I The velocity of a moving frame of reference

[RossBlenkinsop]

actually I think the frame chosen is irrelevant the simple question is if one of the moving light clocks is at rest wrt the point X1 Y1 will the time difference between the electric pulse delivered to the train tracks peak as measured by any other identical clock, not a rest wrt that point

and

as the direction of one of the moving light clocks, and the rate of movement of one of the moving light clocks, in any frame of reference, approaches a state where it is approaching being at rest wrt the point X1 Y1 will the time difference between the electric pulse approach a peak as measured by any other identical clock, not a rest wrt that point

appears to me the frame is irrelevant

any identical clock, in any frame, not at rest wrt the point x1 y1 will tick slower than an identical clock at rest wrt the point x1 y1

 

[RossBlenkinsop]

if an experiment can be devised where a light clock remains at rest wrt the point x1 y1 then that will be the peak tick rate for that clock in any frame and any other identical clock in any other frame will tick slower than that clock

I believe above I have devised such an experiment

 

[Ibix]

the point X1 Y1

This point is only a point in one frame. Basing an argument on the use of "a point" implies a frame.

It is true that your electrical signals are invariant, but this simply reflects the speed of the clock with respect to the rails. The same could be achieved with a radar set.

 

[RossBlenkinsop]

of course the light clock needs to be oriented is such a way that the long axis of the light clock is parallel to the incoming photons from the point X1 Y1

 

[Ibix]

I believe above I have devised such an experiment

Seriously? You think no one in over a century has ever considered two light clocks in relative motion? You're still well inside territory competent undergrads explore routinely. You're just analysing it incorrectly.

 

[RossBlenkinsop]

"the point is only a point in one frame"

a strobe goes off and photons emanate from that point in straight lines in all directions

the speed of photons is invariant in all frames

if in 1 million yrs time I meticulously traced those photons back along their trajectories to the point from which they emanated. is that an arbitrary point ?

 

[RossBlenkinsop]

for me to be wrong would be a breach of the laws of physics

 

[Ibix]

is that an arbitrary point ?

Yes. It depends which frame you use what that point is. Janus' two diagrams demonstrate this clearly. But it should be obvious.

Work in a frame where the light source is at rest. It emits a spherical wavefront. Backtrace the rays and you get to the light source.

Now work in a frame where the lightsource is moving. It emits a spherical wavefront. Backtrace the rays and you get to the place where the light source was, not where it is now. Thus this is a different point from the previous paragraph.

 

[RossBlenkinsop]

because the speed of light is invariant regardless of the elapsed time period elapsed tracing the trajectories of those photons will always lead back to the same point

its almost as if the point is at an absolute position in space

 

[RossBlenkinsop]

Yes. It depends which frame you use what that point is. Janus' two diagrams demonstrate this clearly. But it should be obvious.

Work in a frame where the light source is at rest. It emits a spherical wavefront. Backtrace the rays and you get to the light source.

Now work in a frame where the lightsource is moving. It emits a spherical wavefront. Backtrace the rays and you get to the place where the light source was, not where it is now. Thus this is a different point from the previous paragraph.

In both instances u retrace the photons trajectory to the point from which they emanated ! Just so happens in scenario 1 the actual light itself is at rest wrt the point x1 y1 ...your basically agreeing with me

 

[Ibix]

because the speed of light is invariant regardless of the elapsed time period elapsed tracing the trajectories of those photons will always lead back to the same point

You're clearly not even reading what I write, now. I just explained how this is not the case. Please re-read post #38 and say what you do not understand.

its almost as if the point is at an absolute position in space

This has been known to be meaningless for around three and a half centuries.

 

[RossBlenkinsop]

its almost as if the point is at an absolute position in space

that point cannot move, if it did that would mean the speed of light is not invariant

 

[Ibix]

In both instances u retrace the photons trajectory to the point from which they emanated ! Just so happens in scenario 1 the actual light itself is at rest wrt the point x1 y1 ...your basically agreeing with me

I am not even slightly agreeing with you. You claim that the place where the light is and a place where it isn't are the same place. That is clearly nonsense.

 

[RossBlenkinsop]

because the speed of light is invariant the 2 or more photons on the wave front must be exactly the same distance from the point X1 Y1 for all time

or in other words tracing back along the trajectories will always lead back to the same point, regardless of the frame used or the time period elapsed

 

[RossBlenkinsop]

or in other words the location of that point remains the same over time
and I am pretty sure if the location of something remains the same over time then that is the definition of "not moving"

 

[Ibix]

point X1 Y1

Again, this point is only stationary in one frame. In other frames, this point is moving and does not remain at the centre of the pulse.

in other words tracing back along the trajectories will always lead back to the same point

...but different frames will not agree what this point is and will all regard all other frames' "same points" as changing position.

in other words the location of that point remains the same over time

...according to the frame used to do the backtracing. Every other frame will come up with a stationary point too. But the whole point of different frames of reference is that they don't agree with each other what "stationary" means. They all regard the others' "stationary points" as moving, so there is no "absolutely stationary".

Look. Say the pulse is emitted at the origin in some frame. After time $t$ the pulse is at $x,y$ coordinates that satisfy $c^2t^2=x^2+y^2$. Always centred on $x,y=0,0$.

In another frame, the pulse was also emitted at the origin. After time $t'$ the pulse is at $x',y'$ coordinates that satisfy $c^2t'^2=x'^2+y'^2$. Always centred on $x',y'=0,0$.

But what is the Lorentz transform of $x,y=0,0$? It's $x',y'=-\gamma vt,0$, which is a moving point. The frames do not agree on what "where the light was emitted" means, except at the instant it was emitted.

I don't think I can state it more clearly than that, and it's 1am here. Signing off.

 

[Ibix]

Ugh. Thought of a way that might be clearer to you.

You agree that the strobe light is moving in one frame and stationary in the other. Thus it is (to use your terminology) "at rest with respect to X1,Y1" in one frame and not the other. But one of your light clocks was stationary with respect to the strobe light while the other was stationary in the frame where the strobe light is moving. Thus, which clock is "at rest with respect to X1,Y1" is different in the two frames.

Therefore the two frames disagree which clock ticks fastest.

I've put scare quotes around "at rest with respect to X1,Y1" because it's horrible and potentially misleading notation. It can, however, be made rigorous by adding bouys at the relevant coordinates at rest in the relevant frames. Naturally, they are moving with respect to one another.

Now I'm really going to sleep.

 

[Nugatory]

because the speed of light is invariant regardless of the elapsed time period elapsed tracing the trajectories of those photons will always lead back to the same point

That's just plain wrong, unless you are using the word "point" to mean a point in spacetime as opposed to a point in space (in which case we have more confusion from you using words differently than everyone else and should be using the word "event" because that's something completely different than a point in space).

or in other words the location of that point remains the same over time
and I am pretty sure if the location of something remains the same over time then that is the definition of "not moving"

No, the phrase "not moving" is completely meaningless unless you say what the the object in question is at rest relative to. And even then there's a lot to be said for being precise: "Using the coordinates assigned by a frame in which the spatial coordinates do not change...". This is some of what @Ibix was getting at in the post above when he said

I've put scare quotes around "at rest with respect to X1,Y1" because it's horrible and potentially misleading notation. It can, however, be made rigorous by adding bouys at the relevant coordinates at rest in the relevant frames. Naturally, they are moving with respect to one another.

If you can get hold of a copy of Taylor and Wheeler's book "Spacetime Physics", you will find it very helpful. An internet forum like this one is pretty good at pointing out errors and helping people over isolated hard spots, but not the best way of unwinding misunderstandings.

 

[Janus]

because the speed of light is invariant the 2 or more photons on the wave front must be exactly the same distance from the point X1 Y1 for all time

or in other words tracing back along the trajectories will always lead back to the same point, regardless of the frame used or the time period elapsed

You have three objects, A, B, and C in relative motion with respect to each other and all passing each other the same moment. As they pass each other, a light flash is emitted from them.
According to B, events unfold like this:

However, according to C, events unfold like this:

and according to A, they unfold like this:

Each of them measures the light flash as expanding out away from themselves at c.

If, after the last frame of each of these animations, you were to ask each of them to "retrace the light pulse to its origin, they would trace it back to themselves. But A B and C have separated and in three different points in the last frame, and so they would not agree that the rays trace back to the same spot.

 

[RossBlenkinsop]

well there is an absolute fact

if the speed of light is indeed invariant, regardless of what anyone perceives in any frame, measures in any frame doesn't measure in any frame what ever

if a light strobes at a point X1 Y1 simple maths tells us that 3 photons in the wave front will always triangulate back to the same point in space, for all time or aka that point remains in the same location for all time

if they don't triangulate back to that point then that means the speed of light is not invariant

so which is it is the speed of light not invariant or do the photons triangulate to a set point in space ?

 

[RossBlenkinsop]

there may be difficulty devising an experiment to measure where that point is but never the less
u can't have yr cake and eat it to

 

[Ibix]

if a light strobe at a point X1 Y1 simple maths tells us that 3 photons in the wave front will always triangulate back to the same point in space

Please state this maths. How is it different from what I laid out in #46, and which Janus presented diagramatically in #49? Remember to carry out the maths in two different frames and relate the locations in the two frames. If you do this correctly you will realize that "the same point in space" means different things to different frames. It is not an absolute.

the speed of light not invariant or do the photons triangulate to a set point in space ?

They "triangulate back" to different points according to different frames; the point one frame calls "stationary at the centre of the spherical pulse" other frames call "moving and not at the centre". I have stated this multiple times, both verbally and mathematically, and correct diagrams have been presented to you supporting this. That "a fixed point in space" is a frame-dependent notion, not an absolute one, dates back to Galileo and all of physics assumes the notion.

 

[RossBlenkinsop]

can you explain how a single strobing light with invariant speed photon can triangulate back to multiple centre points ?

 

[Ibix]

can you explain how a single strobing light with invariant speed photon can triangulate back to multiple centre points ?

I already did. See post #46.

 

[RossBlenkinsop]

so it is impossible to conclude that the speed of light is invariant then
ok

 

[Ibix]

so it is impossible to conclude that the speed of light is invariant then
ok

I used the invariance of $c$ in #46...

 

[Ibix]

I repeat: please state the "simple maths" that supports your assertion that there is an absolute frame-invariant point from which the light radiates. You claimed there was some in #50. I know, having done the maths myself and presented a sketch above, that this claim is wrong - so I want to see your maths. Obviously there's a mistake in it somewhere.

 

[RossBlenkinsop]

so what you are saying is if there is a single strobing light that strobes only once and 100 different ppl in 100 different frames, they all agree there is only one light and that it strobed once ,

but 3 photons on that wave front will map back to 100 different points

so what should they conclude from the results of that experiment ?

they cannot conclude there was 100 lights cos they all saw one and they can only conclude it strobed once

they would have to conclude there was 1 light simultaneously in 100 different locations
ok

 

[RossBlenkinsop]

or the other thing they could conclude is that there was one light at one location and there is something wrong with the ,measuring technique

Now

If they conclude there is one light at one location , then all roads lead to Rome

 

[Ibix]

so what should they conclude from the results of that experiment ?

Let's define your experiment better: one person is at rest with respect to the strobe. The other 99 are all in motion with respect to the first and to each other, and all pass the first person simultaneously. At the instant they pass him, he triggers the strobe. All one hundred people agree that the light flash happened at their location. Therefore when they subsequently back-trace the light rays they will always lead back to themselves because they each define themselves to be stationary. But they all agree that they are no longer in the same place. So they all disagree about what "where the flash happened" means.

There's nothing wrong with their measurement procedure. It's just ambiguous what "the same place" means, because there's no absolute standard of rest to define it. I don't really understand why you can't grasp this - it's been said enough times in enough different ways, and your own thought experiments lead to it if you analyse them correctly.

I'm still waiting for the "simple maths" that proves this wrong. It will never be forthcoming, of course, because there is no such thing.