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Post by Progenitor A on Dec 14, 2010 9:24:05 GMT 1
Fix a clock to a rocket on earth, fire it upward so that it gains quite some speeed.
The velocity of the rocket will cause time dilation - time will slow down - thats a tenet of SR.
But as the rocket goes higher in our gravitational field , the clock will speed up -that is a tenet of GR.
Which one wins?
Does the clock remain the same?
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Post by petergriffin on Jan 13, 2011 14:55:19 GMT 1
Its not a simple as you may think, the time dilation is related to velocity, you need to be going close to speed of light for it have a noticable effect, the speeding up of time due to the effect of reducing gravitaional field is related to the mass distorting space and you have to move along way from the mass to have any noticeable effect.
The rocket will dilate time in direct proportion to it speed (or as the speed approachs the speed of light) however, the speeding up of time is in relation to a inversed square rule (gravity is a inversed square field) so the effect demishs quickly as you move away from a mass, thus balancing the two effects would be difficult.
There would be a point on the rockets flight where the two did balnce each other out, but to have it cancel out during all the trip would mean rocket slowing down all the time.
So in summary yes the effects would cancel out at some point on journey, but to have them match during all the flight whilst matmathically possible would be impratical.
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Post by speakertoanimals on Jan 13, 2011 15:11:57 GMT 1
Not quite true. It isn't a LINEAR relationship!
The GPs sateliites (which DON'T travel at close to lightspeed) are sensitive enough to detect both effects, and for them (I think), the gravitational effects (runs faster) outweighs the speed effects (runs slower).
But the original question is still slightly silly, because the correct answer is -- depends on your EXACT path, as you might expect when you have competing effects which depend on your exact speed and your exact height. So, in general, you would expect some paths where the clock runs slower, some where the net effect is it runs faster, and some where the effects cancel.
And before anyone says it, this is a DIFFERENT question to the time experienced by a thrown ball that came up elsewhere, because in this case, we have a rocket, not freefall under gravity as in the thrown ball case..............
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Post by Progenitor A on Jan 13, 2011 16:38:03 GMT 1
Its not a simple as you may think, the time dilation is related to velocity, you need to be going close to speed of light for it have a noticable effect, the speeding up of time due to the effect of reducing gravitaional field is related to the mass distorting space and you have to move along way from the mass to have any noticeable effect. The rocket will dilate time in direct proportion to it speed (or as the speed approachs the speed of light) however, the speeding up of time is in relation to a inversed square rule (gravity is a inversed square field) so the effect demishs quickly as you move away from a mass, thus balancing the two effects would be difficult. There would be a point on the rockets flight where the two did balnce each other out, but to have it cancel out during all the trip would mean rocket slowing down all the time. So in summary yes the effects would cancel out at some point on journey, but to have them match during all the flight whilst matmathically possible would be impratical. I do not recall saying that it was simple. In fact you do not have to anywhere near the speed of light for the effect to be noticeable, as evidenced by the adjustment of the GPS Satnav clocks having to be speeded up to compensate for their orbital velocity (but not quite as much as would be the case if it were not also within our gravitational field -where the effect is to run faster as the rocket rises than earth-bound clocks). But in principle it is simple to find the postion above the earths centre where the dilated time due to velocty (-t d) us equl to the time contraction due to gravity (+t c) It evidently occurs when The magnitude of (-t d) = magnitude of (+t c) |
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Post by speakertoanimals on Jan 13, 2011 16:59:12 GMT 1
We seem to have a parrot about..................DOes he really think no one will notice, when he just repeats what I said in the post directly above (and doesn't even acknowledge that I've already said it!).
Dearie me, is adding 'as speaker correctly pointed out above' too much to expect?
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