Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: gem on 12/09/2022 00:04:25
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Hi all,
previously it has been discussed that time dilation is linked to energy potential, therefore different planets can have the same surface value of g but different escape velocity's.
Therefore how would it be possible to calculate the time dilation for a box with no windows accelerating at a rate of one g ? (in empty space)
:) ;)
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previously it has been discussed that time dilation is linked to energy potential, therefore different planets can have the same surface value of g but different escape velocity's.
It's not about energy potential (units Joules), not g (meters/sec² or F/kg), and not escape velocity (meters/sec). This has already been stated on several replies on other threads on this topic. It's about gravitational potential (units of Joules/kg).
For instance, the gravity on Venus is a little less than it is here (but close). You weigh a little less there. Escape velocity of Venus is a little less than that of Earth. Nevertheless, clocks run slower there because the gravitational potential is less there.
Escape velocity from Saturn is over thrice that of Earth (and you also weigh a little bit more than on Earth), but clocks on its surface run faster than on Earth because the gravitational potential is less on Earth.
Therefore how would it be possible to calculate the time dilation for a box with no windows accelerating at a rate of one g?
There's nothing with which to compare it. A clock isn't dilated relative to itself. If you want an answer to this question, you need to put another clock somewhere. Maybe it's positioned in a fixed location elsewhere in the box, in which case, relative to the box, the lower one (having lower potential in the accelerating frame) runs slower than the upper one. Maybe it's not accelerating with the box, in which case the dilation is dependent on the chosen coordinate system in which to take the measurements. There's no gravity at all in this scenario, so it's purely a special-relativity situation.
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Hi all,
Halc isnt escape velocity the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero ???
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My apologies, but this post seems to have escaped me.
Halc isnt escape velocity the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero ???
Pretty much, yes. To be a bit more precise, the escape speed (which is indeed a speed, not a velocity) of object X at location L is the speed relative to X of a small object Y at L at which the sum of the kinetic energy of Y and its gravitational potential energy relative to X is equal to zero. I think this works even if Y is a system of moving/distributed objects.
The frame specifications are necessary since an object's kinetic energy (and also location) is very frame dependent.
Still, the topic at hand is about time dilation and escape velocity is pretty meaningless in an accelerating reference frame. For instance, if you throw a rock up inside the (large enough) accelerating box, it will come back down no matter how fast you throw it.
Time dilation is relative between clocks, and you only specify one clock (in the box somwhere), so your question isn't clear.
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Hi all,
yes Halc, sorry I wasn't clear.
I am wondering if its possible to calculate the time dilation/rate of a light clock in Einstein's classic lift with no windows accelerating at 1g vs one stationary/not accelerating far away from any gravitational effects.
Similar as to how you would calculate/compare the rate of a stationary clock at sea level on Earth vs one stationary/not accelerating far away from any gravitational effects, as per the standard gravitational time dilation equations.
I read somewhere the centripetal/centrifugal acceleration of a mass correlated to time dilation equivalent to the linear velocity of the body in question, but I am not sure how accurate this information is, or if its possible to mathematically relate it to the question I am posing.
:)
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I am wondering if its possible to calculate the time dilation/rate of a light clock in Einstein's classic lift with no windows accelerating at 1g vs one stationary/not accelerating far away from any gravitational effects.
Similar as to how you would calculate/compare the rate of a stationary clock at sea level on Earth vs one stationary/not accelerating far away from any gravitational effects, as per the standard gravitational time dilation equations.
Well, in the latter case, the separation of the two clocks remains constant and one can express a frame independent ration between their rates.
Not so in the former case where each clock is stationary in its own frame and runs faster than the other. In the inertial frame, the accelerating clock runs nearly as fast at first, but slows as it gains speed. In the accelerating frame, it's like dropping a clock into a black hole. It runs at normal rate for a while, but as it falls, it slows and comes to a complete halt at the event horizon and never falls through it (at least not in the accelerating frame).
I read somewhere the centripetal/centrifugal acceleration of a mass correlated to time dilation equivalent to the linear velocity of the body in question
True. In that case, it's about speed relative to some inertial frame and the acceleration is irrelevant other than to keep the circling clock at some constant distance away. Fir instance, I can put a clock in a centrifuge at the north pole and accelerate it furiously (at 30,000 g say) in a r=~6 meter circle moving 1000 mph, and it will stay in sync with a clock sitting on a shelf somewhere near the equator. The only difference is the huge acceleration of the one, and it doesn't make one clock dilated relative to the other.
Anyway, you didn't say anything about centripetal acceleration. I had the impression your box was undergoing linear acceleration, and my answers are based on that impression. Your OP doesn't really say, it just says "accelerating at a rate of one g" and not if the direction of it is fixed or not.