Exploring Time Dilation: The Case of Alice and Bob

[Ryan_m_b]

I understand that the faster one goes the slower time goes but a thought popped into my head recently that I couldn't resolve;

Alice and Bob are at rest relative to each other in an otherwise empty universe (i.e no point's of reference). Suddenly Alice observes Bob moving away from her at .99c. Twenty years later Bob returns having flown away for a decade before turning around. According to my calculations 20 years at .99c would last only 2.8 years for the traveller. My confusion comes when I consider the fact that in Bob's point of view it is Alice who has moved away at .99c for ten years before coming back.

I was under the impression that there were no privileged points of view. So in this scenario when Alice and Bob meet back up whose clock would say 20 years and whose would say 2.8 years and why?

 

[Pengwuino]

The person who experiences proper time is the one who experiences the acceleration. Something has to propel one of them to that velocity.

 

[Ryan_m_b]

The person who experiences proper time is the one who experiences the acceleration. Something has to propel one of them to that velocity.

Thanks but what's proper time exactly?

 

[Pengwuino]

Thanks but what's proper time exactly?

Sadly, I can't give you a good explanation as to what defines the proper time other than it's the time the non-inertial guy reads. The person accelerating is non-inertial since he's being accelerated off to near the speed of light.

 

[Ryan_m_b]

Fair enough, cheers anyway.

 

[Aimless]

I understand that the faster one goes the slower time goes.

This is a common misconception, and it's an important one to clear up first before one tries to get any deeper into the study of relativity. There is no "the faster one goes." So long as one is in an inertial (non-accelerated) reference frame, one always observes oneself to be at rest. Velocity is not an intrinsic property of the universe. Rather, velocity must always be specified with respect to a frame of reference, which means one must specify an observer.

Just as two observers standing at different locations looking at a third object will view that object with different perspectives, so will two (inertial) observers traveling at different velocities with respect to each other see a different perspective with regards to the passage of time. Observer A sees his own clock running normally, and the clock of Observer B running slowly by an amount which depends on the velocity of Observer B with respect to Observer A. Observer B, likewise, sees his own clock running normally, but sees Observer A's clock running slowly. (Actually, the situation here is symmetric, so Observer A sees Observer B's clock run slowly by exactly the same amount that Observer B sees Observer A's clock run slowly.)

Now, as regards to the twin paradox: as I mentioned, velocity is not an intrinsic property of the Universe; there is no default reference frame from which to measure your own velocity. However, the same is not true for acceleration. An Observer in an accelerated reference frame can measure his own acceleration, and will also measure his own clock running slowly. When the one twin leaves on his journey, he is no longer in an inertial reference frame, since he must turn around and come back; thus, the discrepancy between the ages of the two twins upon return is due to the acceleration of the traveling twin.

 

[Ryan_m_b]

This is a common misconception, and it's an important one to clear up first before one tries to get any deeper into the study of relativity. There is no "the faster one goes." So long as one is in an inertial (non-accelerated) reference frame, one always observes oneself to be at rest. Velocity is not an intrinsic property of the universe. Rather, velocity must always be specified with respect to a frame of reference, which means one must specify an observer.

Yes I was aware of this but my terminology was quite simple.

Just as two observers standing at different locations looking at a third object will view that object with different perspectives, so will two (inertial) observers traveling at different velocities with respect to each other see a different perspective with regards to the passage of time. Observer A sees his own clock running normally, and the clock of Observer B running slowly by an amount which depends on the velocity of Observer B with respect to Observer A. Observer B, likewise, sees his own clock running normally, but sees Observer A's clock running slowly. (Actually, the situation here is symmetric, so Observer A sees Observer B's clock run slowly by exactly the same amount that Observer B sees Observer A's clock run slowly.)

Now, as regards to the twin paradox: as I mentioned, velocity is not an intrinsic property of the Universe; there is no default reference frame from which to measure your own velocity. However, the same is not true for acceleration. An Observer in an accelerated reference frame can measure his own acceleration, and will also measure his own clock running slowly. When the one twin leaves on his journey, he is no longer in an inertial reference frame, since he must turn around and come back; thus, the discrepancy between the ages of the two twins upon return is due to the acceleration of the traveling twin.

Thanks for clearing that up

 

[ghwellsjr]

The person who experiences proper time is the one who experiences the acceleration. Something has to propel one of them to that velocity.

Thanks but what's proper time exactly?

Sadly, I can't give you a good explanation as to what defines the proper time other than it's the time the non-inertial guy reads. The person accelerating is non-inertial since he's being accelerated off to near the speed of light.

Every person always experiences proper time whether they are accelerating or not. The time on every clock is called proper time.

Both twin's clocks keep proper time. When only one of them accelerates and later returns to the other one, the proper times on their two clocks will differ with the accelerated clock having elapsed less time. Both clocks are correct.

 

[Cosmo Novice]

I understand that the faster one goes the slower time goes but a thought popped into my head recently that I couldn't resolve;

Alice and Bob are at rest relative to each other in an otherwise empty universe (i.e no point's of reference). Suddenly Alice observes Bob moving away from her at .99c. Twenty years later Bob returns having flown away for a decade before turning around. According to my calculations 20 years at .99c would last only 2.8 years for the traveller. My confusion comes when I consider the fact that in Bob's point of view it is Alice who has moved away at .99c for ten years before coming back.

I was under the impression that there were no privileged points of view. So in this scenario when Alice and Bob meet back up whose clock would say 20 years and whose would say 2.8 years and why?

The difficulty with this question is that the stipulation on the empty Universe makes it difficult to define who is achieveing relativistic speeds and who has rest mass. It must be the inertial accelerator - Bob, whose clock is different.

Proper time is the time for the observer. So for Bob in his FoR he is experiencing proper time and from Alice FoR she is experiencing proper time - both FoR are equally valid.

 

[ghwellsjr]

The difficulty with this question is that the stipulation on the empty Universe makes it difficult to define who is achieveing relativistic speeds and who has rest mass. It must be the inertial accelerator - Bob, whose clock is different.

Proper time is the time for the observer. So for Bob in his FoR he is experiencing proper time and from Alice FoR she is experiencing proper time - both FoR are equally valid.

You need to think in terms of a single FoR that we are defining the postitions and speeds of both observers. The easiest one is one in which they both start out at rest and end up at rest. Speeds are assigned in SR according to a specified FoR. It has nothing to do with whether the universe is otherwise empty or not.

It's not just that Bob's clock is different, the two clocks are different from each other after they reunite.

 

[Cosmo Novice]

You need to think in terms of a single FoR that we are defining the postitions and speeds of both observers. The easiest one is one in which they both start out at rest and end up at rest. Speeds are assigned in SR according to a specified FoR. It has nothing to do with whether the universe is otherwise empty or not.

It's not just that Bob's clock is different, the two clocks are different from each other after they reunite.

Thanks - I am only just really beggining to study SR. :) So essentially my restraining factor was not using a observers FoR but using Alice/Bobs FoR. My misunderstanding came from if we are assuming an empty Universe then I only saw two valid FoR, Bobs and Alice, and they are alone in a Universe - maybe I took this too literally.

Yes I meant both clocks are different - poor terminology on my part.

Thanks again

 

[ghwellsjr]

Thanks - I am only just really beggining to study SR. :) So essentially my restraining factor was not using a observers FoR but using Alice/Bobs FoR. My misunderstanding came from if we are assuming an empty Universe then I only saw two valid FoR, Bobs and Alice, and they are alone in a Universe - maybe I took this too literally.

Yes I meant both clocks are different - poor terminology on my part.

Thanks again

Yes, there doesn't even have to be any observers permanently at rest in your selected FoR. For example, you could use the Lorentz Transform to convert the previously defined Alice & Bob scenario into a FoR where both of them start out and end up moving at 0.99c and then Bob stops and comes to rest in the FoR for a while and then accelerates to an even higher speed so that he can catch back up to Alice, at which point, their two clocks will display the same times on them as what the analysis from the first frame of reference determined.

 

[Cosmo Novice]

Yes, there doesn't even have to be any observers permanently at rest in your selected FoR. For example, you could use the Lorentz Transform to convert the previously defined Alice & Bob scenario into a FoR where both of them start out and end up moving at 0.99c and then Bob stops and comes to rest in the FoR for a while and then accelerates to an even higher speed so that he can catch back up to Alice, at which point, their two clocks will display the same times on them as what the analysis from the first frame of reference determined.

Thankyou, intuitively I had already thought this while thinking the matter through.

 

[harrylin]

I understand that the faster one goes the slower time goes but a thought popped into my head recently that I couldn't resolve;

Alice and Bob are at rest relative to each other in an otherwise empty universe (i.e no point's of reference). Suddenly Alice observes Bob moving away from her at .99c. Twenty years later Bob returns having flown away for a decade before turning around. According to my calculations 20 years at .99c would last only 2.8 years for the traveller. My confusion comes when I consider the fact that in Bob's point of view it is Alice who has moved away at .99c for ten years before coming back.

I was under the impression that there were no privileged points of view. So in this scenario when Alice and Bob meet back up whose clock would say 20 years and whose would say 2.8 years and why?

The point of view of inertial reference systems is "privileged" in the sense that you mean. Bob does not stay at rest in one.

Note: Einstein tried to get rid of that privilege with GR (adding "induced gravitational fields"), but that's another story.

Regards,
Harald

 

[MrNerd]

I asked this on the yahoo answers forums once, and I believe the answer was the accelerated body. Why does this happen? I'm not sure. I haven't taken a course on relativity yet, I've only done a little outside reading and the special relativity covered in my high school ap physics course. The answer does make me wonder if a change in energy in general messes with time, or maybe only changing velocity. This is just a speculative idea that just popped in my head, so don't be abhorred at the ridiculousness of it, please, if it is ridiculous. After all, the ridiculous can sometimes triumph over common belief.

 

[harrylin]

I asked this on the yahoo answers forums once, and I believe the answer was the accelerated body. Why does this happen? I'm not sure. I haven't taken a course on relativity yet, I've only done a little outside reading and the special relativity covered in my high school ap physics course. The answer does make me wonder if a change in energy in general messes with time, or maybe only changing velocity. This is just a speculative idea that just popped in my head, so don't be abhorred at the ridiculousness of it, please, if it is ridiculous. After all, the ridiculous can sometimes triumph over common belief.

It's speculation to talk about cause and effect, but an increase of kinetic energy corresponds to lower frequency. Similarly, an increase in potential energy corresponds to higher frequency.

Interestingly, clocks at the surface of the Earth have about the same natural clock rate at the equator as at the pole. At the equator the Earth is a little expanded due to the rotation, and the force balance corresponds to an equal increase in potential and kinetic energies.

Cheers,
Harald