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traceur
2009-Nov-29, 12:21 PM
somethings i never quite understood:
1) if a planet is moving at X% of the speed of light away from earth (and vise versa), and a spaceship from that planet travels at X% of lightspeed towards earth, what is the time dilation on that spaceship relatively to earth and relatively to its origin? if it then speeds up to reach earth and then slows down to stop relatively to the earth, would it not experience a time dilation relatively to its origin (still moving faster away)?
2) what is the relative speed between two particles of light reflecting off opposite ends of the same object?
3) if a black hole attracts a light particle going directly away from the black hole, would it not innately be traveling slower then lightspeed?
4) is our planet experiencing some time dilation relatively to our star? is are star experiencing time dilation relatively our central galactic black hole?
5) if our galaxy is moving at a certain speed from the point of the big bang, wouldn't moving in the exact opposite direction mean that your moving slower relatively to the rest of the galaxy and thus experience less time dilation then all the other matter? what about moving in the opposite direction of earth's rotation around the sun, or even simply moving east on the same speed the earth rotates around its axis?

please, help me clear this hole of ignorance in my understanding of spacetime.

Ken G
2009-Nov-29, 04:54 PM
somethings i never quite understood:
1) if a planet is moving at X% of the speed of light away from earth (and vise versa), and a spaceship from that planet travels at X% of lightspeed towards earth, what is the time dilation on that spaceship relatively to earth and relatively to its origin?For this you need to calculate two Lorentz factors. The Lorentz factor is 1/root(1-(v/c)^2)), so it only depends on v, so you need the two relevant v values. One is easy, you specified the speed v = 100*X*c that the spaceship moves relative to its origin. The other relevant v is in principle trickier, as it would generally involve the "velocity addition formula" (you can Google it). But in this case it comes out easy-- if the speed of the planet relative to Earth is the same v as the speed of the spaceship relative to the planet, then the speed of the spaceship relative to the Earth is zero. That's because the Earth is seen as moving at v away from the planet, and so is the spaceship, so there's no way to attribute a relative speed between Earth and the spaceship. So the time dilation of the spaceship, relative to Earth, is zero in that case.


if it then speeds up to reach earth and then slows down to stop relatively to the earth, would it not experience a time dilation relatively to its origin (still moving faster away)? The acceleration of the spaceship makes time dilation an incomplete picture of what is happening. In special relativity (no gravity), there are two ways that times disconnect between two well separated objects, one is time dilation and the other is the "relativity of simultaneity." The latter means that if a clock accelerates, it perceives shifts in how it associates its own "now" with the now of various other clocks, and the farther away are those other clocks, the greater the disconnect becomes. This is one way to resolve the twin paradox, for example (I argue it's not a great way to imagine what is "really happening" there, but it is fine for getting the answer right).
2) what is the relative speed between two particles of light reflecting off opposite ends of the same object?The speed of light is always c for any observer, but time in a frame of a photon is singular and can confuse you (time stands still in the frame of a photon, relative to any other frame). So the answer is "c". However, note that the "relative speed between" two objects is not the same as the "rate that the distance between the object changes in some third frame." The latter is a simple algebraic sum, the former is a reference-frame change and requires relativity.

3) if a black hole attracts a light particle going directly away from the black hole, would it not innately be traveling slower then lightspeed?When gravity is present, the difference between the "rate that the distance changes" becomes very subtle. It really all depends on how you choose to coordinatize distance and time. The only way this is not ambiguous is if you have two objects passing each other at a given place and time-- only then is the relative speed an invariant element of the objective reality there. So the answer to your question is, in some coordinatizations yes, in others no.


4) is our planet experiencing some time dilation relatively to our star? is are star experiencing time dilation relatively our central galactic black hole?Time dilation is not something one "experiences." No one thinks they are themselves time dilated, that's always happening to someone else. Also, it's not really "dilation" when we have gravity, because the star thinks time is going fast for the planet, and the planet thinks time is going slow for the star, in a given common way to coordinatize the time.

5) if our galaxy is moving at a certain speed from the point of the big bang, wouldn't moving in the exact opposite direction mean that your moving slower relatively to the rest of the galaxy and thus experience less time dilation then all the other matter?There is no "point of the Big Bang", the Big Bang is something that happened and is happening everywhere in the universe equally. It is an increase with age of distances between widely separated galaxies, that's all it is-- generally it is best not to imagine that any motion is required there.

what about moving in the opposite direction of earth's rotation around the sun, or even simply moving east on the same speed the earth rotates around its axis?It sounds like you are imagining that time dilation is a physically real thing "happening" to someone, but it is just a way of conceptualizing how to transform from your own measurements to other people's measurements. To do that transformation, you need the relative velocity of the other observer, and to account for gravity (start with special relativity before you worry about gravity!).

Swift
2009-Nov-30, 03:20 PM
traceur,

No foul, but I've moved this thread to Q&A; I think you'll get more answers here.