Recent content by Jonathan Stanley

I think you have an interesting point here. If I'm understanding you, the fact that Einstein provides the Lorentz transformation in his work is what makes it so compelling. Since we've tested the Lorentz transformation, and know it works, then whatever details that lead up to seem less...

The next sentence from that translation may help. "We imagine further that at the two ends A and B of the rod, clocks are placed which synchronize with the clocks of the stationary system, that is to say that their indications correspond at any instant to the “time of the stationary system” at...

That is not what was written. Section 2 is regarding a "stationary system" but the rod and clocks are not stationary. "We further imagine that there are two observers at the two watches, and moving with them" Again, we have not reached section 3 yet. Einstein explicitly stated that he...

Einstein establishes definitions in section 1 which form the basis for section 2 equations. I was trying to be more succinct, but maybe I can try rephrasing again. Apologies for the verbosity; I appreciate your interest. In section 1, we have two fixed points (A and B) according to Newtonian...

I'm not sure what distinction this imposes on my original post. Maybe if I restate more verbosely using Einstein's terms: Einstein wrote in section 1: For example, a ray of light proceeds from A at A-time ##t_A## towards B, arrives and is reflected from B at B-time ##t_B##, and returns to A...

See section 2 of the original docs: "Let us suppose that the two clocks synchronous with the clocks in the system at rest are brought to the ends A, and B of a rod, i.e., the time of the clocks correspond to the time of the stationary system at the points where they happen to arrive ; these...

Correct; we're using the translations from his original work. Earlier you wrote: It isn't clear to me if you were saying there was an error with the equations I wrote, or refactor, etc. This is why I am using the word "agree." You have no disagreement with what I wrote?

Thanks, as always, for the illustrative response. Are we in agreement that Einstein established his definition of synchronism according to a stationary "co-ordinate system, in which the Newtonian equations hold" ? Are we in agreement that Einstein's definition of synchronism can be...

At the time ##t _0##, a ray of light goes out ##A##, reflected at ##B## at time ## t_1##, and arrives back at ##A## at time ##t_2##. So Einstein provides: ##t_2-t_0 = (t_1-t_0) + (t_2 - t_1) = \frac{l _{rod}}{c - v _{rod} } + \frac{l _{rod}}{c + v _{rod} }## Where: Rod with ends A and B ##v...

Thanks; I appreciate the analogy. Einstein's wording is propagated along those axes with the velocity ##\sqrt{c^2 - v^2}## He does not say that this is relative to the origin k, so I'm unclear how you are interpreting this to be relative to k?

Thanks Andrew and Peter. Good thoughts. I think I must concede ##c-v## is not the contradiction it appeared to be. However, it appears you both are affirming the contradiction on ##\sqrt{c^2 - v^2}## We know from Einstein's definition, light's speed is: independent of the condition whether...

Good point! I'm quoting: On the Electrodynamics of Moving Bodies (Annalen der Physik, 1905). Translation by Megh Nad Saha in The Principle of Relativity: Original Papers by A. Einstein and H. Minkowski, University of Calcutta, 1920, pp. 1–34: The other common translation is as follows: "it...

From his original thesis, Einstein said light speed is always constant (c). There is very clear evidence for this. Every ray of light moves in the “stationary coordinate system” with the same velocity c, the velocity being independent of the condition whether this ray of light is emitted by a...