1

New Theories / Re: In regards to the 1st Postulate of STR

« on: 24/02/2015 03:42:23 »

In the 'New Theories' section of "Got a new theory on something? Post your hypotheses here..."

This is where you choose defend the pillars of science? Your actions do nothing but make people afraid to freely discuss their ideas on this forum. Great job Ace!

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 24/02/2015 02:57:28 »

Posts #48-#49. And don't bother "explaining", not interested.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 24/02/2015 01:07:05 »

Colin2B + PmbPhy,
It's a hobby...It's a math problem...even if I'm wrong, it's fun to me...stop being so offensive and judgmental! You're both acting like a couple drama queens on here.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 23/02/2015 07:11:21 »

Working things out on another forum right now. Learned to frame the problem in a "relativity friendly" format from another user and have good positive communication going. Thanks for the offer though, and I'll let you know If I come back to this or identify where my logic went astray.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 23:12:08 »

Thanks for stopping by.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 19:03:55 »

My latest edit based upon great feedback. Not interested in arguing older scenarios as I already admitted they were flawed. That was the point of posting in the first place.

PART 1 (One-Way Events)

WRT Einstein’s book (Relativity: The Special and General Theory), Part 1, Chapter 11 gives the Lorentz transformation (LT) as;

t’ = (t-vx/c^2)γ, where γ = (1-v^2/c^2)^-1/2

Referencing Einstein’s book (Part 1, Chapter 11), we merely apply the transformation to two events (i.e. moving electrons) in K from (x = 0) to (x) in unequal times (τ) and (t).

WRT K’:
     τ’ = (τ-vx/c^2)γ

     t’ = (t-vx/c^2)γ

Evaluating the ratio of these times at (v) gives the results WRT K’ as;
*    τ’/t’ = (τ-vx/c^2)/(t-vx/c^2)

Evaluating this ratio at (v = 0) gives the results WRT K as;
     τ’/t’ = (τ-0*x/c^2)/(t-0*x/c^2)
*    τ’/t’ = τ/t

PART 2 (Round-Trip Events)

Referencing Einstein’s book (Part 1, Chapter 11), we merely apply the transformation to two events (i.e. moving electrons) in K from (x = 0) to (x) in unequal times (ϖ) and (T), then from (x) to (x = 0) in these same times (ϖ) and (T).

WRT K’:
     2ϖ’ = (ϖ-vx/c^2)γ + (ϖ+vx/c^2)γ
     2ϖ’ = ϖγ-(vx/c^2)γ+ϖγ+(vx/c^2)γ
*    2ϖ’ = 2ϖγ

     2T’ = (T-vx/c^2)γ + (T+vx/c^2)γ
     2T’ = Tγ-(vx/c^2)γ+Tγ+(vx/c^2)γ
*    2T’ = 2Tγ

Evaluating the ratio of these times at either (v or v = 0) gives the results WRT to K’ or K as;
*    ϖ’/T' = ϖ/T

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 18:54:38 »

Calm down...it's just a math problem. No need to huff and puff in front of the world. Did your teacher act this way when you made mistakes learning in class? I agreed that there were mistakes within my original scenarios, so stop pretending I didn't.

It is obvious that my original presentations suffer many flaws due to the wording and the related mathematical results as a result of this wording. What if I strip out all the extraneous referencing to observers, rest frames, etc.?

Just because you disagree with how someone answers your question does not mean they didn't answer your question. I tried changing the wording of my scenario based upon the wonderful feedback I received from posts like yours. Continually going backwards in the posts (after I make changes based upon replies) is like going to jail over and over for the same crime. Get over it! Do me a favor, don't ever become a teacher...I don't think you have the patience for it.

And what law states I have to answer your questions anyways?

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 04:23:54 »

PART 1 (One-Way Events)

WRT Einstein’s book (Relativity: The Special and General Theory), Part 1, Chapter 11 gives the Lorentz transformation (LT) as;

t’ = (t-vx/c^2)γ, where γ = (1-v^2/c^2)^-1/2

Referencing Einstein’s book (Part 1, Chapter 11), we merely apply the transformation to two events originating in K that travel from (x = 0) to (x) in unequal times (τ) and (t).

WRT K’:
     τ’ = (τ-vx/c^2)γ

     t’ = (t-vx/c^2)γ

Evaluating the ratio of these times at (v) gives the results WRT K’ as;
*    τ’/t’ = (τ-vx/c^2)/(t-vx/c^2)

Evaluating this ratio at (v = 0) gives the results WRT K as;
     τ’/t’ = (τ-0*x/c^2)/(t-0*x/c^2)
*    τ’/t’ = τ/t

PART 2 (Round-Trip Events)

Referencing Einstein’s book (Part 1, Chapter 11), we merely apply the transformation to two events originating in K that travel from (x = 0) to (x) in unequal times (ϖ) and (T), then are reflected back such that they return to their points of origin (x = 0) in this same time (ϖ) and (T).

WRT K’:
     2ϖ’ = (ϖ-vx/c^2)γ + (ϖ+vx/c^2)γ
     2ϖ’ = ϖγ-(vx/c^2)γ+ϖγ+(vx/c^2)γ
*    2ϖ’ = 2ϖγ

     2T’ = (T-vx/c^2)γ + (T+vx/c^2)γ
     2T’ = Tγ-(vx/c^2)γ+Tγ+(vx/c^2)γ
*    2T’ = 2Tγ

Evaluating the ratio of these times at either (v or v = 0) gives the results WRT to K’ or K as;
*    ϖ’/T' = ϖ/T

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 04:14:57 »

It is obvious that my original presentations suffer many flaws due to the wording and the related mathematical results as a result of this wording. What if I strip out all the extraneous referencing to observers, rest frames, etc.?

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 04:03:11 »

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

To 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?

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 22/02/2015 03:24:18 »

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. Of course they will not measure anything different, that is merely a result of the first postulate. Since all the following remarks are based upon this view, I can see how you came to your conclusion.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 21/02/2015 19:06:21 »

Paraphrasing is the cause for much of this confusion (all my mistakes), so let's return to Einstein's definitions as the source instead of my failed attempts.

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.

Within this co-ordinate system scenario given by Einstein, we define an experiment based upon two events;
(A) As seen by an observer in K, a photon propagates (c) from (x = 0) to (x) in a time interval (τ).
(B) As seen by an observer in K, an electron travels in uniform motion (u<c) from (x = 0) to (x), identical length along the x-axis as the photon, in a time interval (t).

Does this clarify the beginning of this scenario?

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 21/02/2015 18:46:43 »

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 A
Worldline B: Worldline connecting origin with event B

Worldline 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.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 21/02/2015 06:41:30 »

When I asked "I think we can come to a common interpretation by "walking the dog" if you're up to it...wadda ya say?", I meant to start at the beginning and step through the progression (changing as necessary in small pieces) of the scenario ensuring that you can follow my logic (as you best understand) until we get to the conclusion. My original writing style was how I think and write, which is obviously not best for a general audience that is used to another style.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 21/02/2015 06:35:17 »

Only 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'?

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 21/02/2015 06:12:11 »

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?

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.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 20/02/2015 02:43:49 »

OK, things are staring to look clearer, but before we confuse ourselves with maths let's be really clear that we are talking about the same things.

Perhaps we can look at it this way as my original choice of words may have not been understood clearly by all...(τ and t indicate time spans, or time intervals measured by a clock).

Which clock? Sorry to labour this but there are 2 clocks, one in the rest frame and one in the moving frame.
For the observer in the moving frame the moving clock measures the same time intervals as when he made the same measurements in the rest frame so T/t is the same. So by doing a physics experiment he sees no difference between the frames. From his point of view he is stationary (because he is moving with the frame) and no Lorentz transforms are required.

For the observer in the rest frame observing the moving frame, he sees the clock in the moving frame measuring time more slowly than the one he has next to him in the rest frame. So the T/t is not the same and this difference is calculated using the Lorentz transforms.

Does the ratio of these two scenarios mathematically equal each other (same race happening in two different inertial frames)? If so, then how? If not, then what would stop us from determining the velocity of the inertial frame at velocity (v) by conducting such a "race" experiment and measuring how the ratio changes with increasing velocity of the inertial frame.

As we can see, it depends who is doing the observing.
For the observer who was stationary and is now moving there is no difference and this is what the postulate is all about. The observer cannot tell by the race experiment whether he is moving or not. He can however, look out of the window and see he is moving away from the rest frame, so would perceive himself as moving.

For the observer who is stationary observing the moving frame, no the ratios are not the same. That's what relativity is all about, frames moving relative to one another.

Again sorry to labour this, but it think there is a confusion of observers.
I hate to say it but I don't think you are comparing light with light!  []

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

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 20/02/2015 00:42:31 »

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.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 20/02/2015 00:36:18 »

My calculations, where γ = (1-v^2/c^2)^-1/2;

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'

You keep posting things like this without defining them. What you said tells us nothing about what those quantities are/mean.

"Utilizing the Lorentz transformations with respect to the stationary laboratory frame, calculate the ratio of the time span it takes for the photon to traverse this distance to the time span it takes for the electron to traverse this distance (τ/t)." Already defined both time variables here.

"When the race occurs within the inertial frame at velocity (v)." Already defined what this velocity is here.

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.

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New Theories / Re: In regards to the 1st Postulate of STR

« on: 20/02/2015 00:28:27 »

Which clock? Sorry to labour this but there are 2 clocks, one in the rest frame and one in the moving frame.
For the observer in the moving frame the moving clock measures the same time intervals as when he made the same measurements in the rest frame so T/t is the same. So by doing a physics experiment he sees no difference between the frames. From his point of view he is stationary (because he is moving with the frame) and no Lorentz transforms are required.

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.