Test your understanding of Special Relativity.
This thread isn't about whether you agree with the theory, it's about whether you understand it well enough to get "correct" answers to textbook problems.

Shall we begin with an easy one?

13. Equal speeds
A and B travel at 4c/5 and 3c/5, respectively, as shown in Fig. 10.36.
How fast should C travel between them, so that he sees A and B approaching him at the same speed?
What is this speed?
Figure 10.36
4c/5 ? 3c/5
* ---> * ---> * --->
A C B

Good question Pete I look forward to a full and thorough elucidation and extrapolation of the solution....

The questions in this thread are taken from a textbook that I chosen pretty randomly, and that is available online (but doesn't seem to be indexed by Google).

Hi QQ! I don't think there'll be much drama with this one, but I've picked out some very tricky others. Some are quite lovely, from a problem designing perspective!

Do those among us who are not mathematicians get to play this game? 7c/10

Hi QQ! I don't think there'll be much drama with this one, but I've picked out some very tricky others. Some are quite lovely, from a problem designing perspective!

Certainly SRT provides us all with an opportunity to flex our dimensional imaginations and visualisations and .......and even our mathematical visualisations.....

SRT allows for terrific scope in problem design as you say.....although some would think a Rubiks Cube is more fun.......ha..... :D

Oops! Sorry, I didn't read the VAF thread beforehand. I didn't know this was directed
to MacM.

Do those among us who are not mathematicians get to play this game?
Of course! But... at least some maths is going to be needed. No calculus, though, just a bit of algebra, maybe some trig.
7c/10
A the risk of sounding like a teacher...
Well done! That's the correct answer for C's velocity according to the old (pre-Einstein) physics.
However, Special Relativity gives a different answer. Can you figure out what that answer is?

Oops! Sorry, I didn't read the VAF thread beforehand. I didn't know this was directed
to MacM.
While the thread was inspired by MacM, It's not specifically for him. Anyone and everyone is welcome to participate!

No Pete. I cannot understand why Special Relativity would give a different answer. Can you elaborate?

Hi 2inquisitive,
Sorry, I thought you knew some SR.

The relativistic velocity addition formula (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html#c2) is useful here.

If A's velocity is 4/5c, B's velocity is 3/5c, and C's velocity is 7/10c, then according to special relativity:
A's velocity in C's rest frame is 5/22 c
B's velocity in C's rest frame is -5/29 c

Which aren't the same magnitude, which means that 7/10 c isn't the correct SR answer.

Hi 2inquisitive,
Sorry, I thought you knew some SR.

The relativistic velocity addition formula (http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/einvel2.html#c2) is useful here.

If A's velocity is 4/5c, B's velocity is 3/5c, and C's velocity is 7/10c, then according to special relativity:
A's velocity in C's rest frame is 5/22 c
B's velocity in C's rest frame is -5/29 c

Which aren't the same magnitude, which means that 7/10 c isn't the correct SR answer.


No, Pete. A's velocity is .1c relative to C, B's velocity is .1c relative to C, and C is moving to the right at .7c. You asked what velocity C should be traveling at for C to see both A and B approach his frame at equal speeds. Velocity
addition formula is used to calculate A's velocity relative to B. That is not a
part of your original question. I knew you were wanting to introduce the velocity addition formula into the example, but you did not word your gedanken correctly for that.

You see, Pete, you did not specify what frame of reference was being used in your example. All velocities had to be in some context in your example. I chose the ICRF
frame of reference. You could use a heliocentric frame of your choosing if you like.

It's not my question, 2inquisitive. It's directly quoted from a Relativity textbook.
Your answer disagrees with the textbook answer.

You see, Pete, you did not specify what frame of reference was being used in your example. All velocities had to be in some context in your example. I chose the ICRF frame of reference. You could use a heliocentric frame of your choosing if you like.
I think it's obvious that the velocities in the question are in an arbitrary inertial frame. You can use the ICRF if you like - would you get a different answer in any other inertial frame?

I think it's equally obvious that this question:
"How fast should C travel between them, so that he sees A and B approaching him at the same speed?"

Is asking what C's velocity in the initial inertial frame should be such that A's velocity in C's rest frame is of equal magnitude to B's velocity in C's frame.

Sorry for attributing the exercise to you, Pete. In my humble opinion, the textbook
gave a inadequately presented exercise, then. You do see my point, what frame was
A's velocity of 4c/5 calculated in? It was not specified it was relative to anything, so
using the movements WITHIN a frame such as the ICRF seemed fair game to me.

While the thread was inspired by MacM, It's not specifically for him. Anyone and everyone is welcome to participate!

I had not posted here in that I had been directed to your post Here and didn't realize it was a currently posted thread but that it was something from archives.

I replied 0.72c.

You do see my point, what frame was A's velocity of 4c/5 calculated in? It was not specified it was relative to anything, so using the movements WITHIN a frame such as the ICRF seemed fair game to me.
Yep that's fair game. I just don't think it makes any difference - I assumed an arbitrary inertial frame, and found the textbook answer of 5/7 c, with A and B both having a speed of 1/5 c in C's frame.
Textbooks often refer to the "ground frame", which is understood to be an arbitrary inertial frame.

Mac,
I replied 0.72c.
Well, that's close enough to the textbook answer of 5/7 c, I guess.

But, we're just warming up!

This one is also quite straightforward - another warm-up. The next one will be more interesting!

26. Passing a train *

Person C stands on the ground.
Train B (with proper length L) moves to the right at speed 3c/5.
Person A runs to the right at speed 4c/5. A starts behind the train and eventually passes it.
Let event E1 be “A passes the back of the train,” and let event E2 be “A passes the front of the train.”

Find Δt and Δx between events E1 and E2 in the frames of A, B, and C.
Show that the invariant interval c²Δt² - Δx² is the same in all frames.

This one is also quite straightforward - another warm-up. The next one will be more interesting!

26. Passing a train *

Person C stands on the ground.
Train B (with proper length L) moves to the right at speed 3c/5.
Person A runs to the right at speed 4c/5. A starts behind the train and eventually passes it.
Let event E1 be “A passes the back of the train,” and let event E2 be “A passes the front of the train.”

Find Δt and Δx between events E1 and E2 in the frames of A, B, and C.
Show that the invariant interval c²Δt² - Δx² is the same in all frames.

Great. I don't want to appear to be a party pooper but I really only do calculations that I need to to pursue my presentations of conflicts with the theory and have no interest in relativity perse since I see it as false.

But I will be watching out of general interest and the possibility of picking up on some false claim being argued. I guess I really should have rounded my result to .71 instead of .72 in that I worked in decimal not fractions and the "8" digit only raised the "2" to a "3" which should have been dropped leaving the 0.71. But I did go through the VAF algebra running the calculation.

by Pete:


Yep that's fair game. I just don't think it makes any difference -
================================================== ==========

Sorry to reintroduce the previous exercise, but I thought I would explain why it DOES
make a difference. I'll try to keep it short. Consider a constellation of satellites orbiting
the Earth in different orbital planes, planes intersecting with each other. By using Special Theory, the satellites would 'see' different relative velocities for each other as
the paths intersected. That leads to different time dilation calculations and a breakdown of simultaneity. By using the ICRF frame in which all satellites are traveling
at identical orbital velocities WITHIN this frame, all time dilations will be identical for all
satellites relative to the ICRF frame and simultaneity does not break down between the
individual satellites in the constellation. No 'velocity addition equations' are used in this
reference system since velocities BETWEEN individual satellites are not calculated. This
is how the GPS system works, how simultaneity does not break down and there are NO errors introduced using this method. GPS works very precisely, currently in the millimeter accuracy range for receivers 'fixed' on the Earth's surface, and multipal satellite readings.

Sorry, 2inq - not in this thread.
When you can show that you understand how to apply SR, then I'll pay attention to your conclusions. Otherwise, how do you know that your conclusions aren't due to a flawed application of the theory?

Great. I don't want to appear to be a party pooper but I really only do calculations that I need to to pursue my presentations of conflicts with the theory and have no interest in relativity perse since I see it as false.
If you can't demonstrate that understand it, how do you justify claiming it to be false?

Come one, just one more! I bet you can't do this one:

29. Simultaneous claps ***

With respect to the ground, A moves to the right at speed c/√3, and B moves to the left, also at speed c/√3.
At the instant they are a distance d apart (as measured in the ground frame), A claps his hands. B then claps his hands simultaneously (as measured by B) with A’s clap. A then claps his hands simultaneously (as measured by A) with B’s clap. B then claps his hands simultaneously (as measured by B) with A’s second clap, and so on.

As measured in the ground frame, how far apart are A and B when A makes his nth clap?

Or if you don't like that one, you might prefer this one...

19. Modified twin paradox ***
Consider the following variation of the twin paradox. A, B, and C each have a clock.
In A’s reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero.
Also, in A’s reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B’s.
Finally, when C passes A, they compare the readings on their clocks. At this event, let A’s clock read TA, and let C’s clock read TC.

(a) Working in A’s frame, show that TC = TA/γ, where γ = 1/√(1-v²/c²).
(b) Working in B’s frame, show again that TC = TA/γ.
(c) Working in C’s frame, show again that TC = TA/γ.

Or if you don't like that one, you might prefer this one...

19. Modified twin paradox ***
Consider the following variation of the twin paradox. A, B, and C each have a clock.
In A’s reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero.
Also, in A’s reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B’s.
Finally, when C passes A, they compare the readings on their clocks. At this event, let A’s clock read TA, and let C’s clock read TC.

(a) Working in A’s frame, show that TC = TA/γ, where γ = 1/√(1-v²/c²).
(b) Working in B’s frame, show again that TC = TA/γ.
(c) Working in C’s frame, show again that TC = TA/γ.

Actually I see them all as mis-appplications of actual physics and a tedious waste of time. I really believe this is why relativity has survived. People are mesmerized by it and don't want to spend the same calculation time to show the failures by applying the claims to actual data and vice versa.

There exist this falicy that if it partially works then it must all be true. It isn't.

Mac,
If you can't be bothered to understand relativity, how can you justify your stance that it is fallacious?

You've asserted time and time again that you understand relativity better than others on this board.

I challenge you to prove it, or be branded a charlatan.

Mac,
If you can't be bothered to understand relativity, how can you justify your stance that it is fallacious?

I have proven I understand relativity by my posts including mathematics of virtually every aspect of relavistic physics. There is nothing to be gained by spending days, even minutes doing such exercises. Either show error in my posts or accept there validity.

You've asserted time and time again that you understand relativity better than others on this board.

I challenge you to prove it, or be branded a charlatan.

I take this statement to be a bit out of context. One can have an equal understanding of what relativity advocates. In that regard I would say that my understanding is more than adequate, basically equal, if not as polished and practiced.

However, where I may have said I understand better than others applies only to recognizing the consequences of what relativity advocates vs what has been emperically supported and hence why it is invalid. This is not a matter of education but analytical willingness or capacity.

The relativists seem unwilling to actually take such physical facts and live with the consequences which can be shown. They prefer to stick with the rhetoric and merely cite the good book. They are not talking physics at that point.

It is not that they can't. It is a matter that they deliberately refuse to. So I would not want your statement to put the wrong impression as to my view of myself.

Being called a charlatan by those that ignore relavistic calculations of a clocks physical tick rate to in turn generate the necessity for the unsupported claim of spatial contraction, hardly seems to be a matter of concern.

I have certainly wrongfully been called worse here. :D

I have proven I understand relativity by my posts including mathematics of virtually every aspect of relavistic physics.
You must be joking, Mac.
You have a chance to prove it now - why don't you take it?

You must be joking, Mac.
You have a chance to prove it now - why don't you take it?

As I have said I find it a complete waste of time to compute circle jerk gendankins for the sake of playing with relativity because relativity is not real. It is invalid. I will only spend time doing such exercises when doing so to demonstrate the falicies of it.

If you find errors in my application or mathematics it is appropriate you point those out but I have no need nor ambition to do tests of the concept I know to be false physics.

Yeah, we believe you, MacM. We'll just take your word for it that you're an expert in relativity.

You must be joking, Mac.
You have a chance to prove it now - why don't you take it?
I agree with MacM, this thread is a decided waste of tiome and proves nothing save one's ability to pull mathematical expressions, expressing nothing, and cranking out the foolishness.
Didn't you see James R's thread to give MacM a chance to prove himself? Did you see my prediction that this thread was placed there to give the James R crowd the opportunity to insult MacM, regardless of what he said? And did that prediction come true? What are you doinf with this thread of yours: preesenting the epilog of the previous james R thread?
Geistk:cool:iesel

I have no need nor ambition to do tests of the concept I know to be false physics.
Mac, if I said that I have no need nor ambition to do tests of UniKEF because I know it to be false, what would you respond?

You've said several times in the past that SR can't handle more than two frames. And yet here are a number of exercises in a foundation relativity text that deal with several frames!

You've presented your "three clock paradox" as a situation in which SR gives inconsistent predictions... and yet when you're given a strikingly similar exercise froma foundation relativity text, suddenly you have no need or ambition to consider it.

Are you afraid that perhaps applying SR does not lead to inconsistencies?

Or are you going to take on the stance that Relativity textbooks don't actually present Relativity?

geistkiesel,
Is it not reasonable to ask that someone who wants to debunk a model of reality should first understand that model?
If there is doubt about someone's understanding, is it not reasonable to put it to the test ?
If someone refuses a valid and harmless test, should the question of their understanding not remain open?

You must be joking, Mac.
You have a chance to prove it now - why don't you take it? To be fair. These problems do not require an understanding of relativity beyond the definition of variables in special relativity equations. I would be much more impressed if you could derive the special relativity equations based solely on the postulates of relativity. Unfortunately, there is no way to prove to me that you didn't just get a derivation from somewhere on the internet - so this idea is basically pointless.

Mac, if I said that I have no need nor ambition to do tests of UniKEF because I know it to be false, what would you respond?

I would say you should first have studied enough and had found proveable errors which precluded it from consideration.

You've said several times in the past that SR can't handle more than two frames. And yet here are a number of exercises in a foundation relativity text that deal with several frames!

I don't believe I have ever said SR cannot handle more than two frames.

You've presented your "three clock paradox" as a situation in which SR gives inconsistent predictions...

I have said using three or more frames makes falsifying SR easier.

and yet when you're given a strikingly similar exercise froma foundation relativity text, suddenly you have no need or ambition to consider it.

Why continue to replicate scenarios. I have progressed here and been able to fine tune my presentation to offset the initial rebuttals which interjected other relavistic aspects as smoke screens to the consequences shown.

Are you afraid that perhaps applying SR does not lead to inconsistencies?

Not in the least. Are you afraid you have no valid rebuttals for the issues I raise. Why not simply point out my error. Why should we spend time working through circular logic problems, when it is known that circular logic is the only reason the mathematics remains consistant?

i.e. - Spatial Length Contraction can only be claimed because you choose to ignore known, calculated time dilation of the moving clock. If you retain the known physical and emperically demonstrated affect of time dilation when doing the trip travel times, it turns out that distance MUST remain constant.

I have no interest in ignoring known physics and conditions and showing that results in some other affect needing to be declared. For what possible purpose?

Further more the suggestion that doing so mandates contraction is not a complete circumstance. You have not excluded the possibility that the moving observer might merely mis-calculate his velocity as being greater covering the same distance in less time.

No SR is a complete waste of time. Simply retain the calculated and physically known affect of time dilation, which is the only correct thing to do in the first place and there is no problem and also no room for contraction.

Or are you going to take on the stance that Relativity textbooks don't actually present Relativity?

Absolutely not. But they present the same circle jerk logic that creates it by distorting physical relationships arbitrarily and in complete disregard of some of their own physical calculations.

To be fair. These problems do not require an understanding of relativity beyond the definition of variables in special relativity equations. I would be much more impressed if you could derive the special relativity equations based solely on the postulates of relativity. Unfortunately, there is no way to prove to me that you didn't just get a derivation from somewhere on the internet - so this idea is basically pointless.

Your suggestion only shows a greater indepth mathematical capacity to make such derivations. Being able to make such derivations in no manner alters results or improves ones understanding of the ultimate principles and physical relationships due to motion etc.

Yeah, we believe you, MacM. We'll just take your word for it that you're an expert in relativity.

1 - I have not ever claimed to be an expert.

2 - I really give a damn what you believe.

3 - The only thing that matters is that you have been unable to rebut the issues I have raised.

Your only posts have been recital of the theory, innuendo, distortion, etc.

Only when you demonstrate physically the issue of reciprocity or post an in depth description of the physics by which it can be achieved will you have made a valid rebuttal.

Only when you justify disregarding calculated and the emperically proven fact of time dilation when calculating trip time between moving observers to claim spatial contraction will you have made a rebuttal.

MacM:

1 - I have not ever claimed to be an expert.

You wrote, above:

One can have an equal understanding of what relativity advocates. In that regard I would say that my understanding is more than adequate, basically equal [to others on this forum], if not as polished and practiced.

I claim to be an expert in special relativity. Are you equal to me in that regard? Yes, or no? Or do you think I am not an expert?

Only when you demonstrate physically the issue of reciprocity or post an in depth description of the physics by which it can be achieved will you have made a valid rebuttal.

I fervently hope you live long enough to see a nice, clear experiment which demonstrates reciprocity, MacM. Not that I expect that something as simple as evidence will change your mind.

Special Relativity knowledge challenge. This is specifically targeted for MacM and Pete. However, I encourage all to participate.

The following derivation derives the lorentz equations of special relativity. Follow the derivation and list the assumptions (postulates) used to derive the theory. That is to say, if a postulate must exist for the use of a given equation, name the postulate and the equation number. Finally state whether you think this is a valid or invalid derivation.

Lorentz Equations Derivation (http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf)

Hi Aer,
This is a bit beyond me... I'm not enough of a mathemetician to evaluate the rigor of a derivation. BUt, I 'll have a go.

Postulate A: Equivalence of inertial reference frames

Equation (1) follows from Postulate A... except that I would have treated v as a variable, i.e.:
x'1 - x'2 = fx(x1 − x2, t1 − t2, v)
t'1 - t'2 = ft(x1 − x2, t1 − t2, v)

I guess it could be OK to treat v as a constant. I'm not sure, so I know straight away that I won't be able to give a definite yes or no on the derivation's validity.

I think that equations (2) and (3) follow from (1) and from the Euclidian nature of O and O', i.e. I think I could go from (1) to (2) and (3) using Euclidean geometry.

(10) is interesting... I think this is a straight logical step, but perhaps there's an assumption I'm missing? Postulate A might be required, but I don't think so.

I don't follow the logic leading to equation (14). To me, it looks like an unsupported leap, but I'm out of my depth. I'm giving up.

I would say you should first have studied enough and had found proveable errors which precluded it from consideration.
And if I presented you with proveable errors which were based on premises inconsistent with UniKEF's premises?
Would you suggest that I did not understand UniKEF, and that I should study the premises and demonstrate understanding before presenting my rebuttal?

I have said using three or more frames makes falsifying SR easier.
And yet it seems that a correct application of SR leads to different conclusion than you suggest?
Perhaps your application of SR to your three-clock situation is erroneous?
Why not do this exercise, and show us that you can get the same answer as the text?

MacM:

You wrote, above:

I claim to be an expert in special relativity. Are you equal to me in that regard? Yes, or no? Or do you think I am not an expert?

If you define an expert as one that is completely knowledgeable as to what the theory advocates you might well be an expert. Not sure you qualify but you certainly are more practiced and polished. But that says nothing for the correctness of your physics.

We are not debating what SRT advocates. We are debating the validity of what it advocates.

I fervently hope you live long enough to see a nice, clear experiment which demonstrates reciprocity, MacM.

Me to. I have always wanted to be imortal. :D

Not that I expect that something as simple as evidence will change your mind.

Far qucker than your innuendo. You might give it a try next time.

Hi Aer,
This is a bit beyond me... I'm not enough of a mathemetician to evaluate the rigor of a derivation. BUt, I 'll have a go. I appriciate the attempt - I'll make comments later as well as provide the full answers. Hopefully someone else will take up the challenge as well.

Postulate A: Equivalence of inertial reference frames

Equation (1) follows from Postulate A... except that I would have treated v as a variable, i.e.:
x'1 - x'2 = fx(x1 − x2, t1 − t2, v)
t'1 - t'2 = ft(x1 − x2, t1 − t2, v) Your postulate "Equivalence of inertial reference frames" is too vague.


I think that equations (2) and (3) follow from (1) and from the Euclidian nature of O and O', i.e. I think I could go from (1) to (2) and (3) using Euclidean geometry. You need not analyse every step - just those that you think make assumptions.

(10) is interesting... I think this is a straight logical step, but perhaps there's an assumption I'm missing? Postulate A might be required, but I don't think so. There is nothing wrong with the posing of equations (10). It merely follows from all results prior.


I don't follow the logic leading to equation (14). To me, it looks like an unsupported leap You are correct to say that it is an unsupported leap.




Now for the answers.

Equation (5),
Postulate: All reference frames must be inertial reference frames. x = vt → v = x/t and v = dx/dt simplifies to v = x/t if there is no acceleration of S' relative to S. In other words, S' & S must be inertial reference frames.

Equation (6),
Postulate: Light travels at a constant speed in all directions for any inertial frame (i.e. the speed of light is constant). So it doesn't matter if you consider S' moving in frame S at velocity v or, S moving in frame S' at velocity -v.

Edit: The rest of the post was made hastily as I pointed out on another forum - I wish I could have corrected it sooner. I'll post the revision in just a few...

Special Relativity knowledge challenge. This is specifically targeted for MacM and Pete. However, I encourage all to participate.

The following derivation derives the lorentz equations of special relativity. Follow the derivation and list the assumptions (postulates) used to derive the theory. That is to say, if a postulate must exist for the use of a given equation, name the postulate and the equation number. Finally state whether you think this is a valid or invalid derivation.

Lorentz Equations Derivation (http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf)

Thanks for the invite but as Pete said such derivation(s) are out of my league. I have done matrix and some calculus but that was over 40 years ago.

Further, if you have read this thread, I really don't have any interest in relativity other than to point out it's kinks.

I read your reply to Pete and found some of your comments interesting regarding contraction.

Your postulate "Equivalence of inertial reference frames" is too vague.
I was assuming this one as common knowledge.
Read "The laws of physics are the same in all inertial frames of reference."

Equation (5),
Postulate: All reference frames must be inertial reference frames. x = vt → v = x/t and v = dx/dt simplifies to v = x/t if there is no acceleration of S' relative to S. In other words, S' & S must be inertial reference frames.
That's not a postulate, it's part of the definition of O and O' stated in the first point of the derivation: Let us consider two inertial reference frames O and O'.. Ie the derivation is explicitly considering inertial frames only, but it does not deny the existence of non-inertial frames.

Equation (6),
Postulate: Light travels at a constant speed in all directions for any inertial frame (i.e. the speed of light is constant). So it doesn't matter if you consider S' moving in frame S at velocity v or, S moving in frame S' at velocity -v.
Your second sentence is a non sequitur to your first.
Your stated postulate is irrelevant to the derivation - the speed of light is only mentioned in passing, not as part of the derivation.
Your conclusion follows from the translational symmetry of the laws of physics, which I think are a consequence of the equivalence postulate.

Equations (12),
Postulate: Given 3 reference frames, one can make a transformation from frame 1 to frame 2, then transform frame 2 to frame 3 - and this would be equivalent to a transformation from frame 1 to frame 3.
That's the concept I was referring to when I expressed uncertainty for equation (10), which you accepted without quibble. Are we looking at the same derivation?

Now this is intriguing. One should expect this to be true for any "transformation". However, it does not hold true for the Lorentz transformations. You need only try an example to prove this to yourself.
Have you tried it? Did you make the mistake of assuming simple velocity addition?
Here's an easy example:

S₁, S₂, and S₃ are inertial frames.
S₂ has velocity v₁₂ = 0.6c relative to S₁.
S₃ has velocity v₂₃ = 0.6c relative to S₂.

(x₁, t₁) = (0 ls, 2 s) is an event in S₁, which we will transform to S₂ and S₃.

γ₁₂ = 1/(1-v₁₂²/c²) = 1.25
γ₂₃ = 1/(1-v₂₃²/c²) = 1.25

Transform from S₁ to S₂:
x₂ = γ₁₂(x₁ - v₁₂t₁)= -1.5 ls
t₂ = γ₁₂(t₁ - v₁₂x₁/c²) = 2.5 s
(x₂, t₂) = (-1.5 ls, 2.5 s)

Transform from S₂ to S₃:
x₃ = γ₂₃(x₂ - v₂₃t₂) = -3.75 ls
t₃ = γ₂₃(t₂ - v₂₃x₂/c²) = 4.25 s
(x₃, t₃) = (-3.75 ls, 4.25 s)

It's immediately clear (because x₁ = 0, and (0,0) is shared between frames) that the velocity of S₁ rel. to S₃ is:
v₃₁ = -3.75/4.25 = -0.88c
and by symmetry,
v₁₃ = 0.88c
γ₁₃ = 2.125

So now we can do a transform directly from S₁ to S₃:
x₃ = γ₁₃(x₁ - v₁₃t₁) = -3.75 ls
t₃ = γ₁₃(t₁ - v₁₃x₁/c²) = 4.25 s
(x₃, t₃) = (-3.75 ls, 4.25 s)

So, in this particular case, transforming from S₁ to S₂ to S₃ is equivalent to transforming from S₁ to S₃.

A general proof is just as easy, but tedious to type.

I could show a proof here that this is true if and only if one of the frames is equivelent to the other, but I do not know how to represent matrices without the use of Latex as is available on physicsforums.
A counter-example will be sufficient.


Like I said, I don't know if the deriviation is valid... but it seems that you don't know either. Are you qualified for this stuff?

We are not debating what SRT advocates. We are debating the validity of what it advocates.
Actually, Mac, we are debating what it "advocates" (perhaps "predicts" is a better word). I suggest that you just don't know what SR does and doesn't "advocate", as evidenced by your failure to apply it in a way consistent with a textbook on SR.

That's not a postulate, it's part of the definition of O and O' stated in the first point of the derivation: Let us consider two inertial reference frames O and O'.. Ie the derivation is explicitly considering inertial frames only, but it does not deny the existence of non-inertial frames.
But, one of the postulates from wikipedia is "The laws of electrodynamics and optics will be valid for all frames in which the laws of mechanics hold good." which is only true of inertial reference frames - not accelerating reference frames. It is another way of stating the same thing IMO - but alas, I will have to build on this later.



Your second sentence is a non sequitur to your first.
Your stated postulate is irrelevant to the derivation - the speed of light is only mentioned in passing, not as part of the derivation. I suppose I will have to build on this as well - but I think you are have pointed out something valid. That is, the fact that speed of light is constant is never used directly, but there is assumed to be a limit to how fast something can travel.


That's the concept I was referring to when I expressed uncertainty for equation (10), which you accepted without quibble. Are we looking at the same derivation? Actually, this is the conclusion I drew as well, at first. But then realized there was something I was overlooking, I will explain later.


Have you tried it? Did you make the mistake of assuming simple velocity addition? No I didn't, and you are right - I should have! I was being lazy and tried to superimpose the assumptions Einstein used on this derivation, when I should have treated the derivation as unique from the get-go.


A general proof is just as easy, but tedious to type.
It would be required for any transformation actually. It should not need proof in a derivation of a transformation.


Like I said, I don't know if the deriviation is valid... but it seems that you don't know either. Are you qualified for this stuff? I would contend that the derivation is semi-valid. That is, because of equation (26) The actual postulate stating "the speed of light is constant" doesn't appear to be used directly. Just that their is some limit to how fast something can move.

Actually, Mac, we are debating what it "advocates" (perhaps "predicts" is a better word). I suggest that you just don't know what SR does and doesn't "advocate", as evidenced by your failure to apply it in a way consistent with a textbook on SR.

Excuse my blutness but horseshit. Point out a specific item please.

But, one of the postulates from wikipedia is "The laws of electrodynamics and optics will be valid for all frames in which the laws of mechanics hold good." which is only true of inertial reference frames - not accelerating reference frames. It is another way of stating the same thing IMO - but alas, I will have to build on this later.
The wikipedia postulates aren't the only ones from which a theory can be derived - they're just the most popularly used for classroom exercises in deriving special relativity.
A postulate is some statement about reality that is required for the construction of some theory or argument, right?

Your suggested postulate required for this derivation was "All reference frames must be inertial reference frames", which implies "Not-inertial frames do not exist".
But, the deriviation does not require that all frames must be inertial, it only stipulates that the transform being derived only applies between inertial frames - it is silent about how to transform to or from accelerating frames. I wouldn't call that a postulate, just a statement of scope of the transform being derived.

It certainly doesn't require that accelerating frames do not exist. (That would be a postulate).


I suppose I will have to build on this as well - but I think you are have pointed out something valid. That is, the fact that speed of light is constant is never used directly, but there is assumed to be a limit to how fast something can travel.
No... the question stays open. During the derivation, a term falls out which does correspond to some frame-invariant speed, but that term would need to be found empirically. In a Newtonian world, the term would be found to be infinity. (This makes sense, right? In a Newtonian world, something that travels instantaneously would travel instantaneously in all frames.)

Note further that this term is not related to the speed of light by this derivation. It's not even strictly related to a limiting speed. All that this derivation shows is that "if a particle moves with velocity c in one reference
frame, it also moves with velocity c in any other reference frame."
Note that this is a discover of the derivation, not a requirement.

I think that further postulates are required to link c in this derivation to the speed of light (such as the postulate you quoted from Wikipedia) or to a limiting speed (such as rules about momentum and kinetic energy, or a causality postulate).

Excuse my blutness but horseshit. Point out a specific item please.
Your "Three clock Paradox".
You have failed to demonstrate the ability to correctly state the predictions of SR in that situation.


Here's a similar textbook exercise:
19. Modified twin paradox ***
Consider the following variation of the twin paradox. A, B, and C each have a clock.
In A’s reference frame, B flies past A with speed v to the right. When B passes A, they both set their clocks to zero.
Also, in A’s reference frame, C starts far to the right and moves to the left with speed v. When B and C pass each other, C sets his clock to read the same as B’s.
Finally, when C passes A, they compare the readings on their clocks. At this event, let A’s clock read TA, and let C’s clock read TC.

(a) Working in A’s frame, show that TC = TA/γ, where γ = 1/√(1-v²/c²).
(b) Working in B’s frame, show again that TC = TA/γ.
(c) Working in C’s frame, show again that TC = TA/γ.

Let me know when you've done it, and we'll check your results.
If you like, you can set v to 0.866c, and just report TA and TC calculated in the three reference frames (or any other frame you like).

Remember, we're looking for textbook results - what does SR actually predict?

But, the deriviation does not require that all frames must be inertial, it only stipulates that the theory being developed can only be applied in inertial frames - it is silent about what applies in accelerating frames. If this is what you mean, then yes, I agree. However - special relativity only applies to inertial reference frames because it assumes (assumption<->postulate) all frames will be inertial reference frames when you use the equations it derives - that's all I'm saying and that's all Special Relativity says.


It certainly doesn't require that accelerating frames do not exist. (That would be a postulate). You are mixing "do not exist" and "do not apply".

As I said, I will comment on the rest later - hopefully tomorrow. I don't want to look at derivations right now. :D

I was editing the relevant paragraph to make it clearer when you replied... sorry!

Correct application of the derived transform requies that it is only used to transform between inertial frames. This does not assume that all frames are inertial. It only means that the derived transform does not apply to accelerating frames.

You are mixing "do not exist" and "do not apply".
When I say "do not apply", that's what I mean.
When I say "do not exist", that's what I mean.
I think that your proposed postulate implied that the derivation requires that accelerating frames do not exist - and I disagree with that implication.

I think we really agree with each other on this point, and are just niggling over the terminology?


Thanks for the exercise - I'm enjoying it!

Your "Three clock Paradox".
You have failed to demonstrate the ability to correctly state the predictions of SR in that situation.

Not so fast. Please give a specific post. As I recall that thread went for quite some time and there were many debates about how to synchronize clocks, etc. The fact is the only rebutals were in the form of fiat and rhetoric. That did not invalidate my point.

Pick a specific issue where I did not know (do not count some mathematical slip) the relavistic process.

I have posted numerous Velocity Addition scenarios and provided calculations for them. A couple very recently. i.e. A = - 0.577c , B = 0.577c; AB relavistic veloicty = 0.866c.

I also answered your first post in another thread where I was challenged to do such a calculation. You admitted I posted a correct answer. 0.72c (Actually 0.713....)

Why should I now continue to do exercises for the same process over and over?

I suggest it is more efficient for you to show error in my arguement that spatial contraction only exists when you disregard the known physical fact that the clock in motion is time dilated than it is for me to repeat SR calculations.

814711
Why don't you try instead to actually address the A/B with relative velocity = 0.866c issue SRT gamma = 2.000; when it is then pointed out that they are mutually dilated because they were launched in opposite directons at 0.433c (ignoring velocity addition) and therefore accumulate no systemic time dilation between them and are instead dilated by a gamma of 1.109 relative to their common rest frame.

In an arbitrary inertial frame:
A has velocity 0.433c
B has velocity -0.433c

You say that "SRT gamma = 2.000", by which I assume you mean that SR predicts that A's clocks will be dilated by a factor of 2 in B's frame, and vice versa.

814711


In an arbitrary inertial frame:
A has velocity 0.433c
B has velocity -0.433c

You say that "SRT gamma = 2.000", by which I assume you mean that SR predicts that A's clocks will be dilated by a factor of 2 in B's frame, and vice versa.

Thank you for that clarification. Now others can see what realy goes on here. Here is an extract of the actual post.

*********************** Extract *******************
Also do not pretend to suggest that I do not understand the contorted suggestion being made by relativity about space-time. Why don't you try instead to actually address the A/B with relative velocity = 0.866c issue SRT gamma = 2.000; when it is then pointed out that they are mutually dilated because they were launched in opposite directons at 0.433c (ignoring velocity addition)
************************************************

Enough said.

Enough said indeed.

You have failed to demonstrate the ability to correctly state the predictions of SR in that situation.

Excuse my blutness but horseshit. Point out a specific item please.
832568
B and C have relative velocity but you cannot determine relavistic affect without knowing their respective velocities to their common rest frame.
(where "common rest frame" is acknowledged to mean "The frame in which the objects were last at rest with respect to each other")

Enough said indeed.

You have failed to demonstrate the ability to correctly state the predictions of SR in that situation.

Pardon me Pete but screw you. I made it very clear in that thread several times that I was disregarding veloicty addition to simplify the demonstration and make it more clear to others that would be confused by the fact that in SR 2+2 does not = 4.

Further more later in that thread when this sort of BS got posted regarding not using ther term I calculated it using the VAF and posted a complete and proper answer. So stick it in your ear. :D

Further more later in that thread when this sort of BS got posted regarding not using ther term I calculated it using the VAF and posted a complete and proper answer.
Not so fast. Please give a specific post.

832568

(where "common rest frame" is acknowledged to mean "The frame in which the objects were last at rest with respect to each other")

What is your point here?

Not so fast. Please give a specific post.

Considering:

1 - You just altered one of my posts to claim I didn't know relativity by trunticating my statement.

2 - That I have posted numerous velocity addition calculations correctly, I am not inclined to go back and search threads and play games. I understand VAF and properly compute it when required. I have frequently posted scenarios which exclude the VAF because its inclusion does not alter the conclusion but confuses the issue.

Have it your way.
Unsupported assertions will get you nowhere.

Excuse my blutness but horseshit. Point out a specific item please.
832668
I have frequently posted scenarios which exclude the VAF because its inclusion does not alter the conclusion but confuses the issue.

Have it your way.
Unsupported assertions will get you nowhere.

Your charge or innuendo regarding my knowledge of relativity, specifically the velocity addition formula, goes nowhere since I have repeatedly posted correct VAF scenarios and resonses to that issue.

I have no need to go and prove further that I have correctly done so in response to you posting an apparent incorrect -0.433c and 0.433c = 0.866c by me, when I continued to point out I was specifically disregarding the VAF but you altered that fact by deleting (trunticating) that part of my post..

Mac, knowing the velocity addition formula is trivial.
Understanding where it comes from, its place in relativity, and how to apply it correctly in non-trivial situations is what you lack. Your choice to ignore it was a case in point. Another is in this post.
What is your point here?
It's another example of your lack of understanding of SR.

Really, Mac, why not read a textbook and find out what relativists really think, instead of just pretending that you know?

Mac, knowing the velocity addition formula is trivial.
Understanding where it comes from, its place in relativity, and how to apply it correctly in non-trivial situations is what you lack. Your choice to ignore it was a case in point. Another is in this post.

It's another example of your lack of understanding of SR.

Really, Mac, why not read a textbook and find out what relativists really think, instead of just pretending that you know?

This post seems to stand all by itself. It doesn't relate to anything I said in the post you cited. Perhaps you might be so kind as to try and be specific.

Did I say something wrong about velocity addition? No.

Did I miswrite the formula? No

Have I computed incorrect veloicties using veloicty addition? No.

Are you claiming you reject the concept of symmetry of motion and the lack of time dilation in such cases? I should hope not.

Be specific and stop casting unsupported innuendo.

I gave you specifics, Mac. Are you incapable of following links? You don't seem to be able to follow threads very well.

Don't make me hold your hand through it, Mac - I haven't got the time.

Why don't you read a book about it? Are you afraid you'll learn something?

Hello Pete,
sorry about not getting back on the derivation issue. I just haven't had the time or desire to do it. As such - I don't want to leave you or anyone else hanging so I will just reproduce my notes on Einstein's derivation (which I think is a lot better anyway). Unfortunately I do not have any of the notes on this computer, but I did post them on physicsforums a long time ago, so I'll reproduce just as much of the notes as appear there:

These are notes on Einstein's derivation of the Lorentz transformations as appear here (http://www.bartleby.com/173/a1.html). Please note that "assumption" is actually a little bit different than "postulate", where an assumption is something that must hold true for the model in which the equations were formed and a postulate is an assumption about the nature of the universe. I believe this was confused before.



x-ct=0 ..............................[1]
x'-ct'=0 ............................[2]
(x'-ct')=l(x-ct) ....................[3]

Equation 3 is "fulfilled in general" which means that x and x' are not the same in equations 1 & 2 as they are in equation 3. Equations 1 & 2 desiginate the coordinates of a photon fired from x=x'=0 at t=t'=0 whereas equation 3's x & x' need not be the coordinate of the said photon (Otherwise equation 3 would simplify from 1 & 2 as 0=l*0 and be useless). Instead, equation 3 is the relative position of the photon to an object at an arbitrary postion x or x'.

assumption:
(1) x=x'=0 at t=t'=0

x'+ct'=m(x+ct) ......................[4]

Equation 4 is an expression that accounts for the relative positions x and x' from a photon fired in the opposite direction, that is along the negative x-axis. It is the use of this equation that causes reciprocity for these two condtions: (1) frame S' moving with speed v relative to S and (2) frame S moving with speed -v relative to S'. This equation is invalid unless the following assumption is made.

assumption:
(2) Light travels at a constant speed in all directions for any inertial frame.

Equations 3 & 4 can be added and subtracted to get equation set 5:

x'=ax-bct
ct'=act-bx
...where: ...........................[5]
......a=(l+m)/2
......b=(l-m)/2

I'll include the rest of the notes as soon as I am on the computer that contains them. If my notes don't seem detailed enough - it is because I wrote them for myself and not others.

I gave you specifics, Mac. Are you incapable of following links? You don't seem to be able to follow threads very well.

Don't make me hold your hand through it, Mac - I haven't got the time.

Why don't you read a book about it? Are you afraid you'll learn something?

I see you and James R both are down to making attacks and not responding in a physics manner. Hmmmm.

I see you are now down to simply whinging, and have given up trying to make actual arguments, MacM.

Mac,
Since you're incapable of clicking a link and following a thread, I'll spell it out for you (this is very tedious, you know.)

In this thread:

XGen said:
What will happens however in the following case:
v<----------B A C---------->

C and B are moving in opposite directions...
[ snip ]
... but their relative velocity used by SRT will be 0!
I said:
In fact, the relative velocity predicted by SR between B and C is 2v/(1+v²/c²)
Then you came up with this gem:
You have just quoted a modified version of the Velocity Addition Formula. It predicts the terminal velocity of a missle fired from a shuddlecraft as viewed by the stationary mothership observer. You have taken v and u being equal as being mathematically equilvelent to 2v. Which is acceptable mathematically.

w = (v + u) / ( 1+ (vu)/c²).

In addition to that fact you are incorrect. Where two objects are launched in opposite directions the relative velocity between them as viewed by them is the collective velocity.

If you want to argue this point I suggest you provide direction to SR's rules on just how you know which formula to apply when you come across two objects in relative motion and know nothing about the origin of that motion. :D

Your reply illustrates your ignorance of special relativity, as anyone with knowledge of the field can see.

Do you have any substantive response, or are you reduced to whinging and wriggling?



Put up or shut up, Mac - you're boring me.

If you want to shut me up, just take the challenge: do the Modified Twin Paradox exercise posted in this thread.

I really don't think you can, and I think you'll go to any lengths to avoid doing it. Prove me wrong!

I see you are now down to simply whinging, and have given up trying to make actual arguments, MacM.

I must repeat my post above.

I see you and James R both are down to making attacks and not responding in a physics manner. Hmmmm.

You call it an attack, I call it a challenge.
Whatever it is, it's a clear indictment of your inability to apply SR.

You call it an attack, I call it a challenge.
Whatever it is, it's a clear indictment of your inability to apply SR.

Ill thought out rhetoric. Show one error in my mathematics. James R has already confirmed the mathematics is correct.

The maths isn't worth a damn if it's applied incorrectly, Mac. Any monkey can plug numbers into a formula.

The maths isn't worth a damn if it's applied incorrectly, Mac. Any monkey can plug numbers into a formula.

So say how you think it was applied incorrectly. You are simply talking nonsense at this point.