MacM:
You're hopelessly confused, obviously. I have added directions "east" and "west" to the two versions, just to be clear.
A and B both end up moving away from C at speed 0.6c. They never go past C. So I don't know what you're saying here.
No you are confused the frames you specify exist over the entire universe so I can place the clocks anywhere in the universe in that frame. I placed them to cross past C simultaneously as stated just to simplify the result. I have not altered your scenario or the actual results that will be supported by emperical data.
So, to summarise, you believe that in version 3, A and B end up ticking at the same rates "physically".
Yes.
]B and D can never cross paths at C. B ends up moving away from C at 0.6c, as does D.
Again you are confusing yourself. You can and I did locate each clock such that the respective velocities you stipulate cross C as stated.
You say "D cries foul"? What on earth does that mean? It's a simple question: do clocks A and B tick at the same rate in the frame of D, or don't they? How can D yell out "Not a fair question!" ? I guess you just want to have a bet each way and not give a definite answer.
I was making the point that your concern about what D "Thinks" is the tick rate isn't and when he sees the data he cried foul. What is so tough about that?
If you think the "illusion of motion" answer is different from the "reality" here, then just give me the reality. You can tell me the illusion, too, if you think that helps, but primarily I'm asking about real tick rates, not any illusional fantasies you want to introduce as a distraction.
I gave you the reality it is the data transmitted as they all cross C.
Anyway, you say B and D are "not dilated to each other due to relative velocity", even though B is moving at 0.88c relative to D. I'm guessing this is supposed to be the "reality". Does D have an illusion that B's clock is dilated?
Yes in case #3. During motion he may see the other ticking more slowly but the reality is it is ticking differently and the accumulated times when they all pass the common point is the physical reality. They all have the same velocity to C which was their common inertial rest frame and that dictates they all are ticking at a common rate
Does B have an illusion that D's clock is dilated?
Still #3 Yes.
Does B have the illusion of D ticking faster or slower? Does D have the illusion of B ticking faster or slower?
#3. Each has the illusion the other is ticking slower but they are ticking the same.
But after all this you haven't even answered the question I asked, which was whether A and B tick at the same rate in frame D.
I believe I did. What D thinks is respective tick rates is not the actual tick rates. So in D's frame A & B should have different tick rates they don't.
You haven't even mentioned A. Why not? If "in reality" B is not dilated relative to D, then is A dilated relative to D "in reality", even though A is not moving relative to D?
Are you confused or just trying to confuse others. I have made no such assertions. In your case #3 A, B & D all have a common dilation to C. What each thinks of the other is irrelevant. In the case of A & D the perception is correct because they are at relative rest. Shsssh.
You seem to have no time dilation between B and D even though they are moving relative to each other, and you don't seem to know whether A and D have time dilation between them even though they are not moving relative to each other. In other words, you're hopelessly muddled and confused.
Sorry but you have been corrected to many time to let this go unchallenged.
In case #3 yu have what is called symmetry that is equal acceleration and velocity to a common reference frame. Under those condition the actual physical time dilaton is equal and hence they all remain synchronized.
What you are attempting to do is re-interject the "Illusion of Motion" and assert thatvthat is physical reality. IT IS NOT and you have not one case of emperical data to support any such nonsense.
So, you're saying you can't answer the question for version 4, even though all of the final speeds are the same as in version 3.
What extra information would you require in order to be able to answer the question for version 4?
No. I'm saying I'm not wasting my time restructuring your scenarios to show what has already been shown. You can generate 100,000,000 different scenarios and they all come down to the only physical time dilation is relative to motion to a common rest frame. Relative eloicty between clocks each having motion then only produce the illyion of dilation to the observers because that is not what accumulated time emperically supports.
Such a simple question, and such a complicated answer.
Such a simple solution and such lengthy overly complicated scenarios.
You say that in frame C, A and B "appear" to tick in synch, but they don't tick in synch in that frame "in reality". Is that correct? In other words, even though A and B are both moving at 0.6c relative to C, they have different tick rates according to you "in reality", though maybe not in "illusion of motion".
Recall that while all left from D and all had D's tick rate the fact that A turned around and returned to D's frame it now ticks at D's rate. which is faster than C's. But from C's frame both A & B have the same relative velocity and each appears to be ticking slower than C from C's frame.
And you say that there's no way to calculate "actual accumulated times" here without more information. What information, exactly?
You can't predict accumulated time unles you have a rest reference accumulated time. Tick rates zare not the same as accumulated time. Comparative tickrates or a dilated rate requires a reference duration from which to calculate accumulated times.
I would think you knew that.
How can you give a definite "no" here, when you couldn't answer the same question at all for version 3?
Considering that in #4 A & B do not have a common velocity relative to D makes that rather easy. With respect to #3 I think you have confused yourself with regard to answers given.
But you can't know that, really, can you?
What? Of course you stipulated it by having them all at common rest but the in #3 didn't move C and in #4 didn't move D. Are you having a breakdown over this?
For example, suppose that prior to the start of version 3 or 4 all of the clocks A,B,C and D were actually accelerated from another clock E, to a speed of 0.5c relative to E, for example. Nothing then changes about the scenarios as written. Do you agree? And yet this completely mucks up your calculations of "reality", because now the "common local rest frame" of all the clocks must be clock E.
And what if clocks A,B,C,D and E were all accelerated from another clock F?[/quote]
Not going here. I've let you go on and on adding more and more tiers of motion in an effort to confuse people or chew up thread time ansering a bunch of questions which all have the same answer. Only the accelerted frame is ever dilated and dilation between frames is directly linked to a common rest frame not just between two moving frames.
In short, your idea of a "common local rest frame" is useless. It can be changed simply by introducing an extra, arbitrary clock. That's exactly what the difference between versions 3 and 4 is, and you agree that it changes the "reality" there, so you must also agree that introducing E and/or F would equally change the "reality". This means that you can never work out what the "reality" is for any situation at all. Which means you have no workable theory for predicting time dilations. As we already knew.
False. I have shown that the only emperically supported prediction is the one based on the stipulated rest frame and not between moving frames. That is why SR introduced the"Frame Switching" requirement to compute dilation, a resting frame is never dilated.
Symmetrical accelerations of particles are known emperically to produce the same dilation regardless of vector. Co-moving (no relative veocity) or opposite directions (maximum relative velocity) to the accelerator (a common rest frame) and the results are the same. In both cases the dilation is the same. The relative velocity of the beams to each other had no affect, only the beams velocity to the accelerator has dilation.
So what you're saying is that no test has ever shown "reality", or ever could. Therefore, "illusion of motion" is all we can ever see. No experiment will ever be able to determine "reality", and therefore your "reality" is a useless concept.
What are you smoking? Every test ever done involves a rest frame (i.e. - the lab) and something in motion. Emperically the motion is always dilated. You have no test or data to support your claim that given two moving objects that they are dilated to each other. And to extend that arguement tyo symmetrical accelerations is just plain foolish since that has been shown to produce equal dilation of both (they remain synchronized) and the only dilation is between them equally to the common rest frame.
Since your "reality" depends on locating a "common local rest frame", and you admit that it is impossible ever to do that, your "reality" is a useless concept. Agreed?
PLEASE get real. Locating an absolute rest frame universally will likely never be located but every inertial frame is a local absolute rest reference.
Stop trying to make it as though I have said things I have not said.