SR and c measurement

[vuquta]

I'm not sure what you're trying to show here. r/c is the time it takes light to travel a distance r. The transforms won't work, and don't purport to work, on a frame traveling at c.

 

I did not say the frame traveled at c. Where did you get this?

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I'm not sure what you're trying to show here. r/c is the time it takes light to travel a distance r. The transforms won't work, and don't purport to work, on a frame traveling at c.

 

While we are on the subject, have you figured out yet, SR requires each frame's light emission point is valid and they diverge after light emission?

 

That implies multiple light spheres.

[swansont]

I did not say the frame traveled at c. Where did you get this?

 

You used those coordinates, yet they are unphysical. You say the LT fails, but you have used coordinates that are not valid. The position r, at a time r/c, is not a possible origin for reference frame that was co-located at t=0.

 

While we are on the subject, have you figured out yet, SR requires each frame's light emission point is valid and they diverge after light emission?

 

That implies multiple light spheres.

 

So?

[vuquta]

You used those coordinates, yet they are unphysical. You say the LT fails, but you have used coordinates that are not valid. The position r, at a time r/c, is not a possible origin for reference frame that was co-located at t=0.

 

So?

 

First, I did not say LT fails. I said LT is not consistent with time dilation combined with the measure at c logic.

 

So, are you contending if the clock at the origin of light emission reads r/c, then it is false that light proceeds a distance r in all directions?

 

That means the measure at c logic of SR is false.

[swansont]

First, I did not say LT fails. I said LT is not consistent with time dilation combined with the measure at c logic.

 

I don't know what "the measure at c logic" means.

 

So, are you contending if the clock at the origin of light emission reads r/c, then it is false that light proceeds a distance r in all directions?

 

OK, I see I mistook what you were trying to show.

 

Where exactly does the transform of (r,0,0,r/c) and (-r,0,0,r/c) fail?

[vuquta]

I don't know what "the measure at c logic" means.

 

It means the light path is precisely the absolute path between the emission point in the frame and the light receiver.

 

 

OK, I see I mistook what you were trying to show.

 

Where exactly does the transform of (r,0,0,r/c) and (-r,0,0,r/c) fail?

 

Oh, Einstein made the following claim:

 

We now have to prove that any ray of light, measured in the moving system, is propagated with the velocity c, if, as we have assumed, this is the case in the stationary system; for we have not as yet furnished the proof that the principle of the constancy of the velocity of light is compatible with the principle of relativity.

 

At the time t = τ = 0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then

 

x² +y² +z² =c² t² .

 

Transforming this equation with the aid of our equations of transformation we obtain after a simple calculation

 

ξ² + η² + ς² = c² τ²

 

The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system. This shows that our two fundamental principles are compatible.5

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

As such, he claims the light sphere by LT translation is also spherical in the moving frame after LT translation.

 

He chose an arbitrary point (x, y, z) on the light sphere x² +y² +z² =c² t² , which is a sphere, translated it and correctly said ξ² + η² + ς² = c² τ².

 

So, he is claiming LT preserved the light sphere again by asserting "The wave under consideration is therefore no less a spherical wave with velocity of propagation c when viewed in the moving system" after LT translation.

 

This requires like the stationary light sphere for all (x,y,z) on the light sphere c² t² is a constant, to make his assertion, it would need to be the case that for all (x,y,z) on the stationary light sphere, c² τ². AFTER translation by LT.

 

But, by using (x,y,z) on the light sphere equal (r,0,0,r/c) and (x,y,z) equal (-r,0,0,r/c), we find different values for c² τ². and hence LT did not preserve the light sphere as Einstein claimed he proved.

[swansont]

But, by using (x,y,z) on the light sphere equal (r,0,0,r/c) and (x,y,z) equal (-r,0,0,r/c), we find different values for c² τ². and hence LT did not preserve the light sphere as Einstein claimed he proved.

 

Show your work.

[vuquta]

Show your work.

 

Agreed.

 

Given the clock in the moving frame is time dilated at the light emission point, that clock will elapse t/γ when the stationary frame elapses t.

 

In particular, when the clock in the stationary frame elapses rγ/c, the clock in the moving frame elapses r/c.

 

If you disagree, then there is no point in proceeding.

[mooeypoo]

I have to be a bit of a pedant here and remind you, vuquta, PLEASE, to be a bit more vigilant with your definitions and math.

 

But, by using (x,y,z) on the light sphere equal (r,0,0,r/c) and (x,y,z) equal (-r,0,0,r/c), we find different values for c² τ². and hence LT did not preserve the light sphere as Einstein claimed he proved.

 

You mean, I assume, (x,y,z,t) to fit (r,0,0,r/c), seeing as you plug in 4 values into a supposedly three-dimensional coordinate system.

 

This might sound pedantic and petty, but it is important. You're forgetting those, and you're confusing us and yourself. It's not the only thing, too. Please try to take the time and be accurate seeing as there seems to be a confusion here on what "coordinate system" means, "reference frame" means, and how things move at c and don't move at c.

 

Without language, we can't communicate. Please try to be a bit more accurate.

[vuquta]

I have to be a bit of a pedant here and remind you, vuquta, PLEASE, to be a bit more vigilant with your definitions and math.

 

 

 

You mean, I assume, (x,y,z,t) to fit (r,0,0,r/c), seeing as you plug in 4 values into a supposedly three-dimensional coordinate system.

 

This might sound pedantic and petty, but it is important. You're forgetting those, and you're confusing us and yourself. It's not the only thing, too. Please try to take the time and be accurate seeing as there seems to be a confusion here on what "coordinate system" means, "reference frame" means, and how things move at c and don't move at c.

 

Without language, we can't communicate. Please try to be a bit more accurate.

 

Yes, I meant 4-D.

[mooeypoo]

Agreed.

 

Given the clock in the moving frame is time dilated at the light emission point, that clock will elapse t/γ when the stationary frame elapses t.

 

In particular, when the clock in the stationary frame elapses rγ/c, the clock in the moving frame elapses r/c.

 

If you disagree, then there is no point in proceeding.

That's not 'showing' your work, it's reiterating your claim.

 

Show your work means show us the math you claim disproves Einstein's.

[swansont]

By "show your work" I meant do the transforms and show the answer.

[vuquta]

By "show your work" I meant do the transforms and show the answer.

 

that is simple algebra.

 

(r,0,0,r/c) results in

 

t' = r/c(√( (c+v)/(c-v)))

 

(-r,0,0,r/c) results in

 

t' = r/c(√( (c-v)/(c+v)))

 

So, the stationary light sphere does not map into the moving light sphere.

 

In other words, for LT to be consistent, it must map to a light sphere in the moving frame with t' = r/c from the stationary light sphere.

 

LT does not do this.

 

Further, LT does not map the origin of the light sphere frame to frame.

 

So, under LT, the origin is not mapped and there does not exists a time in the stationary frame such that the moving frame will see a light sphere.

 

In fact, on the time interval

[r/c(√( (c-v)/(c+v))), r/c(√( (c-v)/(c+v)))]

 

LT claims the moving frame is seeing r/c.

[swansont]

that is simple algebra.

 

(r,0,0,r/c) results in

 

t' = r/c(√( (c+v)/(c-v)))

 

(-r,0,0,r/c) results in

 

t' = r/c(√( (c-v)/(c+v)))

 

So, the stationary light sphere does not map into the moving light sphere.

 

In other words, for LT to be consistent, it must map to a light sphere in the moving frame with t' = r/c from the stationary light sphere.

 

LT does not do this.

 

Further, LT does not map the origin of the light sphere frame to frame.

 

So, under LT, the origin is not mapped and there does not exists a time in the stationary frame such that the moving frame will see a light sphere.

 

In fact, on the time interval

[r/c(√( (c-v)/(c+v))), r/c(√( (c-v)/(c+v)))]

 

LT claims the moving frame is seeing r/c.

 

Show your work.

 

I did the transform substitution and AFAICT it came out just fine.

[vuquta]

Show your work.

 

I did the transform substitution and AFAICT it came out just fine.

 

Yes, they come up wit two different times.

 

That means we do not have a light sphere. If SR is consistent, it should preserve the light sphere such that the result is a light sphere.

 

Worse the clock at the origin of the moving frame moves with the frame and beats time dilated.

[swansont]

If you take the transform equations and use x = ct, then you get ξ² = c² τ². This satisfies the equation for a sphere.

[vuquta]

If you take the transform equations and use x = ct, then you get ξ² = c² τ². This satisfies the equation for a sphere.

 

This is is true for all x = ct?

 

I think not. It is true for one light beam only and not for all mappings.

 

One mapping has ξ² = c² τ², but for another, τ is a different value.

 

How is that a sphere?

 

Also, what does the clock read at the origin of the moving light sphere?

 

2.7 The Sagnac Effect

 

Quantitatively, if we let w denote the angular speed of the loop, then the circumferential tangent speed of the end point is v = wR, and the sum of the speeds of the pulses and the receiver at the "end" point is c-v in the co-rotating direction and c+v in the counter-rotating direction. Both pulses begin with an initial separation of 2pR from the end point, so the difference between the travel times is

 

http://www.mathpages.com/rr/s2-07/2-07.htm

[swansont]

This is is true for all x = ct?

 

It works in general for all x^2 = c^2t^2, because that's the substitution you make. Try it. Transform x and t into the K' system, using general terms, and see what happens. It works.

 

So if you try it and it fails, you are making an error.

 

edit: I think it's in the details of the derivation.

 

For a ray of light emitted at the time τ in the direction of the increasing ξ

 

So the assumption is that you are sending the light in the positive direction. When you use x = ct, how can you come up with a negative x? You are introducing a negative sign that's not in the equation. The transform looks different when you go in the negative direction.

 

 

2.7 The Sagnac Effect

 

Quantitatively, if we let w denote the angular speed of the loop, then the circumferential tangent speed of the end point is v = wR, and the sum of the speeds of the pulses and the receiver at the "end" point is c-v in the co-rotating direction and c+v in the counter-rotating direction. Both pulses begin with an initial separation of 2pR from the end point, so the difference between the travel times is

 

http://www.mathpages.com/rr/s2-07/2-07.htm

 

How is the Sagnac effect relevant here?

Edited April 5, 2010 by swansont

[vuquta]

It works in general for all x^2 = c^2t^2, because that's the substitution you make. Try it. Transform x and t into the K' system, using general terms, and see what happens. It works.

 

So if you try it and it fails, you are making an error.

 

edit: I think it's in the details of the derivation.

 

For a ray of light emitted at the time τ in the direction of the increasing ξ

 

So the assumption is that you are sending the light in the positive direction. When you use x = ct, how can you come up with a negative x? You are introducing a negative sign that's not in the equation. The transform looks different when you go in the negative direction.

 

 

 

I am not operating in the moving frame.

 

First, I send a beam down the positive x-axis at co-location of O and O'.

 

Then, I allow rγ/c to elapse on the O clock. Time dilation forces r/c to elapse on the clock at the origin of the O' clock.

 

Do you see this part?

[swansont]

I am not operating in the moving frame.

 

First, I send a beam down the positive x-axis at co-location of O and O'.

 

Then, I allow rγ/c to elapse on the O clock. Time dilation forces r/c to elapse on the clock at the origin of the O' clock.

 

Do you see this part?

 

You let r/c elapse on the O clock, by the numbers you've previously given.

 

You're using x = ct. How is it that you can come up with a negative value for x for positive t? That's also the reason the transforms are failing — there's a missing (or extra) minus sign.

[vuquta]

You let r/c elapse on the O clock, by the numbers you've previously given.

 

You're using x = ct. How is it that you can come up with a negative value for x for positive t? That's also the reason the transforms are failing — there's a missing (or extra) minus sign.

 

No this does not explain it.

 

It is simple time dilation along the positive x-axis.

 

I am not talking about the negative x-axis right now.

 

So, does the clock at the origin of the moving frame elapse r/c when the clock in the stationary frame elapses rγ/c, or is time dilation false?

[swansont]

No this does not explain it.

 

It is simple time dilation along the positive x-axis.

 

I am not talking about the negative x-axis right now.

 

So, does the clock at the origin of the moving frame elapse r/c when the clock in the stationary frame elapses rγ/c, or is time dilation false?

 

You get what the transforms tell you. If you apply them properly, that is.

[mooeypoo]

Okay, instead of arguing back and forth about how the transforms would look like if vuquta tries them, how about we skip the argument and vuquta actually tries them. Can you try, please, vuquta?

 

That would end this circular argument one way or another; either vuquta *shows* swansont where he is wrong and you can talk about it, or vuquta finds out that he is wrong and you can talk about it.

 

So much more helpful.

[swansont]

Which he can't because at the root of this is the fact the the Lorentz transform is simply math (algebra, and geometry if you consider the symmetry groups involved). It is self-consistent. As such, it is IMPOSSIBLE to come up with a situation where a valid solution to the math contradicts another valid solution. That would be at odds with the math being self-consistent. The only way to get a contradictory answer in the math is to do the math wrong (algebra error, or introduce a constraint that is inconsistent with the math, like the absolute simultaneity arguments we've seen)

 

Now, all of that is completely separate from the physics of whether or not Lorentz Transforms describe what we see in nature. Galilean transforms, for example, are another mathematically consistent bit of math. You can do them to your heart's content and will get consistent answers (if you do them right), but they do not describe reality; they are approximately correct at low speeds and are thus useful, but fail when speeds approach c. There's nothing wrong with the math — it's just that the math doesn't match up with experiment. And science is all about insisting that theory match up with experiment.

 

Proving that the Lorentz transforms give conflicting answers is an exercise in pure math and is impossible, because the math is self-consistent.

 

Proving Lorentz transforms do not describe reality is possible, because science is inductive. It will be exceedingly hard to do, because we have 100+ years of experiment that show that relativity is correct.

 

——

 

I also note that I find the "hydra" approach to this to be quite annoying: one scenario is shot down, and another one pops up to take its place. But they all suffer from the same fatal flaw I've described above. (This is different from the pop-gun-arcade approach of the long line of different, but incorrect arguments that are paraded, as seen in e.g. creationism and global warming arguments. But I digress … )

[vuquta]

Okay, instead of arguing back and forth about how the transforms would look like if vuquta tries them, how about we skip the argument and vuquta actually tries them. Can you try, please, vuquta?

 

That would end this circular argument one way or another; either vuquta *shows* swansont where he is wrong and you can talk about it, or vuquta finds out that he is wrong and you can talk about it.

 

So much more helpful.

 

Sure, but I am also working from another angle that is legal.

 

I am using time dilation and the light sphere.

 

Here is LT. Other places I debate do not think I have a problem with LT and they are correct.

 

x' = ( x - vt )γ

 

t' = ( t - vx/c² )λ

 

The issue under consideration is t = rγ/c and x = rγ..

 

Simple plug and chug.

 

x' = r( λ² - v λ²/c)

 

OK.

 

Now, do you folks want to continue with time dilation and the light sphere?

 

When time elapses in rγ/c at O, the clock at the origin O' elapses r/c, yes or no.

 

If the clock at O' elapses r/c, then light is a distance r in all directions in the frame of O', yes or no.

 

 

If you all do not want to talk, just say so and I will leave. I have plenty other places where I go.

 

Just let me know.

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Which he can't because at the root of this is the fact the the Lorentz transform is simply math (algebra, and geometry if you consider the symmetry groups involved). It is self-consistent. As such, it is IMPOSSIBLE to come up with a situation where a valid solution to the math contradicts another valid solution. That would be at odds with the math being self-consistent. The only way to get a contradictory answer in the math is to do the math wrong (algebra error, or introduce a constraint that is inconsistent with the math, like the absolute simultaneity arguments we've seen)

 

Now, all of that is completely separate from the physics of whether or not Lorentz Transforms describe what we see in nature. Galilean transforms, for example, are another mathematically consistent bit of math. You can do them to your heart's content and will get consistent answers (if you do them right), but they do not describe reality; they are approximately correct at low speeds and are thus useful, but fail when speeds approach c. There's nothing wrong with the math — it's just that the math doesn't match up with experiment. And science is all about insisting that theory match up with experiment.

 

Proving that the Lorentz transforms give conflicting answers is an exercise in pure math and is impossible, because the math is self-consistent.

 

Proving Lorentz transforms do not describe reality is possible, because science is inductive. It will be exceedingly hard to do, because we have 100+ years of experiment that show that relativity is correct.

 

——

 

I also note that I find the "hydra" approach to this to be quite annoying: one scenario is shot down, and another one pops up to take its place. But they all suffer from the same fatal flaw I've described above. (This is different from the pop-gun-arcade approach of the long line of different, but incorrect arguments that are paraded, as seen in e.g. creationism and global warming arguments. But I digress … )

 

Proving that the Lorentz transforms give conflicting answers is an exercise in pure math and is impossible, because the math is self-consistent.

 

Math theory does not model anything.

 

LT models light travel and relative inertial motion.

 

Apples and oranges.

 

 

Well, instead of making proclamations you cannot prove, let's see where I go. Here you are claiming LT is exactly the same thing as math theory.

 

I am betting otherwise, I must put up or shut up.

 

I say we find out whether I can do this one way or the other.

 

I have 3 ways. I am proceeding with the easiest.

Edited April 6, 2010 by vuquta
Consecutive posts merged.

[mooeypoo]

Sure, but I am also working from another angle that is legal.

But you keep claiming A, you were asked to show A, and now you say you have way B.

 

Please stick to a claim. You need to show us the transforms because you claim they fail. Either show it, or stop claiming it.

 

~moo