What Makes the Twin Paradox a Paradox in Einstein's Theory of Relativity?

[marconism]

why do we call the "twin paradox" a paradox in einstein's theory of relativity when we know exactly that the phenomena it describes is possible theoretically

 

[Nereid]

Welcome to Physics Forums, marconism!

I've split your post from the thread you originally posted it to (it was entirely inappropriate there), and started a new thread in S&GR.

 

[TRCSF]

Alright, so you've probably heard it explained as the one twin getting on a spaceship and zooming around at 99+% the speed of light, then when he gets back to Earth he's still young, but his twin brother has aged into an old man. This is as far as most explanations of the paradox gets, but it's only half of the paradox.

The paradox comes in because from the astronaut's reference frame, it's the earthbound twin that's zooming around at 0.99C, so he should be the one that stays young and the twin in the spaceship should be the old one when they reunite.

Turns out there's a solution for that paradox.

 

[jdavel]

macronism,

People who understand SR usually call it the twin "paradox" indicating that they are quoting a generally accepted label for a phenomenon of physics, but not accepting that the word used for the label is correct.

People who don't understand SR call it the twin paradox as if the phenomenon to which it refers is impossible therefore disproving SR.

It sounds to me as though you're in the first group, as most people here are; welcome to the board!

 

[HannonRJ]

There is no "twins paradox". That "paradox" is a misapplication of Einstein's transformation equations.

 

[General_Relativity21]

Doesnt the twin paradox have to assume the round trip was done in one reference frame? in order for the paradox to be true?

 

[yogi]

In his 1905 paper founding the theory of Special Relativity, Einstein raised the issue of what has since been termed the “Clock Paradox.” He opined that Lorentz Transformations result in asymmetrical ageing between inertial frames in relative motion, specifically that clocks in relative motion would appear to run at different rates when measured against one another; and that a clock aboard a spaceship that departs, executes a “turn-around” and returns to its origin, would always accumulate less time than a clock in the frame where the motion is measured. The phenomena was subsequently anthropomorphized by Langevin as the well known “Twin Paradox” wherein a traveling twin returns home to find his stay-behind sibling older than himself. Since, according to Special Relativity, neither twin is able to determine absolute motion with respect to space, the situation appears symmetrical., And because there is mutual agreement as to their relative velocity, each should observe the other twin’s clock rate as altered by the same factor; ergo there should be no age difference when the twins reunite. Most authorities, including Born and Langevin quickly dismissed the paradox by asserting that kinematical symmetry is broken because the traveling twin changes from one inertial system to another during turn around i.e., the traveling twin feels the acceleration and deceleration that is required to change velocity and direction. This proscription was quickly challenged by von Laue who argued that the dynamical aspects of turn-around would be insignificant compared to the ageing effect of an extended voyage. Moreover, the acceleration can be eliminated entirely if the outbound twin simply transfers his clock reading to a passing homeward bound traveler. This is the so called triplet paradox.

This is the origin of the term - while there is agreement as to the fact that the two twins age at different rates, there is still disagreement as to why

 

[jdavel]

yogi,

"...while there is agreement as to the fact that the two twins age at different rates, there is still disagreement as to why..."

But there is agreement that the reasons "why" are all the same. Because in relativity there is always only one reason for anything, and that is that c' = c.

 

[yogi]

That is true in the sense that all roads lead to the same result and all mainstream physics is based upon c' = c. But amongst mainstreamers there is no explanation as to the physics that is uniformly agreed upon - there is only agreement as to the outcome that follows from the transforms.

 

[JesseM]

Most authorities, including Born and Langevin quickly dismissed the paradox by asserting that kinematical symmetry is broken because the traveling twin changes from one inertial system to another during turn around i.e., the traveling twin feels the acceleration and deceleration that is required to change velocity and direction. This proscription was quickly challenged by von Laue who argued that the dynamical aspects of turn-around would be insignificant compared to the ageing effect of an extended voyage.

von Laue's argument as you describe it is totally spurious, because no one argues that the difference in ages somehow only occurs during the period when the other twin is accelerating--the argument about acceleration is just that it allows us to know which twin traveled in a straight line through spacetime between the two events and which twin traveled in a broken line (as seen in any inertial reference frame). This is just like the "right triangle paradox" where you have two twins who walk between two points in space A and B, and one travels in a straight line while the other travels straight away from A, then makes a 90-degree turn, then travels straight until he arrives at B; the twin who made the turn will have walked a longer distance than the twin who didn't, but the extra distance didn't all accumulate during the moments he was turning!

 

[yogi]

Jesse - my old critic. I think you will find there are many who attribute twin ageing differences to the acceleration in one way or another.

Take a look at what Max Born has to say at page 261 of his book "Einsteins' Theory of Relativity"

"...for sufficiently long journeys the short periods of acceleration exert no influence on the beating of clocks. But this holds only when we are judging things from the inertial system of A and not for the measurement of time in the accelerated system of B."

and at page 355:

"...when the system of reference is altered definite gravitational fields must be introduced during the times of acceleration" ...of the three gravitational fields the first and the last have no influence on the relative rates of clocks of A and B since they are at the same points at the moment of departure and return and since a difference of rate occurs in a gravitational field ...only when there is a distance L between the clocks."

Born goes on to attribute the time difference to (gL/c^2)t because there is a turn around acceleration...concluding "Thus the clock paradox is due to a false application of the STR, namely to a case in which the methods of the general theory should be applied."

I think Born is way off base on this - I merely quoted it to show that there are many ways of explaining the twin caper -

and please don't write me a book about it.

Thanks

Yogi





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[JesseM]

Jesse - my old critic. I think you will find there are many who attribute twin ageing differences to the acceleration in one way or another.

Yes, so do I, just like I attribute the longer path length in the "triangle paradox" to the fact that the twin made a 90-degree turn. But that doesn't mean that all the extra path length happened only during the moments he was executing that turn.

I think Born is way off base on this - I merely quoted it to show that there are many ways of explaining the twin caper -

and please don't write me a book about it.

What Born is saying is that if you want to try to consider things from the non-inertial "frame" of the twin who accelerates, you must bring in GR (and even if you do this, I don't think Born is saying that all the age difference happens during the moments of acceleration, although I'm not very well-versed in GR so I can't be sure). My explanation was just about how the two paths look if you stick to analyzing both twin's motions from the point of view of an inertial frame (which doesn't necessarily have to be the frame of the stay-at-home twin), as you must if you want to deal with the problem using only SR. So, I see no conflict between my explanation and the quotes by Born you posted.

 

[jdavel]

yogi,

Two objects, A and B, collide. "While there is agreement as to the fact that the two" objects collided, "there is still disagreement as to why". Most physicists say that A ran into B. But "I think you will find there are many who attribute" the collision to B running in A. I think they're "way off base on this". But it does go to show that "there are many ways of explaining" the collision.

What you are claiming is just as silly as this!

 

[Alkatran]

Triplets paradox:
Let's look at it only from the perspective of the third triplet, ok?

Ok. In 3's frame of reference 2 leaves 1 and starts heading towards 3.

3 heads towards 1 and is passed by 2, 1 is still aging slower than 3. According to 1, 3 is aging slower.

3 reaches 1 and they both agree on how much they aged.


Why? Because when, in 3's reference frame, when 2 and 1 took off, 3 was in a position which, according to 1's frame of reference, was in the past.

 

[yogi]

djavel - I don't know what you are smoking - but its obviously not something one can get at the local tobacco store.

 

[HannonRJ]

Yogi. Please point out the symbol(s) in Einstein's transformation which pertain to physical objects.