Twin Paradox: Explaining the Relativity of Aging

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The Twin Paradox illustrates how one twin, A, who travels in space at high speeds and returns, will age less than twin B, who remains on Earth. The key to resolving the paradox lies in the fact that A experiences acceleration during the trip, while B does not, breaking the symmetry of their situations. Time dilation occurs due to A's high-speed travel and the effects of gravity, which B remains subjected to on Earth. Observations of aging and time can differ based on the reference frames and accelerations experienced by each twin. Ultimately, the paradox is resolved by recognizing that A's journey involves real changes in proper time, leading to a measurable age difference upon reunion.
  • #31
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.
 
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  • #32
the-genius said:
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.
 
  • #33
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 ).
 
  • #34
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?
 
  • #35
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.
 
  • #36
JM said:
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.
 
  • #37
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
 
  • #38
@the-genius

the-genius said:
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.
 
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  • #39
@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.
 
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  • #40
jonnyk said:
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.
 
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  • #41
@dalespam

DaleSpam said:
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.
 
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  • #42
@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.
 
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  • #44
jonnyk said:
@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).
 
  • #45
jonnyk said:
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.
 
  • #46
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.
 
  • #47
yogi said:
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.
 
  • #48
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.
 
  • #49
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?
 
  • #50


spikenigma said:
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.
 
  • #51


DaleSpam said:
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.


as I said, they shoot light beams (or pulses if you want to be specific) at each other to communicate their clock rates

using this, they can calculate [x] years have passed on Earth and [y] years have passed on the rocket, and be in agreement at any given time
 
  • #52


spikenigma said:
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?

Why should the rocket twin be older. After the acceleration, which ends before the birth, they are both in inertial frames in relative motion and so any calculation of time elapsed is reciprocal.They will each "see" each others clock running slower than their own.

Matheinste.
 
  • #53


matheinste said:
Why should the rocket twin be older. After the acceleration, which ends before the birth, they are both in inertial frames in relative motion and so any calculation of time elapsed is reciprocal.They will each "see" each others clock running slower than their own.

Matheinste.

ok then, two further things for clarification:

1)

let's say that Rocket-twin travels back to Earth (very) slowly as to minimise any time dilation and meets up with his twin. Which twin will be older/younger when he lands?

2)

during travel, why will each twin view the others clock as running more slowly than their own?
 
  • #54


spikenigma said:
using this, they can calculate [x] years have passed on Earth and [y] years have passed on the rocket, and be in agreement at any given time
No, they will always be in disagreement unless they agree on a reference frame in which to do the calculations.
 
  • #55


spikenigma said:
ok then, two further things for clarification:

1)

let's say that Rocket-twin travels back to Earth (very) slowly as to minimise any time dilation and meets up with his twin. Which twin will be older/younger when he lands?

2)

during travel, why will each twin view the others clock as running more slowly than their own?

1) The Earth twin will be older because he has remained inertial (for the purpose of this discussion) and so has traversed a longer spacetime interval and so accumulated more time on his clock than the spaceship twin.

2) Because that is what relativity says will happen.

Matheinste.
 
  • #56
Al68 said:
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.

Quite right - you and I have tried previously to get this across when the twin trip analysis creeps into the forum - and as always no one seems to appreciate how simple it is to do the one way trip and double the answer
 
  • #57


DaleSpam said:
No, they will always be in disagreement unless they agree on a reference frame in which to do the calculations.

Earth

Matheinste said:
1) The Earth twin will be older because he has remained inertial (for the purpose of this discussion) and so has traversed a longer spacetime interval and so accumulated more time on his clock than the spaceship twin.

2) Because that is what relativity says will happen.

doesn't this then imply a preferred reference frame?, which was my original point

both twins know that an object that has accelerated will experience time dilation with reference to one that has not.

When they both meet up, they can conclude that it is in fact the rocket that has accelerated and not Earth, even though rocket-twin never underwent any acceleration during his lifetime
 
  • #58


spikenigma said:
Earth



doesn't this then imply a preferred reference frame?, which was my original point

both twins know that an object that has accelerated will experience time dilation with reference to one that has not.

When they both meet up, they can conclude that it is in fact the rocket that has accelerated and not Earth, even though rocket-twin never underwent any acceleration during his lifetime

Only preferred in the sense that one is inertial and the other is not. As far as physics is concerned there is nothing that makes this inertial frame stand out from the infinite number of other inertial frames.

Acceleration is not the cause of time dilation. Each twin will consider the other to have experienced time dilation because they are in relative motion with respect to each other.

For the twins to meet up again one of them must have undergone acceleration. As the Earth twin has remained inertial (for the purposes of this discussion) then the rocket twin must have undergone acceleration.The difference in ages is not directly due to acceleration but to the differences in spacetime paths due to the acceleration of the rocket twin.

I don't really want to get into a deep discussion of the twin "paradox" as it always causes a lot of grief.

Matheinste.
 
  • #59


spikenigma said:
Earth
Then their answers will only apply to the Earth's frame. This reference frame is "prefered" only in the sense that they agreed to use it, it is not preferred in any physical sense. They could have picked any other inertial frame and the laws of physics would look the same (which is the physics meaning of a "prefered" frame).
 
  • #60


DaleSpam said:
Then their answers will only apply to the Earth's frame. This reference frame is "prefered" only in the sense that they agreed to use it, it is not preferred in any physical sense. They could have picked any other inertial frame and the laws of physics would look the same (which is the physics meaning of a "prefered" frame).

perhaps I'll clarify clearly what I mean

relativity (as far as I understand it) means that there is no preferred reference frame, i.e. if two bodies are moving at a constant velocity, no one body can say that it is the other is the one that is moving, or has moved and visa versa. It is supposed to be impossible to tell.

However, in the scenario, both of the twins can tell which one has accelerated - because one is older. Even though neither of them have ever undergone any acceleration
 

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