Re: A little challenge for relativists.

shuba wrote: 
John Kennaugh wrote:

However it can say nothing whatsoever re Galilean Relativity, because in
terms of Galilean Relativity, it introduces an infinity into the maths.


You can use a limit if you want and not worry about whether
anything travels at c, which is a point irrelevant to the
relativity principle per se.  Despite all your protestations and
hand-waving, you still have a lot of work to do to invalidate the
mathematics of Lie groups, and their clear and well-studied
connections to relativity.

You can start with the general case if you wish. It does not prove
relativity is right it only proves in a complex and roundabout
mathematical way that if you assume the second postulate

The derivation proceeds from the first postulate only.

I am NOT writing the following for Shuba's benefit because I am sure he won't bother to read it but just in case anyone else mistakes the chunk of maths he referred to as showing anything relevant I thought I would explain what is going on. The reference Scuba quotes is section 10.8 of:

http://www.courses.fas.harvard.edu/~phys16/Textbook/ch10.pdf

If you look in 10.2.2 of the same chapter the author derives the time dilation equation using a vertical light clock on a train. As standard he got c in both FoR by assuming that time was different in the two and worked out the time dilation equation.

He could have got c in both FoR by assuming that height rather than time was different in the two FoR. Why assume time is the variable not distance? - I will return to that.

In 10.2.3 he has the light travelling horizontally, again he has to get c in both FoR and in this case he assumes distance and time are different in the two frames of reference and derives the length contraction equations.

Above I asked why he assumed time was the variable rather than height. Is there another possible solution by interchanging which you assume varies? The answer to this is no. It only works one way around and the reason for this is that the two variables are intrinsically different mathematically.

## Length can be assumed to change differently in the direction of motion and at right angles to the direction of motion and time cannot.##

By ditching two of what previously were considered axioms of physics Einstein got two variables with which to get his maths to work i.e. to reconcile his assumption of source independence with the PoR. There was only just enough freedom to achieve his aim and what results is an absolutely unique solution.


If you assume that time and distance *are* dependent upon velocity then from the above it should come as no surprise that such an assumption will lead to a unique solution, nor that that unique solution will contain a constant with units of speed, but you cannot make such an assumption and claim that you are basing your maths only on the PoR.

Now let us examine the maths of sec 10.8:

What the maths does is to start with a general set of linear transform equations which do *not* assume that time and distance are velocity dependent but allows for the fact that they *might* be. Then by applying the PoR and the mathematical laws which transforms must obey, the author sets out to comes up with a unique solution containing a constant with units of speed which can then be equated to c.

If he had done what he set out to do then he might have done something significant but look closely. His initial general transforms are what they purport to be - they do not assume time and distance *are* dependent upon velocity they only allowing for the fact that they might be. Note however that if they are not dependent upon velocity the coefficient A = 1.

At one stage he comes up with equation 10.67. Ignoring the fact that it looks suspiciously like assuming the answer, he uses this to make a substitution for A and describes what he has done as:

"All we have done so far is to make a change of variables"

This isn't true because if you take equation 10.67 and make A = 1 then V = infinity. This makes all subsequent maths invalid for the case A = 1. (see note 1). While it started out *without* an assumption that time and distance *are* dependent on v (only that they might be) it has now invalidated the solution which would allow them not to be so. It should now come as no surprise that such an assumption will lead to a unique solution, nor that that unique solution will contain a constant with units of speed.

If you start with the 2 postulates then you can show that there is only one possible set of transforms and that time and distance vary with v.

If you start be assuming that time and distance vary with v and one of the postulates you can derive the other postulate.

If you pretend that you are not assuming that time and distance vary with v when actually you are, you can fool shuba into making an arse of himself.


Note 1 - You may have come across the 'proof' that 1 = 2. In that you divide by (x - 1) which makes the solution invalid for x = 1 which is why when you make x = 1 it appears that 1 = 2.

--
John Kennaugh
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