How to test length contraction by experiment?

I just want to say that The balls are at different speed than the tube. Like a car vs a plane which travel at different speed. So, plane contract more than car. Then, length contraction can put the balls at a location where the tube is not. This is due to length contraction, like shown in LaurieAG's figure, where ellipse B is where the tube is and C is where the balls are.

 

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I am vary familiar with LaurieAG's figure (actually Gron's). It pertains to a wheel rolling from left to right. The perimeter of the wheel is marked with 16 points which are all labeled 1 to 16.

There is an observer whose eyeball is located at point x=0, y=0. The upright ellipse (B) is the actual length-contracted shape of the rolling wheel, and all 16 points marked on the perimeter are actually located on that upright ellipse. You can see them in the purple color.

But that is not what the observer's eyeball sees, with the exception of the point labeled 1. Instead the observer's eyeball collects light which had been emitted from earlier moments in time, all of which hit the eyeball at the same time, and form the apparent tilted shape (C) which the eyeball considers to be the shape of the rolling wheel. But the observer is not seeing the wheel as it exists in one moment of time.

What you seem to be saying is that, due to the fact that all of the points on the perimeter of the wheel have different velocities, that should mean that some of the points on the perimeter of the wheel will not be located on the perimeter of the wheel. That is absurd.

The points on the perimeter of the wheel must always be on the perimeter of the wheel! They cannot fly off unless the wheel breaks apart. Of course an observer's eyeball can see light emitted from different times and conclude a different tilted shape (C), but even then, all of the red colored points 1-16 still represent the perimeter of the wheel, at least in how it is perceived by the observer's eyeball. It just does not appear as an upright ellipse, it is more of a tilted shape. It is an optical illusion, though, as the real shape is the upright ellipse (B).

 

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Thank for this lengthy explanation. I did not know LaurieAG's (Gron's) figure and study. I surely will ponder on it.
I think it is too complex as an evidence for or against the length contraction problem that I'm talking about.

 

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You are welcome. I agree that LaurieAG's diagram is a little off topic, since it addresses how length-contracted objects appear to the eye.

 

I was actually pointing out that the length contraction was applied to the spoke of the wheel to get the emission start point in the extended road frame/plane. Several earlier attempts at the problem had resulted in failure as they used both length contraction and time dilation so any solution for the observer relies on one or the other but not both.

Also, the link to the image I posted clearly states it is Gron's.

 

Astrophysical jet and length contraction

Astrophysical jets are flows of matter that moves at relativistic speed. They are opportunity to see length contraction in action. An astrophysical jet is analyzed to explain the length contraction effect.
Astrophysical jets are ejected from compact objects such as black holes. https://en.wikipedia.org/wiki/Astrophysical_jet#/media/File:M87_jet.jpg is a photograph of the jet ejected by the supermassive black hole at the center of the galaxy M87 which stretches over 5 000 light-years. Matter in this jet moves at almost the speed of light and undergoes relativistic effects.
Almost all predictions of Special Relativity are proven by experiment except one: length contraction. Indeed, it is impossible to accelerate chunk of matter to relativistic speed to directly measure length contraction on Earth. Fortunately, length contraction should occur in astrophysical jets where we could finally see this effect for real.
An astrophysical jet is a moving cloud of particles whose velocity varies from almost the speed of light in the ejection region to very slow thousand light-years away. We name the jets in these 2 regions fast jet and slow jet. The fast jet should be strongly length-contracted while the slow jet should not. Let us compare a moving cloud of particles with the air inside a ball. The air inside a moving ball moves with the ball and would seem denser than the air inside the same ball at rest because the flat moving ball has a contracted surface. In the same way, fast jet should seem denser than slow jet. Since the particles of an astrophysical jet emit photons, the fast jet should be brighter than the slow jet. As the slowdown of the jet is gradual, we expect that the brightness of a jet decreases gradually from the fast jet to the slow jet. However, we do not see such gradual decrease of brightness in the photograph. Why?
Please read the article at
PDF: Astrophysical jet and length contraction https://pengkuanonphysics.blogspot.com/2019/08/astrophysical-jet-and-length-contraction.html
or
Word: https://www.academia.edu/40066246/Astrophysical_jet_and_length_contraction

 

Can the 2 ends of a ruler move in opposite direction?

Here is a problem about length contraction. If we have a ruler of length L, its near end is at x=0 and far end at x=L when stationary. If we put it in motion, its length is contracted to L/gamma. At time t, it moves the distance s. So, its near end is at x=s and far end at x=s+L/gamma. For any s and any velocity, its far end's will be smaller than L if L is sufficiently long. That is, while its near end moves to the right, far end moves the left. This is so weird.
You can see the computation here, page 4 from figure 10 and on, in the article https://pengkuanonphysics.blogspot.com/2019/08/from-michelsonmorley-experiment-to.html
or https://www.academia.edu/40208137/From_Michelson-Morley_experiment_to_length_contraction
Does anyone have an idea?

 

I don't think it is required that the far end ever move toward the left. All that is required is for the far end to move toward the right a lesser distance than the near end.

Instead of considering a perfectly rigid ruler, consider two rocket engines which are a distance of L apart, when stationary. You can easily arrange for both rocket engines to momentarily fire simultaneously in that one inertial frame of reference. But that would mean that the two rocket engines remain a distance of L apart as measured by that inertial frame of reference. However, in the inertial frame of the rocket engines after they momentarily fired, it will be found that the front engine fired before the rear engine, and it will also be found that the distance between the rocket engines increased accordingly.

So, if you want an analogy to the rigid ruler, you would need to start all over. This time make the rear engine fire before the front engine by just the right amount of time so that in the inertial frame of the rocket engines after they momentarily fired, it will be found that they are a distance of L apart. Of course you would need to make the rear engine fire before the front engine by just the right amount of time that they end up a distance of L/gamma apart according to the original rest frame.

 

...something that is expressly forbidden in Einsteinian relativity, so you will get nonsensical results.

 

Thanks for replying. I know the Bell's spaceship paradox and I have used it to propose a test of length contraction in the article
"How to test length contraction by experiment?" which is the hotly debated first post of the present thread http://www.sciforums.com/threads/how-to-test-length-contraction-by-experiment.162037/
and the articles is:
https://pengkuanonphysics.blogspot.com/2019/06/how-to-test-length-contraction-by.html or
https://www.academia.edu/39584663/How_to_test_length_contraction_by_experiment

I proposed to fire 2 electrons in the experiment at exactly the same time with the same energy and to measure their distance. But this paradox leads to contradiction such as: the 2 spaceships stay at constant distance, but will extend the distance their proper frame due to length contraction. So, in this frame the far spaceship gets velocity and kinetic energy. If the spaceships are tided together and the thread breaks, the work that breaks the thread comes from nowhere.

I have explained this and several other contradictions in the article Astrophysical jet and length contraction
https://pengkuanonphysics.blogspot.com/2019/08/astrophysical-jet-and-length-contraction.html or
https://www.academia.edu/40066246/Astrophysical_jet_and_length_contraction

So, the ruler cannot keep constant length, it will contract and the far end will go left.

 

But I did successfully make an analogy to the ruler, and the result was not nonsense. One simply has to fire the rear rocket before the front rocket so that the distance between them goes from L (when they were at rest relative to the frame that is measuring) to L/gamma (when they were moving at constant velocity v relative to the frame that is measuring). This is called relativity-of-simultaneity, and even though it is strange, it is not nonsense.

But you are correct that there are no perfectly rigid objects, especially in SR.

 

The work that breaks the thread comes from the front spaceship accelerating before the rear spaceship does, in the string's own reference frame. I know it seems like a paradox, but it isn't. It's just that (as Dave mentioned) there are no truly rigid objects, and also, there is no such thing as instantaneous acceleration.

No, I don't see how that conclusion follows from the premises we have at hand. The velocity of the left end of the ruler can go from 0 to v before the right end of the ruler does so, and the result is a length-contracted ruler, without any movement in the opposite direction.

 

If length contraction is true, then it should contract the ruler. Let L be its length, when it gets velocity v, it is contracted to L/gamma. Suppose L=10 and at v, L/gamma = 8.

At t=0, its length is 10. At t=1, its velocity is v, and its length is 8 and its near end is at x=1. So, at this moment, its far end is at 1+8=9=10-1. In consequence, it far end has moved 1 to the left, in opposite direction to the motion of the ruler.

 

No. Measuring where the two ends of the ruler are at a given moment in time is not so simple a task as you think.

 

We just apply Lorentz transforms and we have my result.

 

Okay, but your units are off. You have the left end going from x=0 to x=1 in the time between t=0 and t=1. Using conventional units, that would be the speed of light. But assuming your units are arbitrary, then I can just change your scenario to the following:

At t=0, its length is 10. At t=2, its velocity is v, and its length is 8 and its near end is at x=2. So, at this moment, its far end is at 2+8=10. In consequence, its far end has not moved to the left.

In reality, if you apply a force to the rear end of the ruler, that information cannot even reach the front end of the ruler until it travels the length of the ruler at the speed of sound in the ruler material. You would have a much more complicated scenario if you intend to consider such details. I would recommend looking into the bug and rivet paradox.

 

No, that only gives you a length; it doesn't tell you where the two ends are at a given time.

 

Can we just talk about the Lorentz transform without material consideration?

What I'm exposing is an application of the Lorentz transform. There are 3 stages, the Lorentz transform itself, my application and the result.
First stage, the result is: at t=1, the far end is on the left of its former position 10. Is this acceptable? If yes, OK. If no, then the application may be wrong.
Second stage, the application is: the ruler's length is 8 due to length contraction, its near end is at 1 and then, its far end is at 1+8=9<10. Is this a correct application of the Lorentz transform? If no, then where is wrong? If yes, then may the Lorentz transform be wrong?
Third stage, the Lorentz transform is: the ruler's length contracts according to the Lorentz transform. Is length contraction correct? If no, OK. If yes, we should accept the far end to move left.

 

In the frame of the lab, we have x and t of the 2 end in theory.

 

No. Its far end will never be closer than 10.

1. The far end (marked 10) cannot experience contraction until it is moving at relativistic velocities. It takes a finite - non-zero - length of time for the far end to start moving, and then more time for it to accelerate to relativistic velocity.
2. Since the far end is now moving (to the right) by the time it reaches a relativistic velocity, it will have moved beyond the 10 mark.
3. In the time for the far end to reach relativistic velocity, the near end will have moved at least 2.

Looking at it more simply: No Lorentz contraction effects can affect the far end if that part it is not yet moving relativistically. So it can't possibly contract leftward of 10.