Nature of Time Dilation and Length Contraction

Yes, that's correct. Thought experiments that assume SR and perfectly rigid objects are meaningless. The reason is that SR predicts that even if an object is perfectly rigid in its rest frame, it cannot be rigid in any other frame.

It sits closer to length contraction than you might think. Both length contraction and the non-rigidity of moving objects are consequences of the Lorentz transform. This is discussed clearly and succinctly by W. Rindler in his article "Length Contraction Paradox": Am. J. Phys., 29(6) June 1961. The article is very clear, and understandable to anyone who has learned SR at the level of Halliday and Resnick.

 

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przyk, Tom2, you did not read sleeper555's example correctly. Quoted is his stated parameter:

Information does not travel instantly. Assuming a perfectly rigid rod, it will take one year for the observer at one end to SEE the movement, even though the movement would be instantaneous in a perfectly rigid rod.

The next part of his post:

I take this to mean that if the observer at the end of the rod measured its length either before the force was applied, or after all motion had ceased, it would measure one light year in length. Now, assume this observer 'pushed' his end of the rod toward the distant end. The observer could not 'see' the other end of the rod move for one year. His assumption would be the perfectly rigid rod has contracted in length because he could not see the other end move for one year. Did the perfectly rigid rod contract, or was this an incorrect assumption caused by the one year delay in recieving the information from the far end? Again, I am speaking of a hypothetical perfectly rigid rod, not an impulse traveling through a rod that is not rigid.

Of course, STR is based on what the observer 'sees' in his rest frame. Because the 'information' cannot travel faster than the light that carries it, Special Theory speculates the rod cannot be perfectly rigid, that it must contract during the one year time frame. This is only an unproven assumption.

Any amount of time required for an impulse to travel from one end of a compressable rod to the other must be in addition to this one year period of information delay.

 

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If this is the same kind of contraction that came up in the [THREAD=52923]Bug-Rivet paradox[/THREAD], I'm still inclined to make a distinction between physical compressibility and relativistic compression caused by relativity of simultaneity. I'll admit that this is the current fringe of my understanding of SR, so I could easily be missing something.

 

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Actually I didn't read it at all. I read przyk's post about rigidity, and I commented only on that.

Now that I have read the post, it seems that the observer isn't at either of the two ends. Draw the rod, then draw a perpendicular bisector that is 1 light year long. The observer is at the other end of that line segment.

If you set the problem up mathematically you can keep track of the coordinates of the endpoints of the rod in the observer's frame. If you calculate those coordinates at different times you would predict that the absolute value of the difference (aka, the length of the rod) diminishes as the rod accelerates. This has nothing to do with the time required for light from the (moving) far end of the rod to reach the eyes of the observer.

Actually, it isn't based on that at all. SR allows you to calculate the spacetime coordinates of events locally, without regard to the actual position of the observer. After those results are determined, then you can factor in the time required for light from the events to reach your position.

The relativity of rigidity has nothing to do with the information carried to an observer by light from an event. It is a direct consequence of the relativity of simultaneity, as explained in the Rindler paper. In SR this is not purported to be some optical illusion. A bar that is rigid at rest really isn't rigid in any other frame.

In order for the effect to be seen, yes. But you don't have to add the light propagation time in order to calculate the time it takes for the impulse to travel to the other end of the rod. It arrives when it arrives, regardless of who observes it.

 

sleeper555's example is self-contradictory: if the end of the rod moves a year later, the rod gets shorter. He described a perfectly rigid rod undergoing compression. If information travels along the rod at the speed of light, a perfectly rigid rod cannot exist. The fact that electromagnetic effects propagate at c places an upper limit on rigidity.

I think sleeper555 was describing a real (not perceived) contraction.

Illusions caused by the rate of information transfer are usually assumed to be accounted for in relativity thought experiments.

SRT describes what really happens in a reference frame. The fact that information about what is 'really' happening in your frame travels at the speed of light and reaches you after a delay causes optical illusions that are not a part of the theory.

The limit on rigidity is due to a property of the electromagnetic forces in the rod: changes in the electromagnetic field propagate at the speed of light.

If you were applying the force on the rod, at least two years would pass before you saw the other end move.

 

Yes, you're right about that.

That idea seems untenable. If you have a rod that is moving with constant velocity in your frame then its length should be less than its proper length. Furthermore there are no forces acting on it. So if it is true that the length contraction of the rod is brought about by physical compression then the same observer who sees the length contraction should also see a nonzero strain on the rod, if he used a strain gauge.

But in the absence of any stresses, where does the strain come from? If this hypothesis is true then entire field of statics would have to be rewritten to accomodate it.

 

This would not be an interaction that depends on any absolute coordinates. If we move the gravitating object then the effects on light will also move. They are therefore not tied to any absolute coordinates but only the relative location of the gravitating object and the photon in question. So, can you think of any interaction that depends on absolute coordinates?

-Dale

 

You simply MUST capitalize MUST some more

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For the third time now, your MacM transform has a frame variant c (not to mention a prefered reference frame).

-Dale

 

I almost as confused by the responses as I was pondering the original question... If I understand correctly, it seems that if the rod were "perfectly" rigid (maximum possible), then the force applied to one end would travel through it at speed c, but this would beg the question of whether or not the object experiences any compression at all wouldn't it? The observer measuring the length of the rod at a time between the application of force and the movement of the other end would certainly measure the rod to be shorter but is the shorter measurement due to compression or length contraction?

 

This hypothetical question cannot be addressed by SR. Kindly refer to your favorite alternative theory for an answer.

-Dale

 

No, it wouldn't. There would be some physical compression due to the force acting on the rod and there would be relativistic length contraction. If you take away the force so that the rod travels at a constant speed then the compression would cease, but the length contraction would persist.

 

Why not? Couldn't the perfectly rigid bar could be considered a coordinate system, and pushing the bar be considered motion relative to the coordinate system?

 

Absolutely but any time a gedanken stumps the theory the policy is to restort to pragmatic or tangiable issues i.e. - "you can't actually build it", or "you can't actually do that". Knowing all the time that the theory is built on gedankens and is promoted by gedankens which are currently physically unachievable.

 

How could you possibly consider a bar to be a coordinate system? You can touch a bar, not a coordinate system. A coordinate system has no mass a bar does. A bar can be used to transmit information, energy, force, etc., a coordinate system cannot.

The reason that the situation cannot be addressed by SR is that it violates the postulates of SR. It is like asking someone to use Euclidean geometry to analyze the angle of intersection of two parallel lines.

-Dale

 

Modern physics gives accurate predictions in all of the situations that are currently physically achievable. It is hardly a flaw that something which successfully models reality is unsuccessful at modeling unreality.

-Dale

 

No, it can't be so considered. As the Rindler article explains, rigidity is relative. If you assume that a bar can be rigid in every inertial frame then you have left the realm of Special Relativity.

 

DaleSpam, I am not interested in whether the rod is actually perfectly rigid or not, but the relativistic explanation concerning the compression. ONLY the relativistic part, not because of compressed atoms, thus the 'hypothetical perfectly rigid rod' so as to eliminate actual physical compression.

Thanks, Tom2, you are addressing the question. What I don't understand is WHY "rigidity is relative", other than I assume it has something to do with relativity of simultaneity.

 

Then just ask about an inertially moving rod. Even if your inertially moving rod is made out of rubber there is no physical compression if there are no forces acting on it. If there are forces acting on it then any material will be physically compressed.

It sounds like what you are asking for is a physical explanation of length contraction, the same thing that Prosoothus was asking for in the original post. As you can tell from the responses there are at least two pro-SR opinions on the matter. You can read the thread for further details, but in summary some people think of spacetime as a physical thing and others (including me) think of it as a geometric relationship between objects.

-Dale

 

DaleSpam,

Well, how "absolute" do you want to get? There may not be anything more absolute then gravitational fields. It could be that certain particle decay reactions might be linked to local space, but I'm not sure. If the properties of local space (excluding gravitational fields) vary depending on where you are in the universe, then absolute space coordinates might be necessary to understand certain particle decay reactions.

I'm not saying that certain interactions require absolute coordinates of space, I'm just saying that we shouldn't assume that none do.

 

MacM,

That was good.

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