A fresh look at Special Relativity

[studiot]

In considering the derivation of SR I wondered if the two underpinning concepts can be decoupled.

 

Please note that this is not an attempt to debunk SR, rather an attempt to gain insight by strengthening it.

 

The first concept (invariance of certain physical laws between inertial coordinate frames) is purely mechanical and does not depend upon the existence or non existence of any electric phenomena whatsoever.

In other words it is not dependent on light or c or whether there is any light in the system under consideration.

 

At the time of introduction of SR the only experimental data included light in the system, and Maxwell had developed his equations and related them to c, so it is not suprising that the second concept (invainace of c) was introduced.

 

However subsequent observations in systems where light is not present (for instance cosmic muon extended decay time) do not conform to the purely mechanical Galilean relativity (in one dimension) such that

 

X = x - vt

Y = y

Z = z

T = t

 

For translation as observed in two inertial systems, the first denoted by lower case, and the second translating at velocity v along the x axis relative to the first, by upper case

.

As all good physicists do in this situation we start by assuming the next simplest relationship between the variables

 

X = A(x - vt)

Y = y

Z = z

T = Bt + Dx

 

and seeing if we can determine an A, B and D (I have avoided C to preclude confusion with c) to fit the data.

 

Of course we know from history that the Fitzgerald - Lorenz transformations will fit the bill nicely, but as far as I can see,

We still need some something even without their experiments.

 

So I was wondering if the need for a 'speed limit' (though not necessarily its value or form) could be deduced from the first postulate alone?

Edited September 22, 2014 by studiot

[Dekan]

Perhaps the need for a "speed-limit" could be deduced, merely from the existence of our big, extended, complex, spatial Universe. And from the existence of Time.

I mean, suppose there wasn't a speed-limit. So that particles, such as electrons, protons, photons, gravitons, travelled instantaneously from one side of the Universe to the other.

 

That would mean, that there wouldn't really be any distance, or "Space" within the Universe - it'd be just a single point-like object. And everything within it, would happen "at once". So there'd be no Time either. Therefore, from the fact that we do actually observe Space and Time, doesn't it follow that there must be some kind of limiting speed?

Edited September 22, 2014 by Dekan

[studiot]

I wouldn't put to much emphasis on the idea of a speed limit.

It is a consequence of Einstein's second postulate and introduces the equations

 

x² + y² +z² = c²t²

 

X² + Y² + Z² = c² T²

 

These allow us to solve for A, B and D.

 

I have already connected time and space in the simplest way as a bilinear form in the time transformation equation.

 

So I am really perhaps asking are there any other viable equations that could be introduced?

[xyzt]

 

So I was wondering if the need for a 'speed limit' (though not necessarily its value or form) could be deduced from the first postulate alone?

Yes, it can, there are multiple modern formulations of SR that use only the first postulate. Mind you, SR is not a theory of light, so the second postulate has no place in the modern formulations. This thread should be in the main forum, it is not a speculation.

[studiot]

Thank you for the link, xyzt.

 

It will take a while to go through it all.

I have so far read the Wiki article, which promised more in the headline than it supplied in the detail.

[xyzt]

Thank you for the link, xyzt.

 

It will take a while to go through it all.

I have so far read the Wiki article, which promised more in the headline than it supplied in the detail.

Read the references. There are quite a few.

[xyzt]

Thank you for the link, xyzt.

 

It will take a while to go through it all.

I have so far read the Wiki article, which promised more in the headline than it supplied in the detail.

You are welcome, BTW.

[studiot]

My thoughts were stimulated by Turner's reformulation of Newtons 3 laws to one law equivalent to N3, with the first two derivable from this.