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length contraction and the space twins


asprung
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The space twin would appear to carry an effect of time dilution when he returns to earth as it is said he would return younger than his earth twin. What happens to length contraction? I have not heard that he would return smaller.

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I have been told that length contraction is real and involves an actual physical change. Does the space twin shoot up to his former earth size when he enters earth’s time frame? When viewed from the space twin’s time frame time dilution and length contraction should occur in earth’s time frame. What happens to them when the space twin returns to earth?

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Without wanting (because of limited time) to say too much: The usual meaning of time dilatation and length contraction is a local (instantaneous) property. The ratio of the twins agings is the time change experienced integrated over the trajectory. The ratio happens to be the same as the ratio for the local ratio of measured time distances because in the frame chosen to discuss the problem the magnitudes of the velocities of both twins are constant. But conceptually, the local property and the integrated property are really different things.

 

Now to answer the question: With the times you compare the aging of both twins, i.e. the time passed in their frames of reference, i.e. an integrated quantity. The distances passed in either frames are zero by definition so it's not a useful integrated quantity to compare. I wouldn't know what sensible observable to construct from the length contraction (size integrated over time ?!?) but I think its ratio is just the inverse of the time ratios, anyways.

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I have been told that length contraction is real and involves an actual physical change.

 

You've also been told, numerous times, that it is frame-dependent. Length is not an absolute — it depends on who is doing the measuring. The twin who leaves earth never sees his own clock or length as being different.

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It is real relative to a frame of reference. When the twin travels, he is length contracted relative to earth (he notices absolutely zero change to his own length when measured relative to his own frame of reference). However, once he returns to earth, he is once again part of the earths frame of reference. Once he is again part of the same frame of reference as the earth, the length contraction he experienced relative to the earth is no longer apparent.

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I dont understand. If the length contraction is real and physical some expansion must occur for there to be "no longer any length contraction".

 

As measured from the Earth, the twin expands in the direction of deceleration until he is at rest in that frame.

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I dont understand. If the length contraction is real and physical some expansion must occur for there to be "no longer any length contraction".

 

I suspect what you mean by "physical" is incorrect/inconsistent with how everyone else means it.

 

Imagine you have a spring, having 100 coils with a pitch of 1 cm (i.e. the coils are 1 cm apart) so it is 1 m long. If the spring is moving such that gamma =2, the coils will have a pitch of 1/2 cm and the spring will be 0.5 m long. If gamma = 10, the pitch will be 1 mm, and the spring will be 10 cm long. However, in all cases, there is no physical compression of the spring — it is not under any tension, stress or strain. That's what an uncompressed spring looks like in that frame.

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A change in pitch is a physical change.

 

Keep in mind that the spring is in all inertial (and other) frames at all times, although it is always at rest in just one.

 

It is not doing a dance to keep them all happy.

 

It simply is measured differently in each frame.

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It seems that I am being told that the space twin may have multi forms with a single one being chosen by each time frame from which he is viewed. No form being more correct tthan another.

 

Yes. The measurement depends on the frame of the observer.

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  • 4 weeks later...
I suspect what you mean by "physical" is incorrect/inconsistent with how everyone else means it.

 

Imagine you have a spring, having 100 coils with a pitch of 1 cm (i.e. the coils are 1 cm apart) so it is 1 m long. If the spring is moving such that gamma =2, the coils will have a pitch of 1/2 cm and the spring will be 0.5 m long. If gamma = 10, the pitch will be 1 mm, and the spring will be 10 cm long. However, in all cases, there is no physical compression of the spring — it is not under any tension, stress or strain. That's what an uncompressed spring looks like in that frame.

 

I am going to help you out here swansont. What asprung means by "physical" is what is defined in any standard dictionary. Correct me if I am wrong, asprung.

 

Physical means physical as defined by any dictionary.

 

Swansont, are you going to take the stand that there is a physical contraction? YES/NO.

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I am going to help you out here swansont. What asprung means by "physical" is what is defined in any standard dictionary. Correct me if I am wrong, asprung.

 

Physical means physical as defined by any dictionary.

 

Swansont, are you going to take the stand that there is a physical contraction? YES/NO.

 

The problem with using a standard dictionary is that they do not usually use technical definitions that are very precise. Certainly the definitions are not written with relativity in mind.

 

Length contraction is not a physical process. If I were to physically compress and object like a spring and then expand it, it would eventually fail and break. If I continually move from one frame of reference to another, to achieve differing amounts of length contraction, the object I am measuring will not undergo such a failure.

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