[Kryptid]

Does anyone see the string break?

I'm not sure, but if one does, then they both do.

The traveler watches a couple of hours on the Earth to take 4 years on the ship?
Correct?

Nope. The ship must accelerate into order to reach such a very high velocity. That is an acceleration that is not experienced by the observer on Earth. So the situation is not symmetrical.

[Colin2B]

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?

What do you mean by real?

In the example @Kryptid gives further down a traveller can be seen by earth observers to take (say) 4yrs to travel to a distant star - based on the distance they measure. The traveller, however, sees the distance to the star length-contracted and so takes less time to travel that distance. The experience is real for both of them. (Time dilation and length contraction are effectively the same thing).

If you think these effects are not real you will have to rewrite what we understand about electricity and magnetism and also a great deal of chemistry. Good luck with that 

[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?

What do you mean by real?

In the example @Kryptid gives further down a traveller can be seen by earth observers to take (say) 4yrs to travel to a distant star - based on the distance they measure. The traveller, however, sees the distance to the star length-contracted and so takes less time to travel that distance. The experience is real for both of them. (Time dilation and length contraction are effectively the same thing).

If you think these effects are not real you will have to rewrite what we understand about electricity and magnetism and also a great deal of chemistry. Good luck with that 

What is real is what is going on in 4D Minkowski spacetime. We time bound observers only get to see a slice at a time depending on our reference frames. Multiple observers in different reference frames see different things. None of them see the real thing. Relativistic effects are relative not objective.

[Halc]

The gaps between blocks are said to appear because the radius of the circle is taken to be constant.

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.

2) 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.

3) 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.  There are other ways to create non-Euclidean objects.  Find a neutron star and build a sort of feeding trough that encircles it at some low altitude, say 10 km wide and thick. Fill that trough will some material that hardens into some rigid object, and remove the trough. In normal space, the outside radius will be 60π km greater than the inside radius, but with this object the difference will be less than that, depending on how close to the star you build it.  Remove the object from the vicinity of the neutron star and it shatters just like the Ehrenfest object. Ehrenfest found a way to create such an object in flat spacetime using length contraction, but it doesn't work if length contraction isn't real. 

It is my contention that the spokes will maintain their length but will curve due to differing time dilation along the length. The fixed length of the spokes but bent into a curve will result in a reduced radius and the rim holding the blocks will contract as expected. No gaps will appear.

If you content that the curving spokes is what draws the blocks in, that wouldn't work if the blocks didn't actually contract since they would not fit in the smaller radius.  If the radius of a spinning wheel does contract, that is a real effect visible to any observer, so not a relative effect.
This assertion that it is the spokes bending and curving, pulling in the separate blocks is contrary to all accepted physics. It is a fantasy assertion that you cannot support. It seems you are one of those that will hold to your assertions forever rather than show a willingness to learn.

First some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.

No frame reference, so that statement is ambiguous.  It will be running 7 times slower relative to the frame in which the ship is moving at .99c.  Not saying you're wrong, just sloppy.  It's running at normal rate relative to the ship of course.

That is, watching landmarks go by, he sees himself as traveling at almost 7 c.

If there is a grid with mileposts he can watch, then yes. You can call that his proper velocity if you want, which is what you get by simply multiplying his proper acceleration by his proper time under that acceleration. There's no limit to proper velocity since it accumulates additively, not relativistically.

Question for the rest of the world: What are metric mileposts or mile-markers?  Just kilometer markers?  I live close to Canada and still don't hear the term used ever. What do they call (in English) the little signs on the side of the road?

(Either that or he thinks the distances have shrunk.) But after several years of sightseeing, he decelerates and gets back home again, and finds that his twin brother has aged much more than him. He realizes that acceleration really did slow his clock and that he was not traveling as fast as he thought. He was really traveling much slower.

What an absolute way of putting it, but yes, in the brother's frame, he was travelling at nearly c. In his own frame, he wasn't moving at all, only the length-contracted markers were. He knows very well that those moving markers do not mark distances properly and can not move faster than light, as evidenced by the fact that he can see the one's coming at him.  If they were moving at nearly 7c, they'd not be visible at all until they had passed, just like you can't hear a supersonic jet coming at you. So he knows those markers are moving at about .99c and are nowhere near a km apart. To assert otherwise is to assert light moving faster than c, something I'm starting to see a lot of here.

Unlike time dilation due to different relative inertial speeds, time dilation resulting from acceleration is real and has real consequences. This is the resolution of the so-called Twin Paradox.

So I have four observers Alice, Bob, Charlie and Denise.  Alice was always on Earth.  Charlie came to Earth with Denise and Charlie accelerated to Earth frame to marry Alice.  Bob accelearted to match speeds with Denise to marry her.  Denise and Alice have thus never accelerated, and the other two have.
So according to your statement above, time dilation of the clock on Earth is real according to Charlie because he accelerated to Earth frame, but it is not real for either Alice or Denise, neither of whom have ever accelerated.  Meanwhile dilation of the clock on the ship with Bob and Denise is real to Bob (having accelerated to that frame), but not to Denise right there with him.
Sounds very inconsistent that the same clock is really dilated and also not.

Also, length contraction in all 3 scenarios at the top of this post is very real by your definition since there is a very real consequence (observed by anybody) in all three situation.

In the case of the spinning wheel, different portions of each spoke are traveling at different speeds. The time dilation factor increases as one travels up the spoke from the center.

Agree. Any clock nearer the center will run objectively faster than one further out.  ISS clocks run faster than sea-level clocks for this reason, but GR must be invoked to compute exactly how much.

A clock carried up from the axle to a certain point and back down again will have recorded less time than a clock that stayed at the center. The further up the clock is taken, the greater the discrepancy when brought back.

Also how long it spent out there. You'd have to integrate the curve.
If this is not a reasoning why length contraction doesn't actually occur, then you're getting way off topic.

When the wheel was spun up, the different parts experienced different accelerations, and/or different centripetal accelerations as the wheel turns.

In scenario 3, and also the spoked wheel in post 2, nothing was spun up. There was never any acceleration. In scenario's 1 & 2, there is angular acceleration involved.

This is acceleration-based time dilation and it is therefore real. At each level, the clock is slower than at the center and the real speed is less than an observer at that level thinks it is.

Oh, so if I build a clock on the rim of an already-spinning wheel, it will stay in sync with the clock at the axle? If not, what do you mean by this distinction between acceleration-based real time dilation and not-real?
Suppose Bob passes Earth at .866c without acceleration, syncing his clock to Earth when he's in its presence. Both say zero.  After a year, he smashes the clock works, freezing it at its reading of 1 year. He turns around, builds a new clock, sets it to zero and smashes the workings again, freezing it at 1 year as well. He then decelerates.  Now he has two clocks that have never accelerated (at least not while working) that cumulatively account for 2 years, but 4 years have gone by on Earth.
I'm sorry, but your stories are getting sillier and sillier, seemingly in a desperate attempt to not admit you've made a mistake. Einstein never mentioned any distinction between real and fake time dilation, or real and fake length contraction.  Measurements using light would be different than empirically measured if length contraction wasn't real.  All you have to do is time light as it goes from one end to the other and back in a moving train.  Measure the time with stationary synced clocks (OK, you have tried to counter this by flat out denial of the possibility of syncing stationary clocks). It will take way too long if the train is not really contracted.  A history of acceleration of the train plays no role in the equations involved.

Since the angular displacement would vary at each level, the spoke would curve.

Time dilation has no effect on the curvature of the spokes.  They're effectively strings. Time dilation does have an effect on the angular velocity of the wheel.  An observer at the axle would measure a smaller angular velocity than one at the rim, which is why for relativistic wheels, we specify linear rim speed, not radians per second. The spokes are straight unless there is angular stress on them such as the wheel being accelerated by torque being applied at the hub, but no such torque exists in our examples. All measurement are done in steady state.  Yes, if I put enough change in the rate of torque on a real bicycle wheel, the change would need to propagate up the spokes to the rim at the speed of sound, causing a momentary wave to travel up the spoke. That would bend it a bit just like a sideways yank on a garden hose causes a bend to travel up the hose.  A freely spinning wheel has straight spokes so long as there is any tension on them.

[Jaaanosik (OP)]

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?

What do you mean by real?

In the example @Kryptid gives further down a traveller can be seen by earth observers to take (say) 4yrs to travel to a distant star - based on the distance they measure. The traveller, however, sees the distance to the star length-contracted and so takes less time to travel that distance. The experience is real for both of them. (Time dilation and length contraction are effectively the same thing).

If you think these effects are not real you will have to rewrite what we understand about electricity and magnetism and also a great deal of chemistry. Good luck with that 

The example presented by Kryptid is in question, therefore your argument based on Kryptid's comment is in question as well,
Jano

[Jaaanosik (OP)]

...

Nope. The ship must accelerate into order to reach such a very high velocity. That is an acceleration that is not experienced by the observer on Earth. So the situation is not symmetrical.

There are examples where physicists play the tag scenario without the acceleration.
Meaning a spaceship flies by with the required velocity.



The acceleration is not important, but the relative velocity is.
Please, see how the red full line is an 'average' of the acceleration world line.
Please, can we take this discussion to the reciprocal thread?
Jano

[Malamute Lover]

The gaps between blocks are said to appear because the radius of the circle is taken to be constant.

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. The 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 is following a curve and is longer than the straight-line Euclidean distance. An observer on the spinning ring will think the non-spinning ring is expanding so no problem with fitting. Which is which? As with GR problems in general, who is undergoing acceleration? But 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.

2) 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 spokes bend. They cannot stay straight because they have different clock rates along the length. They are not getting squashed. They would act the same even if there were no rim or blocks. The bending of the spokes and the contraction of the blocks match because they both involve the same Lorentz factor. Are you denying time dilation?

As with the two spinning rings above, the geometry has become non-Euclidean because of the accelerations (startup and ongoing). (I really did not want to involve GR because I made an Unbreakable Vow to not ever index another tensor.)

3) 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.  There are other ways to create non-Euclidean objects.  Find a neutron star and build a sort of feeding trough that encircles it at some low altitude, say 10 km wide and thick. Fill that trough will some material that hardens into some rigid object, and remove the trough. In normal space, the outside radius will be 60π km greater than the inside radius, but with this object the difference will be less than that, depending on how close to the star you build it.  Remove the object from the vicinity of the neutron star and it shatters just like the Ehrenfest object. Ehrenfest found a way to create such an object in flat spacetime using length contraction, but it doesn't work if length contraction isn't real. 

Ehrenfest wrote his paradox before General Relativity was developed and did not know about curved spacetime. Ehrenfest assumed 3D Euclidean geometry, not non-Euclidean as you stated. Ehrenfest assumed that the radius could not change, which it certainly can in non-Euclidean geometry when one of the dimensions is time. He therefore assumed contraction was real, which is what led to his claim of a paradox.

A clock on the surface of the cylinder will run slower than a clock inside the cylinder. To an observer on the surface (and therefore to the mechanical properties of the cylinder) the same number of revolutions a minute are taking place even though the cylinder Lorentz contracts and its rotational speed increases to conserve angular momentum. An observer inside with a faster clock will be surprised to not see the cylinder shatter just as he is surprised when his Twin comes back much younger than him.

Contraction is relative, not objective.

It was consideration of Ehrenfest that gave einstein a clue on how to proceed to deal with non-inertial frames in a non-Euclidean geometry.

Spacetime is not going to be flat in the vicinity of a neutron star. (Assume a non-spinning neutron star to avoid certain non-linearities.) Any measurement you try to make on the object will be distorted in the same degree as the object. To an observer on the object, it is a proper circle. It appears distorted to an outside observer because of the different shape of spacetime. When it is brought up into a different shaped spacetime it will be deformed and become damaged.

How will it be deformed? An interesting fact about gravity wells is that as you go lower into the well, a circle equidistant from the center will not lose as much circumference as is loses radius. This is the opposite of the rotating circle model. In that model, centripetal acceleration will increase as one moves outward. The 4D spacetime resembles a curved bottom bowl with curvature increasing as one moves outward from the center.



When it comes to gravity, which according to GR is the same as acceleration (why things fall down faster and faster), the acceleration increases as you move inward. A gravity well looks like this.



As the radius decreases (following the curve) the circumference does not shrink as much as expected by Euclid. More material can be packed into the circumference than in a flatter spacetime.

A circle constructed around the circumference of a gravity well and brought up (along a polar axis) will have too much material in the circumference.  That much material does not fit into the now smaller circumference relative to the radius. It will be crushed around the circumference. Where does the energy come from to crush it? From the force that lifted it out of the gravity well.

(As the circle is brought up along the polar axis it will be subject to differing gravity gradients along its parts. Let us assume that the material has good tensile strength but poor crushing resistance.)

As I said, a gravity well and a rotating circle have opposite spacetime curving. The equivalent of lifting a ring out of a gravity well would be in the rotating circle scenario would be pushing a ring down toward the axle. This is independent of any Lorentz contraction. The ring around the neutron star was not rotating. A ring of stationary solid material being pushed down toward the axle would also be crushed, because it is being forced into a flatter spacetime with less space than it currently occupies.

In both scenarios, the crushing would be experienced by the ring itself and would be objective. But in neither case does it have anything to do with Lorentz contraction, which derives from relative motion.

It is my contention that the spokes will maintain their length but will curve due to differing time dilation along the length. The fixed length of the spokes but bent into a curve will result in a reduced radius and the rim holding the blocks will contract as expected. No gaps will appear.

If you content that the curving spokes is what draws the blocks in, that wouldn't work if the blocks didn't actually contract since they would not fit in the smaller radius.  If the radius of a spinning wheel does contract, that is a real effect visible to any observer, so not a relative effect.
This assertion that it is the spokes bending and curving, pulling in the separate blocks is contrary to all accepted physics. It is a fantasy assertion that you cannot support. It seems you are one of those that will hold to your assertions forever rather than show a willingness to learn.

What I contend is that the blocks bend exactly as expected from their speed. They are not ‘drawn in’. There is nothing to hold them up since the spokes are not straight. The rim of the spinning wheel will contract exactly as if there were never any spokes. I explained exactly how the curving happens. It is due to different clock rates at different points on the spoke and the fact that the spoke is moving in a circle. Do you deny that the clocks will have different rates at different points on the spoke?  Again it is non-Euclidean geometry going on because acceleration is involved.

It seems that you are the one unwilling to learn.

Whether and how much contraction an observer will see depends on the observer. An observer on the spinning wheel sees nothing different because contraction is only visible from another reference frame. Observers on different locations on a spoke and going at different speeds would see contraction but disagree on how much contraction. And an observer in the center would disagree with all of them. Relative, not objective.

First some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.

No frame reference, so that statement is ambiguous.  It will be running 7 times slower relative to the frame in which the ship is moving at .99c.  Not saying you're wrong, just sloppy.  It's running at normal rate relative to the ship of course.

I did provide a reference frame. The frame in which the ship is moving at .99 c is the one before the acceleration, which I explicitly mentioned right there: “accelerated to 0.99 c”. No sloppiness. We are not going ad hom., are we?

That is, watching landmarks go by, he sees himself as traveling at almost 7 c.

If there is a grid with mileposts he can watch, then yes. You can call that his proper velocity if you want, which is what you get by simply multiplying his proper acceleration by his proper time under that acceleration. There's no limit to proper velocity since it accumulates additively, not relativistically.

You have to bring two observers into the same reference frame to judge which one is right, that is, which one underwent acceleration. That will be the one with the slower clock.

(Either that or he thinks the distances have shrunk.) But after several years of sightseeing, he decelerates and gets back home again, and finds that his twin brother has aged much more than him. He realizes that acceleration really did slow his clock and that he was not traveling as fast as he thought. He was really traveling much slower.

What an absolute way of putting it, but yes, in the brother's frame, he was travelling at nearly c. In his own frame, he wasn't moving at all, only the length-contracted markers were. He knows very well that those moving markers do not mark distances properly and can not move faster than light, as evidenced by the fact that he can see the one's coming at him.  If they were moving at nearly 7c, they'd not be visible at all until they had passed, just like you can't hear a supersonic jet coming at you. So he knows those markers are moving at about .99c and are nowhere near a km apart. To assert otherwise is to assert light moving faster than c, something I'm starting to see a lot of here.

His observation is that he is traveling faster than c. Known landmarks are whizzing by at 7 c. Why can’t he conclude that Einstein was wrong? Again, the only way to tell the difference is to bring him back into a frame of reference that did not experience acceleration (which he did) and compare clocks. Or calendars as the case may be.

[Malamute Lover]

Unlike time dilation due to different relative inertial speeds, time dilation resulting from acceleration is real and has real consequences. This is the resolution of the so-called Twin Paradox.

So I have four observers Alice, Bob, Charlie and Denise.  Alice was always on Earth.  Charlie came to Earth with Denise and Charlie accelerated to Earth frame to marry Alice.  Bob accelearted to match speeds with Denise to marry her.  Denise and Alice have thus never accelerated, and the other two have.
So according to your statement above, time dilation of the clock on Earth is real according to Charlie because he accelerated to Earth frame, but it is not real for either Alice or Denise, neither of whom have ever accelerated.  Meanwhile dilation of the clock on the ship with Bob and Denise is real to Bob (having accelerated to that frame), but not to Denise right there with him.
Sounds very inconsistent that the same clock is really dilated and also not.

Time dilation can be seen to be real when a clock that has undergone acceleration and brought back into a common inertial frame with a clock that has not accelerated. Try restating your scenario with some common inertial frame clock comparisons.

Also resolve the contradiction that “Charlie came to Earth with Denise” and Denise has never accelerated. I will presume you mean that Alice and Denise have always been on Earth.

If you attempted to restate your argument with clocks, you would find the flaw in it.

You say that Charlie accelerated to Earth frame. That would mean that Earth was already in an accelerated frame compared to Charlie. Earth clocks were already ticking slower than the clock in the frame of Charlie before they accelerated. By accelerating to match Earth frame, his clock will slow. Maybe you meant that Charlie decelerated and his clock speeded up to match the clocks on Earth.

Will the clock used by Charlie match Earth time? Irrelevant because nowhere does it say they were synchronized in the first place. If Charlie (likewise Bob):

(1) had been on Earth in the first place and synchronized his clock with an Earth clock and then
(2) accelerated away and cruised for a while then
(3) decelerated, reversed direction and accelerated again and cruised for a while and then
(4) come back to Earth and decelerated to the Earth frame,

then after all that comparing the clocks would be meaningful. And it would be found that the Earth clocks were ahead of the Charlie clock. His clock had been slowed by the acceleration and had been running slower while he cruised. The decelerations only brought his clock back to Earth speed not below it.

If somehow, Charlie had stayed still and Earth had done all the acceleration and whatnot, then the Earth clocks would be behind the Charlie clock. Acceleration is not relative. It is real. It is felt. If he saw Earth moving away, he would know who really accelerated by whether or not he felt the acceleration. And the ‘feeling’ could be by a high precision accelerometer so there is no doubt about whether it happened.

Now what about Lorentz contraction? Will Charlie subjectively feel or see any contraction? Say he has a pulse of light bouncing back and forth along the length of the ship and the clock ticks every time the light pulse completes a cycle. Since the length of the ship is contracted, it should take less time for the light pulse to go back and forth, right? And that means the clock should be running faster, right?

But Relativity tells us that clocks run slower by the same mechanism that lengths contract. Since the clock Charlie uses is running slower and by the same Lorentz factor, the Lorentz contraction driven clock speed up is exactly balanced by the Lorentz time stretch. It takes longer for the light pulse to make its round trip according to the Charlie clock. Charlie sees his clock running at the same rate as always and the length of the ship the same as always and the speed of light measured the same as always.

Lorentz contraction is relative, not objective.

Also, length contraction in all 3 scenarios at the top of this post is very real by your definition since there is a very real consequence (observed by anybody) in all three situation.

An observer on the rotating circle has a slowed clock and is unaware of the contraction that has taken place. Despite the increased RPM resulting from bringing the circle smaller (conserved AM remember), a revolution takes as long as it always did to this observer because his clock is slowed. The observer is unaware of any contraction.

Different situations, different observations. Relative, not objective.

In the case of the spinning wheel, different portions of each spoke are traveling at different s
peeds. The time dilation factor increases as one travels up the spoke from the center.

Agree. Any clock nearer the center will run objectively faster than one further out.  ISS clocks run faster than sea-level clocks for this reason, but GR must be invoked to compute exactly how much.

ISS clocks also run slower because they are at orbital speed. Two factors going on. This is very important in setting the clocks in the GPS satellites. (BTW the real problem with GPS satellites is having them know exactly where they are at each moment, not an easy thing considering the Earth’s gravitational field varies from point to point and the Earth is rotating underneath the satellites.)

A clock carried up from the axle to a certain point and back down again will have recorded less time than a clock that stayed at the center. The further up the clock is taken, the greater the discrepancy when brought back.

Also how long it spent out there. You'd have to integrate the curve.
If this is not a reasoning why length contraction doesn't actually occur, then you're getting way off topic.

The clock rate at each level is what matters, not the increasing time difference. It is not length contraction. It is bending of the spokes because of the differential in rates. This is exactly on topic but it shows that the spokes do not reach out as far as you want them to, so you want to dismiss it.

You do not have to integrate anything. The new circumference of the ring is easily calculated from the amount of contraction due to its speed. (To be clear that is tangent speed, not RPM) The new extension from the axle of the bent spoke is the radius related to that new circumference. They both are both related to the same Lorentz factor.

When the wheel was spun up, the different parts experienced different accelerations, and/or different centripetal accelerations as the wheel turns.

In scenario 3, and also the spoked wheel in post 2, nothing was spun up. There was never any acceleration. In scenario's 1 & 2, there is angular acceleration involved.

All the components in all scenarios are following circular paths. The vector is changing. That IS acceleration.

In addition:

1) In the case of the wedding rings, to demonstrate that the two rings were originally the same size (without which the demonstration is meaningless), they must start off at rest with each other. One then must be accelerated by being spun.

2) In the case of the spokes, to (allegedly) create gaps, you must spin the wheel, which you explicitly refer to. Acceleration.

3) In the Ehrenfest scenario, the flaw is that Ehrenfest based everything on an assumption of 3D Euclidean space. As I said earlier, General Relativity, which did not exist yet, uses 4D curved spacetime when acceleration is involved as it definitely is in a rotating framework.

This is acceleration-based time dilation and it is therefore real. At each level, the clock is slower than at the center and the real speed is less than an observer at that level thinks it is.

Oh, so if I build a clock on the rim of an already-spinning wheel, it will stay in sync with the clock at the axle? If not, what do you mean by this distinction between acceleration-based real time dilation and not-real?
Suppose Bob passes Earth at .866c without acceleration, syncing his clock to Earth when he's in its presence. Both say zero.  After a year, he smashes the clock works, freezing it at its reading of 1 year. He turns around, builds a new clock, sets it to zero and smashes the workings again, freezing it at 1 year as well. He then decelerates.  Now he has two clocks that have never accelerated (at least not while working) that cumulatively account for 2 years, but 4 years have gone by on Earth.

“Suppose Bob passes Earth at .866c without acceleration”

Wrong at the start. The is no way that Bob and Earth can have relative speeds of .866 c without acceleration being involved somewhere. If you think it can, come up with a scenario that would explain how it happened other than the bare assumption.

It is clear that Bob has accelerated to .866 c, either personally or by coming from some environment in motion with respect to Earth, or some combination of the two. As a result, his clock is running at half the speed of a clock on Earth, as would be seen if an elapsed time comparison could be made in a common inertial frame.

“Now he has two clocks that have never accelerated”

The first clock was in a reference frame at .866 c as viewed from Earth. The fact that the clock itself never accelerated is irrelevant, the reference frame it is in did.

The second clock was also in a reference frame at .866 c as viewed from Earth. In order to turn around back to Earth, Bob decelerated and then accelerated back up to .866 c as viewed from Earth. Accelerated reference frame again.

Imagine that Bob built a clock after decelerating but before accelerating in the other direction again. That is, the same inertial frame as Earth. Once the ship finished accelerating again and was just cruising, would this accelerated clock tick at the same rate as the new clock Bob built right after the end of acceleration? If Bob set the clock that he built at the turnaround point and the newly constructed clock to zero at the same moment, would they continue to read the same time or not?

If you say that they would not tick at the same rate, then answer this.  If Bob closed his eyes and counted One Hippopotamus, Two Hippopotamus and so on up to Ten, which clock would he agree with about the seconds elapsed. Keep in mind that Bob was accelerated.

It seems that your understanding of Relativity Theory could use some work.

I'm sorry, but your stories are getting sillier and sillier, seemingly in a desperate attempt to not admit you've made a mistake. Einstein never mentioned any distinction between real and fake time dilation, or real and fake length contraction.  Measurements using light would be different than empirically measured if length contraction wasn't real.  All you have to do is time light as it goes from one end to the other and back in a moving train.  Measure the time with stationary synced clocks (OK, you have tried to counter this by flat out denial of the possibility of syncing stationary clocks). It will take way too long if the train is not really contracted.  A history of acceleration of the train plays no role in the equations involved.

All of my statements are derived from straightforward physics textbooks. There is nothing silly about them. I have addressed your arguments in detail, including all of your counterarguments and I see no reason to change my mind about anything. But I do see we are in ad hom territory.

Einstein never mentioned either fake or real time dilation. He talked about, what was that word again? Oh yes, Relativity. Specifically, “On the Relativity of Lengths and Times”, the second numbered section in his 1905 paper On the Electrodynamics Of Moving Bodies

Measurements of time dilation, length contraction, energy content are all relative to the reference frames of the observer and the observed. Different observers in different frames will disagree on what they see, including Lorentz contraction.  (The energy content part appeared in a different paper.)

Moving on to your thought experiment:

First some questions. What is the train moving relative too? Is there an observer in that reference frame? Without reference toa history of acceleration, how can a degree of motion be assigned?

It is not only length that appears modified to an external observer in a different reference frame. It is time as well. I have already presented this argument earlier but I will repeat it here.

he has a pulse of light bouncing back and forth along the length of the train and the clock ticks every time the light pulse completes a cycle. (One clock solves the sync problem.) Since the length of the train is contracted, it should take less time for the light pulse to go back and forth, right? And that means the clock should be running faster, right?

But Relativity tells us that clocks run slower by the same mechanism that lengths contract. Since the clock on the train is running slower and by the same Lorentz factor, the Lorentz contraction driven clock speed up is exactly balanced by the Lorentz time stretch. It takes longer for the light pulse to make its round trip according to the clock on the train. An observer on the train sees the clock running at the same rate as always and the length of the train the same as always and the speed of light measured the same as always.

However the outside observer sees the length of the train contracted and the clock on the train slower.

Lorentz contraction is relative, not objective.

Since the angular displacement would vary at each level, the spoke would curve.

Time dilation has no effect on the curvature of the spokes.  They're effectively strings. Time dilation does have an effect on the angular velocity of the wheel.  An observer at the axle would measure a smaller angular velocity than one at the rim, which is why for relativistic wheels, we specify linear rim speed, not radians per second. The spokes are straight unless there is angular stress on them such as the wheel being accelerated by torque being applied at the hub, but no such torque exists in our examples. All measurement are done in steady state.  Yes, if I put enough change in the rate of torque on a real bicycle wheel, the change would need to propagate up the spokes to the rim at the speed of sound, causing a momentary wave to travel up the spoke. That would bend it a bit just like a sideways yank on a garden hose causes a bend to travel up the hose.  A freely spinning wheel has straight spokes so long as there is any tension on them.

Time dilation causes the curvature of the spokes. Or rather the curvature of spacetime on which the spokes lie, this curvature caused by acceleration, both original and centripetal. You cannot have spinning without original acceleration or else you have no basis for talking about degree of motion. Unless you include the original acceleration, the wheel could be motionless.

I tried to explain it in Euclidean terms as the spokes offset according to the clock rates, but I did not realize at that time that you do not believe in time dilation. (Einstein is not just rolling over in his grave. He is doing 0.99 c in a circle around his major axis.) I really did not want to get into GR spacetime without cause. But now there is cause. The spokes reside in acceleration caused curved spacetime. They do not reach as far out as they would in Euclidean space. The rotating wheel also resides in curved spacetime due to acceleration and has a circumference in that spacetime that matches the tips of the curved spokes. This is necessarily the case since the same Lorentz factor controls both.

Remember that curved bowl?



The circumference does not grow as fast as the radius as you go out from the center. Or to say that the other way around, the circumference shrinks faster than the radius as you move into flatter spacetime at the center. This is what happens in a gravity well also except that the flatter spacetime is outward instead of inward. Which is why that circle built deep in the gravity well of the neutron star gets squeezed around its circumference as it is lifted out of the gravity well, not enough circumference anymore in flatter spacetime.

Admittedly these are not easy concepts unless you are really used to the subject. But to understand relativity at all, you have to first accept the idea of time dilation.

[Jaaanosik (OP)]

...
Are you denying time dilation?
...
Contraction is relative, not objective.
...

Is the time dilation relative, not objective as well?

[Jaaanosik (OP)]

...

Time dilation can be seen to be real when a clock that has undergone acceleration and brought back into a common inertial frame with a clock that has not accelerated. Try restating your scenario with some common inertial frame clock comparisons.
...

The acceleration can be taken out for the time dilation analysis.
You can see the SR reciprocal thread for the discussion.
Have you ever heard about the clock postulate?
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html
Gamma factor does not include an acceleration,
Jano

[Colin2B]

The example presented by Kryptid is in question, therefore your argument based on Kryptid's comment is in question as well,

It wasn’t an argument being presented, just clarification for Malamute Lover

What is real is what is going on in 4D Minkowski spacetime. We time bound observers only get to see a slice at a time depending on our reference frames.

This all we ever see, even for those things we consider real.

Multiple observers in different reference frames see different things. None of them see the real thing. Relativistic effects are relative not objective.

Being relative does not exclude being real/objective
I’ll pick this up in the other thread when I have time, so to speak 
https://www.thenakedscientists.com/forum/index.php?topic=80208.msg610352#msg610352

[Malamute Lover]

...

Time dilation can be seen to be real when a clock that has undergone acceleration and brought back into a common inertial frame with a clock that has not accelerated. Try restating your scenario with some common inertial frame clock comparisons.
...

The acceleration can be taken out for the time dilation analysis.
You can see the SR reciprocal thread for the discussion.
Have you ever heard about the clock postulate?
http://math.ucr.edu/home/baez/physics/Relativity/SR/clock.html
Gamma factor does not include an acceleration,
Jano

The clock postulate goes into GR territory. But then so does acceleration in general. But if acceleration is identical for two clocks originally synchronized in a common inertial frame, if there is an acceleration related effect, it will be the same for both clocks.

[Malamute Lover]

...
Are you denying time dilation?
...
Contraction is relative, not objective.
...

Is the time dilation relative, not objective as well?

Not if it is different for different observers and non-existent in the reference frame in which the time dilation is observed by others. You seem to be assuming a Newtonian Absolute Space and Time. They do not exist.

[Halc]

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.

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.
SR describes all three scenarios perfectly, but not the neutron star scenario since that involves gravity.

The 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.

An 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.

Which 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.

But 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.

2) 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 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.

I notice you did not address the bumper-car track, which also maintains fixed radius, and apparently has the property of you not being able to think of some way to deny the gaps that form between the cars.

3) 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.

There 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.

Ehrenfest 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.

He 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.

A 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.

To an observer on the surface (and therefore to the mechanical properties of the cylinder) the same number of revolutions a minute are taking place

Now you’ve contradicted yourself again.  We have a stationary marker by which a rotation can be measured.  Both observers agree on what one rotation is, but if their clocks are not running at the same pace, they necessarily measure a different time for one revolution.

An observer inside with a faster clock will be surprised to not see the cylinder shatter just as he is surprised when his Twin comes back much younger than him.

The twin apparently doesn’t know his physics then, because if he did, there would be no surprise.  The cylinder doesn’t shatter because it was always spinning.

At this point you go into a bend about gravity and GR, which seems a diversion from the more simple SR topic that you need to master first.  One comment though:

It will be crushed around the circumference. Where does the energy come from to crush it?

It doesn’t take energy to crush something. It seemingly takes force, which means a strong but brittle object can be crushed by expenditure of arbitrarily small energy. The less brittle it is, the more that energy goes into strain and not into failure, so it takes more. I’m assuming insanely brittle and strong materials for our objects else they’d not be able to withstand the centripetal stresses being put on them. Anything else would just fly apart.

Whether and how much contraction an observer will see depends on the observer.

The cases I enumerate above are observed by anybody. They were chosen for that purpose. The measuring rod between ships is also a real consequence.

An observer on the spinning wheel sees nothing different because contraction is only visible from another reference frame.

In all three cases, the observer on the wheel very much sees differences, which are pointed out in the cases above. You seem to agree that one ring fits through the other, something to which all observers agree. You don’t seem to have any fake physics that lets you deny the bumper-car-track thing, nor do you seem to deny the non-Euclidean dimensions of the ‘cylinder’.  OK, the  non-Euclidean dimensions are frame dependent.  A stationary observer will measure normal dimensions, but the inability of the object to change its angular speed is an objective observation.

First some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.

No frame reference, so that statement is ambiguous.  It will be running 7 times slower relative to the frame in which the ship is moving at .99c.  Not saying you're wrong, just sloppy.  It's running at normal rate relative to the ship of course.

I did provide a reference frame. The frame in which the ship is moving at .99 c is the one before the acceleration, which I explicitly mentioned right there: “accelerated to 0.99 c”. No sloppiness. We are not going ad hom., are we?

It’s not an ad-hom.  It’s sloppy because you’re describing ‘what the pilot experiences’ and a pilot always experiences being stopped.  You’re referencing the pilot frame and also the original frame, which makes it confusing. That’s sloppy.
Secondly, the bolded statement is wrong since no observer can experience time dilation. I can look at the GPS clocks and objectively notice I’m running slower than them, but I still don’t experience that dilation.

You have to bring two observers into the same reference frame to judge which one is right, that is, which one underwent acceleration.

Acceleration is absolute (at least in Minkowski spacetime). An accelerometer works inside a box. All observers will agree if something has accelerated. That’s twice you’ve made this mistake.

His observation is that he is traveling faster than c. Known landmarks are whizzing by at 7 c. Why can’t he conclude that Einstein was wrong?

He is free to propose a different theory, but none has been found so far. So are you a relativity denier then? It seems to be your goal here. You resist it at every step of the way.
Such deniers are dime a dozen on sites like this, but then don't go telling me that your stories conform to an established theory and mine don't. I've pointed out several self contradictions with your assertions.

Einstein didn’t just suggest that light speed yielded the same value in any frame. That because quite apparent by all the attempts to measure the difference as was predicted by the prevailing view of the time. So he can’t conclude Einstein was wrong, he’d have to conclude that all the decades of light speed measurement were wrong. Einstein didn’t perform any of those measurements.

[Malamute Lover]

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.

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.
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.

The 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.

An 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.

Which 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.

But 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.

2) 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.

The 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.

3) 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.

There 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.

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.

Ehrenfest 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?

He 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.

A 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.

[Malamute Lover]

To an observer on the surface (and therefore to the mechanical properties of the cylinder) the same number of revolutions a minute are taking place

Now you’ve contradicted yourself again.  We have a stationary marker by which a rotation can be measured.  Both observers agree on what one rotation is, but if their clocks are not running at the same pace, they necessarily measure a different time for one revolution.

Nope. The reduced circumference circle is spinning faster because tangential speed is still the same but the increased time dilation makes an observer on the circumference think a revolution takes as long as if the circumference were still longer.

An observer inside with a faster clock will be surprised to not see the cylinder shatter just as he is surprised when his Twin comes back much younger than him.

The twin apparently doesn’t know his physics then, because if he did, there would be no surprise.  The cylinder doesn’t shatter because it was always spinning.

Based on his first person experience, the traveling twin is convinced Einstein is wrong and speeds greater than c are possible. Not until he gets back into a common inertial frame with his now much older twin is he given evidence that Einstein was right after all and that observations on different reference frames are relative.

At this point you go into a bend about gravity and GR, which seems a diversion from the more simple SR topic that you need to master first. 

I know SR cold which is why I know that when acceleration is in the picture you need to bring in GR and non-Euclidean spacetime. The circumference is smaller and the spokes do not reach as far out because the spacetime they are on is curved.

One comment though:

It will be crushed around the circumference. Where does the energy come from to crush it?

It doesn’t take energy to crush something. It seemingly takes force, which means a strong but brittle object can be crushed by expenditure of arbitrarily small energy. The less brittle it is, the more that energy goes into strain and not into failure, so it takes more. I’m assuming insanely brittle and strong materials for our objects else they’d not be able to withstand the centripetal stresses being put on them. Anything else would just fly apart.

(We are now talking about the material circle constructed around a neutron star being raised out of the gravity well in a differently shaped spacetime.)

There must be some force involved or there would be no crushing at all. Where does the energy come from? It comes from the same source as the energy used to raise it out of the gravity well. It would resist being forced into a differently shaped spacetime. Note that there is no spinning involved here so this is a different problem from the spinning wheel situations.

Whether and how much contraction an observer will see depends on the observer.

The cases I enumerate above are observed by anybody. They were chosen for that purpose. The measuring rod between ships is also a real consequence.

You cannot directly see curved spacetime. Our 3D Euclidean oriented brains do not work that way. You can only see the consequences. I have addressed all of the cases you enumerated and shown how your assumptions are wrong because you do not take into account GR and curved spacetime, which must be considered because acceleration is involved.

An observer on the spinning wheel sees nothing different because contraction is only visible from another reference frame.

In all three cases, the observer on the wheel very much sees differences, which are pointed out in the cases above. You seem to agree that one ring fits through the other, something to which all observers agree. You don’t seem to have any fake physics that lets you deny the bumper-car-track thing, nor do you seem to deny the non-Euclidean dimensions of the ‘cylinder’.  OK, the  non-Euclidean dimensions are frame dependent.  A stationary observer will measure normal dimensions, but the inability of the object to change its angular speed is an objective observation.

The observer on the wheel does not see length contraction which can only be seen from a different reference frame. The observer on the wheel is time dilated relative to another observer and thinks the wheel is the same circumference because it takes the same subjective time to make a revolution relative to a fixed marker. But from a different reference frame nearer to the center, the circumference, being length contracted, is smaller than would be expected from the length of the spokes, a clear indication that spacetime is curved. As with the orbit of Mercury deep in the Sun’s gravity well, the curvature cannot be seem directly but can be inferred from the precession of the elliptical orbit.

An object certainly can change its angular speed by changing the radius. When a spinning skater pulls her arms in, angular momentum is conserved which requires and increase in angular velocity.

First some comments about time dilation. The pilot of a rocket ship that has accelerated to 0.99 c will experience a time dilation factor of about 7. The clock on the ship will be running 7 times slower than before the acceleration.

No frame reference, so that statement is ambiguous.  It will be running 7 times slower relative to the frame in which the ship is moving at .99c.  Not saying you're wrong, just sloppy.  It's running at normal rate relative to the ship of course.

I did provide a reference frame. The frame in which the ship is moving at .99 c is the one before the acceleration, which I explicitly mentioned right there: “accelerated to 0.99 c”. No sloppiness. We are not going ad hom., are we?

It’s not an ad-hom.  It’s sloppy because you’re describing ‘what the pilot experiences’ and a pilot always experiences being stopped.  You’re referencing the pilot frame and also the original frame, which makes it confusing. That’s sloppy.

You first accused me of not mentioning the original frame, which I did implicitly by mentioning acceleration from it. Now you are berating me for mentioning both frames.  You are just looking for something, anything, to nitpick about even if you contradict yourself. That sure sounds like ad hom.

And “a pilot always experiences being stopped”? No, the pilot experiences being accelerated to 0.99 c from his original reference frame. If he decelerates and finds himself in a matching inertial frame that is actually accelerated from the starting frame, is he stopped? Do you have any understanding of the subject at all or was this another ad hom attempt that misfired?

Secondly, the bolded statement is wrong since no observer can experience time dilation. I can look at the GPS clocks and objectively notice I’m running slower than them, but I still don’t experience that dilation.

If you were able to see the GPS clock, it would be going at the same rate as your own clock because it was intentionally set to run slower.

To account for the increased rate of the GPS clock due to lower gravitational level at the 20,000 km orbital altitude (45 μ s a day fast) and the time dilation at 14,000 km/s orbital speed  (7 μ s a day slow), the clock on a GPS satellite is set to run 38 μ s a day slow to match mean sea level clocks. If there were another unadjusted clock on the satellite, then it would be seen to be 38 μ s a day fast.  Note however that even on the adjusted clock running at the same rate as yours, there will be a difference in time readings of .067 to .089 seconds depending which of the 24 active satellites you were comparing against. The time difference is how GPS works.

You have to bring two observers into the same reference frame to judge which one is right, that is, which one underwent acceleration.

Acceleration is absolute (at least in Minkowski spacetime). An accelerometer works inside a box. All observers will agree if something has accelerated. That’s twice you’ve made this mistake.

The mistake is on your side.

Because the accelerometer on the spaceship is time dilated relative to the unaccelerated observer, it’s history will show a steady acceleration all the way up to 7 c just like the pilot felt, while an outside observer will see the spaceship’s acceleration decrease as it approaches 0.99 c. The fact of acceleration is absolute. But because acceleration slows the clock rate as seen by an outside observer but not by anyone on the spaceship, the rate of acceleration is relative.

To prove whose subjective experience is in error requires bringing both clocks into a common inertial frame and comparing them. In this case, the pilot will realize that his clock ran slow even if it did not seem that way to him. He will then accept that Einstein was right after all.

This is basic stuff. Why are you having a problem with it?

His observation is that he is traveling faster than c. Known landmarks are whizzing by at 7 c. Why can’t he conclude that Einstein was wrong?

He is free to propose a different theory, but none has been found so far. So are you a relativity denier then? It seems to be your goal here. You resist it at every step of the way.
Such deniers are dime a dozen on sites like this, but then don't go telling me that your stories conform to an established theory and mine don't. I've pointed out several self contradictions with your assertions.

Einstein didn’t just suggest that light speed yielded the same value in any frame. That because quite apparent by all the attempts to measure the difference as was predicted by the prevailing view of the time. So he can’t conclude Einstein was wrong, he’d have to conclude that all the decades of light speed measurement were wrong. Einstein didn’t perform any of those measurements.

Acceleration is in the domain of General Relativity. A constant speed of light only leads to Special Relativity.  Because the pilot only studied SR, not GR (and how many have studied GR?) he did not know that acceleration was the explanation of the twin paradox. From his SR based viewpoint, it was perfectly valid for him to say that his twin was traveling away from him and should have been time dilated. In SR, the traveling twin will in fact see the other twin’s clock run slower and consider that proof of the other twin being the one in motion.

To prove whose subjective experience is the more credible, it is necessary to bring both clocks into a common inertial frame to determine who experienced less time.  That is the one who was most time dilated.  I say ‘most’ time dilated because the stay at home twin might have flown X-15 rocket planes a lot and the clock he carried with him at all times is going to be behind the clock on his wall at home. But even that clock is going to have less elapsed time than the one in high orbit around the earth.  Keep in mind that all these clocks will run at the same rate when brought into a common inertial frame.

The pilot disbelieving his own subjective experience because he knew Relativity Theory is just silly. Anyway he only knew the easy part. Which you seem to be having trouble with.

BTW the reason for the attempts to determine if light speed would always be measured at the same value regardless of the state of motion was that Maxwell’s Field Theory of Electromagnetism said that it would and the speed that fell out of the equations was equal to the already measured speed of light. This is why Michaelson and Morley conducted their experiments.  Michaelson continued to believe in the luminiferous ether despite the experiments, and also despite Maxwell’s explanation of why the ether was not necessary.  Einstein was not believed by everyone for some time. There are relativity deniers today, to use your phrase. But there are many more relativity misunderstanders, which includes you, I am afraid.

[Halc]

Mod note:
I have moved all the Bell's stuff into a new topic in New Theories:

Split: Bell's paradox: Does the string break?
https://www.thenakedscientists.com/forum/index.php?topic=80334.0

This thread will track the angular momentum question.  There were definitely ideas being pushed that have no business in the main physics section.

My apologies for the brute scalpel work. Whole posts were moved, and some of the dialog moved definitely concerned this thread, and there are still traces of the Bell's discussion in this thread.

[Jaaanosik (OP)]

The paper explains the centroids:



Is the angular momentum calculated in regards to geometric or energy centroid?
Jano

[Halc]

Is the angular momentum calculated in regards to geometric or energy centroid?

Center of mass is what counts, which is the geometric center.

Per wiki:
"angular momentum L is proportional to moment of inertia I and angular speed ω  measured in radians per second.[3]

L=Iω
Unlike mass, which depends only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation and the shape of the matter"

[Jaaanosik (OP)]

Is the angular momentum calculated in regards to geometric or energy centroid?

Center of mass is what counts, which is the geometric center.

Per wiki:
"angular momentum L is proportional to moment of inertia I and angular speed ω  measured in radians per second.[3]

L=Iω
Unlike mass, which depends only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation and the shape of the matter"

I guess then the angular momentum appears to be frame dependent because the geometric mass is frame dependent.
The geometric mass is at the center of the wheel for the axle frame and it is shifted for the outside frame.
The outside frame has non-relativistic frames around itself that your calculation should be correct but with shifted center of mass, right?