Evidence of length contraction

[Adam]

Hello all.

I've recently had something of an epiphany regarding relativity. One of those moments when things become clear and it all makes sense. However, having not actually performed any of the experiments which may or may not support the whole thing, I have a question. Is there evidence of length contraction? If so, what is it? Are there any alternative explanations for it?

Basically it all started making sense in the most amazing way (and it's really far simpler than I had expected), but my understanding of it requires the acceptance of length contraction, which, as I said, I have not personally checked out much.

 

[zefram_c]

No human has ever been able to actually see length contraction for himself. There is plenty of evidence for time dilation, otherwise short-lived fast-moving particles could not reach the distances they are routinely seen to reach. But in the rest frames of those particles, there is no time dilation. According to their frames, how then do they reach farther than they could otherwise? The solution is length contraction: they move for a small time (after which they decay), but the distance they travel (or technically, the distance that the rest of the world zooms by) is contracted in their frame. Does this help?

 

[Adam]

Unfortunately not. I am aware of the muon thing, but unfortunately it seems that without corroborating evidence from the other side of the matter, why not just assume they are traveling very fast? I know it doesn't fit, but it sure is the simple solution.

Okay, how about this. Can someone explain to me the mechanism by which length contraction occurs?

 

[sol2]

Thanks to another poster, of another time

Hear what Clifford Will has to say on the subject, as he describes the difference in rates between one clock on a tower and a second clock on the ground:

A question that is often asked is, Do the intrinsic rates of the emitter and receiver or of the clock change, or is it the light signal that changes frequency during its flight? The answer is that it doesn’t matter. Both descriptions are physically equivalent. Put differently, there is no operational way to distinguish between the two descriptions. Suppose that we tried to check whether the emitter and the receiver agreed in their rates by bringing the emitter down from the tower and setting it beside the receiver. We would find that indeed they agree. Similarly, if we were to transport the receiver to the top of the tower and set it beside the emitter, we would find that they also agree. But to get a gravitational red shift, we must separate the clocks in height; therefore, we must connect them by a signal that traverses the distance between them. But this makes it impossible to determine unambiguously whether the shift is due to the clocks or to the signal. The observable phenomenon is unambiguous: the received signal is blue shifted. To ask for more is to ask questions without observational meaning. This is a key aspect of relativity, indeed of much of modern physics: we focus only on observable, operationally defined quantities, and avoid unanswerable
questions.


5 Justifying the Approximations

We calculated the speed of a satellite in circular orbit and the speed of the
clock on Earth’s surface using Euclidean geometry and Newtonian
mechanics with its “universal time.” Now, the numerator in each expression
for speed, namely rdφ, is the same for Euclidean geometry as for
Schwarzschild geometry because of the way we defined r in Schwarzschild
spacetime. However, the time dt in the denominator of the speed is
not the same for Newton as for Schwarzschild. In particular, the derivation
of equation [3] assumes that the speeds in that equation are to be
calculated using changes in far-away time dt. Think of a spherical shell
constructed at the radius of the satellite orbit and another “shell” that is
the surface of Earth. Then our task boils down to estimating the difference
between far-away time dt and shell time dtshell in each case, which can be
done using our equation [C] in Selected Formulas at the end of this book.

http://www.eftaylor.com/pub/projecta.pdf

 

[zefram_c]

Unfortunately not. I am aware of the muon thing, but unfortunately it seems that without corroborating evidence from the other side of the matter, why not just assume they are traveling very fast? I know it doesn't fit, but it sure is the simple solution.

Indeed it doesn't fit. When we measure their speed, we find it is below c. In their own frames, they must see the universe as traveling backwards at the same speed - otherwise you'd have a situation where A says B is moving at a speed v_a, and B says A is moving at speed v_b > v_a. This is unacceptable.

Okay, how about this. Can someone explain to me the mechanism by which length contraction occurs?

I'm not sure what sort of mechanism you have in mind. Try http://aci.mta.ca/Courses/Physics/4701/EText/LengthContraction.html and the link therein on time dilation to see how it works. However, as far as we know, there is no deeper mechanism to length contraction; it is simply a derivable result of the constancy of c postulate.

 

[Hurkyl]

It doesn't "occur", per se...

Geometrically, it's closely analogous to this:

Suppose you have a needle resting on a table and you're looking at it from the edge of the table. (So you see it from the side, not above)

The apparent length of the needle depends on the angle you look; if someone rotates the needle, it would appear to change size.


The "angle" here is analogous to relative velocity.

 

[Adam]

So if the subject is moving at a constant distance from the observer, such as in an arc?

 

[pervect]

So if the subject is moving at a constant distance from the observer, such as in an arc?

You have the classic "relativistic rotating disk" with it's associated non-euclidian geometry.

See for instance

http://math.ucr.edu/home/baez/physics/Relativity/SR/rigid_disk.html