(09-12-2017, 01:28 PM)Niekie Wrote: I get that there was/is "speculation" about matter having electromagnetic "wave" properties. However, that the invariance of the speed of a wave, and time dilation, can be seen to be associated with measuring waves using waves, regardless of the type of wave, (sound in air, water, steel) then there is really no speculation required.The download is ok, it was a bad internet connection from my side.

Surely the easiest way to explain "special relativity" to anybody is to explain that these phenomena are just properties of waves, rather than these being some "weird" properties associated with "light" and "travelling close to the speed of light".

What matters is not measuring waves using waves, but measuring waves using waves of the same characteristic (limiting) speed. If there would be two aethers, with different characteristic speeds, only very weakly interacting, one could measure also absolute distances and time, simply by comparing both. Like a classical thermometer works by comparing the different expansion of different materials (glass and mercury), one could use similar comparisons to measure absolutes. So, for example, you can measure with high accuracy everything about sound waves, including the speed of the medium where the sound moves, using light waves. So, it is not something about waves in general. And if we would have sound waves of some absolute medium, not influenced by the ether, we could use it to measure the speed of the ether.

It is almost, but not exactly, the speed of the waves which has to be equal. But there is also a caveat: It is the wave equation which matters, not the speed of a particular solution. So, \[ (\square + m^2) \phi = \frac{1}{c^2}\partial _{t}^{2}\phi -\nabla ^{2}\phi +m^{2}\phi =0\] describes waves of a massive scalar particle, with velocity smaller than c, how fast depends on the momentum, while the massless particle \[\square \phi = \frac{1}{c^2}\partial _{t}^{2}\phi -\nabla ^{2}\phi =0\] describes waves with exact velocity c. But nonetheless both wave equations have the Lorentz group as a symmetry group. One can also say they have the same light cone - in one case it describes the limiting speed of the wave, in the other the exact speed.

I agree, the easiest way to explain relativity is by explaining the properties of wave equations. This is what I have tried in my introduction into relativity. Starting with the point of using a Lorentz transformation with the speed of sound instead of c to construct, from a given solution of the sound equation, other, Doppler-shifted solution of the same sound equation. And, then, simply trying to explain the mathematics that this works also for some other, more complex variants of the same wave equation.

BTW, Latex formulas you can write using the \ ( ... \ ) brackets for inline and \ [ ... \ ] brackets for full line formulas. See here for more.