- #1
Endervhar
- 142
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Something must be wrong with my reasoning in the following thought experiment. Can someone, please, point out my error.
This thought experiment involves an empty cosmos which contains three space craft. Two of these, piloted by those intrepid adventurers Alice and Bob, are twenty light seconds apart and maintaining that distance rigorously. Each has a very accurate clock, and these clocks are synchronised. (For simplicity we will say that each reads “00.00” at an appropriate point in the thought experiment) The third craft, piloted by the less well known, but no less adventurous Charlie, is in motion relative to the other two. Relativity tells us that we cannot know which craft is moving and which, if any, is stationary. All we can say is that Alice and Bob are stationary relative to each other and that Charlie is in motion relative to the other two, or they are in motion relative to Charlie.
The distance between Alice and Charlie is closing at “0.8c”. It so happens that as Alice and Charlie pass each other their clocks are synchronised. (Charlie’s clock also reads “00.00”). It seems reasonable, therefore, to assume that Charlie’s clock must also be synchronised with that of Bob, but, of course, synchronicity is also subject to the rules of relativity, and therefore, events that are perceived as synchronous in one frame of reference may not be perceived as synchronous in another.
First, let’s consider this scenario from the point of view of Alice. Her perception is that she is stationary and that Charlie is approaching, and then passing her at 0.8c. According to her clock it takes twenty-five seconds for Charlie to reach Bob. Alice’s and Bob’s clocks remain synchronised, so they both read “00.25”. As Charlie is the one we chose to regard as being in motion at 0.8c, his clock, when he passes Bob, will read “00.15”, because, in his frame of reference it will have taken him only fifteen seconds to travel from Alice to Bob. Thus, relative to Alice and Bob, Charlie is now ten seconds younger than he would have been had he not traveled at 0.8c, relative to Alice and Bob for fifteen seconds (in his frame of reference).
Look at the scenario again, but this time from a F of R in which Charlie perceives himself as being stationary. We saw that Alice and Bob were maintaining a distance of twenty light seconds between their craft. The relative speed at which the gap between Alice and Charlie is closing remains 0.8c. Because we are now regarding Charlie as being stationary, it seems logical, to conclude that Charlie will now measure the time from when Alice passes him, to when Bob passes him as being twenty-five seconds, while Alice and Bob will measure it as being only fifteen seconds, because they have been traveling at 0.8c. In this F of R Alice and Bob will end up being ten seconds younger, relative to Charlie. How can this be? After all, the whole point of looking at this relativistically is to establish that any motion between the various elements in the scenario must be regarded as relative motion. Surely, it should make no difference who is thought of as being in motion; the outcome should be the same; yet, clearly, it is not.
This thought experiment involves an empty cosmos which contains three space craft. Two of these, piloted by those intrepid adventurers Alice and Bob, are twenty light seconds apart and maintaining that distance rigorously. Each has a very accurate clock, and these clocks are synchronised. (For simplicity we will say that each reads “00.00” at an appropriate point in the thought experiment) The third craft, piloted by the less well known, but no less adventurous Charlie, is in motion relative to the other two. Relativity tells us that we cannot know which craft is moving and which, if any, is stationary. All we can say is that Alice and Bob are stationary relative to each other and that Charlie is in motion relative to the other two, or they are in motion relative to Charlie.
The distance between Alice and Charlie is closing at “0.8c”. It so happens that as Alice and Charlie pass each other their clocks are synchronised. (Charlie’s clock also reads “00.00”). It seems reasonable, therefore, to assume that Charlie’s clock must also be synchronised with that of Bob, but, of course, synchronicity is also subject to the rules of relativity, and therefore, events that are perceived as synchronous in one frame of reference may not be perceived as synchronous in another.
First, let’s consider this scenario from the point of view of Alice. Her perception is that she is stationary and that Charlie is approaching, and then passing her at 0.8c. According to her clock it takes twenty-five seconds for Charlie to reach Bob. Alice’s and Bob’s clocks remain synchronised, so they both read “00.25”. As Charlie is the one we chose to regard as being in motion at 0.8c, his clock, when he passes Bob, will read “00.15”, because, in his frame of reference it will have taken him only fifteen seconds to travel from Alice to Bob. Thus, relative to Alice and Bob, Charlie is now ten seconds younger than he would have been had he not traveled at 0.8c, relative to Alice and Bob for fifteen seconds (in his frame of reference).
Look at the scenario again, but this time from a F of R in which Charlie perceives himself as being stationary. We saw that Alice and Bob were maintaining a distance of twenty light seconds between their craft. The relative speed at which the gap between Alice and Charlie is closing remains 0.8c. Because we are now regarding Charlie as being stationary, it seems logical, to conclude that Charlie will now measure the time from when Alice passes him, to when Bob passes him as being twenty-five seconds, while Alice and Bob will measure it as being only fifteen seconds, because they have been traveling at 0.8c. In this F of R Alice and Bob will end up being ten seconds younger, relative to Charlie. How can this be? After all, the whole point of looking at this relativistically is to establish that any motion between the various elements in the scenario must be regarded as relative motion. Surely, it should make no difference who is thought of as being in motion; the outcome should be the same; yet, clearly, it is not.