In the special theory of relativity it is taught that "moving clocks run slow" or more precisely that the if a clock is moving at a speed close to the speed of light relative to me then I will see it tick more slowly than an identical clock which isn't moving relative to me. The internal composition of the clock matters not - whether it's a grand father clock or the average time it takes for a uranium atom to decay this "time-dilation" effect works in the same way and both clocks will slow by the same amount.
Most "proofs" of this concept are done by taking a clock where light bounces between two mirrors and looking carefully at the physics. The problem is that this argument isn't sufficient. How do we know from the study of the light-clock that this really applies to every other clock and that all clocks will slow by the same amount? You might be able to apply special theory of relativity to a swinging pendulum in a grandfather clock but how do you know the effect is true for the uranium atom from first principles?
Of course the answer is straightforward and readily understood but the the point is subtle and is often missed. To understand why it is true for every clock we need to understand how special relativity comes out of the physics. The foundations of the special relativity come from the Maxwell's equations. At the time of their discovery they caused a few problems for physicists. The problem was that the laws of physics the equations specified appeared to depend on who was observing them.
If I throw a ball in a car doing thirty miles an hour then to me that ball might do four miles an hour. To a man stood on the pavement the ball would appear to travel at thirty four miles per hour. In the lingo we say that in the man on the pavement's frame of reference the ball is doing thirty four miles per hour, in the man in the car's frame of reference the ball is doing four miles per hour.
What this means is that I can take a physics problem inside the car and work out how it look outside the car easily. If everything is consistent then I can take what I see on the pavement, then calculate what I would see if I were sitting in the car. Then using the result of this calculation I could calculate what I would see back on the pavement. At the end of all this working out I should get the same result out as I started with.
The problem with Maxwell's equations was that this didn't appear to work for electromagnetic effects. Suppose I had a person shining a torch in a car. I'd use Maxwell's equations to work out the speed of light relative to the person inside the car. Then to check everything's consistent I'd use that result and attempt to calculate how fast light should look to me sat on the pavement. The answer should be the same as my original measurement but alas - No such luck! :\
Physicists of the time concluded that since the ideas behind Newton's laws were so successful that there must be something wrong with Maxwell's equations. They decided that the equations really told the story of a single frame and that all electromagnetism happened in this single frame of reference. The speed of light appeared different in all frames because they were moving at different speeds to this "aether" frame. This theory was called the aether theory and appeared to be a good solution to the problem. Like all good theories it made a solid prediction, you should be able to discover which frame is the "aether" frame by experiment.
In 1887 the famous Michelson-Morley experiment was performed to determine the nature of this aether frame and the result, coupled with other observations confirmed that it did not exist. So now there was a real pickle. Newton's laws were still inconsistent with Maxwell's equations and there's no easy fix in sight.
Einstein, building on the work of others, came up with the solution in 1905. He realised that the problem wasn't in Maxwell's or Newton's equations as such but in how we transform from one frame to another. Like I said up there - if I'm sat in a car doing thirty miles per hour and throw a ball at four miles an hour relative to me then we get the speed of the ball for the guy stood on the pavement by adding the four miles per hour the ball is doing to the thirty the car is doing and arrive at thirty four miles an hour. It was this step that was flawed. Einstein showed that if you used a different rule for transforming between the two frames then you could make Maxwell's equations consistent with Newton's laws.
What all this really meant was a return to the days of Newton. All frames are created equal so there is no 'master' frame. More profoundly it meant a return to the notion that the laws of physics don't depend on the choice of the frame you measure in.
This is why we immediately know that the light clock thought-experiment shows the result must apply to all clocks irrespective of their composition. If the light clock slowed at a different rate to uranium atom's decay-rate, for instance, then the difference between the rates at which they record time would be dependant on the frame you observed it in. This is clearly a contradiction with the idea that the laws of physics are frame independent and this is why it can't be true.
Simon.