Measuring Lorentz Contraction: Is it Real or Just an Illusion?

[Dale]

Bernhard is correct, Einstein clock synchronication is a good convention, not something obligatory. But if you use it and if c is constant, then length contraction is a logical consequence, not an option.

The reason that the synchronization convention is important in this discussion is that length contraction refers to the interval between two events that occur simultaneously in some reference frame. You have to choose some synchronization convention for that.

 

[MeJennifer]

length contraction refers to the interval between two events that occur simultaneously in some reference frame.

Why do you claim that?

Suppose the distance, as measured by a two-way light signal, between A and B is D then a traveler traveling between A and B will always measure the distance to be < D. If the traveler's speed is << c the measured distance is practically speaking D, however if his speed approaches c the distance will approach 0.

 

[Dale]

That is an interesting take on length contraction, I haven't heard it described in terms of two-way light propagation instead of simultaneous measurements.

Are A and B here events or worldlines? I am guessing you mean worldlines.

 

[yuiop]

In Lorentz's early version of relativity (that was superceded by Einstein's Special Relativity) an object moving relative to the hypothetical ether was length contracted by a factor (gamma) that was a function of it's velocity relative to the ether. In this early viewpoint the contraction was a real physical manifestation that was a result of a physical interaction between the moving object and the ether. Imagine we had identical twins, Adam and Bob. If Adam was moving relative to the ether while Bob was stationary wrt the ether, then in the Lorentz version Adam really would be physically contracted. However, the rulers carried by Adam would also be length contracted and his clock would be advancing at a slower rate and that would cause Adam to measure Bob as being length contracted. The end result is that neither Adam nor Bob could actually tell who is really length contracted and who is really stationary with respect to the ether. Einstein argued that since there is no way to detect the ether, then it could be dispensed with and this is the modern mainstream view.

In the lorentz version, the logic system that is applied can be summerized as:

If (length of A) > (length of B) then (length of B) < (length of A)

If (time interval A) > (time interval B) then (time interval B) < (time interval A)

Now while Lorentz logic seams reasonable and intuitive the above statements concern presumed intrinsic physical values but gloss over what is actually measured.

In the Einstein version the relationship is :

If (A measures length A>B) then (B measures length B>A)

If (A measures time interval A>B) then (B measures time interval B>A)

The Einstein version is slightly non-intuitive, but is mathematically correct and at the end of the day we should concern ourselves only with what we can actually measure rather than what we imagine is "really" going on.

The Lorentz version says that if two objects have relative motion, then both objects can not be stationary wrt the ether at the same time and so one of the objects must "really" be shorter than the other. The Einstein version makes clear that we have no way of measuring which object is "really" shorter and the argument becomes philosophical rather than scientific.

 

[matheinste]

Hello kev.

In answer to #54 with regards to your last comment. Whether or not an object local to us is moving relative to us or not i think can be decided and accepted as fact.The length of an object not moving relative to us is defined in SR as its proper length. Perhaps we can think of that as its real length because for us that is what it would be. We can measure it and if we had no knowledge of realative length contraction no question would ever occur about its reality. If a moving object is contracted relative to our non moving object then we can argue that this length is really shorter or not but surely there is an objective reality, as far as anything can be considered real, about the proper length as defined defined and measured by us.

Matheinste.

 

[matheinste]

Hello again kev.

In answer to my #55 on second reading it does not say anything different than your last comment. Sorry.

Matheinste.

 

[Ken G]

The Einstein version is slightly non-intuitive, but is mathematically correct and at the end of the day we should concern ourselves only with what we can actually measure rather than what we imagine is "really" going on.

I agree and have made the same point with regard to both the many-worlds interpretation of quantum mechanics (popular on this forum) and the interpretation of expanding space in cosmology (popular almost everywhere). Einstein's logic sounds more convincing in relativity, for some reason.

 

[Tachyonie]

Can just someone confirm that I am (approximetly :) correct? I expected correction and I am quiet surprised to not get one. :)

Youre traveling close to C to a distant star 10 light years away. However due to the time dilation it would take the crew only 1 year to reach that star, using simple formula 10/1 we get 10 light years per year which is a big nono... therefore you have to make everything smaller to compensate this paradox.

 

[Lojzek]

Can just someone confirm that I am (approximetly :) correct? I expected correction and I am quiet surprised to not get one. :)

I think your conclusion is correct. One of the assumptions of relativistic mechanics (that is used to derive Lorentz transformation) is that the speed of object B in the system of object A is the same as the speed of object A in the system of B. If B travels a distance of L in a time t in the system A, then equalization of relative velocities gives equation:

L/t=L'/t'

or L'/L=t'/t (=1/gamma)

Length contraction is a necessary consequence of time dilation.

 

[yuiop]

Can just someone confirm that I am (approximetly :) correct? I expected correction and I am quiet surprised to not get one. :)

Hi,

Just like to add that no one measures the speed of the spaceship to be 10c when they use their own clocks and their own rulers. The only person that might come to that conclusion would be a person measuring the distance using rulers at rest with the star frame and clocks at rest with the spaceship frame.

(By the way, I am not disagreeing with your statement ;)