Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Martin Fennell on 24/04/2010 12:30:03
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Martin Fennell asked the Naked Scientists:
Hi,
I have just been reading Prof Brian Cox's book "Why E=mc2"
This leads to a question about Special Relativity:
In the classic thought experiment, an astronaut flies close to the speed of light to a close star and then returns. The astronaut has barely aged but the people on earth have aged a lot.
I can follow and understand the maths as presented.
However:
Relative to the astronaut, the people on earth have traveled close to the speed of light in the opposite direction, and I cannot understand why the astronaut does not age a lot relative to the people on earth.
Can you help?
Thanks
Martin
What do you think?
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The situation is not symmetrical: the astronaut changes velocity with respect to the frame of reference of Earth and all of the fixed stars; the Earth changes velocity only with respect to the astronaut.
From the astronaut frame of reference, the distance between the Earth and the star is less, because of Lorentz contraction; let's say is only 300 km (it have to go very near to c for this): at 300,000 km/s it take 1/1000 second to get there, so 2/1000 s is the time elapsed for him, go and back. For people on Earth, if the star is 2 millions light years far away, the astronaut takes 2 millions years + 2 million years = 4 millions light years to get there and come back, so this is the time elapsed on Earth.
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The way I understand it is this, By accelerating near the speed of light the astronaut is applying phenomenal amounts of energy to do so, and matter is a condensed form of energy and matter produces a gravitational field. The more mass, the greater the field, the greater the field the slower matter travels inside the field with respect to things outside it, so the field acts like a sticky glue slowing things down. The rate of difference in time is big approaching speeds of C so one second to the astronaut may be 1000 years to earth for example. Once he slows back down, he is no longer generating the field and no longer in a different time frame or reference and thus travelled forward in time.... kind of :P
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Murchie85, I don't think you need to involve General Relativity and gravitational time dilation into this and I'm not sure the maths would hang together. Lightarrow's special relativity explanation is correct and sufficient, although a rigorous explanation should take into account the acceleration in changing direction (rather than just treating this as an "event"), and therefore (strictly) should involve GR.
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I agree Martin, it's confusing :) Lightarrow sounds eminently reasonable to me. Murchie's idea make me think of gravitons and how they are thought to behave, getting all 'sticky' and clinging in a field created by our relative mass as we accelerate, and thereby build 'mass' and also slow time relative the original frame of reference and most parts of SpaceTime. And I agree that energy expended have to do with it, but in Lightarrow case it's a discussion of symmetry and the principle of equivalence, as I see it.
And in the end it seems to fall back to if you're ready to accept that distances actually contracts 'for real' when going closer to lights speed in a vacuum, or not. If you do then Lightarrow is your man :) If you don't? well? Then you will have to look at time dilation as being the 'real thing' here, and that should mean relative mass as Murchie describes it. For myself I think both are perfectly correct, and that we have both effects coordinating in that accelerating frame. Time dilation as well as Lorentz contraction.
When we talk about time dilation we will find it both in our accelerated frame (rocket), as well in a gravitational 'inertial' uniformly moving frame like earth. Even though the math seems to differ a little. I understand that 'gravitational time dilation' is equivalent to the 'velocity time dilation' at the escape velocity, which seems to mean that you by inserting the 'escape velocity' needed for your gravitational field (earth) in the SR formula (t=t*sqr(1-v^2/c^2) instead of 'v', you will get the equivalent time dilation, well as I understands it? So time dilation exist in all frames of invariant mass, as well as for relativistic, as well as momentum.