- #1
Buckethead
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This is probably common knowledge to relativity aficionados but at Example 7.3 in this paper:
https://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch07Rel.pdf
I was surprised to read the author showing that a ship accelerating at 1g from rest for 1 hour and reaching a speed of 1610km/s as seen by a stationary observer will show exactly the same amount of dilation as another ship flying past the same observer for 1 hour at a speed of 1610km/s. The amount of dilation in both cases is 1.0000144 hr.
The reason I find this counter-intuitive is obvious. The accelerating ship is not going at the maximum speed during the whole trip as is the inertial ship, so I would have thought it would show less dilation.
I thought about this and realized the difference must lie in the fact that the accelerating ship is experiencing gravity in addition to velocity which the inertial ship is not. And since gravity slows time, it is this gravity due to acceleration that is making the two equal.
Is my realization correct? I have read in other threads in this forum that acceleration (i.e. a ship accelerating) does not affect time dilation, only the resulting velocities at each point matter. I apologize that I cannot refer to such posts, but I remember them being in response to questions about the twin paradox. But if that were true, then the two times should be different due to the differences in the sums of the instantaneous velocities during acceleration. Can someone clarify this? Thanks.
https://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch07Rel.pdf
I was surprised to read the author showing that a ship accelerating at 1g from rest for 1 hour and reaching a speed of 1610km/s as seen by a stationary observer will show exactly the same amount of dilation as another ship flying past the same observer for 1 hour at a speed of 1610km/s. The amount of dilation in both cases is 1.0000144 hr.
The reason I find this counter-intuitive is obvious. The accelerating ship is not going at the maximum speed during the whole trip as is the inertial ship, so I would have thought it would show less dilation.
I thought about this and realized the difference must lie in the fact that the accelerating ship is experiencing gravity in addition to velocity which the inertial ship is not. And since gravity slows time, it is this gravity due to acceleration that is making the two equal.
Is my realization correct? I have read in other threads in this forum that acceleration (i.e. a ship accelerating) does not affect time dilation, only the resulting velocities at each point matter. I apologize that I cannot refer to such posts, but I remember them being in response to questions about the twin paradox. But if that were true, then the two times should be different due to the differences in the sums of the instantaneous velocities during acceleration. Can someone clarify this? Thanks.