Q: two planets, moving away from the center at .5c

[MattC]

I have a question for all of you physics experts.

 

Imagine for a moment that at the moment of the big bang, two planets, stars, whatever, are propelled in opposite directions. Exactly opposite directions, for the sake of this thought experiment. One is propelled away from the center in the "left" direction at half the speed of light - this seems feasible to me. Half the speed of light should be obtainable, with enough energy. The other is propelled at the same speed in the opposite direction.

 

Now, these speeds are relative to the center of the big bang. Relative to that center, the speed of these planets/stars/whatever is .5c. Forget gravity slowing them down ... pretend they start out a little faster and .5c is the speed after 10 billion years. Imagine there are no other confusing gravitational pulls confounding things.

 

As I understand it, all speed is relative - not only in the sense of einsteinian relativity, but also in the sense of reference points. I am not moving, relative to the computer I am at, but I am moving relative to the sun, or the moon.

 

In this thought experiment, we have two objects traveling away from each other at .5c, so if you set your reference point to one of them, the other is moving away at the speed of light ... or even more, if we change the parameters of the thought experiment somewhat. If you are one of those planets, and you shine a beam of light at the distant and fleeing planet, the beam of light will travel at the speed of light ... relative to the source, AND the other planet, which is traveling in excess of the speed of light. So as I understand it, time would be very warped for the other planet, relative to the planet with the flashlight. It would have to be going ... back in time, right? Otherwise the light beam would not catch up. At the least, if the relative speeds of the planets was at C, the distant planet would have to not move through time for the light to catch up and hit it at the speed of C.

 

I hope there is a simple answer to this. I've pondered this question a number of times, and always put off doing research, or asking my betters, thinking the answer would come to me eventually. It hasn't.

 

So, experts, how does this work? Does time really stop for that second planet? Or for both, for that matter, since light comes from both? Or is it somehow just impossible for any two particles in the universe to diverge at that rate?

[swansont]

In this thought experiment, we have two objects traveling away from each other at .5c, so if you set your reference point to one of them, the other is moving away at the speed of light

 

 

No. Speeds do not add linearly. An observer may see two objects fly off in opposite directions, each moving at 0.5c relative to him, but the objects will see each other moving at 0.8c

[J.C.MacSwell]

I have a question for all of you physics experts.

 

Imagine for a moment that at the moment of the big bang' date=' two planets, stars, whatever, are propelled in opposite directions. Exactly opposite directions, for the sake of this thought experiment. One is propelled away from the center in the "left" direction at half the speed of light - this seems feasible to me. Half the speed of light should be obtainable, with enough energy. The other is propelled at the same speed in the opposite direction.

 

Now, these speeds are relative to the center of the big bang. Relative to that center, the speed of these planets/stars/whatever is .5c. Forget gravity slowing them down ... pretend they start out a little faster and .5c is the speed after 10 billion years. Imagine there are no other confusing gravitational pulls confounding things.

 

As I understand it, all speed is relative - not only in the sense of einsteinian relativity, but also in the sense of reference points. I am not moving, relative to the computer I am at, but I am moving relative to the sun, or the moon.

 

In this thought experiment, we have two objects traveling away from each other at .5c, so if you set your reference point to one of them, the other is moving away at the speed of light ... or even more, if we change the parameters of the thought experiment somewhat. If you are one of those planets, and you shine a beam of light at the distant and fleeing planet, the beam of light will travel at the speed of light ... relative to the source, AND the other planet, which is traveling in excess of the speed of light. So as I understand it, time would be very warped for the other planet, relative to the planet with the flashlight. It would have to be going ... back in time, right? Otherwise the light beam would not catch up. At the least, if the relative speeds of the planets was at C, the distant planet would have to not [i']move through time[/i] for the light to catch up and hit it at the speed of C.

 

I hope there is a simple answer to this. I've pondered this question a number of times, and always put off doing research, or asking my betters, thinking the answer would come to me eventually. It hasn't.

 

So, experts, how does this work? Does time really stop for that second planet? Or for both, for that matter, since light comes from both? Or is it somehow just impossible for any two particles in the universe to diverge at that rate?

 

As Swansont pointed out speeds do not add linearly, however current theory says two particles can diverge at that rate:

 

1. wrt the observer, but in this case at 0.8C wrt each other

2. 1.0 C wrt each other due to the hubble expansion, although in this case the observer would measure their speeds as greater than 0.5 C

[MattC]

Hmmm. Thank you both for the responses! I'm trying to work out in my head how the time rates would work out for all of the systems in this example.

 

I have another question, on a similar subject

 

Say you have two objects that are stationary (A and B), but distant. A third object © is moving away from these two objects

 

C is moving straight away from A at a rate of x

C is moving away from B, but not straight away, so it's rate, relative to B, is less than it's rate relative to A

 

C is moving fast, so time for C moves noticably slower. C sees time at point A as moving fast. Time at point B is moving fast but not as fast, because the speed of divergence is less.

 

Yet time is moving at the same rates for A and B

 

So if C leaves A for 2 years (and then comes back), in that period 1 year passes for C (and . B sees that C does not return to A for 2 years, yet relative to B, C should perceive that 1.5 years had passed, instead of the 1 year that C actually perceived as passing (because of it's speed relative to A, which is greater than it's speed relative to B).

 

How does this all work out? A and B see things happening on each other without any dilation of time, yet the dilation of time perceived for C would differ.

[MattC]

Double post. I edited it out.

[Janus]

Hmmm. Thank you both for the responses! I'm trying to work out in my head how the time rates would work out for all of the systems in this example.

 

I have another question' date=' on a similar subject

 

Say you have two objects that are stationary (A and B), but distant. A third object © is moving away from these two objects

 

C is moving straight away from A at a rate of x

C is moving away from B, but not straight away, so it's rate, relative to B, is less than it's rate relative to A

[/quote']If A and B are at rest with respect to each other, and C is moving with respect to them, it has the same velocity with respect to both of them; it does not matter whether it is moving directly away from A or B or not. (I am standing on a north bound lane of a freeway, and car A is North of me and driving at 70 mph. A car on another North bound freeway which parallels my own, passes directly West of me also traveling North at 70 mph. Both cars have the same relative velocity with respect to me; 70mph North.

 

C is moving fast, so time for C moves noticably slower. C sees time at point A as moving fast. Time at point B is moving fast but not as fast, because the speed of divergence is less.

C would see time at A as moving slow and at the same rate as B.

[MattC]

Ah, what was I thinking? You're right, the velocity of C stays the same. I was thinking of the rate at which it moves away from A relative to B, but that doesn't matter. What matters is how fast it appears to be moving, and if you saw it, even though it moved away from B slower than it moved away from A, it also moved to the side, from B's perspective, and thus the apparant velocity would be the same. I was having a brain fart.

 

As for the other part, I think I'm right. The whole Q is irrelevant because of that mess up, but C, being the one moving fast, would travel through time less rapidly - so when C came back from it's year long trip, two years would have passed for A and B. The faster you move, the slower time moves for you, so light can catch up.

 

Anyhow, thanks for pointing on that silly flaw in my question!

[Janus]

 

As for the other part' date=' I think I'm right. The whole Q is irrelevant because of that mess up, but C, being the one moving fast, would travel through time less rapidly - so when C came back from it's year long trip, two years would have passed for A and B. The faster you move, the slower time moves for you, so light can catch up.

 

[/quote']

No, because there is no such thing as a state of absolute rest or motion. You can say that C has a relative velocity wrt A, or A has a relative velocity wrt C, but you cannot say that either is the one that is really moving.

 

And it is this relative motion that leads to time dilation. Thus A's clock runs slow according to C and C's clock runs slow according to A.

 

Having said this said this, why is it that C will record only 1 year upon its return and A will record 2 years? The answer is two-fold.

 

1. While A records that C traveled out to a distance of .866 lightyears and returned from that distance at .866c and took 2 years, due to length contraction, C records that its distance from A at turnaround was only .433 lightyears for a total round trip of .866 light years, which at .866c took one year.

 

2. While on the outbound and inbound legs C determines that A's clock ran slow and recorded .25 years on each leg for a combined accumulated time of .5 years, C has to accelerate in order to return to A, And the rules change for an accelerating object. If you are accelerating towards a clock, (As C does towards A when it turns around) that clock will run fast according to you, the further the clock is from you, the faster it runs. Thus as C turns around, A's clock, according to C, will fast forward by 1.5 years.

 

Thus A will see C's clock slow for the whole trip and record 1 year while A's own clock records 2 years.

C will record 1 year on its clock (due to a shorter trip as measured by it), and will see A's clock run slow on the Outbound trip to record .25 years, then advance 1.5 years as C accelerates to turn around, and finally see A's clock run slow again on the return trip, recording an additional .25 years, to accumulate a total recorded time of 2 years.

[RVonse]

Is it fair to say that the universe can not be expanding any faster than the speed of light?

[swansont]

Is it fair to say that the universe can not be expanding any faster than the speed of light?

 

 

No. You can get recessional velocities that at exceed c, even though locally you will never get two objects travelling >c with respect to each other.

[CanadaAotS]

Ok I've always thought this time dialation thing was a little strange, but its been fully proven in labratories and that right?

[eon_rider]

No, because there is no such thing as a state of absolute rest or motion. You can say that C has a relative velocity wrt A, or A has a relative velocity wrt C, but you cannot say that either is the one that is really moving.

 

Very nicely said. Things like motion can appear to be absolute from a specific reference frame, but ultimately the above is the bottom line. (IMO)

[swansont]

Ok I've always thought this time dialation thing was a little strange, but its been fully proven in labratories and that right?

 

Yes. And in the field. There's no way GPS works without relativity being right, and I know GPS works - I found 3 geocaches the other day.