[Malamute Lover]

Several problems here.

In the Ehrenfest paradox, the circumference contracts, not expands, since the wheel is moving.

I didn't state otherwise, in the quote of mine to which you responded or in post 3. Given a spinning radius of 1, it has a contracted circumference of 6.283 and a rest circumference (proper circumference) of 8.796. That's contracting due to spin.  Either the spokes get shorter (reeled in??) as it spins, or the thing perhaps needs to be manufactured already spinning.

Of course, the spokes experience Lorentz contraction. They are moving too. Because they are in motion, and the light from the outer portions takes longer to reach the observer in the center, they appear curved. That is, the observer does not need to look along the length to notice Lorentz contraction. Yes, the spokes get shorter as the rim contracts.  Since the rim is moving along with the blocks, it will experience exactly the same Lorentz contraction as the blocks. No increasing gap sizes.

From the viewpoint of a non-rotating observer at the center of the circle, the blocks would be seen to shrink along with any gaps between them.

Given fixed length radius, the blocks would have no gaps between them when stationary, and as they shrink, gaps would form, allowing more blocks to be inserted in them if you like. You seem to suggest that the gaps shrink as well, which is wrong.  Picture a bunch of roller coaster cars, touching each other while parked in a circular track. As they speed up, the track doesn't change size at all, but gaps must form between the cars as they contract. That's what the recent diagram depicts.  The ring circumference will contract if there's no track and the cars are bolted together. In that case there never are gaps, but the radius goes down as the ring circumference contracts.

But as we have seen, the radius does shrink because the spokes also experience Lorentz contraction and that is visible to the observer in the center.

This could be seen by comparing the observed length of the blocks compared to their width. An observer riding on the rim would not notice any difference in the size of the blocks or the gaps.

He'd very much notice the gaps forming, which were not there at all before. I agree that he'd not notice the ratio of length/width of his own car changing. We're talking about fixed radius here. Fixed spokes or a track or something.

Sorry, no fixed radius when the wheel is spinning.

Why are you making the circumference larger?

I'm not.

And why are the gaps larger?

Different example. Don't mix them. The text of mine you quoted is about gaps forming with blocks moving at a fixed radius.  Post 3 talks about a solid ring contracting as it rotates, reducing the radius. Nothing gets larger with speed.

The increasing gap size points to the blocks shrinking but the rim not shrinking. That is equivalent to the rim expanding relative to the blocks. But the rim will contract as much as the blocks. No gaps.

The radius is assumed to be constant.

Only in the example in post 29, where the radius is held constant with detached objects moving around that fixed path at ever increasing speeds.

Detached objects following a circular track requires an additional force to keep them on track. That is, there must be something comparable to a rim to exert that inward force. This changes nothing. Whatever is keeping the blocks on track will be subject to the same Lorentz contraction.

If you want something that holds the blocks on track but is not itself moving, you are introducing all sorts of complications. For one thing, from the viewpoint of the blocks, the whatever it is outside will be the thing that is moving and will therefore be Lorentz contracted and have a smaller circumference/radius. For another, the force holding the blocks in place will result in the outside influence thing being set in motion and the blocks slowing down. (Newton #3)

The size of the radius can only be determined with a measuring rod.

We have one. You can't measure a stationary track or fixed length spokes moving only perpendicular to their length?  Post 29 shows a sort of track. No spokes. The grey boxes seem to be the track, not spinning with the red stuff.

The spinning disk (grey) and the red boxes on it will all undergo Lorentz contraction along the direction of motion. This will reduce the circumference and therefore the radius. No broken strings.

If we use the rotating stick as the measuring rod, we will see something interesting. It will not appear to be rigid. Light coming the rod from near the rim will take longer to reach the observer in the center and will show the stick at an earlier time in its rotation. The stick will appear to curve and have a length greater than the expected radius.

Appearances or no, the stick (spoke) is in fact straight in an frame where the axis of rotation is stationary. Light 'appearing' to curve is Coriolis effect that you get in a rotating frame. Light does not move in straight lines in a rotating frame. If you photograph the thing from a distant point on the axis, the spoke-stick will appear straight since light takes about equal time to get from any location of the stick to the point of view.

If you photograph the whole thing from a distant point. You will see something different from what an observer at the center sees. But it will still exhibit Lorentz contraction since it is moving with respect to that distant observer. Lorentz contraction is relative. It is not real.

But if the observer in the center holds a measuring rod out to the circumference until sparks fly when it touches the rim, the measured radius would be as expected for a non-rotating wheel. (Actually, the measurement will be a bit too long as it would take time for the light of the sparks to reach the center. But since the speed of light is known, an adjustment could be made for this.)

If the radius is 1, then the light will take time 1 to reach the observer in the center despite it not moving along the spoke. No adjustment is needed.

The observer in the center will not know that contact has been made until a light signal comes back from the rim. In the meantime, the observer is still pushing the rod out beyond the point of contact.  The length of measuring rod that has been pushed out is too much. An adjustment needs to be made to the measured length.

This result contradicts the radius implied by the observations made of the blocks on the spinning wheel.

The blocks are not making any measurement of the radius. They measure proper circumference.

No, the blocks are measuring Lorentz contracted circumference because they are in motion. No gaps.

Length contraction is not real. It is relative.

You're denying that gaps form between the blocks? By your posts above, it seems so. Let me know how that works for you. I stand by my statement that contraction is objectively real and is well illustrated by the Ehrenfest scenario. There is no frame in which those gaps do not form.

I am denying that gaps form because the circumference is contracting along with the blocks. There is no frame in which the gaps do form.

It is impossible to synchronize separated clocks. The two spaceships cannot start at the same time. There is not such thing as the same time.

This is nonsense.
The ships are initially stationary, and begin identical proper acceleration at the same time relative to the frame in which they are stationary. Are you in denial now that clocks can be synced in a given inertial frame? Einstein gives some nice examples of ways to do exactly that.

As I explained in a prior post, the clocks are out of sync when the engines start because each space ship sees a delay in the start of the other space ship’s engine. As a consequence, each space ship sees the other one going slower than itself because it has not been accelerating for as long. No common frame of reference. It is not possible to start the engines at the same time. Distance = time delay.

You appear to be searching for cop-out excuses to avoid explaining a scenario that you apparently don't understand. The ship at the rear could even start out a little before the other, putting initial slack in the string. As the ships and the string gain speed and contract, the string will eventually break, but it takes a bit longer due to that initial slack.

No cop outs going on. I understand the scenarios perfectly. You are the one being inconsistent in the application of Lorentz contraction. It applies to the circumference as much as to the blocks.

As I described in the previous post, even starting at the same prearranged time on previously synchronized clocks, each spaceship thinks the other one is going slower with opposite expectations. Even if you manage to get them agreeing that they are both going at the same speed, the two spaceships and the string would all be in a common inertial reference frame and they would see no Lorentz contraction and no broken string.

As I pointed out in my prior post, an observer in a different inertial reference frame would see the entire complex of ships and strings equally Lorentz contracted and no broken string.

If a string was tied inside a spaceship along the direction of travel, and the spaceship accelerated (slowly) to a high speed, would the string break? It is not material objects that get contracted, it is space itself by appearing to be at different orientations in Minkowski spacetime to different reference frames. This is the point you are missing.

Lorentz contraction is relative, not real.

[Malamute Lover]

The question: Is accelerated observer on the wheel rim going to see/observe/measure the deformation that is not predicted by (a)?
Jano

An observer on the rim is going to see deformations not present in (a) because the different parts between the rim and the center are going at different speeds. But it will not be the same deformations as an observer at the center would see..

[Malamute Lover]

...

Is the deformation real then?

The deformation into an ellipse is frame dependent, but that doesn't make it not real. M-L seems to think otherwise.

The wheel is already accelerated and it has a constant rotation.

Both wheels have identical proper angular velocity. That's not the same as constant rotation. The angular velocity of an object is frame dependent since it can be used as a clock, and time is dilated in a frame in which the object is moving.

If an A1 rim observer connects a string to B1 rim observer at the bottom then is it fair to expect the string to be broken at the top?

If the two wheels are different wheels in the same frame, then the string breaks same as if I attach a string between a moving car and a parked one.
I don't think you mean that, but I don't know what you mean by 'A1 rim' and 'B1 rim'.  They seem to be references to different objects in relative motion, which probably breaks the string.
If you mean a string from one side of a wheel to the other side of the same wheel, then no, that string will not break for either wheel so long as they keep spinning.  The spokes already serve as such a string.

Is the (a) axle observer going to see the string broken?

I cannot figure out where you are putting your string. The (a) axle observer cannot see anything different than the (b) axle observer since, per principle of relativity, linear motion cannot be locally detected. The two wheels might be the same wheel, just considered in two different inertial frames.

Do we have a multiverse here?

?  What brings this up?

The strings not broken for (a) but broken for (b)?

Your description made it sound like one string between the two wheels, so if one sees it break, the other will see the same string break.

Halc,
This is the bottom of the cycloid as seen from (b).
Please, ignore A₀ and B₀, it should say A₁ and B₁ because the speed is close to 0 in the (b) frame, the bottom part of the cycloid, therefore there is almost no gap between the A₁ and B₁ rim blocks from (b) point of view.
The string is attached here at the bottom when there is very tiny gap between the A₁ and B₁ rim blocks.



The wheel makes a half a turn.



The gap grows. Is the string going to break?
I agree both observers will see the same result, either it breaks or it does not.
There is no multiverse, two different outcomes for two different observers.
Jano

There are no gaps because the circumference of the rim has been subjected to Lorentz contraction as well. You are applying contraction only to one part of a moving system when you should be applying it to all of the system.

[Malamute Lover]

I see the problem this way.
The frame (a) sees the rim of the wheel symmetrically. See the figures 13.14 and 13.15.
The frame (b) sees the rim of the wheel asymmetrically. See the figure 2 of the paper.
Both are the inertial frame observers.
The (a) and (b) observers are not on the rim itself though.
If there is an accelerated observer on the rim of the wheel then this local observer will measure either symmetrical centripetal acceleration as predicted by (a) frame or asymmetrical acceleration where the spacing between 'the rim blocks' changes as predicted by (b) or ... completely something else that neither reference frame predicted.
Jano

As already stated, the outside observer who sees (b) is not looking at an inertial reference frame. The spokes are going faster on top and slower on the bottom relative to overall motion.

My apologies, I introduced a new scenario when the axle is accelerated.
Having said that, my last couple of posts are about the textbook and the paper.
There is no acceleration of the axle here, just to make it clear.
Both, (a) and (b) are inertial observers looking at the rotating wheel.
The question stands, is the accelerated wheel rim observer going to see/observe/measure the deformation or not.
What prediction/observation wins for the accelerated observer on the wheel rim? Is it (a) or (b)?
Jano

Neither, the observer on the rim in (b) is yet another frame of reference from the outside observer.  The observed deformations will be different again. Lorentz contraction is relative, not real.

[Kryptid]

Lorentz contraction is relative, not real.

What about it being relative makes it not real?

[Malamute Lover]

Lorentz contraction is relative, not real.

What about it being relative makes it not real?

By relative, I mean that it is observer dependent, which is how Einstein meant it.. Different observers are seeing different things. Which one is real? As I said earlier, what is real is the situation in Minkowski spacetime, Observers in different reference frames see different aspects of that. Nobody sees the 'real; real because it exists in 4 dimensions and we do not see that way.

[yor_on]

This one reminds me a lot of the spinning disk in where different speeds ,depending on where you measure its spin from its center, leads to different contractions, fracturing and breaking it up, according to some interpretations, before you even get to measuring it. Unless made from some very elastic material, probably needing to be 'infinitely' elastic :)

https://en.wikipedia.org/wiki/Ehrenfest_paradox
=

We have apparently black holes spinning close to 'c' though?  Then again, they are themselves a singularity. Then we have the stuff it 'sucks in' (drag with it)  which should follow that spin, I think? You have locally defined a geodesic (uniform motion, aka being locally 'weightless') for each object, but what about the spin here?

And then there is the spaghettification of course, by tidal forces (different gradients of gravity). Which means that even in the absence of any weight, locally defined, gravity still will split you into pieces. the point being that you can't define both a geodesic and a weight. If you define it as those gradients inferring a weight of the object you just left a geodesic. And the same goes for the spin as that also should be experienced as a weight, normally. So the stuff dragged by a black holes spin must then still be a geodesic, if I'm thinking correct, no matter the black holes 'spin' as defined from a far away observer?

https://www.nasa.gov/mission_pages/chandra/news/08-003.html
https://en.wikipedia.org/wiki/Spaghettification

[Jaaanosik (OP)]

Hi all,
Is the Lorentz Contraction real or not real.
What a beautiful 'can of warms' we got open here.
We all want to find out the truth.
If we come close to finding out the truth we will also find the answer to the question of this thread: Is angular momentum frame dependent?

I suggest we all put aside our convictions what is the correct answer and we develop an argument together; we find the answer together.
There are good points on both sides, to show that the LC is not real and also to show that the LC is real.
First, let us discuss how we can show the LC is not real.
I'll make a statement and I suggest we get an agreement if the statement can lead towards the answer.
If we say yes, then we will analyze and prove the statement.

If the Special Relativity is reciprocal then the Lorentz Contraction is not real.

Please, let us discuss the statement above. Do we agree it is a true statement?
Jano

[Kryptid]

If the Special Relativity is reciprocal then the Lorentz Contraction is not real.

Please, let us discuss the statement above. Do we agree it is a true statement?
Jano

What do you mean by special relativity being "reciprocal"?

[Jaaanosik (OP)]

If the Special Relativity is reciprocal then the Lorentz Contraction is not real.

Please, let us discuss the statement above. Do we agree it is a true statement?
Jano

What do you mean by special relativity being "reciprocal"?

Two inertial observers see each other clocks going slower.
Two inertial observers see each other Lorentz Contracted.
Whatever the first inertial observer can say about the second one then the second observer can say the same things about the first one.
There is no preferred reference frame.
Jano

[Kryptid]

Their observations are both equally real.

[Jaaanosik (OP)]

Here is a new thread to discuss the LC: https://www.thenakedscientists.com/forum/index.php?topic=80208.0
Let us keep this thread to the Angular Momentum discussion.

[CPT ArkAngel]

You cannot consider the wheel has a single frame but only as a collection of infinitely small points, each its own frame because they all have a different acceleration. The mistake is that they forget the additional delays between the frames. The proof of that is if you consider all point frames individually, angular momentum is conserved. It is simply an invariant under special relativity because the speed of light is constant and the mass increases as the length decreases.  There is zero problem.

[Malamute Lover]

Lorentz contraction is relative, not real.

What about it being relative makes it not real?

How about different observers seeing different things? Who is right?

[Kryptid]

How about different observers seeing different things? Who is right?

They both are right. Someone travelling near the speed of light might experience only a few hours of the passage of time if they traveled to Alpha Centauri, but someone on Earth watching them through a telescope will see that it took them over 4 years to get there. You can't say that one is right and one is wrong in that case either. They are both correct in their own reference frames. It's the same with length contraction.

[CPT ArkAngel]

Malamute, you forgot that the energy of acceleration cannot propagate faster than the speed of light. There is a delay between the front and the back as soon as you apply a force on an object. Thus the front and the back cannot be calculated as if they were in the same frame. SR and GR are classical theories. In classical physics, any object is inside space and time, it is embedded. Space and time are represented by a continuum, it is not divisible in chunk. The only way to represent an object which is not embedded in space is to picture it by infinitely small particles separated by space so the space is still a continuum. In Newtonian physics, you can considered objects has having a fixed length because space and time are not interwoven, but space is still a continuum and object are also embedded in space, it is just that you can make abstraction of the continuum to solve the problem when the object is solid.

[yor_on]

It's a nice idea and question Jaaanosik. You can always define different frames of reference to that wheel or disk . Let us assume that a spinning disk, or wheel, breaks down, fractures, due to spins being at different speeds, as defined from its center. One of tenets of relativity is that you always will find a logic for why it does, no matter where you as a observer is situated. So presuming you are 'at rest' with its spin at some location you should be able to define a locally coherent explanation for why it fractures, just as you should be able to do with f.ex the https://en.wikipedia.org/wiki/Unruh_effect

Actually it's deeper than than just relativity. It's a question of how this universe is ordered. By logic or by magic.

[Malamute Lover]

How about different observers seeing different things? Who is right?

They both are right. Someone travelling near the speed of light might experience only a few hours of the passage of time if they traveled to Alpha Centauri, but someone on Earth watching them through a telescope will see that it took them over 4 years to get there. You can't say that one is right and one is wrong in that case either. They are both correct in their own reference frames. It's the same with length contraction.

Does anyone see the string break?

[Malamute Lover]

Malamute, you forgot that the energy of acceleration cannot propagate faster than the speed of light. There is a delay between the front and the back as soon as you apply a force on an object. Thus the front and the back cannot be calculated as if they were in the same frame. SR and GR are classical theories. In classical physics, any object is inside space and time, it is embedded. Space and time are represented by a continuum, it is not divisible in chunk. The only way to represent an object which is not embedded in space is to picture it by infinitely small particles separated by space so the space is still a continuum. In Newtonian physics, you can considered objects as having a fixed length because space and time are not interwoven, but space is still a continuum and object are also embedded in space, it is just that you can make abstraction of the continuum to solve the problem when the object is solid.

The rod is being pushed and pulled. A rod being pulled will not break, stretch or whatever until it cannot propagate the energy wave any further. If it were not attached to anything it would simply move in the direction it is being pulled. In the present example it is attached at the other end and the energy wave from the pulled end will meet the energy wave from the pushed end in the middle and the waves will cancel out and the entire rod will be moving at the same speed. Continued pulling and pushing energy (ongoing acceleration) will propagate in the same manner. If we are talking about string, there will be slack on the pushed end that will take up the energy from the pulled end.

[Jaaanosik (OP)]

How about different observers seeing different things? Who is right?

They both are right. Someone travelling near the speed of light might experience only a few hours of the passage of time if they traveled to Alpha Centauri, but someone on Earth watching them through a telescope will see that it took them over 4 years to get there. You can't say that one is right and one is wrong in that case either. They are both correct in their own reference frames. It's the same with length contraction.

Please, check this post: https://www.thenakedscientists.com/forum/index.php?topic=80208.msg610136#msg610136
The traveler watches a couple of hours on the Earth to take 4 years on the ship?
Correct?
Jano