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I've been going far, far too easy on you guys.
Relativity is absolute, is it not? Therefor - when I attach a clock to myself, and run away from you, and return. Who has the slower clock?
It's a trick question. Relativity is absolute. From my frame of reference, you were moving away from me - not the other way around. The two frames of reference cannot be reconciled unless a third frame of reference is called into account.
This, however, creates two possible interpretations for the speed of light. Which collapses relativity and forms an absolute reference.
I'll give you a little bit to digest that.
Your statement "equal velocity" is imprecise as a physical description, as it lacks direction.
Originally posted by -PLB-
I have yet to grasp it fully, and I need to read it some more times and let it sink in a bit more. My initial thoughts on it is that it only means that superluminal communication between two transceivers that have a different velocity is not possible, but between two transceivers with equal velocity it does not seem to cause any violation.
So if you meant "same velocity in the same direction, without any access to another inertial reference frame", then you're right, no problem.
Figure 3 First superluminal transmission. Alice transmits from event P and the signal is instantaneously received by Bob at event Q. Alice and Bob are at rest relative to each other.
By itself, this single use of the ansible doesn’t create a causality violation. If Bob transmits a signal back towards Alice using a conventional light-speed transmitter, she receives it a later time than when she signalled to Bob. Even if Bob re-transmits with his ansible, Alice receives the reply just a little after she sent out her signal. The problems arise when we bring another inertial frame into play.
Originally posted by Arbitrageur
Your statement "equal velocity" is imprecise as a physical description, as it lacks direction.
If you say "two tranceivers in the same inertial frame of reference" meaning both the same velocity and the same direction, then you have to specify if those two transceivers have access to another inertial reference frame.
OK you're right that velocity does imply direction if you are using the term as a physicist and not as a layperson.
Originally posted by -PLB-
I don't follow you. Why can't two transceivers in one inertial frame of reference have different velocities (direction and speed)? Maybe this is just a matter of confusion over the definition of the terms, but I think its important to be in agreement on that. I will respond to the rest later (when we are clear on definitions).
That's right, it's not really even a paradox though it's been called the "twin paradox".
Originally posted by DJW001
It is not a trick question, it is a sloppily constructed form of the "twin paradox."
Originally posted by -PLB-
I see a bright future for superluminal communication, even when its only possible between transceivers that are at a fixed distance from each other.