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I am definitely learning a lot about the specific vernacular used to communicate these physics ideas to others on this forum...thanks for the feedback.

I use the same definitions for the variable "types" as Einstein within his book "Relativity: The Special and General Theory", i.e. the primed variable is with respect to the co-ordinate system K' and the unprimed variable is with respect to the co-ordinate system K. I use the Lorentz transformations in the same manner as well.

In order to satisfy the first postulate, the relationship between their event times must remain unchanged in order to prevent one from ascertaining the motion of the inertial frame utilizing this scenario.

I think we can come to a common interpretation by "walking the dog" if you're up to it...wadda ya say?

EVENTS OCCURRING IN REST FRAME (v = 0)- These events now occur within a reference frame considered to be at rest (rest frame).- The event time for A is; Δτ = x/c.- The event time for B is; Δt = x/u.- The ratio of these event times gives us the relationship between their event times;Δτ/Δt = (x/c)/(x/u) = u/c.

Quote from: HeyBert EVENTS OCCURRING IN REST FRAME (v = 0)- These events now occur within a reference frame considered to be at rest (rest frame).- The event time for A is; Δτ = x/c.- The event time for B is; Δt = x/u.- The ratio of these event times gives us the relationship between their event times;Δτ/Δt = (x/c)/(x/u) = u/c.No wonder I had a problem understanding what it was you were doing. It was as if you actually went out of your way to take a very simple thing and say it in a very complex way. You should have simply said the following: Let x be the distance traveled by a photon and a particle. Let v be the speed of a particle where v < c. Let t be the time it takes the particle travel the distance x and T the time it takes a photon to travel the same distance. Then x = vt = cT. Therefore T/t = v/c.See how simple that was?

No wonder I had a problem understanding what it was you were doing. It was as if you actually went out of your way to take a very simple thing and say it in a very complex way. You should have simply said the following: Let x be the distance traveled by a photon and a particle. Let v be the speed of a particle where v < c. Let t be the time it takes the particle travel the distance x and T the time it takes a photon to travel the same distance. Then x = vt = cT. Therefore T/t = v/c.See how simple that was?

QuoteOnly if you can confirm which clock, which observer, and that you understand what I have written in this and my last post.Just as Einstein defines his primed variables (such as t'), so I define mine. With regards to the Lorentz transformation t' = (t - vx/c^2)γ, which clock and observer does Einstein use for t'?

Only if you can confirm which clock, which observer, and that you understand what I have written in this and my last post.

If that is a format that you understand better, then yes...go with it. The original format makes perfect sense to me, but then again I wrote it which makes me biased to understanding.

QuoteFirst off I've asked you several times what "There are two parallel linear events (A and B) with uniform velocity along the positive x-axis." means and I've yet to get a response. You didn't even state what the worldlines are which are supposed to be parallel. I'm going to assume that you're referring to the following worldlines;Worldline A: Worldline connecting origin with event AWorldline B: Worldline connecting origin with event BWorldline A is the worldline of a photon which is emitted from the origin and moves in the +x-direction and ends up at event A. That means that it's a line which is 45 degrees with respect to the +x-axis (and of course its also a line which is 45 degrees with the ct-axis).Worldline B is the worldline of a particle which moves at a speed less than the speed of light and ends up at event B. That means that it's a line which is greater than 45 degrees with respect to the +x-axis.This means that it is a line which is 45 degrees with respect to the +x-axis (and of course it’s also a line which is 45 degrees with the ct-axis).Therefore it follows that these two worldlines are not parallel. So what in the world do you mean by “parallel events”?I have no idea where you are getting this information or interpretation. When I say parallel, I mean parallel. A photon travels parallel to the x-asix, and an electron travels parallel to the x-axis. Simple geometry, like your car travels parallel to the surface of the road. No need for world lines or tilting through any degrees. You don't understand my original scenario...I get it. No need to keep stating the same thing...I get it.

First off I've asked you several times what "There are two parallel linear events (A and B) with uniform velocity along the positive x-axis." means and I've yet to get a response. You didn't even state what the worldlines are which are supposed to be parallel. I'm going to assume that you're referring to the following worldlines;Worldline A: Worldline connecting origin with event AWorldline B: Worldline connecting origin with event BWorldline A is the worldline of a photon which is emitted from the origin and moves in the +x-direction and ends up at event A. That means that it's a line which is 45 degrees with respect to the +x-axis (and of course its also a line which is 45 degrees with the ct-axis).Worldline B is the worldline of a particle which moves at a speed less than the speed of light and ends up at event B. That means that it's a line which is greater than 45 degrees with respect to the +x-axis.This means that it is a line which is 45 degrees with respect to the +x-axis (and of course it’s also a line which is 45 degrees with the ct-axis).Therefore it follows that these two worldlines are not parallel. So what in the world do you mean by “parallel events”?

I have no idea where you are getting this information or interpretation.

What is "parallel linear events" supposed to mean?

When I say parallel, I mean parallel.

A photon travels parallel to the x-asix, and an electron travels parallel to the x-axis. Simple geometry, like your car travels parallel to the surface of the road. No need for world lines or tilting through any degrees. You don't understand my original scenario...I get it. No need to keep stating the same thing...I get it.

The following scenario utilizes events that are applicable to Einstein’s Special Relativity Theory. What follows requires further analysis regarding application of the first postulate WRT SRT. For information with images, see http://gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/5916.

Okay. Given your responses which clarify what you were trying to do I went over this carefully and now see that your conclusion is wrong.

In accordance with Einstein's "Relativity: The Special and General Theory", the Lorentz transformations will transform an event (event as referenced within "Relativity: The Special and General Relativity) that occurs within K (x,y,z,t) to a system K' (x',y',z',t') or vice versa. Refer to Part 1, Chapter 11 of his book.

Just as Einstein defines his primed variables (such as t'), so I define mine. With regards to the Lorentz transformation t' = (t - vx/c^2)γ, which clock and observer does Einstein use for t'?

When the race occurs within the stationary laboratory frame (v = 0), no calculation is needed (inverse Lorentz transformation reduces to Galilean format) and the ratio of the photon time span to the electron time span WRT the stationary laboratory frame is simply;Photon: τ = τ'Electron: t = t'Ratio #1: τ/t = τ'/t'

When the race occurs within the inertial frame at velocity (v), the calculation of the ratio of the photon time span to the electron time span WRT the stationary laboratory frame IAW the inverse Lorentz transformation is;Photon: τ=(τ'+vx'/c^2)γ Since it is a photon, the second postulate gives x' = cτ' τ=(τ'+v(cτ')/c^2)γ τ=(τ'+v(τ')/c)γ τ=τ'(1+v/c)γ

While you were composing yours, I was composing mine, you beat me to it by moments. I approach it from a different direction, but we reach the same conclusions. Perhaps you can confirm my logic as I see HeyBert creating an invalid conclusion by failing to perform an audit trail of observers and frames. Perhaps between the two responses he will be able to understand how he should be viewing his scenarios.

It appears from your remark that (T' = T) ...

...means that you are assuming I am discussing what K measures in their own frame vs what K' measures in their own frame. This was not at all what I was discussing.

...means that you are assuming I am discussing what K measures in their own frame vs what K' measures in their own frame. This was not at all what I was discussing."

For all the primed variables, the clarification is as follows. IAW Einstein's book "Relativity: The Special and General Theory", the primed variable is with respect to the co-ordinate system K' and the unprimed variable is with respect to the co-ordinate system K.

Of course they will not measure anything different, that is merely a result of the first postulate.

Quote from: HeyBertIt appears from your remark that (T' = T) ...QuoteTo whom are you speaking to? I don't see Colin making any such comment.I was referring to his comment about "Really? Do you believe that? 1=(1+v/c)γ, where γ = (1-v^2/c^2)^-1/2"Can you see it?

To whom are you speaking to? I don't see Colin making any such comment.