Thoughts (of an amateur) on the Solution to the Twin Paradox

[GregAshmore]

Hello, All. I found this forum through a google search. This post could have been attached to the thread started by Bob Guerico on 09-Jan-08, but I felt it would be better to start a new thread.

I've been reading about SR and GR for about a year now. I've been through several iterations of "I get it" -- "Oh, wait a minute" -- "NOW I get it" -- etc. This has given me a respect for the theory, and an awareness that the conclusions I have reached may be in error. So I ask you, as you read what follows, to keep in mind that I am not on a soapbox. I am presenting for review and criticism my current understanding of SR, the Twin Paradox, and its solution.

I'll present my points in logical order:

[1] The equations of SR are not unique to the theory. They are the equations of Lorentz, derived from a different starting point. Lorentz started with the premise that the speed of light is constant relative to a universally absolute frame of reference; Einstein started with the notion that the speed of light is constant relative to the observer.

[2] Einstein's equation relating energy and mass (E = mc^2) is derived from the Lorentz equations. Therefore, the mass-energy equation is consistent with an absolute frame of reference, on the one hand, and a purely relativistic view of the universe on the other.

[3] Experimental evidence which is consistent with the equations of SR does not prove that the speed of light is constant to the observer, because such evidence is also consistent with the premise that the speed of light is constant relative to an absolute frame of reference.

[4] The distinguishing characteristic of SR is that it allows us to work with the equations of physical phenomena without consideration of an absolute frame of reference. If it were not so, then we would have to take into account our relationship with the absolute frame of reference. Einstein put it this way, "If the principle of relativity does not hold...we should be constrained to believe that natural laws are capable of being formulated in a particularly simple manner, and of course only on condition that, from amongst all possible Galileian coordinate systems, we should have chosen ONE (K0) of a particular state of motion as our body of reference."

[5] The essence of the Twin Paradox is that both observers can be shown to be younger. If the Earth is considered stationary, the observer in the rocket is younger. If the rocket is considered stationary, the observer on the Earth is younger.

[6] The solution to the Twin Paradox is to recognize that one observer is in an inertial frame, while the other is not. The Earth is in an inertial frame because it does not accelerate; the rocket is not in an inertial frame because it does accelerate.

[7] A frame of reference cannot exist by itself. Just as it takes two to tango, it takes two frames to reference. The two frames in the statement of the Twin Paradox are the Earth and the rocket. These frames are accelerating relative to each other, and thus are not inertial with respect to each other.

[8] The solution to the Twin Paradox states that the Earth is in an inertial frame. This implies the introduction of a third frame, relative to which the Earth is not accelerating.

[9] If we accept this solution to the Twin Paradox, we implicitly accept that we cannot correctly formulate the relationship between the Earth and the rocket without taking into account a governing third frame of reference. (See [6] above. Also, consider: How is it that we know the Earth is in an inertial frame? Perhaps it is the rocket which is in the inertial frame. To clarify this point, restate the problem, replacing the Earth with a rocket. How can we tell which rocket is in the inertial frame?)

[10] Thus, the Twin Paradox can only be resolved by abandoning the principle of relativity.

I am open to correction.

Greg

 

[JesseM]

[1] The equations of SR are not unique to the theory. They are the equations of Lorentz, derived from a different starting point. Lorentz started with the premise that the speed of light is constant relative to a universally absolute frame of reference; Einstein started with the notion that the speed of light is constant relative to the observer.

But what Einstein postulated was that the laws of physics would work the same in every inertial frame, so even if there was an absolute frame, it would be experimentally impossible to determine which it was, which would mean the idea of a absolute frame would become a purely metaphysical idea. So far all the known fundamental laws of physics do have the property of "Lorentz-invariance", meaning they will obey the same equations in all the inertial frames that are related by the Lorentz transformation.

[6] The solution to the Twin Paradox is to recognize that one observer is in an inertial frame, while the other is not. The Earth is in an inertial frame because it does not accelerate; the rocket is not in an inertial frame because it does accelerate.

[7] A frame of reference cannot exist by itself. Just as it takes two to tango, it takes two frames to reference. The two frames in the statement of the Twin Paradox are the Earth and the rocket. These frames are accelerating relative to each other, and thus are not inertial with respect to each other.

"Inertial" is not relative in this way. Whichever observer accelerates knows that they are objectively the one who accelerated, because they feel G-forces during the acceleration, while an inertial observer in flat spacetime is always weightless.

 

[Ich]

[7] A frame of reference cannot exist by itself. Just as it takes two to tango, it takes two frames to reference. The two frames in the statement of the Twin Paradox are the Earth and the rocket. These frames are accelerating relative to each other, and thus are not inertial with respect to each other.

I think you got the principle of relativity wrong, extending it to acceleration. There is no "accelerating relative to each other", simply "accelerating" is enough. "inertial with respect to each other" doesn't make sense, too. A frame of reference can exist by itself, and you can determine by local experiments whether it is inertial or not.
Try wikipedia for an introduction to the meaning of "acceleration", "inertial frame", and "principle of relativity".

 

[jcsd]

Yes that's how I read it, your mistake Greg is that acceleration is not relative, either a frame is inertial or it isn't inertial. This isn't something that's peculair to special relativity.

Think about Gallilean relativity, non-inertial frames can be distingusihed from inertial frames by the appearance of so-called pseudo-forces. Gallilean relativity exists as a limit of special relativity so there must also exist in special rleativty an absolute distinction between inertial and non-inertial frames.

 

[GregAshmore]

I see my mistake. It's definitely one of those "duh!" moments--perfectly obvious now that it's been pointed out.

Granted that SP is consistent within itself.

This still leaves the question of whether relativity is true.

<<<<<
But what Einstein postulated was that the laws of physics would work the same in every inertial frame, so even if there was an absolute frame, it would be experimentally impossible to determine which it was, which would mean the idea of a absolute frame would become a purely metaphysical idea. So far all the known fundamental laws of physics do have the property of "Lorentz-invariance", meaning they will obey the same equations in all the inertial frames that are related by the Lorentz transformation.
>>>>

I might suggest that 'metagnostic" is more apt than 'metaphysical'. It is beyond our knowledge to determine whether there is an absolute reference frame--but that frame, if it exists, is physical enough.

It seems that relativity is 'metagnostic' in the very same way. Is it possible to show through experiment that behavior of light can be accounted for only if its speed is constant relative to the observer, thus excluding the possibility of an absolute reference frame?

 

[JesseM]

I might suggest that 'metagnostic" is more apt than 'metaphysical'. It is beyond our knowledge to determine whether there is an absolute reference frame--but that frame, if it exists, is physical enough.

It seems that relativity is 'metagnostic' in the very same way. Is it possible to show through experiment that behavior of light can be accounted for only if its speed is constant relative to the observer, thus excluding the possibility of an absolute reference frame?

Yeah, "metagnostic" is a fine word for it, it's a hypothesis about the physical world which is in principle untestable, similar to the different [URL="https://www.physicsforums.com/insights/fundamental-difference-interpretations-quantum-mechanics/"]interpretations of quantum mechanics[/url] which all yield identical physical predictions. Relativity is just a set of postulates about the measurable laws of physics, so it is not incompatible with the idea of an unmeasurable absolute reference frame, with rulers "objectively" shrinking and clocks "objectively" slowing down when they are in motion relative to the absolute frame...this is sometimes known as "Lorentzian relativity", and there's some discussion of ether theories that are experimentally indistinguishable from relativity on this thread.

 

[jtbell]

Granted that SP is consistent within itself.

SR has also been tested experimentally in many different ways. So far it has always been consistent with the results of well-designed experiments, within its range of validity:

Experimental Basis of Special Relativity

This still leaves the question of whether relativity is true.

Physics cannot say whether a theory is "true" in an absolute sense. It can only say whether a theory agrees with experiments that have been done to date.

 

[Dale]

Granted that SP is consistent within itself.

This still leaves the question of whether relativity is true.

Correct, a theory must first be consistent with itself, and then with experiment. I also recommend the page that jtbell linked to above.

However, I would not use the word "true" in a scientific context like this. I would use the words "correct" or "accurate". The reason is that the scientific method of hypothesis testing is designed to answer the question "does the theory accurately predict the results of this experiment", not untestable questions like "is this theory true".

As you have noted, science is fundamentally incapable of deciding between two interpretations of a theory. In the case of special relativity the theory is the Lorentz transform, and Einstein and Lorentz disagreed about the interpretation. No experiment can resolve the dispute because both make the same predictions about any experimental outcome. In the end, IMO, debates about Einstein v. Lorentz are pointless. Pick your favorite interpretation, or better yet, use both whenever they are useful.

 

[jcsd]

I see my mistake. It's definitely one of those "duh!" moments--perfectly obvious now that it's been pointed out.

Granted that SP is consistent within itself.

This still leaves the question of whether relativity is true.

<<<<<
But what Einstein postulated was that the laws of physics would work the same in every inertial frame, so even if there was an absolute frame, it would be experimentally impossible to determine which it was, which would mean the idea of a absolute frame would become a purely metaphysical idea. So far all the known fundamental laws of physics do have the property of "Lorentz-invariance", meaning they will obey the same equations in all the inertial frames that are related by the Lorentz transformation.
>>>>

I might suggest that 'metagnostic" is more apt than 'metaphysical'. It is beyond our knowledge to determine whether there is an absolute reference frame--but that frame, if it exists, is physical enough.

It seems that relativity is 'metagnostic' in the very same way. Is it possible to show through experiment that behavior of light can be accounted for only if its speed is constant relative to the observer, thus excluding the possibility of an absolute reference frame?

DIsagree, if there is no way of determining it is an absolute frame, what property does it have that make sit an absolute frame?

 

[GregAshmore]

DIsagree, if there is no way of determining it is an absolute frame, what property does it have that make sit an absolute frame?

One property would be absolute zero velocity. The mass of an abject absolutely at rest would be its "base" mass (or perhaps "true" mass.)

If we could determine that a particular frame was absolute, and if we found a massive object at rest in that frame, then we would know that mass can exist without motion.

True, in our present circumstances we are not able to distinguish the absolute frame from other frames. But that does not preclude the existence of circumstances which would allow us--or some other being--to make such a determination.

Yes, this could very easily lead to a discussion of metaphysical ideas. No doubt this is not the place for such a discussion. Fair enough. Nevertheless, I think it is also fair to point out the illogic of concluding that a thing does not exist simply because we are unable to detect its existence. Our inability does not exclude the existence of ability; our ignorance does not exclude the possibility of knowledge.

 

[ZapperZ]

One property would be absolute zero velocity. The mass of an abject absolutely at rest would be its "base" mass (or perhaps "true" mass.)

If we could determine that a particular frame was absolute, and if we found a massive object at rest in that frame, then we would know that mass can exist without motion.

True, in our present circumstances we are not able to distinguish the absolute frame from other frames. But that does not preclude the existence of circumstances which would allow us--or some other being--to make such a determination.

Yes, this could very easily lead to a discussion of metaphysical ideas. No doubt this is not the place for such a discussion. Fair enough. Nevertheless, I think it is also fair to point out the illogic of concluding that a thing does not exist simply because we are unable to detect its existence. Our inability does not exclude the existence of ability; our ignorance does not exclude the possibility of knowledge.

This is not physics. It is simply guess work based on things that have not been proven to exist.

Please review the https://www.physicsforums.com/showthread.php?t=5374" that you have agreed to. Pay particular attention to speculative, personal theory. Unless you have something definitive to based what you have said, this violates our Guidelines.

This thread is done.

Zz.