Special Relativity for everyman (or woman) - 6. More on Frames of Reference.

More on Frames of Reference

The Origin of the Frame of Reference, has the coordinates 0,0,0,0 and it is the location of the Nominal Observer and his clock.

There are at least three ways of viewing a Frame of Reference:

1. 1. From the perspective of a Nominal Observer (real or imaginary) located at the Origin, holding, or at least adjacent to, a standard clock. This clock will be measuring Proper Time, as the clock is at all times, at the Origin, with that Frame's Nominal Observer and so will be tracing the path of that Frame of Reference.
2. 2. From the perspective of an Observer, elsewhere in that Frame of Reference, carrying a clock synchronized with the Nominal Observer's Clock. Measurements, made using a synchronized clock and standard ruler, will also be Proper Times and Proper Lengths.
3. 3. From the perspective of a remote Observer who is moving with respect to that Frame of Reference, rather than in it. All measurements are taken by the Frame's Nominal Observer and are then converted (Transformed) by that remote observer to cater for the relative velocity. This is done using the Lorentz Transformation Equations. These Transformed measurements are Coordinate Measurements.

It is immediately apparent that an observer, on any body or at any location in Spacetime, will measure time on his local clock and measure lengths, in his frame of Reference, with his standard ruler and that those measurements will be in Proper units.

Spacetime is Homogeneous and Isotropic. It is the same everywhere, in any direction. It obeys the same basic scientific laws throughout. Therefore, if we place an object within a Frame of Reference, its properties will be the same as they would be in any Frame of Reference. This is one way of stating Einstein's First Postulate of his Theory of Special Relativity.

Let us consider what this means by taking an Event, a flash of light, and examining how it appears from different points of view.

If we take the time and location of that flash of light as the origin of a Frame of Reference it will have the coordinates 0,0,0,0. Light travels away from that event at 'c' in every direction.

After 1 second the light emitted will be measured to have travelled 1 light second in every direction and will have traced out a sphere in Spacetime, radius 1 light second. And it will be a sphere, radius 1 light second in each and every Frame of Reference, only the coordinates of that Event will be different.

There is one rather surprising outcome from these considerations however. For when we define our Frame of Reference, Spacetime is fixed and at rest from our perspective, then surely, one would think, Spacetime must be moving for every other Frame of Reference, that is moving with respect to our 'fixed' Frame of Reference.

Yet as soon as one thinks this way, one has fallen into the trap, and failed to grasp the essential meaning of Relativity. Everything is Relative. No Frame of Reference is fixed and at rest absolutely; yet each and every Frame of Reference is fixed and at rest from its own perspective.

No, there is not, nor ever can be any one preferential Frame of Reference. For if Spacetime were at rest in only one Frame that Frame would take precedence having simpler Laws of Science than other Frames of Reference.

Again I say No! For the simple reason that Spacetime is at rest as observed from any Frame of Reference.

Each and every Frame of Reference is a Map of Spacetime, with the origin of that Frame of Reference as the fixed centre of that Map.

From the perspective of any observer, at rest in any Frame of reference, every other entity or Frame of Reference is moving, in Spacetime, relative to that Frame of Reference! That is each and every Frame of reference is moving relative to every other Frame of Reference or Map of Spacetime (for if they are not moving they are different parts of the same Frame of Reference).

I have repeated myself, ad nauseam, in the passage above, because it is describing the fundamental principle of Relativity: Everything is Relative.

This is the most fundamental and I may say surprising facet of Relativity, and one that so many eminent scientists, indeed the whole scientific establishment have, as yet, failed to grasp; determined as they still are to see everything relative to some particular Frame of Reference, thereby failing to recognize that that particular Frame too, must also interact in exactly the same way relative to other Frames as those Frames interact with it.

AS A IS TO B, SO B IS TO A

So let us try and picture this, shall we?

Let us take for an example a train moving along a railway track. A lightning strike hits the track, as the very centre of the train is passing that point on the track. How is the flash of the lightning observed from the track and from the middle of the train. Fig. 1

Fig. 1

This is a practical example of our original event the flash of light and two frames of reference, the track and the train, that are moving relative to one another.

Now as we saw in the earlier discussion, each will see the light travel at 'c' relative to their Frame of Reference, so the observer on the track will measure the light travel equal distances, in the each direction, along the track as the train moves away. Fig. 2

Fig. 2

while the observer on the train will measure the light travel equal distances, in each direction along the train, as the track moves away from the train. That same observer on the train, will see the light reach both ends of the train at the same time; although when that happens, the two ends of the train will no longer be equidistant from the observer on the track. Fig. 3

Fig. 3

So which one is correct, the observer on the train or the one on the track?

As we have just seen, they both are, hence the need for Einstein to explain it!

Think about it! At the moment of the flash of light both B and B' are coincident at the flash of light.

The two Observers are located, one at B on the Track and one at B' on the Train, which coincide when the flash of light occurs. So each Observer, at rest in Spacetime as they Map it, will observe the light travel at 'c' in all directions in their Frame of Reference. The light will, therefore, reach the points, A and C on the track, and A' and C' on the train, at the same time. It is the observers B and B' who are each moving away from the other and so are no longer at the location of the flash of light, AS MEASURED IN THE OTHER FRAME.

The important fact to realize here is that every observer will measure the light expanding evenly from the initial event, the flash of light, within his own Frame of Reference! But that every other Frame of reference, will be moving away from him. Exactly as we see in our 'thought experiment' with the train .

A paradox, or a conundrum at the very least, one might think, yet the answer is a simple one: there is only one expanding sphere of light that is mapped as being at rest in each and every observer's view of Spacetime!

For each and every observer the light expands evenly in their Spacetime, while all other observers are moving through that expanding Sphere of light; thus the stationary observer's inevitable conclusion that the moving observer cannot see the light travelling evenly in both directions.

Note: that it is only in the measurement, relative to a stationary observer, that the space and time of the moving observer, is distorted.

So how is this distortion, of the moving observer's view and measurements of Spacetime, experienced by those concerned, how do we relate the stationary observer's measurements with those of the moving observer?

At which point we ask those two venerable old rogues, Time Dilation and Length Contraction to step forth and take a bow!