Was Einstein lucky when not considering twin paradox as paradox?

[adoion]

hi,

Einstein did not even consider the twin paradox as problematic at all, he argued that it is a simple consequence of his special relativity?

obviously he never gave a explanation of why the two twins don't age the same he instead left it to others to do so.

was Einstein just having a hunch witch turned out to be just a lucky guess?

 

[Nugatory]

Einstein did not even consider the twin paradox as problematic at all, he argued that it is a simple consequence of his special relativity?

obviously he never gave a explanation of why the two twins don't age the same he instead left it to others to do so.

was Einstein just having a hunch witch turned out to be just a lucky guess?

The twin paradox was properly understood by Einstein and other physicists from the beginning; no one who understands relativity has ever thought that it is problematic. It only started being called a "paradox" later, when we realized that it could be used as a teaching tool like the other "paradoxes" of relativity, such as the classic pole-barn and bug-rivet problems (google will find both of these online).

There is an interesting and important problem associated with the twin paradox (and these other "paradoxes") but it's not a problem of understanding. It's how to explain them to someone who is still learning special relativity, and teachers have been working on that one for a century now.

 

[adoion]

The twin paradox was properly understood by Einstein and other physicists from the beginning; no one who understands relativity has ever thought that it is problematic. It only started being called a "paradox" later, when we realized that it could be used as a teaching tool like the other "paradoxes" of relativity, such as the class pole-barn and bug-rivet problems (google will find both of these online).

There is an interesting and important problem associated with the twin paradox (and these other "paradoxes") but it's not a problem of understanding. It's how to explain them to someone who is still learning special relativity, and teachers have been working on that one for a century now.

All right so how did Einstein understand the twin paradox, did he consider the acceleration of the traveling twin witch goes out of the scope of special relativity or did he argue that the traveling twin uses 2 inertial frames of reference?

 

[ghwellsjr]

hi,

Einstein did not even consider the twin paradox as problematic at all, he argued that it is a simple consequence of his special relativity?

obviously he never gave a explanation of why the two twins don't age the same he instead left it to others to do so.

was Einstein just having a hunch witch turned out to be just a lucky guess?

Of course not. He described in his 1905 paper the result and calculated the difference in "aging" between two clocks starting out together but one remaining inertial while the other one takes a trip and circles back to the inertial clock. You can read about it here at the end of section 4:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

 

[Nugatory]

All right so how did Einstein understand the twin paradox, did he consider the acceleration of the traveling twin witch goes out of the scope of special relativity or did he argue that the traveling twin uses 2 inertial frames of reference?

There's a widespread misconception that you need general relativity in situations involving acceleration, but it's just not true; special relativity handles acceleration just fine. You can google for "Rindler coordinates" for one example, and you'll find another example (a clock experiencing uniform circular motion due to the Earth's rotation) in Einstein's original 1905 paper to which ghwellsjr gave you a link above.

This misconception propagates because very few first-year courses and textbooks cover this material. The math is appreciably more complex and introduces no new physical insights, so the examples and problems in these courses and books generally don't include acceleration.

 

[adoion]

Of course not. He described in his 1905 paper the result and calculated the difference in "aging" between two clocks starting out together but one remaining inertial while the other one takes a trip and circles back to the inertial clock. You can read about it here at the end of section 4:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

as far as I can tell there is no explanation of the twin paradox just a similar statement in his paper, a statement without deeper inside in why this has to be or a consideration of what would happened if we assume the Earth is moving and the rocket twin is still. as I said just a statement confusingly written for modern standards I guess.
and if he was so precise about this statement then why was there a need anyway to clarify this "PARADOX". if it was just stated for educational purposes and a couple of different explanations where given??

 

[Nugatory]

and if he was so precise about this statement then why was there a need anyway to clarify this "PARADOX". if it was just stated for educational purposes and a couple of different explanations where given??

One of meanings of the English word "paradox" is "something that appears at first glance to be contradictory, but with deeper understanding is not". We're using this definition when we speak of the "paradoxes" of special relativity, and we use a student's ability to properly explain them as a measure of the student's understanding of SR.

 

[phinds]

as far as I can tell there is no explanation of the twin paradox just a similar statement in his paper, a statement without deeper inside (sic) in why this has to be or a consideration of what would happened (sic) if we assume the Earth is moving and the rocket twin is still.

Einstein certainly understood, as would a physics 101 student, that relative to the Earth, the stay at home twin was not accelerating whereas the traveling twin was and thus they are not symmetrical. He probably didn't feel that that needed to be pointed out.

 

[stevendaryl]

as far as I can tell there is no explanation of the twin paradox just a similar statement in his paper, a statement without deeper inside in why this has to be or a consideration of what would happened if we assume the Earth is moving and the rocket twin is still. as I said just a statement confusingly written for modern standards I guess.
and if he was so precise about this statement then why was there a need anyway to clarify this "PARADOX". if it was just stated for educational purposes and a couple of different explanations where given??

Einstein starts off, in his derivation of the Lorentz transforms, with:

Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good...​

This line is not explained in any more detail, but the way I interpret it is that it means an inertial system of coordinates. In a noninertial coordinate system, the laws of Newtonian mechanics don't hold good--that is, objects can accelerate relative to a noninertial coordinate system without any physical force being applied.

So from the very beginning, Einstein was talking about a special set of coordinate systems. In the case of a rocket taking off from the Earth, turning around, and returning, there is no inertial coordinate system in which the rocket is at rest at all times.

 

[PeroK]

as far as I can tell there is no explanation of the twin paradox just a similar statement in his paper, a statement without deeper inside in why this has to be or a consideration of what would happened if we assume the Earth is moving and the rocket twin is still. as I said just a statement confusingly written for modern standards I guess.
and if he was so precise about this statement then why was there a need anyway to clarify this "PARADOX". if it was just stated for educational purposes and a couple of different explanations where given??

Special Relativity is not, solely, the Twin Paradox! The point of the 1905 paper was not to explain this one aspect of SR, but (with beautiful insight and simplicity) to prove that (given the postulates which are clearly stated) time and distance are not universal for all observers, and to provide quantitative predictions for the experimentalists to verify.

If you are saying: "Einstein didn't explain the twin paradox very well". Well, maybe so, but that was not what he was trying to do.

By limiting your interest to this one "paradox", you are missing the whole essence of SR. Why not read the paper and try to understand what it is saying?

 

[ghwellsjr]

All right so how did Einstein understand the twin paradox, did he consider the acceleration of the traveling twin witch goes out of the scope of special relativity or did he argue that the traveling twin uses 2 inertial frames of reference?

Of course not. He described in his 1905 paper the result and calculated the difference in "aging" between two clocks starting out together but one remaining inertial while the other one takes a trip and circles back to the inertial clock. You can read about it here at the end of section 4:

http://www.fourmilab.ch/etexts/einstein/specrel/www/

as far as I can tell there is no explanation of the twin paradox just a similar statement in his paper, a statement without deeper inside in why this has to be or a consideration of what would happened if we assume the Earth is moving and the rocket twin is still. as I said just a statement confusingly written for modern standards I guess.
and if he was so precise about this statement then why was there a need anyway to clarify this "PARADOX". if it was just stated for educational purposes and a couple of different explanations where given??

It's not an issue of one clock moving and the other clock not moving, it's that one clock is inertial and the other clock is not inertial.

In his 1905 paper, Einstein only considered Inertial Reference Frames (IRF's) and he described the "twin paradox" using the IRF in which the inertial clock was stationary. You only ever need one IRF to define a scenario. It doesn't matter whether the clocks are stationary, moving inertially at a constant velocity in any direction, or changing speeds and/or directions (accelerating), one IRF is all you need. But if you want, you can transform the coordinates of all the significant events according to the defining IRF to another IRF that is moving with respect to the defining IRF and this will make the stationary clock move at some constant speed but it is still inertial and it will make the other clock move at different speeds, even being stationary during some part of the scenario, but it is still non-inertial.

So when you define a scenario according to one IRF where the first twin remains inertial on the Earth and the other twin travels away from the Earth at a constant speed and direction and then turns around and travels back at that same constant speed but in the opposite direction, there are two more different IRF's in which the traveling twin is at rest during each half of the trip and the Earth twin is moving inertially but you must consider the entire scenario from each of these two IRF's. The Time Dilations of the twins will be different in each of these three IRF's but they will all explain the difference in aging between the twins identically.

Perhaps a concrete example will help. Let's consider a typical Twin Paradox. I'm going to depict the Earth twin in blue and the traveling twin in red. The traveling twin departs Earth at a speed of 0.6c and after 8 years according to his clock, he turns around and spends another 8 years coming back at the same speed. When he reunites with the Earth twin, they find that the Earth twin has aged 25 years while the traveling twin has aged 16 years. The dots on this diagram mark off one-year increments of time for both twins:

Please note that in this IRF, it is only the traveling twin whose clock is Time Dilated by a factor of 1.25 during the entire scenario. This is because his speed is 0.6c during the entire scenario according to this IRF. Also note that the Earth twin is inertial during the entire scenario while the traveling twin is not inertial during the entire trip.

For the next two IRF's and their diagrams, I'm going to refer to the Earth twin as the inertial blue twin and the traveling twin as the non-inertial red twin.

First we're going to transform to the IRF in which the non-inertial red twin is at rest during the first part of the scenario. The diagram looks like this:

Note how the inertial blue twin is moving at -0.6c during the entire scenario and so his clock is Time Dilated by 1.25 the entire time. During the first part of the scenario, the non-inertial red twin's clock is not Time Dilated because he is not moving. But at his time of 8 years, he starts moving at -0.882c where his Time Dilation is now 2.125 and after 8 more years he catches up to the inertial blue twin who has aged 25 years by the time they reunite.Finally we're going to transform to the IRF in which the non-inertial red twin is at rest during the last part of the scenario:

This is similar to the previous IRF so we can use the same numbers but in different orders but the net result is that the twins age by the same amounts.

I hope this is clear and removes all your confusion. If not, ask.

 

[Fantasist]

Special Relativity is not, solely, the Twin Paradox! The point of the 1905 paper was not to explain this one aspect of SR, but (with beautiful insight and simplicity) to prove that (given the postulates which are clearly stated) time and distance are not universal for all observers, and to provide quantitative predictions for the experimentalists to verify.

If you are saying: "Einstein didn't explain the twin paradox very well". Well, maybe so, but that was not what he was trying to do.

By limiting your interest to this one "paradox", you are missing the whole essence of SR. Why not read the paper and try to understand what it is saying?

It seems to me that the OP read and understood Einstein's paper very well. What he is asking is, whether there is any information why Einstein did not check the consistency of his time dilation calculation by changing the rest frame to the other observer/clock. Was it deliberate or an oversight?

 

[stevendaryl]

It seems to me that the OP read and understood Einstein's paper very well. What he is asking is, whether there is any information why Einstein did not check the consistency of his time dilation calculation by changing the rest frame to the other observer/clock. Was it deliberate or an oversight?

Checking your work isn't usually part of the final paper.

 

[adoion]

It's not an issue of one clock moving and the other clock not moving, it's that one clock is inertial and the other clock is not inertial.

In his 1905 paper, Einstein only considered Inertial Reference Frames (IRF's) and he described the "twin paradox" using the IRF in which the inertial clock was stationary. You only ever need one IRF to define a scenario. It doesn't matter whether the clocks are stationary, moving inertially at a constant velocity in any direction, or changing speeds and/or directions (accelerating), one IRF is all you need. But if you want, you can transform the coordinates of all the significant events according to the defining IRF to another IRF that is moving with respect to the defining IRF and this will make the stationary clock move at some constant speed but it is still inertial and it will make the other clock move at different speeds, even being stationary during some part of the scenario, but it is still non-inertial.

So when you define a scenario according to one IRF where the first twin remains inertial on the Earth and the other twin travels away from the Earth at a constant speed and direction and then turns around and travels back at that same constant speed but in the opposite direction, there are two more different IRF's in which the traveling twin is at rest during each half of the trip and the Earth twin is moving inertially but you must consider the entire scenario from each of these two IRF's. The Time Dilations of the twins will be different in each of these three IRF's but they will all explain the difference in aging between the twins identically.

Perhaps a concrete example will help. Let's consider a typical Twin Paradox. I'm going to depict the Earth twin in blue and the traveling twin in red. The traveling twin departs Earth at a speed of 0.6c and after 8 years according to his clock, he turns around and spends another 8 years coming back at the same speed. When he reunites with the Earth twin, they find that the Earth twin has aged 25 years while the traveling twin has aged 16 years. The dots on this diagram mark off one-year increments of time for both twins:

View attachment 75242​

Please note that in this IRF, it is only the traveling twin whose clock is Time Dilated by a factor of 1.25 during the entire scenario. This is because his speed is 0.6c during the entire scenario according to this IRF. Also note that the Earth twin is inertial during the entire scenario while the traveling twin is not inertial during the entire trip.

For the next two IRF's and their diagrams, I'm going to refer to the Earth twin as the inertial blue twin and the traveling twin as the non-inertial red twin.

First we're going to transform to the IRF in which the non-inertial red twin is at rest during the first part of the scenario. The diagram looks like this:

View attachment 75243​

Note how the inertial blue twin is moving at -0.6c during the entire scenario and so his clock is Time Dilated by 1.25 the entire time. During the first part of the scenario, the non-inertial red twin's clock is not Time Dilated because he is not moving. But at his time of 8 years, he starts moving at -0.882c where his Time Dilation is now 2.125 and after 8 more years he catches up to the inertial blue twin who has aged 25 years by the time they reunite.Finally we're going to transform to the IRF in which the non-inertial red twin is at rest during the last part of the scenario:

View attachment 75244​

This is similar to the previous IRF so we can use the same numbers but in different orders but the net result is that the twins age by the same amounts.

I hope this is clear and removes all your confusion. If not, ask.

the thing is that you can use all 3 of those diagrams interchangeably on both the Earth twin and the traveling twin.

1. inertial frame is fixed at the Earth twin and it is determined what time he calculates has passed .
in this case the traveling twins time goes slower as he goes away from the Earth twin, but also as he returns to the Earth , at the same amount.
the traveling twin uses 2 IRF, in this case.

2. IRF is fixed to the traveling twin. the Earth is moving away from the traveling twin who is at rest. the traveling twin will measure that the Earth twins time goes slower by the same factor as the Earth twin measured before for the traveling twin.
in this case the Earth twin uses 2 IRF, if he would believe that the Earth is moving, one on the trip away and one for the trip back.

3. the last possibility is that both agree to use a IRF in witch the Earth twin moves at a speed $v_1$ and the traveling twin with a speed $v_2$ and in this case just like in the first case the traveling twin changes speed and the traveling twin is the one who would use 2 IRF.

so the first 2 cases are absolutely symmetric and they would both measure that the other twin is younger at the end so both would have to be older and younger at the same time when they meet.
only with the presence of a third observer (case 3.) is the asymmetry obvious and that is only if the third observer doesn't travel at the same speed (direction and velocity) as the traveling twin.

even if we take acceleration into account, the acceleration can be attributed to the Earth as well as to the traveling twin, so symmetry again.

so again if somebody thinks he can correct me please do so id really like to know?

 

[Dale]

2. IRF is fixed to the traveling twin. the Earth is moving away from the traveling twin who is at rest. the traveling twin will measure that the Earth twins time goes slower by the same factor as the Earth twin measured before for the traveling twin.
in this case the Earth twin uses 2 IRF, if he would believe that the Earth is moving, one on the trip away and one for the trip back.

This frame is not inertial. The I in IRF stands for Inertial, so this is not a valid IRF.

In any IRF (remember I stands for Inertial), if you do the calculation you will get that the "travelling" twin is younger on reunion. That is the point of ghwellsjr's exercise above.

so the first 2 cases are absolutely symmetric and they would both measure that the other twin is younger at the end so both would have to be older and younger at the same time when they meet.

No, only the first case is even self consistent. The second case is not self consistent since it uses the time dilation formula for an IRF for a reference frame which is not inertial. This is a self-contradiction which invalidates the second case, regardless of any other case.

 

[adoion]

This frame is not inertial. The I in IRF stands for Inertial, so this is not a valid IRF.

In any IRF (remember I stands for Inertial), if you do the calculation you will get that the "travelling" twin is younger on reunion. That is the point of ghwellsjr's exercise above.

if you have only 2 point particles an nothing else, how do you determent witch one is accelerating?
so what is your opinion, what would be the IRF ( I stands for inertial) in this case??

 

[Dale]

Two point particles with nothing else is inconsistent with the twins paradox scenario.

 

[adoion]

Two point particles with nothing else is inconsistent with the twins paradox scenario.

hows that?

 

[stevendaryl]

if you have only 2 point particles an nothing else, how do you determent witch one is accelerating?
so what is your opinion, what would be the IRF ( I stands for inertial) in this case??

An object travels inertially if it is not acted on by any external force. We have a pretty good idea of what forces are relevant in space: Collision forces (which are ultimately electromagnetic in nature, for ordinary macroscopic objects), electromagnetic forces, gravity. That's basically it. If those forces are approximately zero, then the object is moving approximately inertially.

 

[Dale]

hows that?

As stevendaryl mentioned if you have two point particles and nothing else then they will travel inertially only. If one were to turn around without anything else then the conservation of momentum would be violated.

 

[adoion]

As stevendaryl mentioned if you have two point particles and nothing else then they will travel inertially only. If one were to turn around without anything else then the conservation of momentum would be violated.

witch one would be turning around? if anyone of them would be acted upon by an external force witch one would be accelerating in this case? you can always say that the other one is accelerating.

 

[Dale]

witch one would be turning around?

Neither. That is why two point particles with nothing else is inconsistent with a twins scenario. They would both travel inertially.

 

[adoion]

Neither. That is why two point particles with nothing else is inconsistent with a twins scenario. They would both travel inertially.

ok so what ingredient needs to be added??

 

[Orodruin]

you can always say that the other one is accelerating.

This seems to be the source of your misunderstanding and is simply not true. Unlike velocity, (proper) acceleration is absolute and can be measured without ambiguity.

 

[adoion]

This seems to be the source of your misunderstanding and is simply not true. Unlike velocity, (proper) acceleration is absolute and can be measured without ambiguity.

could you please explain how you would measure it in the above example I gave?

 

[Orodruin]

If you put an accelerometer on the accelerating object, it will show a non-zero value.

 

[harrylin]

hi,

Einstein did not even consider the twin paradox as problematic at all, he argued that it is a simple consequence of his special relativity?

obviously he never gave a explanation of why the two twins don't age the same he instead left it to others to do so.

was Einstein just having a hunch witch turned out to be just a lucky guess?

Despite the presentation in textbooks of a "twin paradox" in special relativity (as a student exercise), there never was anything really paradoxical about the "twin paradox" in that context. SR only accepts inertial coordinate systems as reference for the Lorentz transformations as Einstein already illustrated in 1905, with his clock prediction. Langevin presented in 1911 the example with a space traveller -from both perspectives- to illustrate how a change of velocity is "absolute" in SR. You can read that example starting from p.50 here:
http://en.wikisource.org/wiki/Translation:The_Evolution_of_Space_and_Time

The twin paradox only appeared with Einstein's development of general relativity. According to original, 1916 GR, acceleration is relative in the sense that 'coordinate systems in arbitrary states of motion are qualified' so that the traveller can rightly claim to be "in rest" all the time. You can read Einstein's 1918 answer to this problem as advanced by critics here:
http://en.wikisource.org/wiki/Dialog_about_objections_against_the_theory_of_relativity

 

[adoion]

If you put an accelerometer on the accelerating object, it will show a non-zero value.

if the external force is uniform like for example far away from an electric charge where the lines of force are almost parallel and same in magnitude.

in this case the accelerometer and the object would be accelerated the same and you would conclude that the other object is accelerating.

also how would you be sure that the accelerometer is not acted by a force instead of the objet who's force it is supposed to measure.
also the accelerometer introduces a third object or observer in the system if you have only the accelerometer and one object then once again you wouldn't know witch one is accelerating

 

[Fantasist]

I When he reunites with the Earth twin, they find that the Earth twin has aged 25 years while the traveling twin has aged 16 years. The dots on this diagram mark off one-year increments of time for both twins:

View attachment 75242​

This is not consistent with your diagram, which shows only 20 years on the blue scale, not 25.

I
For the next two IRF's and their diagrams, I'm going to refer to the Earth twin as the inertial blue twin and the traveling twin as the non-inertial red twin.

First we're going to transform to the IRF in which the non-inertial red twin is at rest during the first part of the scenario. The diagram looks like this:

View attachment 75243​

Note how the inertial blue twin is moving at -0.6c during the entire scenario and so his clock is Time Dilated by 1.25 the entire time. During the first part of the scenario, the non-inertial red twin's clock is not Time Dilated because he is not moving. But at his time of 8 years, he starts moving at -0.882c where his Time Dilation is now 2.125 and after 8 more years he catches up to the inertial blue twin who has aged 25 years by the time they reunite.Finally we're going to transform to the IRF in which the non-inertial red twin is at rest during the last part of the scenario:

View attachment 75244​

This is similar to the previous IRF so we can use the same numbers but in different orders but the net result is that the twins age by the same amounts.

I hope this is clear and removes all your confusion. If not, ask.

You evaluated further above the age difference from the viewpoint of the 'inertial blue twin'. How can you say that the subsequent consideration evaluates the age difference from the viewpoint of the 'non-inertial red twin', when the latter in fact never occupies the reference frames for which you claim time dilation here (you evaluate the time dilation in a third reference frame which moves opposite to the 'non-inertial red twin')?

 

[tom.stoer]

adoion, the only thing which is paradoxical in the twin paradox are the explanations. The proper time each twin measures on his own wrist watch is related to the "path length" of his/her trip through spacetime. for different paths we expect different "length". Consider two different paths with different lengths from New York to Boston. Why would you talk about a paradox at all?

 

[Fantasist]

As stevendaryl mentioned if you have two point particles and nothing else then they will travel inertially only..

Inertial motion is what Special Relativity is based on, and Einstein obtained the time dilation conclusion on this basis only (without considering any symmetry-breaking accelerations etc.) . That was the OP's point.

 

[harrylin]

if the external force is uniform like for example far away from an electric charge where the lines of force are almost parallel and same in magnitude.

in this case the accelerometer and the object would be accelerated the same and you would conclude that the other object is accelerating.

also how would you be sure that the accelerometer is not acted by a force instead of the objet who's force it is supposed to measure.
also the accelerometer introduces a third object or observer in the system if you have only the accelerometer and one object then once again you wouldn't know witch one is accelerating

While I don't entirely follow your arguments, an accelerometer is indeed insufficient. Note that identically the same problem occurs in classical mechanics. See my clarifications in posts #17 and #25 here [edit: replaced by direct links]:
https://www.physicsforums.com/threads/acceleration-and-the-twin-paradox.779110/#post-4898903
https://www.physicsforums.com/threads/acceleration-and-the-twin-paradox.779110/page-2#post-4900264

 

[Fantasist]

The twin paradox only appeared with Einstein's development of general relativity

That's clearly incorrect. The 'twin paradox' problem implied by the inertial frame scenario in Einstein's theory was already known since about 1911 (still several years after Einstein's 1905 paper appeared; see http://en.wikipedia.org/wiki/Twin_paradox ). It seems more like Einstein developed GR in order to be able to include non-inertial scenarios and thus 'get out of jail' with the twin paradox issue here.
I found a further interesting article in this respect here http://www.iisc.ernet.in/~currsci/dec252005/2009.pdf

 

[harrylin]

That's clearly incorrect. The 'twin paradox' problem implied by the inertial frame scenario in Einstein's theory was already known since about 1911 (still several years after Einstein's 1905 paper appeared; see http://en.wikipedia.org/wiki/Twin_paradox ). [..]

Sorry if my clarification was not clear enough. As I as well as others here remarked, there was no such paradox known in the context of SR alone, and it was still not paradoxical in that context in 1911 - the so-called "twin paradox" of textbooks is just an SR student exercise. Note also that Einstein started developing GR from about 1907.

 

[stevendaryl]

ok so what ingredient needs to be added??

A particle can't accelerate without a force. So to have two particles, one of which accelerates and the other doesn't, you have to have a force that applies to one and not the other.

Most thought experiments involving Special Relativity just assume contact forces: A rocket is accelerated by throwing matter behind it.

 

[stevendaryl]

Inertial motion is what Special Relativity is based on, and Einstein obtained the time dilation conclusion on this basis only (without considering any symmetry-breaking accelerations etc.) . That was the OP's point.

SR was developed by considering inertial FRAMES, not inertial MOTIONS. Motions are described relative to a frame, but the motions themselves are not confined to be inertial in SR.

The assumptions that led to SR were that:

1. The laws of physics in their simplest form look the same when described from the point of view of any inertial frame.
2. The speed of light has the same speed in any inertial frame.
3. Empty space is the same in all directions and at all locations and at all times.

These (possibly together with the assumption that Newtonian physics works in the limit of small velocity) allow you to derive the laws of SR, and those rules (possibly together with assumptions about the nature of idealized clocks) allow you to predict what happens when a clock undergoes noninertial motion.

SR is not in any way restricted to inertial motion--it (or more precisely, the usual mathematical formulation of it) is restricted to using inertial frames to describe motion, but the motion itself is not required to be inertial.

The situation is no different from in Newtonian physics. The whole point of Newton's laws (and SR are intended to be a replacement of those laws) is to describe how objects move when acted upon by forces.

 

[Fantasist]

Sorry if my clarification was not clear enough. As I as well as others here remarked, there was no such paradox known in the context of SR alone, and it was still not paradoxical in that context in 1911 - the so-called "twin paradox" of textbooks is just an SR student exercise. Note also that Einstein started developing GR from about 1907.

It may be merely a student exercise today, but exactly what we are discussing here was a serious issue for Einstein already before he published his GR, which was discussed by leading scientists at the time. I quote from the Wikipedia article

Starting with Paul Langevin in 1911, there have been various explanations of this paradox. These explanations "can be grouped into those that focus on the effect of different standards of simultaneity in different frames, and those that designate the acceleration [experienced by the traveling twin] as the main reason...".[1] Max von Laue argued in 1913 that since the traveling twin must be in two separate inertial frames, one on the way out and another on the way back, this frame switch is the reason for the aging difference, not the acceleration per se.[2]

 

[Fantasist]

SR is not in any way restricted to inertial motion--it (or more precisely, the usual mathematical formulation of it) is restricted to using inertial frames to describe motion, but the motion itself is not required to be inertial.s.

Nobody said that SR is necessarily restricted to inertial motion, but its conclusions do not in any way depend on non-inertial motion. Einstein derived his results (including time dilation) using inertial motion only.

 

[stevendaryl]

That's clearly incorrect. The 'twin paradox' problem implied by the inertial frame scenario in Einstein's theory was already known since about 1911 (still several years after Einstein's 1905 paper appeared; see http://en.wikipedia.org/wiki/Twin_paradox ). It seems more like Einstein developed GR in order to be able to include non-inertial scenarios and thus 'get out of jail' with the twin paradox issue here.
I found a further interesting article in this respect here http://www.iisc.ernet.in/~currsci/dec252005/2009.pdf

It is completely false to say that the Twin Paradox required General Relativity for its resolution. It's also false that General Relativity is needed to be able to describe noninertial coordinate systems (such as the coordinate system of the traveling twin). Additional mathematics is required, but no additional physics is required. Mathematically, if you have a description of the laws of physics in an inertial coordinate system, then calculus alone will allow you to get a description in a noninertial coordinate system. That's true in exactly the same way that Newtonian physics, described in rectangular coordinates, is sufficient to figure out what physics looks like in spherical coordinates. There are no additional physical principles involved, just calculus.

So the "resolution" to the twin paradox described in the paper isn't, from the point of view of modern understanding, a "General Relativity" solution. It's a Special Relativity solution using generalized (non-inertial) coordinates. Einstein falsely believed that "general covariance"--the principle that the laws of physics have the same form in any coordinate system, whatsoever--would uniquely imply what that laws must be. That isn't true. You can take any laws (Newtonian physics, for example) and rewrite them in a generally covariant form.

But what you find when you rewrite the laws of physics in terms of general coordinates is that there are additional terms in the equations that were not present in inertial coordinates. These are terms that are sometimes called "inertial forces" and they look like position-dependent forces that affect the motion of all objects (regardless of their physical composition) in the same way. These "inertial forces" look like gravitational fields. Einstein's insight was to suppose that real gravitational fields are similarly inertial forces due to using noninertial coordinates. Working out how this could be the case leads to General Relativity.

In retrospect, General Relativity was not needed to describe things from the point of view of an accelerated coordinate system. That description is derivable from SR alone. And that description has terms that are "gravity-like", but all within SR. GR is only needed if you want to describe real gravity, due to the presence of massive objects.

 

[stevendaryl]

Nobody said that SR is necessarily restricted to inertial motion, but its conclusions do not in any way depend on non-inertial motion. Einstein derived his results (including time dilation) using inertial motion only.

I just explained why your phrasing is not the best way to say it. Einstein derived his results using inertial FRAMES only. The results themselves describe both inertial and noninertial motion. So it is a fact that a clock which (from the point of view of any inertial frame) accelerates away and then accelerates back to its original location will show less elapsed time than a clock that remains stationary in that frame. That is a fact that depends on noninertial motion (since it's a fact ABOUT noninertial motion), and it follows from Einstein's SR. It depends on noninertial motion, but it doesn't depend on a noninertial FRAME.

 

[Fantasist]

I just explained why your phrasing is not the best way to say it. Einstein derived his results using inertial FRAMES only. The results themselves describe both inertial and noninertial motion. So it is a fact that a clock which (from the point of view of any inertial frame) accelerates away and then accelerates back to its original location will show less elapsed time than a clock that remains stationary in that frame. That is a fact that depends on noninertial motion (since it's a fact ABOUT noninertial motion), and it follows from Einstein's SR. It depends on noninertial motion, but it doesn't depend on a noninertial FRAME.

Where in Einstein's 1905 paper do you read that time dilation results from non-inertial motion?
I read the following there

From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by 1/2*t*v^2/c^2.

where v (according to the earlier definitions) is constant (i,e, the motion is inertial).

 

[Dale]

ok so what ingredient needs to be added??

An external field which would accelerate one particle and not the other or a third particle which interacts with one and not the other.

 

[adoion]

An external field which would accelerate one particle and not the other or a third particle which interacts with one and not the other.

I already added this in my last example as you can see, but this doesn't help.

 

[stevendaryl]

I found a further interesting article in this respect here http://www.iisc.ernet.in/~currsci/dec252005/2009.pdf

I consider that paper deeply misleading. It's possible that the confusion in that paper is an accurate reflection of the confusion of physicists (including Einstein himself) in the early days of relativity. But just because people were confused about it in the past doesn't mean that we need to confuse ourselves in the same way.

The paper has the following line:

Einstein needed the general relativistic physics to resolve the twin paradox in special relativity, and admitted so.

Einstein may have believed that he needed general relativity to describe things from the point of view of the traveling twin, but if so, he was mistaken. The mistake was probably caused by the fact that the relationship between general covariance (which is pure mathematics) and general relativity (which is a theory of physics) was not clearly understood.

The so-called "general relativistic" solution to the twin paradox proceeds as follows:

1. Describe the situation from the point of view of the accelerating twin.
2. From the point of view of this twin, there are inertial forces involved when the twin turns around.
3. Invoking the equivalence principle, these inertial forces are equivalent to a gravitational field.
4. According to General Relativity, clocks within a gravitational field experience gravitational time-dilation.
5. Using gravitational time dilation, you can work out the differential elapsed times on the clocks of the two twins.

What's convoluted and downright circular about this argument is that time dilation due to inertial forces is derivable from pure Special Relativity. As a matter of fact, gravitational time dilation was discovered by Einstein several years before he even completed GR. Einstein, using his "Elevator" thought-experiment, deduced that there had to be gravitational time dilation and gravitational bending of light from SR and the equivalence principle. The logical order was this: In the noninertial frame of an elevator accelerating in empty space, there is apparent position-dependent time dilation and bending of light. If we assume that a gravitational field on the surface of a planet is equivalent to the apparent gravitational field inside an accelerating elevator, then there must be position-dependent time dilation and bending of light due to a gravitational field, as well.

So Einstein derived gravitational time dilation from considering noninertial frames, not the other way around. So it's completely circular to invoke a theory of gravity to explain effects aboard an accelerating rocket. It's not wrong, but it's ridiculously convoluted.

1. You derive gravitational time dilation for a rocket at rest on a planet by invoking the equivalence principle and transforming to the case of a rocket accelerating in empty space.
2. Then you derive time dilation on board an accelerating rocket by transforming it to the case of a rocket at rest on a planet and using gravitational time dilation.

It works, but you could get the same result without ever mentioning the planet at all. You introduce it only to transform it away.

 

[stevendaryl]

Where in Einstein's 1905 paper do you read that time dilation results from non-inertial motion?

I'm saying that the case of a noninertial clock is a deduction from Einstein's paper. His paper doesn't explicitly derive that case, but that's the whole point of having a "theory". A theory can be used to derive an infinite number of special cases.

The result of the twin paradox, that the traveling twin will be younger than the twin who travels inertially when they reunite, is a special case derivable from the theory introduced in Einstein's 1905 paper.

 

[DrGreg]

Where in Einstein's 1905 paper do you read that time dilation results from non-inertial motion?

In the English translation On the Electrodynamics of Moving Bodies at the top of page 11, the final paragraph of §4.

"Thence we conclude that a balance-clock at the equator must go more slowly, by a very
small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions."​

(I assume you realize that circular motion, around the equator in this case, is non-inertial motion.)

 

[stevendaryl]

if the external force is uniform like for example far away from an electric charge where the lines of force are almost parallel and same in magnitude.

in this case the accelerometer and the object would be accelerated the same and you would conclude that the other object is accelerating.

also how would you be sure that the accelerometer is not acted by a force instead of the objet who's force it is supposed to measure.
also the accelerometer introduces a third object or observer in the system if you have only the accelerometer and one object then once again you wouldn't know witch one is accelerating

If there is a force that affects all objects in exactly the same way, independent of what they are made out of, then you are exactly right--such a force would be unobservable using an accelerometer. It would only be observable by looking at larger-scale phenomena--tidal forces: how that force changes from place to place and from moment to moment. That's what gravity is. I believe that you could lump any such "universal" force in with gravity.

Such universal forces require a treatment that goes beyond Special Relativity. So the development of SR does not take into account such forces. It's not a complete theory, in that sense.

 

[ghwellsjr]

This is not consistent with your diagram, which shows only 20 years on the blue scale, not 25.

Yes, you are correct, I put down the wrong number in post #11, twice, in fact. I guess I was looking at the coordinate time of the reunions for the second and third diagrams. Anyway, thanks for catching this.

You evaluated further above the age difference from the viewpoint of the 'inertial blue twin'. How can you say that the subsequent consideration evaluates the age difference from the viewpoint of the 'non-inertial red twin', when the latter in fact never occupies the reference frames for which you claim time dilation here (you evaluate the time dilation in a third reference frame which moves opposite to the 'non-inertial red twin')?

I never used the term "viewpoint". I used the term "defining IRF" to specify the scenario and then I talked about transforming the coordinates of all the significant events to two other IRF's moving at different speeds with respect to the defining IRF.

Both twins "occupy" all three IRF's. In the defining IRF, the blue twin, who remains inertial is not moving but the red twin is moving at a constant speed, although he changes direction half-way through, making him non-inertial. The second IRF was chosen so that the red twin would not be moving during the first part of the scenario but he starts moving at his time of 8 years making him non-inertial while the blue twin is always moving inertially. The third IRF was chosen so that the red twin would not be moving during the last part of the scenario but he started out moving until his time of 8 years making him non-inertial while the blue twin is always moving inertially. I thought I made all these points clear in post #11.

I don't consider any of these diagrams to be showing the "viewpoint" of either twin. I would have had to draw in light signals going between the twins to show their viewpoints and they would be exactly the same in all three IRF's.

 

[PeroK]

It seems to me that the OP read and understood Einstein's paper very well. What he is asking is, whether there is any information why Einstein did not check the consistency of his time dilation calculation by changing the rest frame to the other observer/clock. Was it deliberate or an oversight?

In my opinion:

a) No one who understands SR would ask whether Einstein was "lucky", with the implication he missed all the potential paradoxes and was fortunate that others resolved these paradoxes and, luckily, left his theory intact.

b) No one who understands SR very well would obsess over the twin paradox and fail to grasp the lack of symmetry vis-a-vis the role played by an accelerating reference frame.

 

[adoion]

To sum up a little bit,

A reference frame is inertial if there are no fiction forces present like coriolis and centrifugal forces, witch are associated with rotating reference frames. Then we also have fiction forces due to linearly accelerating reference frames.

but how does one make sure that a force is or is not fictional? one has to find the source of the force or one has to find other reference frames in witch those forces disappear and one is left with the simples form of laws, especially Newton's second law, the les forces there are to consider the simpler it is.

the point is that we would always have terms in the equation of Newton's second law $F=ma$ witch would be always present, like the coriolis term for example, and one would be forced to state Newton's second law in a more complicated form including those additional terms instead of adding these terms every time a new calculation needs to be made, this is valid for a rotating system.
obviously Newton's first law would have to be restated in a rotating reference frame as "all bodies tend to rotate around at a fixed radius or with uniformly changing radius unless acted upon by an force".
all of this is more complicated.

if the reference frame is linearly accelerating then one wouldn't need to do anything with Newton's laws and they would take their simplest form anyway. objects that move under the influence of the same force as the Reference frame would appear to stand still or move uniformly and objects that would appear to accelerate would be the once that move with different accelerations than the reference frame.
anyways, we would have just a shift in perception of what's accelerating and what's not and not a change in laws.
the law of gravity for example would have the same form, just that the masses in the universe would appear to accelerate a little bit faster or slower in a particular direction, than in another reference frame.

in the twin paradox, motion is uniform (constant velocity and direction) until the turn around where obviously an acceleration happens.
whatever the source of the acceleration might be is nowhere mentioned in the statement of the paradox so it can be anything.

both of the twins must make their measurements from their point of view and since in both cases the laws of physics take their simplest form, both of them are correct in assuming that their reference frame is inertial and that the other one is accelerating.