« on: 06/08/2020 00:52:24 »
The ring is treated as having negligible thickness, in which case it is Euclidean and can be spun up to speed. If not, it is a case of the concrete think poured around the neutron star, making it scenario 3. It shatters if you try to spin it. If already spinning, a thick ring is non-euclidean and does not undergo any angular acceleration.There are actually three distinct scenarios.
1) You have a solid ring that spins. It contracts as you spin it. A shrinking ring (that reduces in radius from any perspective) seems awful real to me. Using this scenario, I can pass one wedding ring through another identical one by spinning it. That's real contraction, or it couldn't be done. It isn't observer dependent.
You are sort of describing such a thing below, except with superfluous spoke that will bend because they're too long, so they serve no purpose other than to be deformed by being squashed.
The geometry of the spinning ring is non-Euclidean. It was not only accelerated up to speed, it is under continuous acceleration as it spins. SR is not a good guide here.
SR describes all three scenarios perfectly, but not the neutron star scenario since that involves gravity.
This is incorrect. The thickness is irrelevant. The ratio of the circumference to the radius, which follow a curved spacetime, is less than 2π. The curved radius is no longer in Euclidean geometry. The circumference is shorter than it was before rotation caused the spacetime curvature.
Circular acceleration (spin up or centripetal) is like gravitational acceleration but the direction of increasing curvature is reversed. To an observer on the axle, the circle has become smaller and faster. But to the time dilated observer on the circle, a rotation takes as long as ever so the speed did not change.
QuoteThe acceleration requires the use of GR. Because the spacetime is curved, the distance from the spinning ring to the non-spinning ring is greater.It doesn’t matter whether GR or SR is used since spacetime is completely flat in the example, and SR handles acceleration just fine. Spinning a ring doesn’t bend spacetime. It just bends the ring.
You are incorrect again. Acceleration bends spacetime. The spacetime is definitely non-Euclidean.
SR does not handle acceleration at all. It is restricted entirely to inertial reference frames.
QuoteAn observer on the spinning ring will think the non-spinning ring is expanding so no problem with fitting.He will think no such thing any more than anybody thinks the traveling twin made everybody on Earth age faster. He knows very well that his ring is the one spinning and shrinking since rotation is absolute, not relative. Everybody knows it, on the ring or not. That’s what makes it a real consequence.
(This is now the two wedding rings, not the spinning wheel.)
Acceleration is absolute in that it is experienced by the accelerating observer. The magnitude of the acceleration is not absolute in that time dilation disassociates proper acceleration from that measured by an inertial frame observer. The traveling twin thinks he is continuing to accelerate at the same rate – which he can feel - and therefore exceeds c as evidenced by the speed of the landmarks going by. Einstein must be wrong, he thinks. An inertial observer never sees the twin exceed c, inferring that the acceleration is declining.
While rotation is real because it induces acceleration, the magnitude of the rotation is not absolute, again because of time dilation.
An observer on the periphery of the spinning ring will not experience any shrinkage of his ring. His ring is as big as ever and he can prove that by walking around it and it takes just as many steps as ever, being unaware of any contraction in himself. The other ring must be expanding, he thinks. Who is right? Bring both rings into the same inertial reference frame and compare clocks. That will tell who experienced acceleration.
QuoteWhich is which? As with GR problems in general, who is undergoing acceleration?Acceleration is also absolute. There’s no question what undergoes it. Surely you know at least this much.
Who is undergoing acceleration is the way one tells which is which. I have said this several times very clearly so there was no need for you to misinterpret it. Yes, I know that much and a lot more.
The fact of acceleration is absolute, being felt by the accelerated body. But the magnitude of acceleration is not absolute because of time dilation. This is why the pilot of the spaceship and the inertial frame observer disagree on how fast the ship is going.
QuoteBut the question can only be settled by bringing the two rings into a common inertial reference frame and comparing clocks, just like with the Twins. It cannot be settled by comparing observations.The two rings are in a common inertial frame, and a clock on one runs objectively slower that the other, just as is observed with the ISS.Observation of a clock is completely unnecessary since the one ring passing through the other is objective. You can measure the two rings with a relatively stationary ruler and observe (from any frame) that the one ring is unchanged and the spinning on is contracted. The clocks are more evidence, but not necessary to observer the real consequence.
As predicted, you’re just refusing to accept hard evidence. It seems you’re not even denying the contraction now, suggesting instead that the stationary ring might have instead expanded due to the proximity of this spinning ring. No theory suggests any such thing.
Until you compare clocks, you will not convince the observer on the spinning ring that he was wrong and that his ring contracted, which he did not see, and that the other ring did not expand, which he did see.
Quote from: Halc2) Spoke scenario, or the roller coaster track, which is essentially the same scenario. Here the radius is held constant by the non-contracting straight spoke, or by the stationary track. There is no solid ring, but a series of detached adjacent blocks. If there are spoke, you have essentially a row of independent pendulums. If a track, you have a row of 'bumper cars'. Spin it up and gaps form between the blocks, and more can be inserted if you like.
Observers in any frame will agree on this, but you seemingly are in denial of it.
The roller coaster thing and the spoke thing are not the same. In the spoke thing, the blocks are being held against centripetal force by the rim which is moving with them. In the roller coaster thing, the cars are being held against centripetal force by an outside track which is not rotating with them. (If it is rotating with them, then this is exactly the spoke scenario, in which the wheel contracts when the geometry becomes non-Euclidean and the spokes curve.)
As the cars accelerate, they push the track in the opposite direction. (Newton’s Third Law.) That is the acceleration will not be as much as expected, half of the energy going into the track. (No problem. They have powerful engines and lots of fuel.) If the mass of the track is the same as that of the cars, the track will rotate at the same speed and it will contract in exactly the right proportion to match the contracting circle of the cars. No gaps.
If the track is more massive than the cars, it will be going slower than the cars going and would not contract as much as if it were equal in mass. But remember that the cars are on a contracting circumference because their speed is bending spacetime. What is holding them in a circular orbit rather than flying out in a straight line and crashing into the track?
As it turns out, the track is going to contract with the cars. How? Lense-Thirring frame dragging. (The names are Austrian and are pronounced LENsuh TEERing).
Rotating masses drag spacetime with them. That is part of GR. It has been demonstrated in polar orbit satellites where gyroscopes precess toward the Earth’s axis. The degree of dragging is related to the radius, the angular momentum of the body and the radius at which the dragging is measured. The speed of the track and the path of the cars is initially the same. But they are spinning in opposite directions. As the cars continue to accelerate, the track will also accelerate but not as quickly because it is more massive.
As the cars get up to relativistic speed, their mass energy (as determined by an inertial frame outside observer) increases as per the Lorentz factor. Where is the energy coming from? Time dilation. The engines are running at the same power level but from the outside the cars are not accelerating as quickly as the drivers think. The energy difference between driver perceived acceleration and external observer perceived acceleration is going into mass-energy.
As with all characteristic affected by the Lorentz factor, the mass-energy grows quickly as lightspeed is approached. The mass-energy of the cars is growing faster than the mass-energy of the slower accelerating more massive track. The L-T frame dragging strength is growing faster for the cars than for the track. The cars are dragging the spacetime frame of the track toward them. Again since it is all related to the Lorentz factor, everything matches and comes out equal. The track and the expected car path shrink (go non-Euclidean) at the same rate. No gaps.
Your naïve, incomplete and partially incorrect knowledge of Special Relativity does no good in situations involving acceleration where General Relativity must be applied.
QuoteThe spokes bend.They do not. You have no way to back this fantasy. Yes, time dilation and width contraction varies along its length, but neither has any reason to curve the string, which would have zero effect on that dilation.
Not a fantasy but a consequence of GR, which you need to deal properly with acceleration. But you are in denial of GR. I find it curious that you had no problem with the spinning wedding ring contracting but you deny that [i[your[/i] circle can contract. Do you really think that the wedding ring could contract in a purely Euclidean space?
You are in denial that acceleration requires GR and that GR uses non-Euclidean geometry to deal with it. If you do not know the rules, do not try to play the game.
QuoteThere is no curved spacetime in the scenario. Spacetime is completely flat, lacking a source of gravity in the description. He found it paradoxical that a solid could exist in Euclidean Minkowski spacetime that exhibited non-Euclidean properties, but of course SR predicts it.Quote from: Halc3) The actual Ehrenfest scenario where he takes a non-Euclidean 3 dimensional solid (a spinning cylinder) and declares it paradoxical when its non-Euclidean properties are illustrated. If the object is rigid, it shatters as soon as you attempt to change its angular speed. That shattering is an objective effect that any observer in any frame will witness.Ehrenfest wrote his paradox before General Relativity was developed and did not know about curved spacetime.
Naïve Minkowski spacetime relates to SR, not GR. It is not non-Euclidean, having been developed years before GR. Minkowski spacetime is 4D but all dimensions are straight. General Relativity is much hairier involving semi-Riemannian manifolds with varying metrics.
QuoteEhrenfest assumed 3D Euclidean geometry, not non-Euclidean as you stated.If he assumed the object was Euclidean, then he was mistaken. Spacetime is in that instance, but not the object. No rotating object can be.
The rotating object exists in non-Euclidean spacetime. Of course, it is in a non-Euclidean form. What are you trying to say here?
QuoteHe therefore assumed contraction was real, which is what led to his claim of a paradox.Contraction being real is what is demonstrated, because it resolves the paradox. The radius doesn’t change because the spin never does. The object was never stationary, and he does not suggest that it ever was.
If the spin was always there, then the spacetime was always non-Euclidean. Centripetal acceleration, remember.
QuoteA clock on the surface of the cylinder will run slower than a clock inside the cylinder.Indeed. An objective consequence admitted by the guy who denies it. Hmm…
How is this real consequence explained if time dilation isn’t real? It isn’t relative since the observer on the edge also sees the clock in the middle run faster.
“Neither dilation nor contraction are real, except when I have to admit otherwise”. Great stance.
Acceleration is real because it cannot be denied by those who experience it. Acceleration puts different observers in different reference frames. Time dilation is observer dependent. Different observers will disagree on the rate of a single clock. Those in possession of the clock deny that there is any time dilation, whereas they cannot deny acceleration. But they can argue about the degree of acceleration. Time dilation is relative not objective. Bringing two clocks into a common inertial frame will allow comparison, with the slower clock the one that experienced more acceleration.
Time dilation and length contraction are relative. Two spaceships not in a common inertial frame will both see the other’s clock as running slow and their own clock as running properly. Who is right? Neither one. Time dilation is relative. Bring them into a common inertial frame and the two clocks will run at the same rate. But one will be behind the other because it got accelerated more. Agreement on who is right cannot not be done in separate reference frames and not by directly comparing clock rates. Relative, not objective.
A very fast spaceship passes a stationary one, relative to some specific inertial reference frame. Both will see the other as contracted and having a slow clock. If contraction is real then why don’t the observers on the two ships see the other observers get crushed with blood and guts shooting out their sides? And why would that happen? Because another ship passed at a different speed?
Sorry, but you are still wrong. Lorentz contraction is relative, not objective.