Lorentz Transformation Applicability Re: EM & Casuality

[danmay]

Hi,
From what I've learned so far, Lorentz transformation meets certain criteria, such as the constancy of EM wave propagation speed in vacuum, &/ casuality, among others.

My question is, why would it/would it not be applicable to phenomena that have nothing to do with EM interaction? In other words, why is SR, as we know of it now, valid for phenomena other than light & EM wave?

Is the only other way then to assume that some sort of casuality (applicable to all phenomena) is not being violated?

 

[bcrowell]

Hi, danmay,

Welcome to PF!

IMO causality is fundamental, and E&M is not. The FAQ below may be helpful, along with the paper by Pal it references.

-Ben

FAQ: Is the c in relativity the speed of light?

Not really. The modern way of looking at this is that c is the maximum speed of cause and effect. Einstein originally worked out special relativity from a set of postulates that assumed a constant speed of light, but from a modern point of view that isn't the most logical foundation, because light is just one particular classical field -- it just happened to be the only classical field theory that was known at the time. For derivations of the Lorentz transformation that don't take a constant c as a postulate, see, e.g., Pal (2003).

One way of seeing that it's not fundamentally right to think of relativity's c as the speed of light is that we don't even know for sure that light travels at c. We used to think that neutrinos traveled at c, but then we found out that they had nonvanishing rest masses, so they must travel at less than c. The same could happen with the photon; see Lakes (1998).

Palash B. Pal, "Nothing but Relativity," (2003) http://arxiv.org/abs/physics/0302045v1

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[danmay]

First of all, thank you Dr. Crowell for your welcome and response.

I read through the paper by Palash B. Pal, "Nothing but Relativity," (2003) <http://arxiv.org/abs/physics/0302045v1/>. Just to recap, the author assumed (1) the existence of space, time, and speed, (2) the non-existence of a privileged observer, besides a difference in relative uniform motion, (3) the isotropy of space, and (4) the homogeneity of space and time. He derived transformations that entail the constant--with respect to the speed of relative motion--factor K, whose value for our universe must correlate with experimental evidence.

In our case, such experimental evidence entails (a) the existence of an invariant speed c and (b) velocity composition that does not yield a result greater than c from speeds originally less than c. Consequently, K = c^(-2). Would I then be correct to say that the particular version of Lorentz transformation consistent with SR as we know it, requires (a) & (b), even though Lorentz transformations in general do not require such criteria?

Any comments would be welcome! Btw, in the thread title & the first post, I meant causality not casuality :)

-Daniel

 

[GrayGhost]

Hi,
From what I've learned so far, Lorentz transformation meets certain criteria, such as the constancy of EM wave propagation speed in vacuum, &/ casuality, among others.

My question is, why would it/would it not be applicable to phenomena that have nothing to do with EM interaction? In other words, why is SR, as we know of it now, valid for phenomena other than light & EM wave?

SR was developed to show that light's invariant speed was compatible with the principle of relativity, the LTs relating the measure of space and time between 2 material entities for the special case of inertial motion. Therefore, SR should apply to anything that moves. The LTs were designed for the POV of material entity, and so they must apply to (and be valid for) anything material. The theory first assumes the 2 apriori postulates true, and so c exists in the model that relates the measure of space and time between 2 material POVs.

GrayGhost