A relativity question.

[lifegazer]

scenario
Let's imagine a super-massive wheel as big as a galaxy (or even bigger if necessary), with fixed spokes/radials joining the circumference to the center.
Now, let's consider 3 points within that wheel upon a single radial. One point on the circumference(z), one point at center(x), and one point somewhere inbetween the other two, but much closer to the center(x) than the circumference(z).
Imagine the wheel is positioned so that gravitational considerations are approximately equal anywhere within the wheel. Hence, given that the wheel is stationary (at the start), we can say that an observer at each of our three points will be having an almost identical experience of time to one another. I.e., their clocks will all run the same and show the same time if they meet up.
... Now, the wheel begins to rotate so that the observer at position (z) on the circumference eventually accelerates to an extremely high velocity (c/2 for example). The other two observers, of course, are not moving very fast at all.

Question:-
All three observers share the same solid radial. The positions of other galaxies wrt that radial must be the same for all three observers, in reality. I.e., the galactic nightsky must appear to be in the same position for all three observers. If not, then howso? And if so, then in what sense do they all experience time differently?

I've posted this in philosophy because I might make philosophical claims which the science mob won't understand. Rather, they'll refuse to understand.

 

[Stimpson J. Cat]

The positions of other galaxies with respect to the wheel will not appear the same for all three observers, because they are now moving relative to each other, and this causes length contraction effects along the directions of relative motion. Also, it is not acceptable to talk about a rigid wheel in this type of case. No matter how physically strong the wheel is, two things are going to happen.

1) The wheel is going to bend when the torque is applied to get it rotating, due both to its own inertia, and to the fact that the wave of shearing force that travels along the spokes, ultimately causing the atoms to move, will travel with a finite speed that is much less than the speed of light. For example, if the torque is applied at the center of the wheel, then the point at the circumference will not even feel a force until millions of years later!

2) Due to special relativity, even in the absence of any deformation, the wheel will appear deformed to all three of the observers, and will appear to be deformed differently to all three.

I've posted this in philosophy because I might make philosophical claims which the science mob won't understand. Rather, they'll refuse to understand.

How delightfully presumptuous of you. Are you familiar with the phrase "poisoning the well"?


Dr. Stupid

 

[Atlas]

Fun Facts about us and our Galaxy...

Our solar system is about 30,000 light years out from the galactic centre and orbits around it at a speed of 250 kilometres per second. The astronomer Harlow Shapley, in the 1920s, was the first to realise that we are not at the centre of the Milky Way.

Containing over 100 billion stars and different types of interstellar gas and dust, the "body" of our galaxy is shaped like a great disc 300 light years thick and 100,000 light years across. It is a spiral galaxy, and our Sun is about two thirds of the way out from the centre along one of the spiral arms.

The galaxy is slowly rotating: our Sun takes about 250 million years to do one orbit of the galactic centre. Hence our solar system must have made only 20 or so orbits around the Milky Way since the Sun began to shine about 5 billion years ago.

Can someone comment on lifegazer's wheel from the perspective of point z addressing galaxies existing above our galactic plane as well as a galaxy in our plane of spin that is (at a moment in time) in front of us flying toward us at up to c/2 and one behind us flying away at up to c/2. I like this stuff but I have to be reminded everytime what I should expect in my frame of reference.

 

[epepke]

scenario
Question:-
All three observers share the same solid radial. The positions of other galaxies wrt that radial must be the same for all three observers, in reality. I.e., the galactic nightsky must appear to be in the same position for all three observers. If not, then howso? And if so, then in what sense do they all experience time differently?

Once the wheel is rotating, the observers will be under centripetal acceleration, that is, toward the center of the wheel. The observers near the center of the wheel will perceive the observers toward the outside as moving more slowly. This would occur even with uniform acceleration, but it is complicated by the fact that the acceleration is not uniform. The observer near the rim of the wheel experiences more centripetal acceleration, and so that clock will go even more slowly.

Using the raw GR equations to solve this case is a real pain, but fortunately, there's a trick to get it by superposing a simple solution from SR with a simple solution from GR.

The observer at the rim, also, will not see the same picture of the stars, because the universe will appear to be contracted in the direction of travel. If he looks along the direction of the axle of the wheel, he will see a distorted picture, much like one would get by taking the hemicylindrical magnifying "glasses" (OK, plastics) common on some rulers (that magnify up and down but not side to side), placing it over a picture, and rotating the lens. I believe this effect is used on television sometimes when someone has been slipped a mickey and is passing out. Just put a Panavision lens on a non-Panavision camera and rotate it. Cheap and effective.

Furthermore, there would be other time distortions as well when the wheel was being sped up and slowed down, because that imparts acceleration in another direction to the outer. This leads to a funny situation, because this has now changed the net direction of acceleration for the three clocks. At about this time, the math starts to get a bit hairy.

Once you do this, starting up the wheel, letting it run for a while, and stopping it, all three observers will agree on how many times they went around. They will not agree on what time it is. They will agree on how fast the wheel was turning based on their measurements of accelerometers, calculated in some inertial frame of reference, say a spacecraft outside the wheel.

But wait! They'll all agree on how many times they went around. They'll disagree on what their clocks read. So, if they divide the number of times they went around by the elapsed time on their clocks, they'll get different speeds for the the wheel. Isn't that a paradox?

No; it bleeding well isn't. Acceleration is not relative in the sense that people usually think about when they think about relativity. . You can tell you're accelerating without comparing to anything else outside you, because all your coffee cups fall to the stern of the ship and so forth and so on. Once you start rotating things, you have acceleration, including one I didn't talk about. If the observer in the center of the wheel decides to take the elevator up to the rim, he and/or she is going to be experiencing Coriolis acceleration.

A rotating body, which is held in place by Kevlar or something and would break apart otherwise, is not an inertial frame of reference.

An inertial frame of reference is in Special Relativity, something moving at a uniform speed in a straight line. General Relativity adds to this something falling in a gravitational field, such as a satellite in orbit. The idea in GR is that what in classical physics we would call acceleration is really the absence of acceleration. (Given that and the ideas of SR, it is possible to derive all of GR. Not easy, mind you, but possible.)

But not a big wheel or something swung around on a tether. Using GR and sometimes SR, you can calculate exactly what happense, but it is not relative.

[edited to add]

Perhaps somebody is going to tell me that I'm wasting my time, but maybe some person will find this explanation of some value. Even if not, I find it a personally valuable exercise to go through just for my own clarity of thought.

 

[Upchurch]

Imagine the wheel is positioned so that gravitational considerations are approximately equal anywhere within the wheel.

Well, first, there is a physical problem here. Assuming that there is no other matter in the universe and that the spokes of the wheel are essentually massless, the observers at x and y will feel no net gravitational force due to the symmetry of the ring, but the observer at z will feel the full gravitational force fo the entire ring. Then...

Hence, given that the wheel is stationary (at the start), we can say that an observer at each of our three points will be having an almost identical experience of time to one another. I.e., their clocks will all run the same and show the same time if they meet up.

This sort of syncronisity would be impossible given the distribution of the gravitational force. You might be able to make this assumption for x and y, but z is already under acceleration.

All three observers share the same solid radial. The positions of other galaxies wrt that radial must be the same for all three observers, in reality. I.e., the galactic nightsky must appear to be in the same position for all three observers. If not, then howso?

Well, for the size of ring as you're proposing, there will be quite a distance seperating x and z. As such, nearby galaxies will have varying locations for each observer.

And if so, then in what sense do they all experience time differently?

Well, since x is the only observer who is in an inertial reference frame (i.e. not accelerating), x will observer y's clock ticking slower and z's clock ticking slower still.

I've posted this in philosophy because I might make philosophical claims which the science mob won't understand. Rather, they'll refuse to understand.

I'm guessing that's because you'll try to make a physical claim that is inconsistant with known physics, which you won't understand. Rather, you'll refuse to understand.

 

[Dancing David]

I think that the paradox is apparent from the start in that LG has suggested the the wheel is going to hold toether no matter what. If we were to think about each of the points as seperate but under the same conditions, then whatever effects of relativity occur are not going to be as mind bending. the fact the mote z is traveling at half the speed of light is going to impact the observation of z's frame, same for x and y.

But by joining them together, there is a paradox, not that the wheel wouldn't fracture. And the frames for each are different, although I think I don't understand what epekeke is saying.

Which brings up the question, if god tosses a pizza crust in the air and imparts enough momentum to the crust that the outer edge is traveling close to the speed of light, how long will it take for god to eat the pizza?

 

[lifegazer]

The positions of other galaxies with respect to the wheel will not appear the same for all three observers, because they are now moving relative to each other, and this causes length contraction effects along the directions of relative motion.

A wheel rotates 360 degrees for all points upon any specific radial of that wheel. So, imagine that the universe was like a clock - all points upon our radial will start-off at noon, for example, and will arrive at the midnight-radial simultaneously, whether they perceive of that reality or not. In fact, this is the essence of the problem, since if they share the same radial - regardless of their differing velocities - then why are the observers along the various points of the radial perceiving things differently, as Einstein shows us that they do?
[Note: I am not arguing that Einstein was wrong about relativity. Rather, I aim to show that what he taught us has hugely significant philosophical importance in relation to ~reality~ itself.]

Also, it is not acceptable to talk about a rigid wheel in this type of case. No matter how physically strong the wheel is, two things are going to happen.

Give me a break. Like anyone is going to build a wheel as big as a galaxy in the first instance.

1) The wheel is going to bend when the torque is applied to get it rotating, due both to its own inertia, and to the fact that the wave of shearing force that travels along the spokes, ultimately causing the atoms to move, will travel with a finite speed that is much less than the speed of light. For example, if the torque is applied at the center of the wheel, then the point at the circumference will not even feel a force until millions of years later!

I understand. But let's imagine a technology which enables us to impart an equal rotating force upon all parts of a wheel, simultaneously, so that all radials remain straight.

2) Due to special relativity, even in the absence of any deformation, the wheel will appear deformed to all three of the observers, and will appear to be deformed differently to all three.

Why? I want you to detail the reasons why. That's the point of this thread.

How delightfully presumptuous of you. Are you familiar with the phrase "poisoning the well"?

Are you familiar with the term "been there before"?

 

[lifegazer]

The observers near the center of the wheel will perceive the observers toward the outside as moving more slowly.

Why? You can't get any slower than the initial stationary position, and the wheel is now accelerating to achieve c/2 for point-(z) on the circumference. I see no sense in your statement.

The observer near the rim of the wheel experiences more centripetal acceleration, and so that clock will go even more slowly.

I'm aware that the faster one moves, the slower one's clock registers time. The question is why? In what sense? Afterall, the universe itself cannot be affected by our actions if it is distinctly real from our own minds. In other words, a galaxy residing at noon-position in the galactic-sky will always be in the noon position, no matter what velocity we attain.

Relativity doesn't alter the fact that there are 360 degrees in a complete rotation. Given that all points on a rigid radial complete 360 degrees simultaneously, regardless of their differing velocities, and given that all points will pass "galactic-noon" at the same moment, in what sense can we say that observers along different points of that radial have experienced time differently, unless we acknowledge that the time each observer experiences is completely given to awareness by their own mind?
[creeping towards my idealistic point upchurch, so resist the temptation to move to science please]

The observer at the rim, also, will not see the same picture of the stars, because the universe will appear to be contracted in the direction of travel.

The observer at the rim traverses 360 degrees in the same time as all other observers along that radial. This is a fact imposed upon those observers by the circumstances of this scenario. The only question here, is why those observers perceive the passage of time differently. Why do they see "galactic-noon" at different moments given the alleged absoluteness of lightspeed?

 

[lifegazer]

Well, first, there is a physical problem here. Assuming that there is no other matter in the universe and that the spokes of the wheel are essentually massless, the observers at x and y will feel no net gravitational force due to the symmetry of the ring, but the observer at z will feel the full gravitational force fo the entire ring.

Then I shall ordain a moon to be placed beyond the wheel, counteracting those forces, to equalise gravity along the entire radial. Or something like that. I just wanted to obliterate the complications of gravity from the starting-point of the scenario. Theoretically, it must be possible.

As such, nearby galaxies will have varying locations for each observer.

Are you suggesting that galaxies dance to our individual tune? Or are you acknowledging the fact that the position of a galaxy is dependent upon where the mind puts it in our awareness?

Well, since x is the only observer who is in an inertial reference frame (i.e. not accelerating), x will observer y's clock ticking slower and z's clock ticking slower still.

Actually, all points existing upon a moving radial, are moving also. There can be no part of a rotating wheel that is not also rotating.

I'm guessing that's because you'll try to make a physical claim that is inconsistant with known physics, which you won't understand. Rather, you'll refuse to understand.

I'm aiming to show that Einstein discovered God for us. Are you in contact with Randi? It's about time he mixed with the peasants, me thinks.

 

[Atlas]

The only question here, is why those observers perceive the passage of time differently. Why do they see "galactic-noon" at different moments given the alleged absoluteness of lightspeed?

Well I'm not up on angular momentum and time distortions like many others of you might be, but if this is as lifegazer says: The only question here... It puts me in mind of a thought experiment story attributed to Einstein when he was a child. I'll put it in terms of the Earth and sun.

If a man in a ship burst from inside the sun traveling at the speed of light toward Earth how much time would pass from the perspective of an observer on the earth.... 93 million miles / 186000 mi per sec = 500 seconds or 8.33 minutes

How much time would pass from the perspective of the man in the ship... 0 seconds

As a boy Einstein pictured a clock on the sun side of his ship as he sat on the Earth side looking back at it. He noted that he was traveling away from the clock as fast as light from the clock was reflecting to his eyes. That may be a kid's perspective but it also may be close to the awareness issue that lifegazer is addressing.

I don't know if this helps but it seems a simple example of the frame of reference issue that's involved.

 

[Atlas]

Are you suggesting that galaxies dance to our individual tune? Or are you acknowledging the fact that the position of a galaxy is dependent upon where the mind puts it in our awareness?

Lifegazer,
This question addressed to Upchurch seemed odd to me. We see in our own night sky all the stars and galaxies race around the North Star. Actually it's our own Earth's rotation that gives us this nightly procession. It's a beautiful dance.

But in terms of two points 50 light years apart on your wheel - any galaxy above them that happened to be midway between them would cause the observer in the center of the wheel to look outward toward the rim and upward while an observer on the rim would be looking inward toward the center and up.

We definitely have our unique spatial perspectives based on location. It's true of drivers on our roads going to the same location from different starting points. So, "dependent on where the mind puts it's awareness" seems an odd phraseology for an observer's location.

 

[epepke]

I'm aware that the faster one moves, the slower one's clock registers time. The question is why?

That's an easy question, and it is easily answered. I'll present the one-page version.

There are two ideas behind relativity:

1) That you can't really tell if you are moving in a straight line or how fast you are going except by comparing your motion to something else.

2) That the speed of light is the same for all observers, regardless of their motion or the motion of the source of light.

Idea 1 dates at least from Galileo.

Idea 2 dates from the middle of the 19th century, from Maxwell's equations.

For about a half century, people tried to prove one or the other wrong, and they failed. So maybe both are right.

Take these two ideas as inputs.

Make a clock by taking a long stick. Put a mirror at one end. Put a flash bulb and a light detector and some electronics at the other end. The flash bulb flashes. The light travels to the mirror and bounces back. The electronics detect the return pulse and send out another flash. That's one ticktock. You could actually make one of these for about $50 bucks with parts from Radio Shack.

Now give someone a clock like this. Put him and/or her in a spaceship, holding the stick up and down. The spaceship moves side-to-side past you. For the person on the ship, the light just goes up and down. For you, because the ship is moving side-to-side past you, the light travels a zig-zag pattern, like a triangular sawtooth. A zig-zag patter is longer than just up and down.

As you see it the light takes a longer path relative to the path the person on the spaceship sees. From 2, the light always has to travel at the same speed. Since you see the path as longer, at the same speed, the light has to take longer to get there. So you see the ticktock as taking longer. So in your frame of reference, the spaceship-person's clock runs more slowly.

Furthermore, all of the spaceship-person's clocks have to run like that. Because if they didn't, then he and/or she could compare another clock to the lightstick clock and, from the difference, figure out how fast the ship was moving. But that would conflict with 1, which says that it isn't possible.

That is really all there is to the theory of special relativity.

Now, I've seen you go to great lengths to confuse yourself, and I can't stop that, but it really is this simple.

 

[uruk]

the galactic nightsky must appear to be in the same position for all three observers. If not, then howso

I'm looking into this, but. My initial answer is no because of the enormous distances and the speed of light which limits the speed at which information reaches the observers.

I think Einstien himself posited a thought experiment similar to this about a spinning disk with a clock and rod on the inner circumfrance and another clock and rod on the outer circumfrance showing time and length contraction. I need to dig up the book and slogg through the math (which I'm very bad at) .

But the position of the stars would be different for each observer due to their relative positions within the galaxy and the distances they are from each other. This has to do with of course the speed of light. When we look up at the night sky the stars we see are not actually in the same positions we are observing them because the light takes time to reach us. In the time it has took the light to reach us from position they would have moved to a different position. Actually some of the stars may not actually be there any more. they may have gone nova by now but we won't know about it untill the light reaches us.
therefore even if the wheel were perfectly rigid the observers would still not observe their position as rotating simultaneously.
Also they would actually see the wheel warping. they would see this because of time light would take to travel the distances.

Note this has nothing to do with the mind creating any reality for itself but rather with the amount of time it takes for information to reach it from some distance. That time has to do with distance and speed.

 

[RussDill]

scenario
Let's imagine a super-massive wheel as big as a galaxy (or even bigger if necessary), with fixed spokes/radials joining the circumference to the center.
Now, let's consider 3 points within that wheel upon a single radial. One point on the circumference(z), one point at center(x), and one point somewhere inbetween the other two, but much closer to the center(x) than the circumference(z).
Imagine the wheel is positioned so that gravitational considerations are approximately equal anywhere within the wheel. Hence, given that the wheel is stationary (at the start), we can say that an observer at each of our three points will be having an almost identical experience of time to one another. I.e., their clocks will all run the same and show the same time if they meet up.
... Now, the wheel begins to rotate so that the observer at position (z) on the circumference eventually accelerates to an extremely high velocity (c/2 for example). The other two observers, of course, are not moving very fast at all.

Question:-
All three observers share the same solid radial. The positions of other galaxies wrt that radial must be the same for all three observers, in reality. I.e., the galactic nightsky must appear to be in the same position for all three observers. If not, then howso? And if so, then in what sense do they all experience time differently?

I've posted this in philosophy because I might make philosophical claims which the science mob won't understand. Rather, they'll refuse to understand.

These questions have already been explained quite well by einstien himself. He looked into this sort of thing. He called it a "rigid rotating disk".

TRY RESEARCHING FIRST

 

[lifegazer]

Well, for the size of ring as you're proposing, there will be quite a distance seperating x and z. As such, nearby galaxies will have varying locations for each observer.

I do understand this, since the distances between x and z might be as much as (or even more than) a 100,000 lightyears. But the point of using the nightsky as a reference, here, is to know when we have rotated 360 degrees after motion has begun.
The question is, will all three observers acknowledge the completion of a full circle, simultaneously, or not?
Then, if yes, in what sense do we say that they have experienced time differently? If no, then we have a paradox that can only be explained in terms of the mind, imo.

So, what's your answer to this question?

 

[Stimpson J. Cat]

lifegazer,

A wheel rotates 360 degrees for all points upon any specific radial of that wheel. So, imagine that the universe was like a clock - all points upon our radial will start-off at noon, for example, and will arrive at the midnight-radial simultaneously, whether they perceive of that reality or not.

Incorrect. Under special relativity, simultaneity is frame dependant. What appear to be two simultaneous events in one frame of reference, are not simultaneous in another. And the notion that you can say that they are simultaneous in some absolute sense, regardless of whether they perceive that or not, simply contradicts the basic premises of special and general relativity.

In fact, this is the essence of the problem, since if they share the same radial - regardless of their differing velocities - then why are the observers along the various points of the radial perceiving things differently, as Einstein shows us that they do?

The problem is that you are implicitly assuming things which contradict the premises of Einstein's theory. You are assuming that when the wheel is in motion, you can still somehow claim that the radials are still straight lines from all reference frames. They simply are not.

[Note: I am not arguing that Einstein was wrong about relativity. Rather, I aim to show that what he taught us has hugely significant philosophical importance in relation to ~reality~ itself.]

Actually, we all know that perfectly well. The significant philosophical importance of his theory in relation to reality itself, is that reality does not work the way our intuition says it should. Our intuition tells us that special relativity leads to all sorts of paradoxes, because the theory makes predictions which do not agree with our intuition. The big philosophical point of all of this, is simply that our intuitive notions of how the World works, are not always very accurate.

Also, it is not acceptable to talk about a rigid wheel in this type of case. No matter how physically strong the wheel is, two things are going to happen.
--------------------------------------------------------------------------------

Give me a break. Like anyone is going to build a wheel as big as a galaxy in the first instance.

That is beside the point. You can not make a meaningful point about what a theory says about reality, by constructing a thought experiment whose conditions are, according to that theory, physically impossible. If your hypothetical wheel does not conform to the laws of physics, then how can you expect a scientific theory to be able to describe its behavior? If you start by assuming some magical wheel that violates the laws of physics itself, then you might as well quit right there, because you have just thrown special and general relativity out the window.

1) The wheel is going to bend when the torque is applied to get it rotating, due both to its own inertia, and to the fact that the wave of shearing force that travels along the spokes, ultimately causing the atoms to move, will travel with a finite speed that is much less than the speed of light. For example, if the torque is applied at the center of the wheel, then the point at the circumference will not even feel a force until millions of years later!
--------------------------------------------------------------------------------

I understand. But let's imagine a technology which enables us to impart an equal rotating force upon all parts of a wheel, simultaneously, so that all radials remain straight.

Simultaneous from which reference frame? As soon as the wheel is moving, what constitutes an application of equal torque simultaneously to the whole wheel, to one of your observers, will look like a very uneven and non-simultaneous application of torque, from the point of view of the other observers.

2) Due to special relativity, even in the absence of any deformation, the wheel will appear deformed to all three of the observers, and will appear to be deformed differently to all three.
--------------------------------------------------------------------------------

Why? I want you to detail the reasons why. That's the point of this thread.

This has already been explained by other people in this thread. It is basic special relativity. When an observer is moving relative to something, he sees a contraction along the direction of motion. Given the non-uniform motion of rotation, this implies an overall distortion of the wheel. It will appear, to all of the observers, to be twisted. And the degree of twisting will be dependant on the observer.

And just to nip this whole thing in the bud, the fact that space and time do not transform under different reference frames according to the way our intuition says they should, does not in any way imply any sort of idealism. Even under classical mechanics, how things appear to an observer depend on that observer's position and velocity relative to that thing. All Einstein s's work did was to show that when high velocities, and strong gravitational fields are involved, that dependence does not work exactly the way we originally thought it did. None of Einstein's work suggests that reality is not objective, nor that our minds somehow construct or influence objective reality. All it suggests is that objective reality does not work quite the way we originally thought it did.


Dr. Stupid

 

[Lothian]

Can you lot please stop messing up this thread with science and just accept Lifegazer is right in his philosophical claim that a big wheel proves there is a god...or that we should be nice to each other...or something.

 

[MRC_Hans]

*sniiiip*

Are you familiar with the term "been there before"?

Very much. I have clear memories of last time a poster here, who also did not understand relativity, insisted that everybody explained it to him, and no matter how many times and how many ways they explained it, he still did not understand, and kept claiming they were wrong

We also had one on gravity (not with the same poster)...

Hans

 

[Upchurch]

I do understand this, since the distances between x and z might be as much as (or even more than) a 100,000 lightyears. But the point of using the nightsky as a reference, here, is to know when we have rotated 360 degrees after motion has begun.
The question is, will all three observers acknowledge the completion of a full circle, simultaneously, or not?

Not. Can't really use special relativity since there is only one inertial reference frame, as I said. However, since there are, say 100,000 light years between x and z, x will could make several revolutions and still not have seen z budge.

If no, then we have a paradox that can only be explained in terms of the mind, imo.

If that is your opinion, it only goes to demonstrate that you don't really understand what relativity is in the first place. There is no need to rely on imaginary dream worlds in order to explain natural phenomena. Like most "paradoxes" the dilemma can be resolved with a broader understanding of the situation. In this case, step back from your Newtonian understanding of physics and view the universe through general relativity.

But you're not going to try that, are you?

 

[RussDill]

I do understand this, since the distances between x and z might be as much as (or even more than) a 100,000 lightyears. But the point of using the nightsky as a reference, here, is to know when we have rotated 360 degrees after motion has begun.
The question is, will all three observers acknowledge the completion of a full circle, simultaneously, or not?

Get this in your head lifegazer, there is no such thing as simultaneously in relativity. Perhaps it might be helpful to use a third observer outside the disk, and time everything from there. Then, you can do all the math, and answer the questions very easily (actually, rigid rotating disks are kinda difficult since the disk becomes non-ecludian, but still, it is just math)

Then, if yes, in what sense do we say that they have experienced time differently? If no, then we have a paradox that can only be explained in terms of the mind, imo.

You question is non-sensical is relation to relativity. You have to ask the question in respect to a particular observer. If you want to show me a paradox, work out the math.