Ok. You assumed that they both started off from common point with same acceleration, although that wasn't a known. Now suppose one of rockets didn't have same acceleration, but lets say, stayed around earth orbit, thus being very close to frame of earth. Now we have to touch twin issue. Departing ship reaches 0.866c relative to earth and other ship. But, neither ship knows the fact. Can they detect which case is true?Originally posted by Janus
For this time dilation, their relative velocity would be .866c.
If each astronaut slept for 10 hrs by their own clock, they will each figure that they are 8.66 light-hours apart when they wake, and that according to the signal received from the other ship, only 5 hrs has passed for the other astronaut (after correcting for transmission delay and Doppler effect)
Both astronauts will measure that while 10 hrs have passed for them, only 5 have passed for the other.
Now, on one hand, the mutually observed time dilation should be measured on both ships as you said, but on other hand, when departing ship returns, it must show real retardation of time. This means, that on one ship, time retardation must have been real, not just measurement due to dopler effect and light travel time for signal.
Astronauts have slept for the whole duration of acceleration, and waken up only when relative inertial motion is achieved.
Wouldn't this lead to answer:
In this case, the one in the moving ship would measure 10 hrs as having passed for him, and 20 hrs for the other astronaut (near earth).
For the astronaut on near-earth ship, if he measured 10 hrs for him, then he would measure only 5 hrs as passing for the astronaut in the departing ship?
You also assumed that each ship can measure how much time passed on other ship. This implies coded time signals. But lets omit that for a start and only assume that single bzzzz signal is available, thus only clock rate comparison is possible. What kind of bzz signal frequency shifts would either ship measure?
This is same case as twin journey. Only that ship in such 'field' would make virtual journey. If not supposedly short signal propagation time between ships, compared to real motion, this would be pretty much like real twin journey.In the second case, I assume that you are talking about putting one ship inot some "time retardation field".
In this case, the one in the field would measure 10 hrs as having passed for him, and 20 hrs for the other astronaut.
For the astronaut outside the field, if he measured 10 hrs for him, then he would measure only 5 hrs as passing for the astronaut in the field.
You wouldn't have the same situation/measurements as you did with the actual relative motion.
Now, I'm wondering, trying to keep in mind all of relativity, IS there any special difference between real motion as we know it, and virtual motion that results from time retardation? If time retardation is real, which it appears to be, then, although we currently know of no other way to cause it, would effects of time retardation be equivalent to relativistic motion?
Please, Janus, patience. This is "thought experiment (tm)", where pigs have not only wings, but they actually can fly. Relax, I know its considered impossible technologically. I only want to focus on what either ship CAN measure, and equivalence between the cases that they would detect. Idea I want to test here, is that do they really have any chance to detect whether they are moving relativistically, or sitting next to each other one being in field "where pigs have wings". Because if they can't, then there is really no reason to say there is any real difference, other than that it would be counterintuitive.If you are talkng about some Super-duper technology that mimics relativistic effects perfectly while the astronauts sit next to each other, then you are talking about somethign along the lines of "If Pigs had wings".
Such technology would in all likelyhood violate Relativity and causality, and if such technology could exist, then the rules of Relativity don't apply. Therefore invoking such technology does nothing towards increasing understanding of Relativity,
Sure. Thats why its interesting to consider what would ship inside 'time retardation field' measure, and what would lab equipment outside it measure. Somehow, when we talk about such forced time dilation, we tend to assume that there exists space in which we first have to move, while there really is no separate existence of space without time and interaction.Both time and space are relative. Whenever you deal with relativity, you must consider both time dilation and length contraction together.
Hmm. Are you completely confidently positive here? Timeflow for one of twins is retarded. Signal it generates in such frame, should have higher frequency when received by earth twin. Dopler redshift shifts it back down, but imho there should be difference in measured received signal by standards of each ship. You can transform the effects to common frame only IF you know relativistic velocity first. But without prior knowing it, the only way is to rely on assumption that atomic clocks on both ships are of same type, and find v by comparing clock rates.Relative velocity between two frames as meaured from those frames will always be the same.
This depends, as I understand, on geometry of trajectories taken.Relative velocity between two frames as measured from a third frame moving wrt to the both of the first two, will not be that same as the relative velocity of the two as measure from either of the two.