Curve Space-time from Spinning disc?

[lucas_]

Please see attached illustration (from Discover September 2004. Einstein 100 years special issue).

Is it correct that one key to Einstein's thinking is to analyze a spnning disk. That "Since the rim of the disk travels faster than the center of the disk, the theory of relativity states that the rim is compressed more than the center. If so, the disk must be distorted (its circumference is no longer pi times its diameter). So The surface of the disc, is in fact, curved?"?

 

[PeterDonis]

Please see attached illustration (from Discover September 2004. Einstein 100 years special issue).

This is a good example of why it's not a good idea to learn science from pop science articles. The article's description is highly misleading. See below.

Is it correct that one key to Einstein's thinking is to analyze a spnning disk.

It's possible that it played a role, but I don't think the connection the article is claiming is valid.

First, a key distinction: the article discusses curved space, but space is not the same as spacetime, and the curvature of the "space" of a spinning disk has nothing whatever to do with spacetime curvature. Spacetime in the case of the spinning disk is flat.

Second, the "space" of the spinning disk isn't even a 3-dimensional spatial "slice" cut out of 4-dimensional spacetime. It's an abstract "space" that you get by performing a particular mathematical operation (the technical term is "quotient space"), and doesn't correspond to any actual 3-dimensional space at all.

Third, the "rubber sheet" model that the article describes is not an analogue of the curved "space" of the spinning disk. Why? Because the curved "rubber sheet" space is an actual 3-dimensional spatial "slice" cut out of the 4-dimensional spacetime of a static gravitating mass. However, this "space" is curved because of the particular way it is cut from the spacetime; there are other ways of cutting such slices that make the spatial slices flat. So once again, the curvature of the "rubber sheet" space is not the same as the curvature of the spacetime; the latter is there no matter how we cut spatial slices out of the spacetime.

 

[FactChecker]

Einstein himself wrote some books that motivate his theory. You should look there. One should be careful not to take too literally any description that is meant to help visualize the concepts but is not valid physics.

 

[lucas_]

This is a good example of why it's not a good idea to learn science from pop science articles. The article's description is highly misleading. See below.
It's possible that it played a role, but I don't think the connection the article is claiming is valid.

First, a key distinction: the article discusses curved space, but space is not the same as spacetime, and the curvature of the "space" of a spinning disk has nothing whatever to do with spacetime curvature. Spacetime in the case of the spinning disk is flat.

Second, the "space" of the spinning disk isn't even a 3-dimensional spatial "slice" cut out of 4-dimensional spacetime. It's an abstract "space" that you get by performing a particular mathematical operation (the technical term is "quotient space"), and doesn't correspond to any actual 3-dimensional space at all.

Third, the "rubber sheet" model that the article describes is not an analogue of the curved "space" of the spinning disk. Why? Because the curved "rubber sheet" space is an actual 3-dimensional spatial "slice" cut out of the 4-dimensional spacetime of a static gravitating mass. However, this "space" is curved because of the particular way it is cut from the spacetime; there are other ways of cutting such slices that make the spatial slices flat. So once again, the curvature of the "rubber sheet" space is not the same as the curvature of the spacetime; the latter is there no matter how we cut spatial slices out of the spacetime.

Thank you.

How about the analogy of the moving clock up and down explaining time dilation. Is it real or incorrect? Watch this video (it's explained towards the end) which is winner of the 2017 Breakthrough Junior Challenge where 1 video out of 11,000 entries around the world was selected (winner takes home $400,000). Is there any flaw in of the explanation of the winning entry "Relativity and the Equivalence of Reference Frames"?

https://breakthroughjuniorchallenge.org/winners/2017
(just click on the 2017 winner entry)

 

[lucas_]

Thank you.

How about the analogy of the moving clock up and down explaining time dilation. Is it real or incorrect? Watch this video (it's explained towards the end) which is winner of the 2017 Breakthrough Junior Challenge where 1 video out of 11,000 entries around the world was selected (winner takes home $400,000). Is there any flaw in of the explanation of the winning entry "Relativity and the Equivalence of Reference Frames"?

https://breakthroughjuniorchallenge.org/winners/2017
(just click on the 2017 winner entry)

The Light clock with 2 mirrors at the end and moving seems to be valid:

http://www.emc2-explained.info/The-Light-Clock/#.XRbu6vZuKYg
Why can't this be done in actual experiment where laser light bounces in mirror and it is moving. Then observer or detector in the moving device compares the time to the stationary observer?

 

[PeterDonis]

The Light clock with 2 mirrors at the end and moving seems to be valid

Sure, the light clock is a well-known thought experiment that is often used to teach SR.

Why can't this be done in actual experiment where laser light bounces in mirror and it is moving

It could, but probably nobody has thought it necessary to go to the trouble since there is so much other evidence already that confirms SR.

However, I don't see what any of this has to do with the subject of this thread.

 

[FactChecker]

The video just gives a brief hint at what is going on. There is also length contraction, the relativity of simultaneity, and other effects. The effect on time is roughly correct, but the other effects complicate things. By using the Doppler effect as an example, the video also implies that people in the same inertial reference frame might disagree with each other about the relativity effects, but they would not.

 

[lucas_]

The video just gives a brief hint at what is going on. There is also length contraction, the relativity of simultaneity, and other effects. The effect on time is roughly correct, but the other effects complicate things. By using the Doppler effect as an example, the video also implies that people in the same inertial reference frame might disagree with each other about the relativity effects, but they would not.

Can you give an example about this thing where people "

in the same inertial reference frame might disagree with each other about the relativity effects, but they would not."?​

 

[FactChecker]

People in the same inertial reference frame do observe different frequencies due to the Doppler effect. But their observations about the time and length changes in a fast-moving object are the same.

 

[lucas_]

Sure, the light clock is a well-known thought experiment that is often used to teach SR.
It could, but probably nobody has thought it necessary to go to the trouble since there is so much other evidence already that confirms SR.

However, I don't see what any of this has to do with the subject of this thread.

The Spinning disc example in Discover was written by Michiu Kiku. Someone as knowledgeable as Einstein. So if it's misleading. Then I just fathomed whether the light clock was another common misleading example. So the spinning disc is not commonly used?

Also is it not General Relativity can be derived from Special Relativity. Or is the concept separate. So a universe could have special relativity without general relativity. Or does the former implies the latter?

 

[PeterDonis]

The Spinning disc example in Discover was written by Michiu Kiku. Someone as knowledgeable as Einstein.

But it's still a pop science article. It's not peer reviewed. Nobody is telling the author that what he writes is misleading. He's just writing what sounds good to him and works to sell articles and magazines and books. Whereas in a textbook or peer-reviewed paper, there are other experts involved who can keep the author from writing misleading things.

Then I just fathomed where the light clock is another common misleading example.

Why? The fact that one particular video happened to say something misleading while discussing the light clock, does not mean the light clock itself is misleading. You just need to stop looking at pop science articles and videos and start looking at textbooks and peer-reviewed papers.

So the spinning disc is not commonly used?

Commonly used for what? As a pedagogical example in textbooks and peer-reviewed papers? Sure, it is.

is it not General Relativity can be derived from Special Relativity

No, it's the other way around. Special relativity is a special case of general relativity, in which spacetime curvature is zero.

So a universe could have special relativity without general relativity.

Only in the sense that a universe in which spacetime was flat everywhere could be described using SR without having to use the full machinery of GR. But such a universe could not contain any matter or energy, which means it could not contain any people.

 

[lucas_]

But it's still a pop science article. It's not peer reviewed. Nobody is telling the author that what he writes is misleading. He's just writing what sounds good to him and works to sell articles and magazines and books. Whereas in a textbook or peer-reviewed paper, there are other experts involved who can keep the author from writing misleading things.
Why? The fact that one particular video happened to say something misleading while discussing the light clock, does not mean the light clock itself is misleading. You just need to stop looking at pop science articles and videos and start looking at textbooks and peer-reviewed papers.
Commonly used for what? As a pedagogical example in textbooks and peer-reviewed papers? Sure, it is.
No, it's the other way around. Special relativity is a special case of general relativity, in which spacetime curvature is zero.
Only in the sense that a universe in which spacetime was flat everywhere could be described using SR without having to use the full machinery of GR. But such a universe could not contain any matter or energy, which means it could not contain any people.

Ok. Last question about Michiu Kiku before I donate the Discover magazine. Is it true that without relativity, our bodies' molecules would fall apart? I don't think it's because of something moving at relativistic speed. But without relativity, there is no spin too? So can one say relativity doesn't only work for relativistic speed?

 

[lucas_]

But it's still a pop science article. It's not peer reviewed. Nobody is telling the author that what he writes is misleading. He's just writing what sounds good to him and works to sell articles and magazines and books. Whereas in a textbook or peer-reviewed paper, there are other experts involved who can keep the author from writing misleading things.
Why? The fact that one particular video happened to say something misleading while discussing the light clock, does not mean the light clock itself is misleading. You just need to stop looking at pop science articles and videos and start looking at textbooks and peer-reviewed papers.

I meant since the spinning disc was misleading, I wondered whether light clock in general was misleading too. But you referred to that particular video concerning the light clock as misleading. Which part of it? It won $400,000. Almost 1/3 the Nobel Prize out of 11,000 choices. So I ought to know why was its light clock example misleading?

Don't worry. I'd start looking at textbooks next month at library (if I can understand it). So I just need to know these basic for bird eye views.

Commonly used for what? As a pedagogical example in textbooks and peer-reviewed papers? Sure, it is.
No, it's the other way around. Special relativity is a special case of general relativity, in which spacetime curvature is zero.
Only in the sense that a universe in which spacetime was flat everywhere could be described using SR without having to use the full machinery of GR. But such a universe could not contain any matter or energy, which means it could not contain any people.

 

[haushofer]

Your paper claims that quantum mechanical spin is demanded by relativity. I don't see how. Spin is an inherent property of particles enforced upon us by experiments. There is no physical law which says that matter should have spin, let alone spin 1/2. It follows from considerations that this inherent property explains the zeeman-effect, the periodic table etc. So I don't understand that claim.

 

[PeterDonis]

Is it true that without relativity, our bodies' molecules would fall apart?

The argument given in the image you show can't be right, since the statement "relativity requires that all particles spin like tops" is false; spin zero particles exist and are perfectly compatible with relativity. So the argument seems bogus to me.

It is true that you can't have atoms as we know them without fermions (particles that obey the Pauli exclusion principle, which says that no two fermions can be in the same state). But I don't see any way to argue from relativity that fermions must exist.

 

[PeterDonis]

you referred to that particular video concerning the light clock as misleading.

No, I didn't. I haven't even watched the video. I think you are confusing me with @FactChecker here.

 

[lucas_]

Your paper claims that quantum mechanical spin is demanded by relativity. I don't see how. Spin is an inherent property of particles enforced upon us by experiments. There is no physical law which says that matter should have spin, let alone spin 1/2. It follows from considerations that this inherent property explains the zeeman-effect, the periodic table etc. So I don't understand that claim.

Whoa. If it was written by Tom and Gerry. We could doubt it. But not when it was written by a highly regarded esteemed physicist of highest caliber (Michio Kaku). This is the full context. I won't share other images, just this for scrutiny:

 

[lucas_]

This was the article by Michio Kaku http://discovermagazine.com/2004/sep/einstein-in-a-nutshell

 

[lucas_]

This was the article by Michio Kaku http://discovermagazine.com/2004/sep/einstein-in-a-nutshell

If Michio third claim was false. How about his first and second claim (see illustration above):

1. "Moreover, since relativity governs the properties of electricity and magnetism, all modern electronics would come to a halt, including generators, computers, radios, and TV.". Relativity really governs the
properties of electricity and magnetism?

2. "Without relativity, Earth would freeze solid", "The nuclear furnace that drives the sun and stars would shut down without relativity. If there were no E=mc^2, the universe would suddenly become dark and cold, making life impossible". True?

 

[jbriggs444]

Argument from authority does not fly. And Kaku's pop science presentations are infamous here.

 

[Nugatory]

How about his first and second claim (see illustration above):

Both claims have it backwards. We develop and use physical theories to describe how the universe behaves. Relativity does not “govern the properties of electricity and magnetism” - the properties of electricity and magnetism compel us to accept relativity as an accurate description of the universe.

 

[Nugatory]

Whoa. If it was written by Tom and Gerry. We could doubt it. But not when it was written by a highly regarded esteemed physicist of highest caliber (Michio Kaku).

You want to be careful here. Doing physics and describing physics are different skills; many bad popularizations have been written by good physicists.

If you want understanding as opposed to entertainment, there is no substitute for the real thing: peer-reviewed publication and serious textbooks. It’s more work, but infinitely more rewarding.

 

[lucas_]

The argument given in the image you show can't be right, since the statement "relativity requires that all particles spin like tops" is false; spin zero particles exist and are perfectly compatible with relativity. So the argument seems bogus to me.

It is true that you can't have atoms as we know them without fermions (particles that obey the Pauli exclusion principle, which says that no two fermions can be in the same state). But I don't see any way to argue from relativity that fermions must exist.

But is it not spin occurs when special relativity is added to Schrodinger equation which produced Dirac equation that included spin? So doesn't this mean spin and relativity is connected. So Michio illustration may be just a simplified statement that if there was no relativity, there was no Dirac equation that can make particles execute the Dirac equation so no spin can be possible (you don't have spin in the non-relativistic Schrodinger Equation)?

 

[PeterDonis]

If it was written by Tom and Gerry. We could doubt it. But not when it was written by a highly regarded esteemed physicist of highest caliber (Michio Kaku).

Go back and read my post #11 again. Your confidence in pop science articles is misplaced. And if you're going to refuse to believe us here when we explain to you why your confidence in pop science articles is misplaced, and instead keep arguing from authority, why are you even bothering to ask the question?

 

[PeterDonis]

is it not spin occurs when special relativity is added to Schrodinger equation which produced Dirac equation that included spin?

No. There were non-relativistic treatments of spin before the Dirac equation was discovered.

 

[lucas_]

No. There were non-relativistic treatments of spin before the Dirac equation was discovered.

Can you please share some peer review reference(s) about the equations for spin (0, 1/2, etc) without using relativity?

 

[PeterDonis]

the equations for spin (0, 1/2, etc) without using relativity?

"Equations for spin" is a bit of a misnomer. In quantum mechanics, "spin" is an observable on a Hilbert space that is separate from the "configuration space" on which the position and momentum observables are defined. We can define the Hilbert spaces for a given spin (spin 1/2, spin 1, etc.) without using relativity at all. Most QM textbooks will discuss this.

In order to link the above quantum mechanical "spin" observable with the usual classical understanding of angular momentum, the standard technique is to look at representations of the group that describes the symmetries of spacetime. In relativity, this group is the Poincare group; in non-relativistic classical mechanics, it is the Galilei group. Both groups have SU(2) as the subgroup that describes rotations, and the irreducible representations of SU(2) are labeled with the standard "spin" indexes of 0, 1/2, 1, etc.

The references in the Wikipedia articles on the representation theory of the Poincare and Galilei groups are a decent starting point for digging into the gory details of all this; I have barely scratched the surface above.

https://en.wikipedia.org/wiki/Representation_theory_of_the_Poincaré_group
https://en.wikipedia.org/wiki/Representation_theory_of_the_Galilean_group

 

[PeterDonis]

The references in this Wikipedia article, along with the discussion in the particular section I link to, might also be useful if you want to understand the basic QM model of spin (which, as noted in my previous post, does not require relativity):

https://en.wikipedia.org/wiki/Spin_(physics)#Mathematical_formulation

 

[lucas_]

The references in this Wikipedia article, along with the discussion in the particular section I link to, might also be useful if you want to understand the basic QM model of spin (which, as noted in my previous post, does not require relativity):

https://en.wikipedia.org/wiki/Spin_(physics)#Mathematical_formulation

I'm now convinced to stay away from pop sci. But for laymen like us. If we don't read the pop-sci. How do we know what to read or focus on in textbooks.

But pop-sci is almost akin to disinformation, isn't it. For 4 facts, 2 were already refuted.

1. Spinning disc can cause space to be curved - FALSE
2. Relativity is what cause spin - FALSE

Please address the 3rd and 4th claim of Michio which is:

3. "Moreover, since relativity governs the properties of electricity and magnetism, all modern electronics would come to a halt, including generators, computers, radios, and TV.". Relativity really governs the
properties of electricity and magnetism?

4. "Without relativity, Earth would freeze solid", "The nuclear furnace that drives the sun and stars would shut down without relativity. If there were no E=mc^2, the universe would suddenly become dark and cold, making life impossible". True?

For 3 above. Relativity doesn't really govern the properties of electricity and magnetism? If not, then what governs them? And what is the relationship of relativity to electricity and magnetism (all I know is they are part of symmetry when using special relativity, maybe this is the context that without relativity, there is no electricity and magnetism?)

For 4 above. At least this may be true that without relativity, there would be no E=mc^2 or sun, right?

I'd not ask other items. I'm now convinced why only peer reviewed references were allowed in PF. Without, we would spend so much time just sorting through the disinformation in the sources.

 

[PeterDonis]

How do we know what to read or focus on in textbooks.

In general, unless you already have a good background in the subject of a textbook, you should not try to pick and choose; you should just read the textbook and work the problems.

Relativity doesn't really govern the properties of electricity and magnetism?

I would say this is backwards; the fact that the properties of electricity and magnetism (and, as we now know, the properties of all fundamental interactions) are Lorentz invariant, rather than Galilei invariant, is what makes relativity the correct theory, rather than non-relativistic mechanics.

without relativity, there would be no E=mc^2

It depends on how you interpret that equation. The best current interpretation is that it is simply an expression of a unit conversion: the conventional units of energy are the conventional units of mass, times $c^2$. In itself this equation says nothing about whether rest mass and other forms of energy can be inter-converted.

It is true that no one has ever developed a non-relativistic theory in which rest mass and other forms of energy can be inter-converted, for example by a particle and antiparticle annihilating each other and producing radiation. However, that could just be due to historical accident--that by the time experiments showed that such reactions were possible, relativity had already been developed and shown to give more accurate predictions in many other experiments, so there was no incentive to try to develop a non-relativistic theory of such reactions. In itself this does not prove that a non-relativistic theory of such things is impossible, or that they would be impossible in a hypothetical alternate universe where relativity was not true.

More generally, claims of the sort Kaku is making are not claims about physics anyway. They are just sensationalistic claims made to sell books, articles, and TV shows. Neither Kaku nor anyone else can do experiments in some alternate universe in which relativity is not true, so nobody knows for sure what would or would not be possible in such a universe.

 

[lucas_]

In general, unless you already have a good background in the subject of a textbook, you should not try to pick and choose; you should just read the textbook and work the problems.
I would say this is backwards; the fact that the properties of electricity and magnetism (and, as we now know, the properties of all fundamental interactions) are Lorentz invariant, rather than Galilei invariant, is what makes relativity the correct theory, rather than non-relativistic mechanics.
It depends on how you interpret that equation. The best current interpretation is that it is simply an expression of a unit conversion: the conventional units of energy are the conventional units of mass, times $c^2$. In itself this equation says nothing about whether rest mass and other forms of energy can be inter-converted.

It is true that no one has ever developed a non-relativistic theory in which rest mass and other forms of energy can be inter-converted, for example by a particle and antiparticle annihilating each other and producing radiation. However, that could just be due to historical accident--that by the time experiments showed that such reactions were possible, relativity had already been developed and shown to give more accurate predictions in many other experiments, so there was no incentive to try to develop a non-relativistic theory of such reactions. In itself this does not prove that a non-relativistic theory of such things is impossible, or that they would be impossible in a hypothetical alternate universe where relativity was not true.

More generally, claims of the sort Kaku is making are not claims about physics anyway. They are just sensationalistic claims made to sell books, articles, and TV shows. Neither Kaku nor anyone else can do experiments in some alternate universe in which relativity is not true, so nobody knows for sure what would or would not be possible in such a universe.

I heard about E=mc^2 since grader. Do you have any peer reviewed reference(s) exactly how they are derived? Or is it ad-hoc only? About Michio statement "If space and time become distorted, then everything you measure with meters and clocks also becomes distorted, including all forms of mass and energy", it may have a iota of truth in it? I want to see the exact derivations or proof of it. I heard about E=mc^2 since a grader and now need to see it in detail and in full glory. Thank you.

 

[lucas_]

This is a good example of why it's not a good idea to learn science from pop science articles. The article's description is highly misleading. See below.
It's possible that it played a role, but I don't think the connection the article is claiming is valid.

First, a key distinction: the article discusses curved space, but space is not the same as spacetime, and the curvature of the "space" of a spinning disk has nothing whatever to do with spacetime curvature. Spacetime in the case of the spinning disk is flat.

Second, the "space" of the spinning disk isn't even a 3-dimensional spatial "slice" cut out of 4-dimensional spacetime. It's an abstract "space" that you get by performing a particular mathematical operation (the technical term is "quotient space"), and doesn't correspond to any actual 3-dimensional space at all.

Wait. First I know LET discussion is banned (although historical discussion of it not banned). But we are not discussing the details but historical context. I'm just pointing out that Michio Kaku may have it in mind in the analogy of the spinning disc. For if the material physically contract, then in the spinning disc, the inner part contracts more than outside so curvature is actually initiated so here we have LET GR in its full glory? Just state if it is possible. Because Michio Kaku article in Einstein 100 year anniversary is one of the most powerful pop-sci articles about relativity written so it's justified to at least tell the truth whether Michio spinning disc is an example of actual LET GR. If it works, just say yes or no to not violate that details of LET would not be discussed. We are not discussing details of it but I was just asking if Michio example of it can work and historical context.

Remember also when Einstein fist cooking up general relativity. He wasn't using the Minkowski interpretation of space-time. So with regards to Michio statement "One key to Einstein's thinking is to analyze a spinning disk. Since the rim of the disk travels faster than the cetner of the disk, the theory of relativity states that the rim is compressed more than the center. If so, the disk must be distorted" Just see the illustration in the OP. Maybe Einstein really thought of it and it was LET GR in its full glory? Note historical discussion of LET is allowed according to Forum rules. Only details of LET not allowed. So the historical discussion is justified.

Third, the "rubber sheet" model that the article describes is not an analogue of the curved "space" of the spinning disk. Why? Because the curved "rubber sheet" space is an actual 3-dimensional spatial "slice" cut out of the 4-dimensional spacetime of a static gravitating mass. However, this "space" is curved because of the particular way it is cut from the spacetime; there are other ways of cutting such slices that make the spatial slices flat. So once again, the curvature of the "rubber sheet" space is not the same as the curvature of the spacetime; the latter is there no matter how we cut spatial slices out of the spacetime.

 

[Nugatory]

Do you have any peer reviewed reference(s) exactly how they are derived? Or is it ad-hoc only?

Googling for “E=mc^2 derivation” will find some good derivations, and any first-year textbook (such as Kleppner and Kolenkow) will cover this.

Be aware that $E=mc^2$ is a special case (the mass is at rest so the momentum $p$ is zero) of the more general $E^2=(m_0c^2)^2+(pc)^2$. A pretty good rule of thumb is that if whatever you’re reading doesn’t eventually get around to that more general relationship... it’s not giving you the whole story.

 

[phinds]

@lucas_ as others have already pointed out (a point you seem to have taken to heart) your faith in pop-science is very seriously misplaced. I would add to that that your belief in Kaku is even MORE misplaced. He is one of the worst popularizes in terms of reliability and accuracy.

You can find numerous threads here on this site pointing out his flaws. Here are a couple from off-site

http://rationalwiki.org/wiki/Michio_Kaku

http://scienceblogs.com/pharyngula/2011/02/16/why-do-physicists-think-they-a/

 

[Nugatory]

For if the material physically contract, then in the spinning disc, the inner part contracts more than outside so curvature is actually initiated so here we have LET GR in full glory?

No, the spacetime is still flat. The disk is experiencing internal stresses because different parts of it want to move in different directions; either these stresses distort it (as Kaku describes) or it breaks.