How to test length contraction by experiment?

Right. And the picture actually seen by a moving ball is, depending who you believe, different again. Terrell effect maintains that a perfectly rigid, non-rotating object in it's proper frame, will appear rotated and distorted from another inertial frame in constant relative motion:
https://en.wikipedia.org/wiki/Terrell_rotation
I actually think that is mistaken. It's pov is that rays of light emanating from different parts of the object must have started out at different times in order to arrive at the observer simultaneously. Which would be true if said object emitted a phased pulse. [Or was radar/lidar illuminated by the observer.] In fact, we normally assume continuous illumination of object by a fixed wrt object external source e.g sun, and then there should imo be just the normal Lorentz contraction seen. True also if the observer (but not object) is in say circular motion.
However, in the case shown in fig. of #54, retardation effects will be evident when it comes to snapshot of the other circulating balls. They will have distorted positions over and above that of Lorentz contraction of the circular track. Precisely because the notion behind Terrell rotation - varying signal delay - then comes into effect.

 

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This may be similar PengKuan.

The image below is from a SR based relativistically rolling ring solution from an old forum (solution summary link below, they were hacked so they reinstated a backup from 2014 but the hacker kept getting back in so they locked new members).

A is the wheel frame, B is the axle frame and C is a Euclidean plot (or plane based on the road frame) of photon emissions from 16 points around the rim of the rolling ring that were timed so that all photons emitted arrive at the camera at point 0 on the road at the same time.

While the emission point locations are on the circumference of the ring the length contracted spoke length determines the emission point.

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http://www.thephysicsforum.com/spec...elativistic-rolling-wheel-ii-3.html#post12639

 

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If more balls fit along the perimeter, when in motion, then that must be a physical fact. It cannot be a visual effect.

 

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Hi Laurie AG! Thank you for the very nice chart, and the link! I had forgotten about that convo. It was very enlightening.

 

The solution shown above is the only one I have seen that goes anywhere near replicating Ovyind Gron's Figure 9 Part C 'optical appearance' solution in his paper "Space geometry in rotating reference frames:A historical appraisal". Unfortunately this excellent paper is behind a paywall now.

Incidentally the straight line distance between each emission point and the camera is the actual time/distance traveled by the emitted photons at c. The legends of the columns in the spreadsheet have the variables/equations.

 

Thank for this link and drawing. This is a analyze new for me.

It deal with wheel in space which is has not external limit of space, so the perimeter of the disk can be a ellipsoid. But in my case, there is a circular tube that contains the electrons. From the view of an electron, the other electron are on a ellipsoid, but the tube should be an ellipsoid of different form because its speed is not the same. So, in the moving frame of an electron, the other electrons are not in the tube, which is not physical.

 

If the balls are touching each other, then there can be more balls in the ring. This means that the balls are contracted in the direction of the motion.

However, here the balls are only point like electrons and the space between them do not contract. Why does matter contracts but not space? This is not consistent since relativity is about space, not matter.

I'm not suggesting that you are wrong nor the theory. But if a theory lead to multiple interpretations, then it need some clarification. Indeed, any aspect of the experiment should fit into the theory at the same time. Length should contract, but the circumference should be 2PI R, the position of the electrons are seen as on an ellipse but should stay inside another ellipse which is the tube of the accelerator, the diameter of the balls should contract in the direction of the motion, but the space between should not since the circumference is 2 PI R....

 

PengKuan;

This is the only one I know.
In the graphic, U describes all motions.
A and B are space cans of length 2 and separated by a gap of 2.
A and B use the same program to accelerate to a target speed requiring 4 time units.
Each can contracts producing an expanding gap (the values are just approximations).
Any flexible connection between A-front and B-back will fail if stressed to its limit.
This case does not include all cases. The 2 cans could be connected via a rigid material, producing an assembly that could withstand a slow constant acceleration.

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Thanks for remembering my very old post and the lengthy discussion about it.

Yes, in the co-moving frame, length should increase. In this case, an electron see the distance from him to the next becomes longer. Since the radius does not contract, the electron will conclude that the circumference is longer than
2PI R . Which is not geometrically correct. This is how Einstein get the idea of curved space. But here the circle is one-dimensional.

The ellipse on which rest the electrons and the tube of the accelerator do not fit together. But they should be of the same geometrical form so that the electrons circulate in the tube.

 

You have one inertial frame where the tube is not moving at all, and in that frame the tube is a circle. Let's call that the Lab frame, meaning it is the laboratory where you are performing your experiment.

Now please imagine a different inertial frame where the bottom electron in your diagram is stationary for one instant of time. In that inertial reference frame, the whole tube is moving horizontally at constant speed, and so the whole tube is contracted to an ellipse. It's height stays the same as the original circle, but the width is contracted.

In that inertial frame, all of the other electrons are located at different places inside that ellipse. In that frame, the top electron in your diagram is the one that is most length contracted, but all of the other electrons are length contracted to various degrees

This new inertial frame is the one that most closely approximates the non-inertial reference frame of the bottom electron. So let's call this new frame the reference frame of the bottom electron.

Yes, that is what I meant.

Okay, let me try to clarify. In the lab frame, the tube is a circle. There is empty space inside the circle. In the frame of the bottom electron, the tube is an ellipse, so the empty space inside the circle is contracted to an ellipse as well.

I think your concern is that you think the Ehrenfest paradox is a real paradox. But it isn't really, not in theory.

 

This is basically what I'm trying to describe:

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Assume steady illumination from an external source stationary wrt ring. Then even for the middle (lab frame) fig., an observer there will see the circulating balls not exactly as shown but as each ball would have been had it continued in a straight line for a distance equal to its instantaneous velocity times the signal delay time from ball to observer. Hence at a larger radius than the ring itself. This is not 'unphysical' - remember we are dealing with visual effects. The basic idea of apparent or virtual present position is set out when deriving the Lienard-Wiechert potentials and radiation formulae for arbitrarily moving charge. See e.g.:
http://farside.ph.utexas.edu/teaching/em/lectures/node129.html

It gets more complicated for the last figure because the observer (a given circulating ball) is not itself in uniform relative motion, so signal delay between it and any other ball is more complicated than for an inertial observer. And more complex again if illumination is via radar/lidar from the observer.
Bottom line - be very careful to spell out and set out all the relevant factors when evaluating any given scenario.
And we are drifting quite away from the OP topic!

 

My posts and diagrams in this thread are not considering any visual effects at all. I don't know where you got that idea.

The standard configuration of SR, and the Lorentz transformation equations, is that each inertial reference frame has a spacial coordinate system AND assumes Einstein-synchronized clocks located everywhere throughout the whole coordinate system. The spacial coordinate system provides three spacial dimensions (x, y, z) and the pre-synchronised clock at the location of any event provides the fourth variable (t).

Knowing the coordinates (x, y, z, t) of any event, you can always calculate how much delay there will be if the light from that event has to actually reach any distant observer's eyeball. But that is a secondary consideration. No distant observers are actually required, because if there is an Einstein-synchronised clock located right at the event, then that serves as a very local observer, with essentially zero distance between itself and the event.

As for drifting off-topic, yes that is true. I am also assuming physical balls, not electrons or any other charged particles. My bad.

 

So in particular the last fig. in #71 is not meant to illustrate what the chosen ball actually 'sees' as a snapshot? I'm confused. What does it show then?

[Edit: I'd best expand on my comments in #72 re your middle fig. of #71. There must be finite distance between any lab frame observer and at least all bar one of the circulating balls. My unstated assumption was that of an observer located anywhere along the symmetry axis of the constraining ring. Then there is equal magnitude of (apparent present position) minus (actual present position) for all the balls wrt observer.]

But the reference ball is not itself in an inertial reference frame! That of itself makes a fundamental difference.

Given there is always spatial separation between any two balls, I'm not following your reasoning here. Seems to me we either discount SR effects entirely (assuming then v << c), or we must analyze it according to what signal delay dictates. I linked to that reference article for a reason.

Re balls vs charges - PengKuan swapped there. There are important differences between electrodynamics of moving charge vs snapshot visuals of neutral balls, but the common factor is the principle of apparent or virtual present position. It's only essential to take into account when dealing with non-uniform i.e. accelerated motions. Which is the case dealt with here.

 

PengKuan #7;

Objects in motion can contract, space does not. The circular path remains constant. The guide for accelerated particles is not in motion relative to the lab, therefore does not change dimensionally.

 

Why Matter contracts but not space? In LIGO, the void space in the arms are stretched allowing the gravitational wave detection.

 

This an explanation for Bell's spaceship paradox. We see that the length of the moving string lengthens.

 

I'm not sure that all balls stay inside the tube because the balls and the correspondent points on the tube have different velocity. Thus, they are not on the same trajectory.

 

If all balls stay inside the tube in the "lab frame", then they also must stay inside the tube in the "bottom ball frame". To think otherwise is to think you have proven SR incorrect. I would suggest you think this through a little more carefully before jumping to such a conclusion.

Now tell me, do all balls stay inside the tube in the "lab frame" or not? If not, why not?

 

It is meant to show where the balls would actually be located, as opposed to where they would "appear" to be located.

No distant observers are necessary. Imagine there is an ant walking around on the roof of your office building, and your boss tells you that he wants to know exactly where that ant is located at any given moment in time. He marks the whole roof with x and y coordinates everywhere. Note that there are an infinite number of x and y values between x=1 and x=2 but he can mark it as accurately as he chooses. Perhaps he marks only 1.00 1.25 1.50 1.75 and 2.00. Or perhaps he marks 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 and 2.0. It is a thought experiment, so this is not really a matter of concern.

But he only gives you two choices as to how to achieve this task. You can choose 1 or 2:

1. Set up a video camera on the moon, record the ant walking around on the x and y coordinates, and use the time stamp on the video. Simply adjust the time stamp value by the amount of time it takes for the light to travel from the earth to the moon in order to get the actual time coordinate, t.

-or-

2. Set up a video camera at each x and y marking, just 1/16" above the roof, and synchronise all of their clocks. Use all of them to record the ant walking around on the x and y coordinates, and use the time stamp on all of the videos. Now the time stamp values do not really have to be adjusted as 1/16" is too small to worry about the time it takes light to travel.

Either method would work, in principle. But SR assumes that there is a lattice of an infinite number of synchronised clocks, located at every spacial coordinate. So SR is more equivalent with method 2 above.

I am not really considering the non-inertial frame of one of the balls. I am considering an inertial frame in which one of the balls is momentarily at rest.

In post #70 I said to PengKuan, "Now please imagine a different inertial frame where the bottom electron in your diagram is stationary for one instant of time. In that inertial reference frame, the whole tube is moving horizontally at constant speed, and so the whole tube is contracted to an ellipse... This new inertial frame is the one that most closely approximates the non-inertial reference frame of the bottom electron. So let's call this new frame the reference frame of the bottom electron."