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Quote from: Jaaanosik on 30/07/2020 20:30:04Quote from: Malamute Lover on 30/07/2020 20:08:58Quote from: Jaaanosik on 30/07/2020 19:57:09The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,Two different reference frames seeing things differently is what relativity is all about. How can this be reconciled with this: "The laws of physics take the same form in all inertial frames of reference."The spokes of the wheel are traveling at different speeds as they go around. This is not an inertial frame of reference.Quote from: Jaaanosik on 30/07/2020 20:30:04QuoteNonetheless I fall to see that total angular momentum is not conserved. Can you, please, elaborate how you see it?JanoAs I said earlier.“QuoteThis situation is quite similar to the spin Hall effect in various systems, where variations in the intrinsic AM(spin) are compensated at the expense of the centroid shift generating extrinsic AM. […] However, in addition to the shape deformations, a rotating body also acquires mass deformations. The y >0 and y <0 sides of the wheel have different velocities in the moving frame and their constituent particles acquire different local γ-factors. Owing to this, the y >0 particles become heavier than the y <0 particles. [page 2 of the article, the same page as the spoked wheel pictureThe spokes on the top are denser, as seen in the picture and heavier. The energy centroid is higher than the geometric centroid. Looks to me like overall angular momentum is conserved, but redistributed. “There is a tradeoff between intrinsic and extrinsic AM with the shift in energy centroid generating extrinsic AM compensating for the changes in intrinsic AM, just like the text of the paper says. Where does it say anything about non-conservation of AM? If that had been demonstrated by the paper, it would have been shouted long and loud as something totally new and ultra-important.
Quote from: Malamute Lover on 30/07/2020 20:08:58Quote from: Jaaanosik on 30/07/2020 19:57:09The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,Two different reference frames seeing things differently is what relativity is all about. How can this be reconciled with this: "The laws of physics take the same form in all inertial frames of reference."
Quote from: Jaaanosik on 30/07/2020 19:57:09The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,Two different reference frames seeing things differently is what relativity is all about.
The world lines lose the symmetry in (b), they are asymmetric.This is the problem, two different frames show different analysis.They do not agree on the world lines. This is not good.They do not agree on physics,
QuoteNonetheless I fall to see that total angular momentum is not conserved. Can you, please, elaborate how you see it?Jano
Nonetheless I fall to see that total angular momentum is not conserved.
This situation is quite similar to the spin Hall effect in various systems, where variations in the intrinsic AM(spin) are compensated at the expense of the centroid shift generating extrinsic AM. […] However, in addition to the shape deformations, a rotating body also acquires mass deformations. The y >0 and y <0 sides of the wheel have different velocities in the moving frame and their constituent particles acquire different local γ-factors. Owing to this, the y >0 particles become heavier than the y <0 particles. [page 2 of the article, the same page as the spoked wheel picture
Quote from: Jaaanosik on 30/07/2020 22:27:05I 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.JanoAs 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.
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
Quote from: Malamute Lover on 30/07/2020 22:31:36Quote from: Jaaanosik on 30/07/2020 22:27:05I 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.JanoAs 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
...I repeat, the observer of (b) is not looking at an inertial reference frame. There are continuous velocity changes as the wheel goes round (velocity being a vector). That is the whole point of the paper is that the relativistic effects seen in (b) are due to acceleration and not even straight line acceleration. This is why the energy centroid moves. And as I have already quoted from the paper, that movement balances the books on AM conservation.
Quote from: Jaaanosik on 30/07/2020 22:27:05I 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.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
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.
Quote from: Malamute Lover on 30/07/2020 23:00:14...I repeat, the observer of (b) is not looking at an inertial reference frame. There are continuous velocity changes as the wheel goes round (velocity being a vector). That is the whole point of the paper is that the relativistic effects seen in (b) are due to acceleration and not even straight line acceleration. This is why the energy centroid moves. And as I have already quoted from the paper, that movement balances the books on AM conservation.The observer (a) is not looking at an inertial reference frame as well.
Quote from: Malamute Lover on 30/07/2020 23:00:14...I repeat, the observer of (b) is not looking at an inertial reference frame. There are continuous velocity changes as the wheel goes round (velocity being a vector). That is the whole point of the paper is that the relativistic effects seen in (b) are due to acceleration and not even straight line acceleration. This is why the energy centroid moves. And as I have already quoted from the paper, that movement balances the books on AM conservation.The observer (a) is not looking at an inertial reference frame as well.There is an observed velocity change for (a) observer too.The (a) sees one centripetal acceleration to the center of the wheel and the rim blocks are equally spaced.The (b) sees normal and tangential accelerations but their sum should point to where?Energy centroid, different location?If an observer is on the rim and a measurement is done, what is the direction of the acceleration?Is the spacing/contraction change of the rim blocks real for the rim observer or not?Jano
The Fig. 13.15 shows 'the rim blocks'. Is the length contraction real?
We connect the A0 block and B0 block with a string.Is the string going to break when the wheel accelerates and the gap grows between A1 block and B1 block?
Quote from: Jaaanosik on 31/07/2020 11:54:13The Fig. 13.15 shows 'the rim blocks'. Is the length contraction real?It's very real. Length contraction is not just a visual effect. It is entirely real. If radius is held constant as depicted, then real gaps must form between the blocks, which will be quite apparent to any observer.I brought this up in post 3.
QuoteWe connect the A0 block and B0 block with a string.Is the string going to break when the wheel accelerates and the gap grows between A1 block and B1 block?The string will break, just like in Bell's spaceship 'paradox'. The only difference here is that they're moving in a circle instead of a straight line, but length contraction is real in both cases.
Quote from: Jaaanosik on 31/07/2020 11:54:13The Fig. 13.15 shows 'the rim blocks'. Is the length contraction real?It's very real. Length contraction is not just a visual effect. It is entirely real. If radius is held constant as depicted, then real gaps must form between the blocks, which will be quite apparent to any observer.I brought this up in post 3.QuoteWe connect the A0 block and B0 block with a string.Is the string going to break when the wheel accelerates and the gap grows between A1 block and B1 block?The string will break, just like in Bell's spaceship 'paradox'. The only difference here is that they're moving in a circle instead of a straight line, but length contraction is real in both cases.
Several problems here. In the Ehrenfest paradox, the circumference contracts, not expands, since the wheel is moving.
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.
Why are you making the circumference larger?
And why are the gaps larger?
The radius is assumed to be constant.
The size of the radius can only be determined with a measuring rod.
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.
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.)
This result contradicts the radius implied by the observations made of the blocks on the spinning wheel.
Length contraction is not real. It is relative.
Bell’s spaceship ‘paradox’ is not a paradox at all.
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.
Is the deformation real then?
The wheel is already accelerated and it has a constant rotation.
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?
Is the (a) axle observer going to see the string broken?
Do we have a multiverse here?
The strings not broken for (a) but broken for (b)?
...Quote from: Jaaanosik on 31/07/2020 15:31:03Is 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.QuoteThe 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.QuoteIf 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.QuoteIs 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.QuoteDo we have a multiverse here?? What brings this up?QuoteThe 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.
This is the problem in physics.Over a hundred years after the SR paper and the relativists do not agree on the Lorentz contraction.
This is the bottom of the cycloid as seen from (b).
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.
Halc,I am not sure we understand each other. I'll try again.There is no more angular acceleration in (a) frame.The wheel is already up to speed, accelerated and it has the shape on the right from this figure 13.15.The gaps are already created in the (a) frame.
We also know that the wheel rim blocks in (b) have 0 speed at the bottom of the cycloid.
The question is if it is OK to assume the spacing is like this for the (b) reference frame.
That's why it is a half a turn, 180 degrees, from the bottom to the top for already rotating wheel as seen from (b).
Quote from: Malamute Lover on 31/07/2020 14:31:35Several 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.
QuoteFrom 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.
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.
QuoteThis 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.
QuoteWhy are you making the circumference larger?I'm not.QuoteAnd 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.
QuoteThe 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.
QuoteThe 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.
QuoteIf 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.
QuoteBut 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.
QuoteThis 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.
QuoteLength 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.
QuoteIt 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.
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.
The question: Is accelerated observer on the wheel rim going to see/observe/measure the deformation that is not predicted by (a)?Jano