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 accleration 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 accleration" 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 accleration 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 'theres 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?

 

[the-genius]

I think there is an interesting consequence of this time dilation.
After return since the traveling twin is younger, it implies that he he is bacward in time. So, even though he may occupy same position in space with another twin (means he hits the other twin), he is at different time, so he won't collide. I mean he will be like a ghost.

 

[ZikZak]

I think there is an interesting consequence of this time dilation.
After return since the traveling twin is younger, it implies that he he is bacward in time. So, even though he may occupy same position in space with another twin (means he hits the other twin), he is at different time, so he won't collide. I mean he will be like a ghost.

Um... No. He is not a ghost or "backward in time." He's at the same time and place as his twin.

 

[Mentz114]

JM:

This implies that 'home' twin and 'traveling' twin agree on who is younger when they reunite.

All inertial observers will agree on the which twin is younger. Because this quantity is based on proper-interval which is Lorentz invariant.

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

They're wrong. There's nothing more to be said ( I don't have time to explain SR ).

 

[JM]

To Cantab Morgan et al: Re your reply #30. Yes, here's something specific. It is usual to explain the twin paradox by introducing rockets or acceleration at the turnaround point. Yet Einstein obtained his clock paradox without any rockets or accelaration. If we look for an explanation of Einsteins result we should look within his analysis, and not invoke sometthing he ignored ( acceleration). I believe his 'paradox' can be explained as a correct outcome of hiis analysis, and that 'time dilation' is involved.
Has no one else looked at the 1905 paper for explanation, and if so what did they find?

 

[Dale]

Relativity has progressed since 1905. I don't see the point in restricting ourselves to what Einstein wrote about in those very early days. In any case, you cannot possibly have a turnaround without acceleration.

I agree with Cantab Morgan. Please read the FAQ and get back to us on any specific point you don't understand. Show some good-faith effort to not waste everyone's time on things that are well explained in the FAQ.

 

[ZikZak]

To Cantab Morgan et al: Re your reply #30. Yes, here's something specific. It is usual to explain the twin paradox by introducing rockets or acceleration at the turnaround point. Yet Einstein obtained his clock paradox without any rockets or accelaration. If we look for an explanation of Einsteins result we should look within his analysis, and not invoke sometthing he ignored ( acceleration). I believe his 'paradox' can be explained as a correct outcome of hiis analysis, and that 'time dilation' is involved.
Has no one else looked at the 1905 paper for explanation, and if so what did they find?

Relativity does not belong to Einstein. It belongs to physics. Not everything Einstein said was right, or the best way to interpret the theory. Einstein moved on from 1905, and so should we.

 

[cristoper]

I found this defense of Relativity by Einstein helpful when I was struggling with the Twin Paradox:

http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

 

[jonnyk]

@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.

JK- You probably know that in case of a gravitaional field the ones in the stronger field at the bottom age slower than those further away as per GR don't you? So if a massive object pulls a less massive object towards it, the less massive one will perceive all reactions on the more massive one as being slower than the same would in it's own reference frame. SO when a human being is being accelrated to the earth, which si mroe massive, he/she would perceive say all heart beats of human beings on the surface of the Earth slower than his own. AGAIN all this is real. So for more significance if say we lived on a black hole and there was a tall building, the ones at the top would not just appear to be aging more fast for the ones at the bottom and when they come back down everythings normal, NO, but when they come back down theyr ACTUALLY much older and prooably much more knowledgeable than the bottom ones since ALL NATURAL PROCESSES SLOWED DOWN for the ones at the bottom.
Note that people on the ground of the black hole are accelerating MORE than the ones whor still further away in an absolute sense. By applying GR and SR we cannot tell how much an object approaching us has accelerated from absolute rest, where rest is itself relative and absolute rest on every level means nothing since nothing would be going on to form anything as well, but we can determine the ratio of acceleration between us and the object starting from our and it's existence in the form of mass.

 

[jonnyk]

@the-genius
I would like to explain your example further. Remember that real time dilaiton is dependant on ACCELERATION NOT VELOCITY. Say two rockets initially at rest wrt Earth in space start accelrating towards each other to a speed of 50000 km/hr. Now theyd be approaching each other with 100,000 km/hr. This means that there would now be APPARENT time dilation only. That means that although both of them will now age equally wrt each other and will experience no difference in age once they both woudlve slowed down simulatanously, each one of them will see the other as acting slower optically AS LONG AS THEYR STILL SPEEDING AWAY FROM EACH OTHER.

 

[Dale]

Remember that real time dilaiton is dependant on ACCELERATION NOT VELOCITY.

The http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Clock_Hypothesis" says "the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives". It has been experimentally validated up to accelerations of about 10^18 g. I don't know what you mean by "real" time dilation, but whatever you mean it needs to be consistent with the clock hypothesis.

 

[jonnyk]

@dalespam

The http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Clock_Hypothesis" says "the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives". It has been experimentally validated up to accelerations of about 10^18 g. I don't know what you mean by "real" time dilation, but whatever you mean it needs to be consistent with the clock hypothesis.

JK- That experiment was done relative to the Earth which where we knew that the plane was accelrating whilst the Earth was not so the clock on the plane would be slower than that left on earth. If you have two rockets in space set a distance apart, initially at rest wrt the earth, then you accelrate BOTH of them towards each other, youd ofcourse have a real time difference between the clock on Earth AND those onboard those rockets BUT NOT between the clocks onboard both rockets even though they too experienced a +ve velocity wrt each other. In other words once the rockets are slowed down simulatanously i.e. one with the same deceleration as the other, and both brought back to earth, one would find both clocks from both rockets synchronised as before and both of them out of synch with the one on Earth that was initially in synch with them too.

 

[jonnyk]

@dalespam
Clock hypothesis: "the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives"

And this is exactly how it is. the two rockets ARE NOT INERTIAL wrt each other because we have the Earth as reference to them which is the inertial frame here.

 

[jonnyk]

Check this out:
http://en.wikipedia.org/wiki/Twin_paradox

 

[JesseM]

@dalespam
Clock hypothesis: "the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives"

And this is exactly how it is. the two rockets ARE NOT INERTIAL wrt each other because we have the Earth as reference to them which is the inertial frame here.

The rockets are not inertial, but you can still define their position as a function of time from the perspective of any inertial frame (i.e. in that frame's space and time coordinates), and thus define the velocity of each rocket as a function of time v(t), and from the perspective of this inertial frame the rate that each rocket's clock is slowed down as a function of time is always \sqrt{1 - v^2/c^2}--it only depends on the instantaneous velocity, not the instantaneous acceleration. If in this frame the rockets depart from another at time t0 and reunite at time t1, then if you know one of the rocket's velocity as a function of time v(t) in this frame, you can always calculate the total time elapsed on that rocket's clock between meetings with the other rocket using the equation \int_{t_0}^{t_1} \sqrt{1 - v(t)^2 /c^2} \, dt, which will give you the correct answer (and you'll get the same answer regardless of what inertial frame you use, in spite of the fact that each frame defines the velocity as a function of time v(t) differently, and also assigns different time-coordinates to the departing and reuniting).

 

[Dale]

And this is exactly how it is. the two rockets ARE NOT INERTIAL wrt each other because we have the Earth as reference to them which is the inertial frame here.

Please read carefully what JesseM said. As he said, the time dilation on the rocket's clock is a function of the rocket's velocity in the inertial frame, not a function of their acceleration.

Also, the two rockets are not inertial. This is an absolute statement not a relative one. You do not need to specify the reference frame and saying that they are not inertial wrt each other doesn't make any sense.

 

[yogi]

The twin Paradox again - it is never going to be correctly explained by invoking acceleration - even though Einstein fell into his own trap in 1918 by attempting to rationalize the difference in aging by introducing a pseudo G field at turn around to account of the age difference - this lead to a lot of papers and books erroneously claiming the Twin Paradox required General Relativity to be fully explained.

Break the probem into two trips - one outbound and one inbound - no initial acceleration - simply start the clocks at zero when the hi speed spaceship flies by Earth - and stop the spaceship clock when it reaches Alpha Centuri - pass the reading to a spaceship headed toward Earth and start the clock in the second spaceship when it passes Alpha Centuri - stop the second clock when it reaches earth.

 

[JesseM]

Break the probem into two trips - one outbound and one inbound - no initial acceleration - simply start the clocks at zero when the hi speed spaceship flies by Earth - and stop the spaceship clock when it reaches Alpha Centuri - pass the reading to a spaceship headed toward Earth and start the clock in the second spaceship when it passes Alpha Centuri - stop the second clock when it reaches earth.

Acceleration per se is not the key, what's important is the geometry of the two paths through spacetime whose time you want to measure. If you have two events in spacetime and two worldlines between them, one of which is a "straight line" through spacetime (corresponding to the worldline of an inertial observer moving at constant velocity) and one of which is "bent", then the total amount of time along the bent path (even if you measure it using a few different clocks that pass off readings when they meet rather than a single clock that follows the entire path) will always be less than the time along the straight-line path. This is directly analogous to the fact that on an ordinary 2D plane, if you pick two points in the plane and draw two spatial paths connecting them, one of which is straight and the other being bent, then the bent path will always have the greater distance, because a straight line is the shortest distance between two points. If the bent path was made up of two straight segments connected at a sharp angle, you could measure the distance either by having a single car drive the entire path with its odometer running (making a sharp turn at the bend), or by having two cars driving in straight lines along each segment, with the first car passing its odometer reading to the second when they cross paths at the bend.

 

[Al68]

Why not just look at a one way trip where the ship doesn't return, but just comes to rest with Earth and stays there indefinitely?

The answer is the same (divided by two) and the reason for it is clearer.

Then just double that answer.

 

[spikenigma]

a slight variation

reading through this thread has been interesting

instead of creating a new thread, I'd like to offer a little variation if I may:

A Rocket is an arbitrary distance from Earth, it accelerates up to a constant 0.7c

As the rocket hurtles past Earth at that constant speed, two twins are born, one on Earth and one on the rocket. Rocket-twin and Earth-twin know that they were both born at the same time.

They then communicate with each other with (VERY powerful lasers). Rocket-twin asserts that he is stationary and that the Earth is moving away from him at 0.7c, Earth-twin asserts that the Earth is stationary and Rocket-twin is moving.

If Rocket-twin is older than Earth-twin, doesn't that make Earth the preferred reference frame?

 

[Dale]

If Rocket-twin is older than Earth-twin, doesn't that make Earth the preferred reference frame?

How do you determine which is older? Because they are separated you must use some simultaneity convention. Then the answer applies only to that frame.