Twin Paradox revisited


by Physicist1231
Tags: paradox, revisited, twin
Physicist1231
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#19
May12-11, 06:03 PM
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Quote Quote by DaleSpam View Post
Why would you need to know what speed you have achieved? And relative to what?
how would you know the rate of seperation actually is changed to (or even caclulate the acceleration if you do not know the actual coordinate speeds that the individuals are going.

Is the rate of seperation mentioned (.5c) and proper velocity as mentioned by your link?
DaleSpam
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#20
May12-11, 06:12 PM
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Quote Quote by Physicist1231 View Post
how would you know the rate of seperation actually is changed to (or even caclulate the acceleration if you do not know the actual coordinate speeds that the individuals are going.
You don't need to calculate acceleration, you can measure it.

Look, this isn't complicated. Pick any reference frame you like (inertial or not) and evaluate the integral I provided in post 8. If you don't have enough information to evaluate the integral (as in this case) then your problem is incompletely specified.
Physicist1231
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#21
May12-11, 07:01 PM
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Quote Quote by DaleSpam View Post
For any clock travelling along any path P in an arbitrary coordinate system [itex]x^\mu[/itex] with metric g the time recorded on the clock is:
[tex]\int_P \sqrt{g_{\mu\nu}x^{\mu}x^{\nu}}[/tex]

Whether a particular person was asleep at some time is irrelevant.
Not trying to play dumb but can you explain this formula a little better? What does each variable represent?
1MileCrash
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#22
May12-11, 07:26 PM
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Quote Quote by Physicist1231 View Post
why though? How do you know what speed you have achieved if you dont know what speed you were going prior to the acceleration?
Since acceleration is absolute, we will get the same result for all reference frames. Therefore, you know your acceleration in terms of net change.

You can define your speed/direction to be X. You can define your acceleration to be a net change in speed of 1 unit. This net change can be negative or positive. We will say that you accelerate in direction "A." All reference frames will observe that change of speed of 1 unit, regardless of the relative speed of and direction of X.

However, all reference frames will not agree on whether or not you slowed down, sped up, start moving, or stopped moving, or changed direction, because the motion is still relative.

For example, a frame which measures X as 50 mph going in direction "A" will observe you speed up to 51 mph.

A frame which measures X as 50 mph going in direction "B" will observe you slow down to 49 mph.

A frame which measures X as 0 mph will observe you to start moving in direction A at 1 mph.

A frame which measures X as 1 mph in direction B will observe you stop moving.



As you can see, that initial speed of X can be whatever we want, but the net change in speed will always be 1 MPH and is therefore absolute. Acceleration is a change in speed, what the speed started and ended at is relative, but the difference between the two is absolute.


Granted you can get the relative speeds from the other reference point but both parties (measuring each other) will percieve the same thing.

Person A sees Person B moving at .5c and vice versa. At this point there have been no change of speeds

With this rate of seperation person A thinks that B is aging slower due to how he percieves B and B thinks that A is aging slower because of how he percieves A.

Who is right? In this case they cannot both be actually right since they are percieving the same ratio. Or are they both wrong and both aging at the same rate?
Actually, they are both right. In A's reference frame B is aging slower. In B's reference frame A is aging slower. They don't agree, because they are in different reference frames. Bring them back together in the same reference frame, and they must agree (read on.)

The (named) paradox lies in the fact that if they are brought within the same reference frame, they can't perceive one another as being younger, and this is true. However, that can never happen. Bring them back together by accelerating them at equal amounts will render them agreeing on their age (how much time has passed.) An unequal amount of acceleration will make them agree that one is absolutely younger than the other.

When they are in the same reference frame, they must observe the same thing, and they will agree on everything. This is because for them to be in the same reference frame after speeding away from one another, one or both must accelerate. If they both accelerate at equal amounts, they agree that they are the same age. If A accelerates more than B, they will both agree that A is the younger twin. If B accelerates more than A, they will both agree that B is the younger twin.

Does that make sense?



This brings up the point of Actuallity and Perception. What is being percieved and what is actually happening?
It doesn't really work that way.
kmarinas86
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#23
May12-11, 08:15 PM
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Quote Quote by Physicist1231 View Post
According to what I have researched in Relativity (thanks to you guys) there is no such thing as absolute motion, time, or distance. I had a question about this paradox mentioned.

Paraphrase:

Two people that are exactly 20 years old are on earth. One decides to fly to planetX and some fraction of C. When he comes back he will be older.

This is further explained because the person on earth could watch the flyers clock and it would be slowing down for the acceleration thus age slower.

With this said here is my question.

Those same two people at the exact age of 20 are in space with no other objects to define a relative speed for. They feel no acceleration so they assume they are at rest.

They fall asleep because it is boring and there is not much to do out there. They wake up to find that the distance between them is increasing dramaticly. They have a rate of seperation (according to both observers) of .5C (I am intentionally not saying who is actually moving since speed is relative only). According to each individual they are at rest and the other person is moving.

Again they get bored and fall asleep. When they wake up the find that the distance between them is decreasing at the same rate it was increasing. So now the closing velocity between them is .5c

If there is no "absolute speed, motion, or time" then when they get back together who has aged? Since speed is relative and we assumed the person on the earth was "motionless" that he did not age as much. But now we could have the same setup but dont have the earth to compare motion to so we dont know if we are still ot the other person is still. We just have a rate of seperation.

Any Ideas?
There is no absolute motion, but there can be an absolute difference of two motions. This does NOT mean that acceleration is absolute. The time experienced by different non-inertial observers can change that (i.e. the s inside m/s^2).

The twin on the rocket is affected by the thrust of propellant, while the twin on the Earth is not. Dynamical effects occur on the first twin which do not occur on the second.

The motion of the twin on the Earth is not changing as rapidly as the motion of the twin in the rocket ship.

The paradox is solved by GR.

Quote Quote by Physicist1231 View Post
why though? How do you know what speed you have achieved if you dont know what speed you were going prior to the acceleration.
A car going from 0 to 60 on the road may be going 30,000 to 30,060 relative to some distant planet. The key is that the car "feels" the difference between the two velocities. It was not important to measure the car's speed relative to planet X, or whatever. The same goes for a rocket.

Devices have been developed to measure the effects of acceleration. Simply measuring a force is sufficient for such a task, which is what accelerometers do. Distance itself doesn't need to be measured.

Proper acceleration is NOT relative to an observer, but coordinate acceleration is. The proper acceleration is what you should consider as relevant to the Twin Paradox. Basically, it is the acceleration received by physical, non-fictitious forces. Such forces involve the transfer of kinetic energy to or from a given body. Such forces are defined by direct interaction on the body. This is what causes the difference between the twin on the Earth and the twin on the relativistically-fast rocket. The rocketing twin has gained much more kinetic energy in the process, and is therefore mechanically subject to a literal slow-down of its clocks.

This effect persists even after acceleration has stopped. For example, the time dilation of relativistically-fast mu-mesons from outer space persists in such a manner that even after they have accelerated, their clocks have slowed down to the effect they do not decay until the particles collide with the Earth's atmosphere. This is a physical effect not attributed to the their coordinate motions relative to some arbitrary observer.

The acceleration requires a literal build up of inertial mass. So the rocket twin somehow gains inertial mass. The mass is derived by the energy released by the reaction causing the rocket to gain momentum. The Earth twin has no such contribution to its inertial mass.
kmarinas86
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#24
May12-11, 08:58 PM
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Quote Quote by 1MileCrash View Post
Actually, they are both right. In A's reference frame B is aging slower. In B's reference frame A is aging slower. They don't agree, because they are in different reference frames. Bring them back together in the same reference frame, and they must agree (read on.)

The (named) paradox lies in the fact that if they are brought within the same reference frame, they can't perceive one another as being younger, and this is true. However, that can never happen. Bring them back together by accelerating them at equal amounts will render them agreeing on their age (how much time has passed.) An unequal amount of acceleration will make them agree that one is absolutely younger than the other.

When they are in the same reference frame, they must observe the same thing, and they will agree on everything. This is because for them to be in the same reference frame after speeding away from one another, one or both must accelerate. If they both accelerate at equal amounts, they agree that they are the same age. If A accelerates more than B, they will both agree that A is the younger twin. If B accelerates more than A, they will both agree that B is the younger twin.

Does that make sense?
You need to distinguish the difference between proper acceleration and coordinate acceleration.

If you do not take GR into account, what you tend to end up with is a misleading notion of symmetry, where the distance between the twins is understood to be the same for both, and that the rate change of this distance is the same for both, and that the rate of change of the rate change of this distance is the same for both. This is where most people get it wrong.

The truth is that proper acceleration is what matters in this situation. That is to say the acceleration which can be measured with the body being accelerated. It is the consequence of physical forces acting on the body in question.

SR simply doesn't deal with proper acceleration. That's one the reasons why GR is relevant here.

When you say this:

"In A's reference frame B is aging slower. In B's reference frame A is aging slower. They don't agree, because they are in different reference frames. Bring them back together in the same reference frame, and they must agree (read on.)"

The first three sentences relate to a Special-Relativistic effect (connected to relative velocity), while the last one is the result of a General-Relativistic effect (connected to accumulated time delay that results from an increased inertial mass due to accumulated proper acceleration).

Another note I would like to make is on this use of the word "agree" that we see so often when comparing observers. The person on the Earth saying that he/she aged 10 microseconds more than the person on the rocket, who in turn says that he/she aged 10 microseconds more than the person on the Earth is not agreement between the observers, but nor is either claim in agreement with the reality. What is 10 microsecond "less aged" in this case is the image received by other observer. It makes no sense to say that other person aged 10 microseconds less just because his/her image took 10 extra microseconds to get to the observer. This Special-Relativistic effect, which is misattributed to a "reduced aging rate" of the "other" twin, is simply due to the fact that the light, just like any other wave, is subject to the Doppler effect.

To claim that there is a difference in aging occurring with relative velocity alone is just as errant as saying that the aberration of light means that the observed object is physically distorted in a way depending the reference frame. They are only time delays (http://www.youtube.com/watch?v=wteiuxyqtoM) and optical distortions (http://www.youtube.com/watch?v=JQnHTKZBTI4) of the image received. Observing the image of the object the moment it is received is not evidence of a simultaneous event any more than the sound of thunder or the image of lighting is evidence of a simultaneous event.
DaleSpam
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#25
May12-11, 09:28 PM
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Quote Quote by Physicist1231 View Post
Not trying to play dumb but can you explain this formula a little better? What does each variable represent?
P is the path, x is the coordinate location of the clock, and g is the metric. It is the equation of the arc length along a curve, called the space-time interval in relativity. In other words a clock measures the length of its worldline in spacetime.
harrylin
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#26
May13-11, 06:47 AM
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Quote Quote by Physicist1231 View Post
According to what I have researched in Relativity (thanks to you guys) there is no such thing as absolute motion, time, or distance. [...]
That statement is baseless if you use Newton's definition of absolute motion or even current concepts of rotation (see next); it's therefore better to say that measurements of motion, time and distance are relative to the used reference system.

A careful reading of the first paper on this topic may be useful to avoid this kind of misunderstandings. You can find a translation here:

http://en.wikisource.org/wiki/The_Ev...Space_and_Time
(in particular p.46 - 53)

Cheers,
Harald
Physicist1231
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#27
Feb9-12, 11:43 AM
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Quote Quote by DaleSpam View Post
Because acceleration can be directly measured with an accelerometer without reference to any external object. Velocity cannot.

See: http://en.wikipedia.org/wiki/Proper_acceleration
and http://en.wikipedia.org/wiki/Covariant_derivative
Then what about teh Wiki page defining an accelerometer?

An accelerometer is a device that measures proper acceleration, also called the four-acceleration. For example, an accelerometer on a rocket accelerating through space will measure the rate of change of the velocity of the rocket relative to any inertial frame of reference.

Thus it uses and extenal FOR to determine acceleration so how can acceleration be deemed "absolute" when time and velocity are not deemed so?

(just to clear things up, i do believe that absolute acceleration is properly defined and can be attained, my argument is that the componenets that make up acceleration should also be as well based on this logic)


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