How to test length contraction by experiment?

Thanks. I think you are the only one who has got my point. I do not deny length contraction, but I want to see it. For example, take 2 co-moving muons. In their frame, they are D distance apart. When they move in the atmosphere at the speed 0.999 c, D should be contracted, say, D/gamma.

Then, we should see if D and D/gamma are really the case.

 

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If one take a rod with a moun at each end, we will have 2 mouns moving with constant distance between them. Without the rod, these moun should move the same way. Then, let D be the distance between them. What is the distance in the frame of Earth?

 

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However long your rod was.

Note that there's no way to
- place two muons at the ends of a rod,
- accelerate the rod to .9999c,
- ensure two muons are traveling at the exact same speed in the exact same direction.

So, while the idea might work as a thought experiment, it has nothing to do with a practical experiment, which is what you declared your goal to be.

So, do you want a thought experiment, or a practical experiment?

 

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My proposed experiment is to accelerate 2 electrons. We know their distance in the 2 electron guns, then we detect their positions in the fly.

 

You're missing the point. That won't measure length contraction.

Look:
How do you know when to fire the second electron gun?
How will you know when the second electron one is passing the first one?
Hoe will you measure the velocities of the electrons before they've reached your detector?

Here is your setup, with one spatial dimension replaced with time.
Electrons travel straight from left to right, and the passage of time is tracked from top to bottom.
How does this demonstrate anything?

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Very nice drawing. Thanks.

The electron guns are triggered at the same time. In the frame of the electrons, the distance between them equals that between the guns. Once they reach the detectors, we know their positions. The voltage in the guns gives the velocity.

 

OK, diagram updated. Now what?

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How, exactly, does the voltage "give" us the velocity?
Because we set it to a certain voltage and we know what velocity that is equivalent to?

Except that the velocity is what it is - including any velocity on account of length contraction.
So, you aren't showing any before and after.

 

The linear accelerator at Stanford performs experiments on a regular basis using electrons. At speeds approaching c, the em fields are deformed, and electric field intensities increase as measured by electronic equipment. This is indirect evidence of length contraction. The idea originates with O. Heaviside who derived a deformed magnetic field from Maxwell's equations. Heaviside discussed the idea with Fitzgerald who presented it to Lorentz, who had similar but incomplete ideas, while forming his 'electron theory', circa 1880's. There are other phenomena that rely on lc for their explanation [1].

There is also a visual effect not usually considered that is counter-productive.

When a rod approaches at speeds in the near c range, and specifically with an offset from the observer, the light from the far end leaves before the light from the near end. The composite image will show the rod longer than its rest length.[1] As it approaches it will continuously contract to its rest length at closest approach then to a lower limit depending on its speed.


ref.

[1] length contraction, Wikipedia, June 2012

 

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On the left an earth observer describes a group of muons descending from an altitude of 1 unit to the ground (g) at .95c in et = 1.05.

On the right a computer/video device moving with the group records the ground moving at them at .95c on a collision course. The computer has 1 unit of distance to the ground from the starting altitude, stored in memory. Inspectors analyze the data recovered from the wreckage and reconstruct the experiment. Using SR they conclude the onboard clock was running slow by a factor of .32 which is in good agreement with the clock reading of .33. By substituting a device there was no loss of life.

 

Suppose the voltage is 10 Volt. Then the electron will get 10 eV of energy. The kinetic energy of an electron is:
E=1/2 m v2
So, we get the velocity of the electron v

In the diagram, we have 2 distances. The distance between the 2 Ding and that between the 2 Pow. The Ding-distance is the distance of the moving electrons. The Pow-distance is the distance when the electrons were at rest. So, Ding-distance could be the contraction of Pow-distance.

However, it seems that Ding-distance = Pow-distance.
Is it wrong with respect to Relativity?

 

Is the electric field deformed only in x direction or in xyz direction? Is its form measured like magnetic field line? If we do not know that, then the deformation is a derivation from length contraction. Then, length contraction should be precisely measured. Otherwise, the interpretation of experiment are not reliable.

This why the detection of the ends should be right in front of the rod, not deviated.

 

Time dilation confirmed.

 

Exactly. They're both doing exactly the same thing - have the same velocity and travel the same distance - so there's no reason it wouldn't take the same time.


Note, by the way, that - even if this did work the way you were expecting - and one electron (somehow) took less time than the other - you still wouldn't be measuring length contraction, you'd be measuring time dilation.

The velocity formula is v=d/t (or t=d/v).

So, for each electron:
e: t=d/v
e': t'=d'/v'

Since v=v' and d=d',
it must follow that t/t' is what would show a discrepancy (if the experiment worked as you expected).

 

I do not expect that "one electron (somehow) took less time than the other". I'm suggesting that in the frame traveling with the electrons, the electrons are static. So, they do not drift away from each other. That is, the distance between them stays constant in time and equals Pow-distance.

On the other hand, Ding-distance is the distance between the electrons measured in the frame of the laboratory. So, Ding-distance should be a contraction of Pow-distance. That is,
Ding-distance = Pow-distance / gamma

Ding-distance should be shorted than Pow-distance. The higher the velocity, the shorter Ding-distance should be. But if Ding-distance = Pow-distance as shown in your diagram, the length between the electrons is not contracted, which is contradictory to Special Relativity.

 

No it shouldn't.

Nor should it be.

It isn't.

You are misinterpreting length contraction. I will post an explanation later.

 

Except that they do. The electrons - in their frame - see the other moving away.

Because of the relativity of simultaneity, each electron does not see the other fired at the same moment. They are separated in time.

That's the lesson learned from Bell's Spaceship Paradox.

If the leading electron - right after exiting the gun - were to look back at the trailing electron, it would not immediately see the trailing electron being fired. It takes time for that event to propagate (at c) to where the leading electron experiences it. Thus the trailing electron is still accelerating even as the leading electron speeds away. The distance between them increases over time.

 

Declining to give any credit to the usual crew over at PF - yet again?:
https://www.physicsforums.com/threads/length-contraction-of-a-pair-of-electrons.973723/

 

Maybe I am, maybe not.

 

If the leading electron looks back at the trailing electron and sees it delays in time, does this mean that it is drifting away? In a gravitational field, we are all accelerated downward. Do we see the ground drifts away below us?

For the 2 electrons, let us put them on the 2 ends of a rod just to help us reflecting. The 2 ends at time t=0 are 2 time-like events, that is, they are not causally linked. The motion of one end does not need to be seen by the other to be executed. So, simultaneity or not in their frame do not affect the position in space of the 2 electrons.

As taught in text books, the ends of a moving rod are not simultaneous, but they are at constant distance from one another whatsoever. The head end looks back at the trailing end and see it delayed. But so what? They are tied by the rod and stay at the same distance apart.

We have learned no lesson from Bell's Spaceship Paradox, otherwise, it would not be a Paradox without explanation now.

So, your " Except that they do " is wrong. As the 2 ends of the rod do not see " the other moving away ", the electrons on these end do not move away from the other.

 

Thanks for the link, but you have ruined his effort to hide it.