Light sphere question


by cfrogue
Tags: light, sphere
cfrogue
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#577
Dec9-09, 05:23 PM
P: 687
Quote Quote by JesseM View Post
Why do you say it's false? If we set y and z to zero (so we're only looking at where the light is on the x-axis), then x' + y' + z' = t'c reduces to t'c = x' which is the same as ct' = x'.
Because we proved there exists two different t's in O such that ct' = x' is satisified and this violates logical consistancy.

So, I am saying that is not the way to approach the SR light sphere.

If it is approached as t increases and each point is transformed to satisfy,
x' + y' + z' = τc
then we have logical consistancy.

On the other hand, if we include x', we get different length radii for each directiion due to the simultaneity difference in each direction of the light ray in O.

It can only be approached as taking each spacetime coord in O and LT'ing it, then applying
x' + y' + z' = τc


That is why I say the normal logic of ct' = x' does not work.

The following points in O satisify that condition

t1=r/(λ(c-v)) for the ray point right and
t2=r/(λ(c+v)) for the ray point left.

If you run these through LT with x=+ct and x=-ct as appropriate, you will find two different satisfactions of the equation ct' = x' at two different times in O which creates two different light spheres which is a logical inconsistancy.
cfrogue
cfrogue is offline
#578
Dec9-09, 05:29 PM
P: 687
I have concluded LT will not give me the center of the light sphere after and time t in the frame of O.

I realize Einstein assumed it is at vt.

Does anyone have anything else on this that I am not seeing?
cfrogue
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#579
Dec9-09, 05:34 PM
P: 687
Also, if you run this point through LT,

x = λvt/(1+λ)

t' = t( t - vx/c )λ

You will find t' = t with collinear relative motion.

Thus, we must be very careful not to conclude LT decides time dilation between frames.
JesseM
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#580
Dec9-09, 05:48 PM
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Quote Quote by cfrogue View Post
Because we proved there exists two different t's in O such that ct' = x' is satisified and this violates logical consistancy.
What violates logical consistency? I don't see anything illogical about the fact that there can be two events with values of (x,t) that satisfy ct = x, and with t being different for each event, such that when you apply the Lorentz transformation to the (x,t) coordinates of each event to get the (x',t') coordinates of the same event, then both events can have (x',t') coordinates that satisfy ct' = x' but with the new feature that the t' coordinate is the same for each event. Are you saying this is illogical or impossible?
Quote Quote by cfrogue
That is why I say the normal logic of ct' = x' does not work.

The following points in O satisify that condition

t1=r/(λ(c-v)) for the ray point right and
t2=r/(λ(c+v)) for the ray point left.

If you run these through LT with x=+ct and x=-ct as appropriate, you will find two different satisfactions of the equation ct' = x' at two different times in O which creates two different light spheres which is a logical inconsistancy.
Again, what's a logical inconsistency? These events occur at different times in O, so naturally they are part of two different light spheres at different times in O. The equation ct = x was never supposed to define a single light sphere, rather it is an equation defining all points that lie on the light cone in 1D, it can include events at different times in O. Exactly the same is true of the equation x' + y' + z' = τc, τ is a variable so this too is the 3D version of a light cone which includes events that lie on the path of the light at different times in O.
JesseM
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#581
Dec9-09, 05:50 PM
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Quote Quote by cfrogue View Post
I have concluded LT will not give me the center of the light sphere after and time t in the frame of O.

I realize Einstein assumed it is at vt.
Why have you concluded that? The center of the light sphere in O' is always at x'=0, and if you apply Lorentz transformation to some event which has an x' coordinate of 0 you'll always get an event whose x and t coordinates satisfy x=vt. Do you disagree? If not, what's the problem?
cfrogue
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#582
Dec9-09, 05:56 PM
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Quote Quote by JesseM View Post
Why have you concluded that? The center of the light sphere in O' is always at x'=0, and if you apply Lorentz transformation to some event which has an x' coordinate of 0 you'll always get an event whose x and t coordinates satisfy x=vt. Do you disagree? If not, what's the problem?
I get x=(vt)λ
JesseM
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#583
Dec9-09, 06:00 PM
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Quote Quote by cfrogue View Post
I get x=(vt)λ
Suppose the event has coordinates x'=0, t'=T' in O'. Then the coordinates in O are:

x = gamma*(x' + vt') = gamma*vT'
t = gamma*(t' + vx'/c^2) = gamma*T'

So, x/t = (gamma*vT')/(gamma*T') = v, and if x/t=v then x=vt.
cfrogue
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#584
Dec9-09, 06:02 PM
P: 687
Originally Posted by cfrogue
Because we proved there exists two different t's in O such that ct' = x' is satisified and this violates logical consistancy.
Quote Quote by JesseM View Post
What violates logical consistency? I don't see anything illogical about the fact that there can be two events with values of (x,t) that satisfy ct = x, and with t being different for each event, such that when you apply the Lorentz transformation to the (x,t) coordinates of each event to get the (x',t') coordinates of the same event, then both events can have (x',t') coordinates that satisfy ct' = x' but with the new feature that the t' coordinate is the same for each event. Are you saying this is illogical or impossible?
No, I am saying uisng that method creates two different light spheres. I gave you the points. Use them and apply the radius in both directions.

Quote Quote by JesseM View Post
[
Again, what's a logical inconsistency? These events occur at different times in O, so naturally they are part of two different light spheres at different times in O. The equation ct = x was never supposed to define a single light sphere, rather it is an equation defining all points that lie on the light cone in 1D, it can include events at different times in O. Exactly the same is true of the equation x' + y' + z' = τc, τ is a variable so this too is the 3D version of a light cone which includes events that lie on the path of the light at different times in O.
I have been down this road.

It does not achieve anything. I created two different light spheres in O' because of the simultaneity differential of the direction of the light rays in O.

Yet, if I do strictly point by point transforms as suggested by Einstein, I have a consistant resolution.
cfrogue
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#585
Dec9-09, 06:03 PM
P: 687
Quote Quote by JesseM View Post
Suppose the event has coordinates x'=0, t'=T' in O'. Then the coordinates in O are:

x = gamma*(x' + vt') = gamma*vT'
t = gamma*(t' + vx'/c^2) = gamma*T'

So, x/t = (gamma*vT')/(gamma*T') = v, and if x/t=v then x=vt.
Good one.

Thanks. That works.
DaleSpam
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#586
Dec9-09, 06:15 PM
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Quote Quote by cfrogue View Post
I clearly see a difference of when an event will occur concerning light and time dilation.
Obviously. Time dilation requires Δx=0 and Δx never equals 0 for light, so there will always be a difference.
Quote Quote by cfrogue View Post
It is false that

ct' = x'
You already agreed it was true, and it was proved conclusively several different ways. If you want to suddenly go back and ignore the previous 570 posts then I am done with this. What is the point of continuing the conversation if you will just ignore that amount of proof?
atyy
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#587
Dec9-09, 06:20 PM
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Quote Quote by cfrogue View Post
Yet, if I do strictly point by point transforms as suggested by Einstein, I have a consistant resolution.
Yes, that is the only way to do it, and that is what I've been doing all along, although that was not apparent to you. Regardless, this is correct, and fundamental.
cfrogue
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#588
Dec9-09, 06:48 PM
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Quote Quote by DaleSpam View Post
Obviously. Time dilation requires Δx=0 and Δx never equals 0 for light, so there will always be a difference.
You already agreed it was true, and it was proved conclusively several different ways. If you want to suddenly go back and ignore the previous 570 posts then I am done with this. What is the point of continuing the conversation if you will just ignore that amount of proof?
I am the one that introduced ct' = +-x'.

That was my argument.

You did not prove anything to me about this.

Then, I discovered it created two light spheres. You agreed.

The question for you is how do you create logical consistancy with ct' = +-x'?

I would like to see this.
cfrogue
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#589
Dec9-09, 06:48 PM
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Quote Quote by atyy View Post
Yes, that is the only way to do it, and that is what I've been doing all along, although that was not apparent to you. Regardless, this is correct, and fundamental.
Agreed.
cfrogue
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#590
Dec9-09, 07:22 PM
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Quote Quote by atyy View Post
Yes, that is the only way to do it, and that is what I've been doing all along, although that was not apparent to you. Regardless, this is correct, and fundamental.
Well, you could be more specific.

NGC String Band Bolero
DaleSpam
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#591
Dec9-09, 10:07 PM
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Quote Quote by cfrogue View Post
The question for you is how do you create logical consistancy with ct' = +-x'?

I would like to see this.
We already demonstrated this more than 500 posts ago. If you would like to see it just use your browser to review the thread.
atyy
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#592
Dec9-09, 10:47 PM
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Quote Quote by cfrogue View Post
That is why I say the normal logic of ct' = x' does not work.

The following points in O satisify that condition

t1=r/(λ(c-v)) for the ray point right and
t2=r/(λ(c+v)) for the ray point left.

If you run these through LT with x=+ct and x=-ct as appropriate, you will find two different satisfactions of the equation ct' = x' at two different times in O which creates two different light spheres which is a logical inconsistancy.
Yes, these imply that there are two light spheres in O at two different times. But that is not a problem, since there are an infinite number of light spheres in O, one for each t.

Thus t1=r/(λ(c-v)), x1R=ct1 is one side of the light sphere in O at t1, whose other side must be t1=r/(λ(c-v)), x1L=-ct1, which by the LT you can check does lie on a light sphere of O'.

Smilarly, t2=r/(λ(c+v)), x2L=-ct2 is one side of the light sphere in O at t2, whose other side must be t2=r/(λ(c+v)), x2R=ct2, which by the LT you can check does lie on a light sphere of O'.
jtbell
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#593
Dec10-09, 01:07 AM
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With 592 posts plus this one, this thread has by far the most posts of any thread in the Relativity forum, ever. It's long overdue time to give it a rest. Thread closed.


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