Light sphere question

cfrogue

Also, if you run this point through LT,

x = λvt/(1+λ)

t' = t( t - vx/c² )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

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?
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'² + y'² + z'² = τ²c², 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

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

I get x=(vt)λ

JesseM

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

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.

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

Good one.

Thanks. That works.

DaleSpam

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?

atyy

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

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

Agreed.

cfrogue

Well, you could be more specific.

NGC String Band Bolero

DaleSpam

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

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

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.