The Actual Solution To The Ehrenfest Paradox (Relativistic Spinning Disk)

[Dubbelosix]

I did elaborate that the paradox is issued incorrectly. There are no true rigid bodies in relativity. While the Lorentz contraction is a Lorentz rotation, a sphere while rotated as shown by Penrose, its apparent size can still appear smaller. There should be no exception in nature the subtle differences are uniquely misunderstood. A spinning planet that us warm, bulged at the equator analogous to a classical transform. The quantum case for a particle spreads out like a disk. There is also one last point, there is no rigidity on nature and no true pointlike particles.

Edited August 1, 2020 by Dubbelosix

[LaurieAG]

Hmm, that's an interesting idea. Can you elaborate on it a bit?

 

-Anssi

Hi Anssi,

 

The 2xpi discrepancy could merely be the difference between the standard Compton wavelength, the reduced Compton wavelength and the nature of universal matter calculations and observational data calculations as the Λ in ΛCDM is just 1 of 3 lambda's involved. Wikipedia describes the differences between the reduced/standard forms and the different types of equations they are used in. Gravitational mass and inertial mass are essentially the same while the CMBR is observed photons of a specific wavelength.

 

https://en.wikipedia.org/wiki/Compton_wavelength#Distinction_between_reduced_and_non-reduced

The reduced Compton wavelength is a natural representation of mass on the quantum scale. Equations that pertain to inertial mass like Klein-Gordon and Schrödinger's, use the reduced Compton wavelength.^[2]:18–22 The non-reduced Compton wavelength is a natural representation for mass that has been converted into energy. Equations that pertain to the conversion of mass into energy, or to the wavelengths of photons interacting with mass, use the non-reduced Compton wavelength.

 

The following link is to my last post on an Against The Mainstream (ATM) thread on another forum. At the bottom of the post you will find a link to an image of the ΛCDM ratios as I can't post images here.

 

https://forum.cosmoquest.org/showthread.php?174969-Simple-Universal-DM-halo-calculations&p=2514394#post2514394

 

I was surprised that Δc, the virial overdensity constant used in the ΛCDM model is half of that as used for galaxies.

 

https://en.wikipedia.org/wiki/Virial_mass#Virial_radius

 

This definition is not universal, however, as the exact value of Δc depends on the cosmology. In an Einstein–de Sitter model, it is assumed that the density parameter is due to matter only, where Ωm = 1. Compare this to the currently accepted cosmological model for the Universe, ΛCDM model, where Ωm = 0.3 and ΩΛ = 0.7; in this case, Δc ≈ 100. Nevertheless, it is typically assumed that Δc = 200 for the purpose of using a common definition, and this is denoted as r200 for the virial radius and M200 for the virial mass.

[AnssiH]

I did elaborate that the paradox is issued incorrectly. There are no true rigid bodies in relativity. While the Lorentz contraction is a Lorentz rotation, a sphere while rotated as shown by Penrose, its apparent size can still appear smaller. There should be no exception in nature the subtle differences are uniquely misunderstood. A spinning planet that us warm, bulged at the equator analogous to a classical transform. The quantum case for a particle spreads out like a disk. There is also one last point, there is no rigidity on nature and no true pointlike particles.

I'm not familiar with Penrose's argument on this matter, but I touched the topic of people trying to solve the paradox with additional dynamics, and why that is immediately off-topic.

 

Of course there are no "rigid bodies" because there's no infinite information speeds holding objects together. But the point of the paradox is to question how does purely abstract geometry work in terms of relativistic transformation. A single inertial frame is expressed in euclidean coordinate system by definition, therefore a snapshot of a disk must also be expressible as euclidean no matter what inertial frame we take the snapshot from.

 

Or in other words, the coordinate transformations ought to be self-consistent as long as we do everything correctly.

 

The only reason why so many people argue that the solution is non-euclidean disk is that they misapply Lorentz length contraction in this situation.

 

And the reason why many people suggest that additional dynamics (such as centrifugal force) might improve the situation seems to be somewhat desperate attemp to solve a problem they can't otherwise solve. Really, they just have a wrong perspective on what Lorentz transformation represents, that's all.

 

This quote from Oyvind Gron's research is very much to the point;

 

"...should relativistic kinematics not be self-consistent, it would seem hard, on logical grounds, to accept the view that the addition of dynamical arguments might improve the situation."

 

-Anssi

[AnssiH]

Hi Anssi,

 

The 2xpi discrepancy could merely be the difference between the standard Compton wavelength, the reduced Compton wavelength and the nature of universal matter calculations and observational data calculations as the Λ in ΛCDM is just 1 of 3 lambda's involved. Wikipedia describes the differences between the reduced/standard forms and the different types of equations they are used in. Gravitational mass and inertial mass are essentially the same while the CMBR is observed photons of a specific wavelength.

 

https://en.wikipedia.org/wiki/Compton_wavelength#Distinction_between_reduced_and_non-reduced

 

The following link is to my last post on an Against The Mainstream (ATM) thread on another forum. At the bottom of the post you will find a link to an image of the ΛCDM ratios as I can't post images here.

 

https://forum.cosmoquest.org/showthread.php?174969-Simple-Universal-DM-halo-calculations&p=2514394#post2514394

 

I was surprised that Δc, the virial overdensity constant used in the ΛCDM model is half of that as used for galaxies.

 

https://en.wikipedia.org/wiki/Virial_mass#Virial_radius

That's quite interesting. This is a topic I'm not too familiar with so I can't say much. But I noticed people quite aggressively defending "conventional views" on that other forum. I must say that in general the whole general topic of dark matter, dark energy, big bang theory etc, is so full of shaky assumptions, crude approximations and dependencies to rather fragile aspects of our current theories, that I find little bit silly to take any of it as much more than highly hypothetical musings.

 

I mean, it's hard to think of a more arrogant thing to say than "we know the age of the universe" or "we know what happened at [math]10^-11[/math] seconds after the universe came to existence."

 

Combine that with rather embarrassing statements suggesting some kind of childish "origins" philosophy, like "universe was born out of nothing" and "before the big bang there was nothing because time did not exist", I honestly think the theory says more about human psychology (the need to "know") rather than about the universe itself.

 

Wow that went off topic fast... :D

 

Anyway, that reminds me of another little detail; I wonder if anyone has ever seriously attempted to explain the galaxy rotation curves by modeling the EM and/or gravity propagation "environment" (the "space") as being dictated entirely by the nearby massess influencing it. I mean, sort of Mach's principle, but taking into account a possible dragging effect of the rotating galaxy itself.

 

I don't have any specific details to propose, but just pointing out the obvious - if the rotating galaxy itself influences the "space" for EM or the gravity propagation, it would seem to lead into a situation where the outer parts of the galaxy must rotate faster in order to stay in stable orbit. Because from their perspective, the whole "space" they are in is also rotating by some degree (influenced by distant stars and by the local galaxy). This could also potentially explain why the rotation curves are not symmetrical around the whole disk.

 

I could guess this might not be a popular way to model things after the advent of General Relativity, but at the same time it seems entirely valid possibility at least superficially, and doesn't seem to rule out any observations usually associated with GR.

 

At any rate, it's probably not a bad idea to view matter and space as just the different aspects of the same "thing" - or at least take the stance that things can be modeled this way. There are a lot of successful models already taking clear steps to this direction. To me it always seems a bit naive to define space and matter as two different entities, when at the same time we are forced to define clear dependencies between them.

[LaurieAG]

At any rate, it's probably not a bad idea to view matter and space as just the different aspects of the same "thing" - or at least take the stance that things can be modeled this way. There are a lot of successful models already taking clear steps to this direction. To me it always seems a bit naive to define space and matter as two different entities, when at the same time we are forced to define clear dependencies between them.

 

Yes Anssi, :) there's also the higher level paradox that the BB theory has 'nothing' outside of it, something that we can't really observe anyway, and 'something' outside of our BB 'bubble' is not considered because we can't observe it lol, even though it would remove the need for 'dark matter'. ;)

[AnssiH]

Yes Anssi, :) there's also the higher level paradox that the BB theory has 'nothing' outside of it, something that we can't really observe anyway, and 'something' outside of our BB 'bubble' is not considered because we can't observe it lol, even though it would remove the need for 'dark matter'. ;)

Yeah I noticed the comments about this when reading that thread on the other forum. Seems kind of strange to assume that beyond our observational boundary nothing would influence things inside our boundary...

 

But throughout the history of natural philosophy we have found - to the surprise of most people - that we are further and further away from the center of the universe. And step by step we have found that we are smaller than we think. Again this really says more about the human psychology than the universe...

 

And on that token, the common Big Bang view just really does place us in a remarkably special location, doesn't it. 13 and some billion years for the age of the universe, that is ridiculously small number. The same model places the heat death of the universe at a number that is too large for me to type. Let's just say in the range of 1 googol or so. The point is, that just happens to place us right next to the birth of the universe.

 

There's this illustration from Carl Sagan to compare human history to the age of the universe

"...Sagan goes on to extend the comparison in terms of surface area, explaining that if the Cosmic Calendar [entire history of the universe] is scaled to the size of a football field, then "all of human history would occupy an area the size of [his] hand"

 

I think he perhaps meant that to illustrate how small we are, but to me it does the opposite. The area of his hand is still ENORMOUS if we really think human history occupies that much of the entire temporal universe that has ever existed. Come on now people.

 

And what comes to the observations of stars like Methuselah - right in our backyard - that appear to measure as older than the age of the entire universe, I have two things to say;

 

First, we've been able to get the age "almost" (but still not quite) to fit inside the age of the universe only by trimming the numbers by furiously looking for different sources of observational and theoretical uncertainties, and always chosen to push the number as small as we possibly dare. Now if that's not an extreme case of confirmation bias, I don't know what is.

 

Second, and more importantly, even if we one day manage to push that age within valid limit for the Big Bang theory, I think this illustrates again just how remarkably close to the beginning of the universe we have placed ourselves. We are so special, that we are literally witnessing the first generation of stars. Wow, let's all feel lucky together.

 

Anyway, in addition to taking into account what might lie beyond our observation limits, I think there's a lot of interesting possibilities also in refining very fundamental aspects of our models. The nature of space, matter, and information propagation. Of course it's possible there's something like dark matter and nothing changes, but these conventional theories certainly seem to get disproportionate amount of attention. I guess when a view preserves the largest number of existing beliefs, it tends to resonate with people the most, on average. Indeed, we've seen this effect throughout the history of science.

 

This thing;

https://www.discovermagazine.com/the-sciences/mysterious-dark-flow-is-tugging-galaxies-beyond-the-universes-horizon

 

where they find the galaxy clusters appear to be all anomalously moving, and in a coherent direction no less... It didn't contain much details, but that description makes me speculate the possibility that our observable universe is just a small portion at the edge of a larger orbital or otherwise circular structure. I say "otherwise circular" because I wouldn't necessarily propose gravitational mechanisms over distances where light potentially redshifts to zero energy... But I mean, that type of hypothesis could easily yield apparent "coherent direction" to galaxy clusters from our perspective (because they all "fold away" towards the center of the circular structure). Again making us smaller, and placing us yet another step away from the "center" of the universe.

 

Oh, one more thought. About the idea of explaining galaxy rotation curves by associating information propagation speeds to the bodies surrounding the situation (dominated by the rotating galaxy itself), I have not found why this has not been considered, but if you think about the general relativistic frame-dragging;

https://en.wikipedia.org/wiki/Frame-dragging

 

As you probably know, I usually don't view spacetime as much more than a mental construct - I think it's more rational to view universe as actually dynamic with a universal simultaneity beyond our ability to measure that simultaneity. That view basically models universe as a dynamic space where information propagation speeds are taken as dynamic (as oppose to the notion of simultaneity taken as dynamic), which also suits nicely this idea of modeling matter and space as the flip sides of the same coin.

 

In terms of observable effects of course everything works the same way - just that in my view, the flow of time is not just an illusion of a mind, but rather the interaction dynamics themselves obey relativistic relationships as far as all natural observers can measure with realistic devices (bound by the same interaction speeds). After all, we are all natural observers...

 

So, if you read the frame-dragging description through that lense, it looks in fact quite intuitive - it just that the bodies of the universe define entirely the very structure where information propagates - thus nearby moving elements can be seen as "dragging" that environment and will impact measurements accordingly. Rotating body is really more accurately just a collection of moving elements, dragging the "space" around them along.

 

It doesn't seem like a stretch to me at all to extend this effect to the scale of the entire galaxies. Why no one has attempted this, I have no idea...

 

-Anssi

[LaurieAG]

And on that token, the common Big Bang view just really does place us in a remarkably special location, doesn't it. 13 and some billion years for the age of the universe, that is ridiculously small number. The same model places the heat death of the universe at a number that is too large for me to type. Let's just say in the range of 1 googol or so. The point is, that just happens to place us right next to the birth of the universe.

...

And what comes to the observations of stars like Methuselah - right in our backyard - that appear to measure as older than the age of the entire universe, I have two things to say;

 

First, we've been able to get the age "almost" (but still not quite) to fit inside the age of the universe only by trimming the numbers by furiously looking for different sources of observational and theoretical uncertainties, and always chosen to push the number as small as we possibly dare. Now if that's not an extreme case of confirmation bias, I don't know what is.

 

Second, and more importantly, even if we one day manage to push that age within valid limit for the Big Bang theory, I think this illustrates again just how remarkably close to the beginning of the universe we have placed ourselves. We are so special, that we are literally witnessing the first generation of stars. Wow, let's all feel lucky together.

 

Anyway, in addition to taking into account what might lie beyond our observation limits, I think there's a lot of interesting possibilities also in refining very fundamental aspects of our models. The nature of space, matter, and information propagation. Of course it's possible there's something like dark matter and nothing changes, but these conventional theories certainly seem to get disproportionate amount of attention. I guess when a view preserves the largest number of existing beliefs, it tends to resonate with people the most, on average. Indeed, we've seen this effect throughout the history of science.

...

where they find the galaxy clusters appear to be all anomalously moving, and in a coherent direction no less... It didn't contain much details, but that description makes me speculate the possibility that our observable universe is just a small portion at the edge of a larger orbital or otherwise circular structure. I say "otherwise circular" because I wouldn't necessarily propose gravitational mechanisms over distances where light potentially redshifts to zero energy... But I mean, that type of hypothesis could easily yield apparent "coherent direction" to galaxy clusters from our perspective (because they all "fold away" towards the center of the circular structure). Again making us smaller, and placing us yet another step away from the "center" of the universe.

...

Oh, one more thought. About the idea of explaining galaxy rotation curves by associating information propagation speeds to the bodies surrounding the situation (dominated by the rotating galaxy itself), I have not found why this has not been considered, but if you think about the general relativistic frame-dragging;

https://en.wikipedia.org/wiki/Frame-dragging

 

Anssi, whether we like it or not we are at the center of the visible universe and there's nothing much we can do about it apart from constructing our models to reflect this limitation, otherwise we just tie ourselves in knots with paradoxes. I bet the ancient Greeks always observed what happened at the finish line despite Zeno's mathematical constructs. :)

 

Over a decade ago or so they referred to movement of galaxies you refer to as the Hubble flow but they have more recently redefined the definition as describing the motion of galaxies due solely to the expansion of the Universe, a subtle but very important difference.

 

The DM Halo model and the Virial theorem is entirely based on something outside the baryonic matter in our galaxy that changes the mechanics of stars on the outer edge of the baryonic matter part. In a minimalist WIMP model context we have 5 massive 'particles', that are the same weight as the baryonic matter part of our galaxy, floating around in a halo 1000 times the volume of the baryonic matter part but weakly interacting with it.

 

If you look closely at my avatar you will see a feed back loop screen capture I made over 20 years ago. I called the setup an "Opto-Electric Lag Inferometer" because the frame dragging shown in the image is due to the camera being at 3 minor angles to the monitor screen and the lag is due to the electric component of the loop (in ferro over a meter ;) ). That's why I have always suggested an astronomical observation point that does not sit on the surface of the earth, does not rotate/orbit around our sun and does not rotate/orbit around the center of our galaxy to remove 3 angles of spin from our observations so we can see what our universe is really like.

 

 

[OceanBreeze]

Anssi, whether we like it or not we are at the center of the visible universe and there's nothing much we can do about it apart from constructing our models to reflect this limitation, otherwise we just tie ourselves in knots with paradoxes. I bet the ancient Greeks always observed what happened at the finish line despite Zeno's mathematical constructs. :)

 

 

 

Yes and no. We are at the center of Our visible universe, but our visible universe is not the same as the visible universe as seen from the Andromeda Galaxy, for example. Since Andromeda is 2.5 million light-years from Earth, an observer there will be able to see further in the direction away from Earth and we can see further in the direction away from Andromeda. Both Andromeda and Earth are at the center of different visible universes. In fact, two identical telescopes located at different places on Earth will each have slightly different visible universes that they are each at the center of.

 

There is no one single visible universe that is THE Special visible universe for everybody.

[Dubbelosix]

Let's put something into perspective here, dark matter halos have not been directly observed

 

Dark matter halo - Wikipedia

https://en.m.wikipedia.org › wiki › Dark...

Edited August 8, 2020 by Dubbelosix

[Dubbelosix]

Their existences are only inferred upon.

[LaurieAG]

Yes and no. We are at the center of Our visible universe, but our visible universe is not the same as the visible universe as seen from the Andromeda Galaxy, for example. Since Andromeda is 2.5 million light-years from Earth, an observer there will be able to see further in the direction away from Earth and we can see further in the direction away from Andromeda. Both Andromeda and Earth are at the center of different visible universes. In fact, two identical telescopes located at different places on Earth will each have slightly different visible universes that they are each at the center of.

 

There is no one single visible universe that is THE Special visible universe for everybody.

Until we can go to the Andromeda galaxy/send a probe and view the visible universe from that location, or any other, we will be stuck with viewing the same 'special' visible universe from our own limited perspective. That's the point I was making.

 

I have no doubt that light travels at the same velocity in all frames and that there is no preferred frame. I also said that more than just a frame is required to solve certain problems (like Gron's Fig 9 Part C) without distorting the geometry (and I haven't seen any successful solution that uses frames as opposed to Gron's 'optical appearance' plot 'at retarded points in time').

[AnssiH]

So, going back to the topic of the OP, it seems to me that it would make sense to publish this solution somewhere. I mean we have over a century of silly solutions, so maybe it's time... There must be people out there who'd be interested of understanding how it actually pans out under SR. I'm absolutely confident this is correct solution because it just falls out of purely SR logic without violating anything in SR.

I could write a cleaned up, clearer, more concise / focused version. Maybe add a clarifying picture or two if it feels necessary. (Any feedback for anything that felt unclear in the OP is welcome)

 

Albeit I feel like it would also be valuable to point out the exact error(s) in the solutions published thus far...

 

But I have no good idea of what would be a good avenue for publishing the solution so it reaches people who are interested and capable of verifying its legitimacy. As in, other than just talking about it on internet forums to fine folks like you :D

 

Any thoughts / ideas?

[AnssiH]

On 8/13/2020 at 9:06 AM, AnssiH said:

So, going back to the topic of the OP, it seems to me that it would make sense to publish this solution somewhere. I mean we have over a century of silly solutions, so maybe it's time... There must be people out there who'd be interested of understanding how it actually pans out under SR. I'm absolutely confident this is correct solution because it just falls out of purely SR logic without violating anything in SR.

I could write a cleaned up, clearer, more concise / focused version. Maybe add a clarifying picture or two if it feels necessary. (Any feedback for anything that felt unclear in the OP is welcome)

 

Alright,I gave this a stab. Here's what I have so far;
https://www.dropbox.com/s/p4msczv4028rd8i/Kinematic Solution To The Ehrenfest Paradox.pdf?dl=0

I'm failing on the "concise" part a bit, although more than half of the length is extra discussion. I feel like this whole thing could be explained in one page, but then I look at all the silly solution suggestions out there in published papers, and my confidence to the "one-page approach" being enough vanishes... I just don't know which detail is the one everyone keep missing here when they insist on paradoxical solutions 🤷‍♂️

Anyway, perhaps some online journal would be interested of publishing something like this. Let me know what you guys think about it, especially @LaurieAG... Does it sound about clear, or is it too rambling?

-Anssi

Edited January 4, 2021 by AnssiH
changed link to the article

[LaurieAG]

Hi Anssi,

Your paper has to have lots of comments as you aren't just addressing one paradox.

You could possibly improve the clarity by adding a number/title to each section to define which type of paradox, as identified in the (numbered?) list at the start,that  you are addressing in that section.

Also don't forget that the S in SR means special and examples are deliberately constructed to give consistent and non paradoxical outcomes.

Good luck. 🙂

[AnssiH]

4 hours ago, LaurieAG said:

You could possibly improve the clarity by adding a number/title to each section to define which type of paradox, as identified in the (numbered?) list at the start,that  you are addressing in that section.

Hmm yes, that could make it easier to follow... 🤔

OTOH I'm also on the fence for completely removing all the extra commentary as it's not strictly needed... but then I also feel like some readers might be stuck on one of those solutions, and unable to see its problems without pointing it out... Anyway, good feedback, I'll need to think about what to do...

Thanks!

-Anssi

[nucleardomo]

I am going to suggest to AnssiH that his argument fails on two levels:

1. we constantly talk of transformations of intervals in relativity - both special and general. By continuity this allows one to in some cases talk of macroscopic distances, and so is not some fatal constraint, but that is not even crucial here...though it leads to the following argument from simple analysis ( in the calculus/differential geometry sense)....

2. more to the point, the argument itself depends on considering a situation in which the comparison of some already tiny distance in someone's frame of instantaneous reference would fail on account of the "pole through the barn door catastrophe" that a relativist would recognize. But that is a red herring - the identification of a fast enough travelling frame for rod B to imply that a side-by-side rod A would burst the thought experiment box merely signals that you have chosen to wide a "diffrerentail length" to have a sufficiently local inertial frame. Yes, once the rotating rod A would presumably burst the containment in your thoughts you are being told by the mathematics that a tinier delta-length in well in order - one where the rotation of the ends becomes negligible compared to ta tangential length. There will always be a scale at which this is possible, so your argument fails on its own premise that somehow even infinitesimal extents cannot be compared. Indeed, the Lorentz contraction effect witnessed by B (and on its side by A), come back just as in a first-year text book.

best regards,

 

D Barillari

 

[Jaro]

I am almost convinced by the arguments in this post. I say almost because there is one troubling feature that I cannot resolve using the same arguments. And it is this:

If all the clocks on the spinning wheel are synchronized with each other, and they are synchronized (though ticking slower) with clocks in the stationary frame, then the coordinates representing constant time for both rotating and stationary observers are lines in the plane perpendicular to the time coordinate. However, suppose that the short rods the wheel is composed of were to decouple from the spokes and fly out in a straight line. To an observer in the stationary frame, who has not seen these rods be part of a rotating structure a moment go (all he sees is a rod moving in a straight line), the rods would now be Lorenz contracted and two clocks attached to the end of each rod would not be synchronized to him.

So, my issue is the apparently discontinuous transition from one coordinate system in which all observers agree on lengths and the synchronicity of clocks to one where they do not.

Thank you for addressing this point.

 

Edited September 14, 2022 by Jaro