Twin Paradox: Explaining the Relativity of Aging

[the-genius]

I know very little about relativity. I have heard that it implies that-----
if A and B be two tweens. If A goes in a space trip and then return to B at earth, he will be younger than B.

What I am confused is, It must be same thing whether A went away from B in his space trip on the ship or B went away from A ( in B's earth-Ship!). Then how can it be that A Is younger. It will be impossible I think to determine who went for the space-trip and who didn't.

Please feel free to ask for clarification if you don't get me.

 

[HallsofIvy]

I am sure that there have been dozens of threads on this. Basically, the situation is not symmetric because A accelerates (and acceleration is NOT "relative") and B doesn't. Also, B remains deep in the Earth's gravity well while A does not.

 

[Timmaay322]

Well, if you know very little about it maybe you should read about it before you ask questions on why it doesn't make sense.
Here is a good explanation of it that helped me out.
http://en.wikipedia.org/wiki/Philosophy_of_physics"

 

[Dale]

Here is a good FAQ on the subject: http://www.edu-observatory.org/physics-faq/Relativity/SR/TwinParadox/twin_paradox.html

 

[jonnyk]

@thegenius
Infact time dilation can be used to determine whether an approaching object is the one which was accelrating towards oneself or vice versa. Say for example suddenly we experienced the moon coming towards us. If we exerience the radioactive decay of a certain element, which is always constant in the same refrence frame, taking place on the moon at a lesser rate than we would normally experience on Earth then we would know that it was the moon accelerating towards the Earth and vice versa.

 

[the-genius]

Suppose that A and B are in void. Then if A sees B acclerating away then how would he know(or what is the difference betwn) that if it is B or himself or both who is "indeed" moving away from the other.
Won't Both see the other move in exactly same way (with respect to path followed and the velocities)?

 

[Dale]

Read the FAQ

 

[quZz]

Suppose that A and B are in void. Then if A sees B acclerating away then how would he know(or what is the difference betwn) that if it is B or himself or both who is "indeed" moving away from the other.
Won't Both see the other move in exactly same way (with respect to path followed and the velocities)?

That's a nice question =) Though it is completely useless in case of the real world, but still, if there were only two elementary particles in the whole Universe, for example an electron and a positron, how would they interact? =)
I guess we have to take GR into account... any ideas?

 

[robphy]

This is one of my favorite papers on this topic:

http://www.jstor.org/stable/2309916
"The Clock Paradox in Relativity Theory"
Alfred Schild
The American Mathematical Monthly, Vol. 66, No. 1 (Jan., 1959), pp. 1-18

 

[jonnyk]

@thegenius

Suppose that A and B are in void. Then if A sees B acclerating away then how would he know(or what is the difference betwn) that if it is B or himself or both who is "indeed" moving away from the other.
Won't Both see the other move in exactly same way (with respect to path followed and the velocities)?

JK- If A can take a look at Bs behaviour inside his spaceship and A sees that Bs heart rate is under the min of any human in our frame of reference then A would know that B is the one who accelerated more wrt to him thus being closer to c than him.

 

[jonnyk]

@all
These so called paradoxes would only arise if the time dilation effect was only apparent i.e. once the spacecraft stopped both the observer on the rocket and the one on say Earth now havnt actually undergone any real age differences whislt when one observer was speeding close to c it appeared to be so for the former. HOWEVER this is not the case. The reactions actually do slow down for the external world and the astronaut can really come back younger than any human who was previously younger than the astronaut. This effect is not only as long as hes/shes traveling close to c for the outisders. NO it lasts even if he/she slows down back into their reference frame. He/shed still be having aged less than all others.

 

[Cantab Morgan]

In a number of these posts, we have been sloppy in our use of the term, "accelerating." You can always tell whether you are accelerating. You can feel it. So I think we've occasionally used the term "accelerating" to mean "moving relative to each other."

I'm also struggling to understand and agree with some of what jonnyk has written, but without complete success. If two objects are approaching each other very quickly, I don't think relativity allows us to bless the reference frame of just one. So I'm not following how time dilation would reveal that one has accelerated and the other hasn't. If they exchanged radio transmissions, wouldn't each observer perceive the other as aging slowly?

 

[phyti]

In a number of these posts, we have been sloppy in our use of the term, "accelerating." You can always tell whether you are accelerating. You can feel it. So I think we've occasionally used the term "accelerating" to mean "moving relative to each other."

I'm also struggling to understand and agree with some of what jonnyk has written, but without complete success. If two objects are approaching each other very quickly, I don't think relativity allows us to bless the reference frame of just one. So I'm not following how time dilation would reveal that one has accelerated and the other hasn't. If they exchanged radio transmissions, wouldn't each observer perceive the other as aging slowly?

They perceive each other as aging faster.
There has also been sloppy use of transformations.

 

[the-genius]

If acceleration isn't relative then can you answer this:
suppose I place you and your friend in space, far from everything else and also far from each other. Then I will apply gravitational pull on one of you only thus acclerating one of you. Each of you will see other acclerating away. Now to find who is the one I am applying force to acclerate, what experiment would you carry out to find if you are in "real acceleration" or not?
(if you throw a stone, it will still appear to go away in uniform velocity whether you are acclerating or not, as my gravitaional force acts not only on you but everything you throw.)

Also answer my these elementary question about the two clock A and B.
If I move away clock A and bring it back to B, which will be slower?

If Clock A moves away from clock B (as seen by clock B) with uniform velocity then will the time on clock A continue to change with that of B or maintain a constant differnce (from the synchronized time)?

Suppose Clock A revolve round clock B (then for B, A is acclerating as velocity is constantly changing), what effects will be there on the times, they record.

 

[JM]

Hi the-genius, here's what I think. The paradox originated in Einstein's paper 'On the Electrodynamics of Moving Bodies' published in 1905. First the theory is based on the kinematics of rigid bodies, so forces causing motion and any resulting deformations are excluded. Let's take our two astronauts,with their clocks, in space suits to deep space and place them together facing each other. The theory denies any place that is at ablolute rest, so only relative motions are important. So if astronaut A sees B moving away and then returning, then B sees A moving an exactly equal path. And if A calculates B to be younger when they reunite, then B sees A to be younger. This natural outcome of the theory can be traced to the properties of light, in particular the postulate that the speed of light c is a universal constant. JM

 

[Mentz114]

If acceleration isn't relative then can you answer this:
suppose I place you and your friend in space, far from everything else and also far from each other. Then I will apply gravitational pull on one of you only thus acclerating one of you. Each of you will see other acclerating away.

It's not possible to selectively apply a gravitational field. In any case, when you introduce gravity SR no longer applies globally.

If you imagine your two spaceships at rest wrt each other, a long way from any matter, then the only way for them to separate is for one or both to use rocket engines. If they went on different journeys and met up again, their clocks would show the proper time each had experienced. Find out what 'proper-interval' means, because the twin scenario depends only on that.

Also answer my these elementary question about the two clock A and B.
If I move away clock A and bring it back to B, which will be slower?

It depends on whose journey through space-time had the shortest proper-interval.

 

[the-genius]

JM--You said-->"The theory denies any place that is at ablolute rest, so only relative motions are important. So if astronaut A sees B moving away and then returning, then B sees A moving an exactly equal path. And if A calculates B to be younger when they reunite, then B sees A to be younger. This natural outcome of the theory "
How can both be younger than the other when they meet. Isn't it paradoxical.

 

[Cantab Morgan]

Yes, you have exactly articulated the "paradox."

The resolution is that one of the astronauts has to fire his rockets to turn around and come back. He can feel that. He knows he's the one that was accelerated.

 

[the-genius]

How do you FEEL cantab Morgan?\
You will feel that you are acclerating only when the forces(that accelrates you and the rocket) on the particles of your body are applied by say the wall of the rocket. If every-particle of your body were to fire their own rocket (very hypothetical) you won't feel it. Just as you don't feel you are acclerating towards the Earth or at rest when you are at free fall (as each particle would be applied the gravitational force)

 

[Cantab Morgan]

How do you FEEL cantab Morgan?\
You will feel that you are acclerating only when the forces(that accelrates you and the rocket) on the particles of your body are applied by say the wall of the rocket. If every-particle of your body were to fire their own rocket (very hypothetical) you won't feel it. Just as you don't feel you are acclerating towards the Earth or at rest when you are at free fall (as each particle would be applied the gravitational force)

Good question. When I say that I can feel an acceleration, I mean that I can detect whether or not I'm in an inertial reference frame. I can do so by, say, letting go of a pencil. If it just floats there, then my rocket engines must be off. If the pencil flies away from my hand, then my rocket engines must be on.

Remember Newton's First Law: "Inertial reference frames exist." I can always tell when I'm in an inertial frame because that's the one where unperturbed particles will have constant velocities. My claim is that the twin who has to turn around and come back must leave an inertial reference frame to do so. He thereby discerns that he is the younger twin.

 

[the-genius]

You din't quite get me Cantab Morgan.
If you are in a closed box and in free fall (acclerating towards earth), then if you let go your pencil, it will still appear to float, However, from the precpective of earth, you and the pencil are both acclerating towards the earth. How can you tell you are acclerating and not still.

 

[Cantab Morgan]

You din't quite get me Cantab Morgan.
If you are in a closed box and in free fall (acclerating towards earth), then if you let go your pencil, it will still appear to float, However, from the precpective of earth, you and the pencil are both acclerating towards the earth. How can you tell you are acclerating and not still.

Well, I suppose I can't tell, but that has nothing to do with the twins.

 

[the-genius]

It has this to do with the twins.
If you can't tell in this case, the traveling twin too, can't tell if he is acclerating (due to this time not by the rocket engine but by gravitational field that acclerates every thing on the rocket (like the case of free fall)). So, the condition appears to be symmetric.

 

[JM]

Hi the-genius. I see you have read my entry. First let me reiterate, special relativity is based on Kinematics, so its results have been obtained without accelarations, and its our task to understand the results without them. You are right, they can't be both younger. The calculations are done with the Lorentz Transforms. I consider these equations to represent propagating light waves. In order for A to calculate a time there must be a light ray involved, for example A might use a ray pointed at B. For symmetry B might use a ray pointed at A. Thus they are both solving the same problem, and must get the same result. But what they are calculating is not an age, but the answer to a wave problem. There is a way to find age, though.

 

[Cantab Morgan]

It has this to do with the twins.
If you can't tell in this case, the traveling twin too, can't tell if he is acclerating (due to this time not by the rocket engine but by gravitational field that acclerates every thing on the rocket (like the case of free fall)). So, the condition appears to be symmetric.

Ah. Well, I'm afraid we can't build a gravity powered spaceship. I don't know how to turn gravity on and off like an electromagnet, so I don't think there's any way to do what you are proposing.

My trajectory in the falling elevator is not the required trajectory that the twin has to follow. (There and back again.) So, you can't invoke the Einstein equivalence principle to claim that the traveling twin can somehow be shielded from discerning that he is the traveling twin.

 

[the-genius]

I didn't mean that Cantab Morgan. I meant, suppose you needn't need to use your rocket engine, simply an external gravitational field (my be from a star) will acclerate you.
Your trajectory in falling elevator will be the required trajectory that the twin has to follow if the twin is also acclerated by gravitational field of say, a Star.

 

[Mentz114]

Hi the-genius,

there's no twin 'paradox' in SR.

It depends on whose journey through space-time had the shortest proper-interval.

You've introduced a gravitational field which means that general relativity applies - but even so there's no paradox. All observers will agree on another observers proper time.

I suggest you give some thought to this - or change your monicker.

 

[Dale]

Hi the-genius, when you involve gravitational sources then you are talking about GR instead of SR. However, the geometrical approach of SR applies to GR also. Simply integrate the metric along each worldline. All observers will agree which is shorter.

 

[JM]

Dear Mentz 114, I hope it's polite to address another contributor. I am intrigued by your comment #27 that 'there's no paradox in SR'. In view of the volume of discussion, a generally accepted explanation would be very valuable. I tend to agree that any observer can calculate what other observers see. This implies that 'home' twin and 'traveling' twin agree on who is younger when they reunite. Most writers seem to think that this is not OK, which is the idea of the paradox. Can you tell us more?

 

[Cantab Morgan]

Most writers seem to think that this is not OK, which is the idea of the paradox. Can you tell us more?

Happily, the laws of physics need not be ratified by popular vote.

Very helpful explanations were cited in the links posted towards the beginning of the thread. But, it would be fun to discuss any parts of them that you didn't find compelling. Can you quote something specific from them that left you unconvinced?