Not All That Much of a Paradox, Really

The Twin Paradox is trivially resolved using Triplets. NO clock gets accelerated. Time intervals are defined using explicit physical contact for start and stop. The more space a clock traverses the less elapsed time it records, by the book. This is old stuff.

It is the reference frames that matter, not their contents or histories. Velocity is trivially relative and time with it. No external reference (e.g., Mach's Principle) is required.

I was just going to email you about this, too.

My kookometer rgistered high levels of kookosity as well, though independent measurements on the John Baez scale were inconclusive.

I agree with you that:

(1) Einstein gave us "not much of a paradox," so what problem is actually being solved?

(2) Absolute space is not new -- it's Newton.

(3) The sounds vaguely like Mach's principal.

(4) The press release's "science writer" obviously had no clue.

(5) I mean, we feel sorry for Katrina, and the Saints in the Superbowl and all, but, c'mon.

(6) "space shuttle ... travels near the speed of light" -- that's not the Space Shuttle that I worked on at NASA. More like that episode of Star Trek where the Enterprise was rejiggered by aliens to go, like, humongously faster.

(7) " the paradox is that the earthbound twin is the one who would be considered to be in motion" -- except it was the dud in the pimped shuttle who actually accelerated.

(8) Kak and Kook are both palindromes starting and ending with "K", but that's less than even an ad hominem argument.

(9) Yes, Special Relativity doesn't work. Makes it imposssible for a wheel to revolve. We know that. Einstein knew that. That's why he invented General Relativity. Is this about a modification to GR? Or what?

(10) In my interview for the position of Mission Planning Engineer on the Voyager fly-by of Uranus, I was asked to explain the Twin Paradox. I described it in the context of the Robert Heinlein novel where the twins had instantaneous telepathic contact, and the traveler came home to marry his great-great-great grand-niece. Got me the job.

Please keep us informed as the breaking story, ummm, breaks down.

His solution didn't happen to involve the use of nullity at some point, did it?

I never thought of the twin "paradox" as a paradox at all. When it was explained to me in high school, it just seemed to be a non-intuitive result on how the universe worked. Plus I thought Einstein did a good job of explaining it for someone like me who is not an expert in physics.

I winced at the boast at the end of the press release:

"The implications of this resolution will be widespread, generally enhancing the scientific community's comprehension of relativity. It may eventually even have some impact on quantum communications and computers, potentially making it possible to design more efficient and reliable communication systems for space applications."

The paper itself is just as wince-worthy. The author claims that the explanations of the paradox in terms of shifting reference frames and in terms of acceleration are "inconsistent" with each other, failing to realize that they are actually the same thing, and that an instantaneous shift in reference frame is still an impulse acceleration.

Fundamentally, the paradox is resolved because the two twins travel along worldlines of different spacetime length, rendering the "paradox" an obvious consequence of geometry with direct analogy to ordinary Euclidean plane geometry: it is no more "paradoxical" than the fact that the length of a hypotenuse is different from the sum of the lengths of the other two sides of a triangle.

He then proceeds to introduce a preferred reference frame defined by "distant objects", the motion with respect to which is detectable and upon which the results of local experiments depend, "disproving" Einstein's relativity.

Actually, as far as I can tell, he merely shows that you can measure your speed relative to a distant object, and incorrectly infers that the distant object's rest frame is a preferred rest frame.

It's the same mistake that leads some crackpots to insist that the cosmic background radiation is an "aether" which violates the laws of relativity, because it pervades the universe and we can measure our motion with respect to a CMBR-isotropic frame.

I am at a loss to explain what the author thinks probability distributions of speeds and relative entropies have to do with it.

As an engineer I'm wincing with the rest of you, but, Chad, lighten up on the physic's kook = engineer line of reasoning. There's a certain arrogance and hubris that just pisses me off when physicists look down there noses at mere engineers...as if we have trouble understanding real physics.

I thought the problem of the rigid disk in SR had more to do with rigidity — that you can't spin a disk up to speed without violating the Born condition (the limiting case of large Young's modulus). Rotation doesn't idealize well

As an engineer I'm wincing with the rest of you, but, Chad, lighten up on the physic's kook = engineer line of reasoning.

I wasn't trying to say that engineers are kooks-- though I did leave that interpretation open-- but rather noting that he's not a physicist, but is claiming to have solved an outstanding problem in physics.

A physics professor making grand pronouncements about problems in biology would also be a kook signifier. What matters is that the problem under discussion is outside the training of the person making the announcement.

I was very close to sending you that link, too, because even as an engineer who had *lousy* relativity and QM training in school, and whose attempts to properly re-educate himself ended (with some success, I think) about eight years ago... I thought that press release was rather dorky, too.

Christ, the twin's paradox is straight SR. It falls directly out of some not-obvious, but straight-forward geometry, and I really suspect I could solve numerical problems about it from first principles instead of just crunching formulas. In short, once you get your head around the geometry, it makes sense. And if I can understand it, what's this guy's excuse?

Jonathan vos Post wrote:
Yes, Special Relativity doesn't work. Makes it imposssible for a wheel to revolve. We know that. Einstein knew that. That's why he invented General Relativity.

Huh? I'm not quite sure what you're getting at, but I am sure that turning on gravity doesn't make it any easier for wheels to turn.

C'mon, anon. Follow Blake Stacey's hotlink. Really cool, though my prolonged discussions with Kip Thorne and other physicists tell me that the problem is not a big deal, if you can tolerate long messy equations, and be willing to accept good numerical simulation results.

Kak's website has a "High resolution picture for press". That should tell you something...

Jonathan Vos Post wrote: "space shuttle ... travels near the speed of light" -- that's not the Space Shuttle that I worked on at NASA.

Correct. That one goes 25 times the speed of light. They wouldn't have put it on the Headline News crawl if it wasn't true.

"Kak's solution assumes that the universe has the same general properties no matter where one might be within it"

Isn't that simply a very loose statement of one aspect of relativity - that the laws of physics are the same regardless of the origin of one's reference frame? Actually , isn't that just a roundabout way of saying 'conservation of momentum'?

The problem with this statement is not just that the twin paradox is resolved and no problem - it's that there's probably a half-dozen ways, if not more, to resolve it without issue in the context of special and general relativity, and they're all in agreement. Taylor and Wheeler's Spacetime Physics is a good source for this. I just lectured on the twins in class today. I call 'kook'!

It would be great if some sciencebloggers got hold of the paper as it appears in the "International Journal of Theoretical Physics", and gave a thorough review of the actual content of the paper, without any regard to who wrote it.

It is basically the same as the version in arxiv, but the one in the journal may have some changes and it also has a formal stamp of approval by virtue of peer review. I've read it; and it is excruciatingly bad -- how it got past review is the major question I have on the whole fiasco.

The IJTP online paper is DOI 10.1007/s10773-006-9281-2

I was able to get it through a University library with a subscription. A direct link to the journal is http://www.springerlink.com/content/e4670q159464473r/?p=e2bde9490c89476…

The arxiv paper was linked above. It is http://arxiv.org/abs/physics/0605199

Jonathan:

Anon. is right: special relativity has no problem with revolving wheels. It has a problem with infinitely rigid revolving wheels, but in reality, no such wheel exists or even can exist, so that's hardly an objection to the validity of SR. Switching to general relativity doesn't solve anything: you can't have infinitely rigid wheels there, either, and even if you could, no such wheels exist.

The issue is not "infinitely rigid" whee4ls, but "rigidly rotating wheels."

Very subtle difference. Several brilliant mathematicians and physicists addressed the problem.

The page linked to (via John Baez) has more, and I had siscussed what was claimed to be an unsolved proble, on that page with current experts.

There are quite a few fringe papers out there that are a little similar to this one. The sociological problem with explaining SR to these people is that SR requires that the believer assume that all frames of reference are equivalent. This grates against a natural inclination to believe that there is a unique frame of reference. Maybe the thinking goes something like "the universe is unique, therefore there should be a unique reference frame for the activity in it".

The fringe viewpoint is not kooky as such. One can always suppose that there is a preferred reference frame but that to detect it requires energies that are beyond our ability to perform. This postulate cannot be disproved using usual SR.

Our experiments deal only with particle energies far, far, lower than the Planck energy. One can suppose that there are more or less infinitely many ways of continuing our physics to Planck energies. Since a preferred reference frame at high energies cannot be disproven, one must include in the set of continuations all the continuations that involve a preferred reference frame (and violate Lorentz symmetry at high energies). My guess is that there are a lot more continuations that violate Lorentz symmetry than there are that obey it.

Jonathan:

A "rigid wheel" in theoretical physics is different from a real wheel. No real wheel moves "rigidly", according to Born's (or other) definitions. Special relativity has no problem with real "rigid" wheels, such as train wheels, gears, etc. There is an interesting literature on what constitutes an acceptable definition of "rigid rotation" in special relativity (there is a nice Wikipedia history of the literature), but it is irrelevant to the behavior of real wheels which actually exist. The Relativity FAQ page you keep citing supports this; you have misunderstood its implications.

" The Relativity FAQ page you keep citing supports this; you have misunderstood its implications."

Then so has John Baez, with whom I discussed this by email. Then so is Prof. Kip Thorne at Caltech, with whom I discussed this face-to-face.

In none of this was Subhash Kak in the loop, nor should he be, nor does he likely care nor understand. But thanks for taking the time to check it out. Fascinating concepts.

some weeks ago I had to referee a paper about paradoxa in SR. I am very relieved to see that this discussion is *not* about the paper I refereed. without going into the details, the author claimed he had solved all paradoxa in SR. for sure he did, but he did it by essentially removing SR. and voila, suddenly he understood everything. too bad that SR has been pretty well confirmed. anyway, the problem was that the paper was such a confusingly written mess of thought-experiments that I had to take apart the whole thing to find out what he had actually done. in the end I was annoyed, for me it was a complete waste of time. I wonder when it started that scientists began to work with thought-experiments if there actually are REALLY experiments to look at?!

sometimes I think it would help if we'd just stop calling these things 'paradoxa' because it leaves people with the impression that there is something we haven't understood in SR.

Best,

B.

Is "International Journal of Theoretical Physics" a reputable journal...? How did this get through peer review?

The Definitive Answer to the Twin Paradox:

(And yes, I know what I am opening myself up to with a title like that; and god forbid if I make a mistake in this :-) ).

Pick an inertial frame, any inertial frame. Take your two twins and start them off together. Then let them do whatever movement you want; either, or both, can follow various near-luminal tracks. At the end, finally bring them back together again. Which one is older?

What you do is, for each twin, figure out his proper time. You do this by integrating ds over his path (in the inertial frame that you picked) over the course of the two flights. ds is of course defined by

ds^2 = dt^2 - dx^2 - dy^2 - dz^2.

You can parameterize your integration however you like.

During their flight, while they are not together, it is always possible to find some other inertial frame in which one twin is older than the other (and, of course, vice versa). Always. (You find their current age in this frame by integrating the path up to the current time, as time is defined in that inertial frame.)

However, once you bring them back together and compute the total proper time for each, you will get one and only one result that tells you which is the older twin. And you will get the exact same result (with the exact same ages) regardless of what inertial frame you initially chose.

That is because the proper time is an invariant. It is invariant because it doesn't change as you move from one inertial frame to another (unlike specific coordinates, like time). That's why it's called an invariant. And it is invariant because it is a true scalar quantity, unlike the 4-vector quantity, space-time.

There is no paradox.

Jonathan:

I am quite certain that neither Baez nor Thorne claimed that real, physically realizable disks, which are subject to internal stresses and deformatins, obey an idealized conception of "rigid rotation" such as Born rigidity.

Ambitwistor: That's true. The web site maintained by Don Koks (not to be confused with Kak!) for John Baez says, however, just before the references:

"To settle the question definitively, it seems one has to perform a full-blown, hairy GR calculation. Perhaps someone has done this; perhaps someone has turned the vague notion of 'infinitely rigid' into a formula for a stress-energy tensor, plugged that into the Einstein field equations, and solved. If the Gentle Reader knows of a reference, please let me know."

That suggests strongly that the solution for a non-ideal rotating disk in GR, being accelerated from motionless to spinning, which induces all sorts of time-dependent distortions, has NOT yet been solved.

Baez and Koks agreed that this meant no such solution had been derived by anyone they knew or could find in the literature. I discussed with several physicists whether or not we should, as a team, solve this "full-blown, hairy GR calculation."

Kip Thorne, whom I have known since the 1960s, told me (to paraphrase):

(1) True, nobody has done that hairy solution;

(2) Who cares?

(3) It can be ground out by symbolic math software (such as Mathematica) to any sufficient approximation, once properly formulated. But the output will indeed be very long and very messy and very unlikely to give interesting insights.

(4) The non-ideal solid rotating wheel can be done numerically by either of several applications packages, including those of his colleagues.

(5) Stars, galaxies, black holes, are not solid anyway, and their GR rotations and distortions and gravity waves are numerically and semi-analytically solved, so again, who cares about solid general relativistic wheels?

It's a harder problem than the Twin Paradox which is not a paradox. Sorry if I was unclear.

As Robert Heinlein said: "A paradox can be paradoctored."

It's true that nobody (to my knowledge) has dervied a full analytic solution for a "realistic" torqued disk in GR. That does not mean, however, that either GR or SR cannot handle "real" rotating disks. Both of them can. Of course, the SR solution neglects the gravitational field of the disk, which will become important for very relativistic systems, but is not necessary in general to describe a realistic rotating disk. This is contrary to your claim that it is impossible for wheels to rotate in SR.

Kip Thorne's response is pretty much what I would say if asked about working out an analytic GR solution to a rotating disk.

I think, Ambitwistor, that we agree far more than we disagree. I apologize for any lack of clarity in my writing, and (for that matter) in my thinking.

SR ignores gravitational field, and gravitational radiation carrying away quadrupole and higher terms of the aspherical pulsating twisting, wriggling "solid" disk. SR also ignores the Stress which itself deforms space-time.

"Realistic rotating disk" begs the question of what we mean by "realistic." That has proven, even here, to depend upon assumptions.

Of course there are no "rigid" rods and "rigid" disks as conceived in the 19th century. Of course SR claims that rigid disks can't revolve. There was a flurry of papers published in 1905 and 1906 to address this. Clever pseudosolutions: spokes of wheel curve into "integral signs", wheel buckles, and so forth. One author wrote that in SR rigid wheels simply can't turn. Einstein wrote that this solution was correct. In the real world, wheels turn.

There is a gap between the real world and science, and between science and axiomatic mathematics.

There is many a slip between cup and lip.

Jonathan Swift (1667-1745):

So, naturalists observe, a flea
Has smaller fleas that on him prey;
And these have smaller still to bite 'em;

["a Rhapsody"]

Great fleas have little fleas upon their backs to bite 'em,
And little fleas have lesser fleas, and so ad infinitum.
And the great fleas themselves, in turn, have greater fleas to go on;
While these again have greater still, and greater still, and so on.

[De Morgan: A Budget of Paradoxes, p. 377]

Big wheels have bigger wheels
who fund them and who bite 'em
small wheels have smaller wheels
so on, ad infinitem

But none of these, as Einstein says,
can rotate if it's rigid
heat energy will warm them up
if they begin too frigid

Rigidity's impossible
if wheels are to revolve
GR can tell us everything
but this is hard to solve.

[me, just now]

Explanation of Twins Paradox by Aether Wave Theory (AWT). The AWT reconciles the ancient aether concept with the findings of relativity and Newtonian mechanic by using of the insight, in dense particle system the diffusional patterns are having the character of foam, i.e. can serve for the energy spreading in transversal waves preferably (compare the condensing supercritical vapor as a model of vacuum). For such waves the absolute reference frame is undetectable by the same way, like the underwater motion for the capillary waves at the water surface, which leads to the relativistic phenomena.

DHTML applet animation: http://superstruny.aspweb.cz/images/fyzika/relativity/twins.htm

AVI Movie: http://superstruny.aspweb.cz/images/fyzika/relativity/twins.htm

Jonathan,

I'm not exactly sure what you are claiming about SR and rotating wheels, but as I understand the FAQ entry (which is by Michael Weiss, actually, not John Baez), it's saying that it is an open question as to whether Born rigid rotation is possible in GR; it's clearly impossible in SR. However, I don't take this to be a claim, as you said in your first message, that SR "makes it impossible for a wheel to revolve". I don't think that there is any evidence that GR has any nonnegligible role in the physics of actual wheels.

It seems to me that the issues with a rigidly rotating wheel can be understood, in simpler form, by considering a Born-rigid rod, instead. Suppose you have a rod that is a billion miles long but is light enough to swing around with one hand (a fun toy to have, but I'm sure you could poke your eye out with that thing). What happens when you hold one end and swing it in a slow circle? Obviously, the rod can't remain straight, because then far enough down the rod, the particles would have to travel faster than light. So the rod must bend: the angular velocity of various sections of the rod can't be constant, but must go to zero as you get farther from the center of the rotation.

I think that the rigidly rotating wheel is in the same boat. If you think of a bike wheel, with a bunch of spokes connecting the center hub to the outer rim, then each spoke is an example of my rotating rod. When you try to rotate the wheel, the spokes bend backwards, so that the rim has a smaller angular velocity than the center hub. The wheel can rotate, but only by stretching and deforming.

The issue is not what happens at constant angular velocity. The hard-to-compute part is what happens when there is torque, changing angular velocity, and waves propagating in highly nonlinear ways, that eventually damp out. These waves are limited to the speed of light, and defining the 4-D coordinates is tricky.

Yes, Michael Weiss wrote the page, Don Koks maintains the page, and John Baez links to it. I doubt that Subhash Kak knows any of this.

Stranger than crackpots are those who are (or used to be) experts in one field, pontificating on another field, without being familar with the literature. Not throwing stones from glasshouse, I've made that mistake, and still do at times.

This applies in fiction as well. Professional science fiction writers hate it when a mainstream fiction author thinks they have a brilliant new idea, and publish a novel on it, heedless that it has been done better decades ago in the SF literature, and oin more sophisticated ways since then by those who read the classic.

Any Literature is a networked discussion between writers. You can't step twice into the same conversation. Waves pass through genres and literatures. They're variously called trends, schools, subgenres, revolutions.

And that brings us back to revolutions.

What goes around comes around.

Don Koks emailed me as follows.

============================

Since you all got that email, maybe you all have an interest in the
subject of rotating wheels. First, I only read the faq for the first time
after receiving Jonathan's email, so I was a little surprised to see
"Baez and Koks agreed that this meant no such solution had been derived
by anyone they knew". (Doesn't anyone pause to take note of who the
authors of these faq entries are?)

Anyway, my take on the wheel is this. I see no reason to invoke GR.
SR is a self-consistent theory that shouldn't need excursions into GR
for help in solving its conundrums. I think the main difficulty with
rotation is that it's very hard to draw pictures of planes of
simultaneity, and thus it's hard to develop a good feel for the subject.

However, since you are all probably familiar with the "pole in the
barn" conundrum, let me put a new spin on that old story.

Suppose we -could- make a wheel that was spinning relativistically.
Perhaps it was spun up by attaching micro-rockets to each of its atoms,
and then having each burn appropriately to allow the wheel to attain an
unbuckled spin.

In that case, let's build a barn around the wheel, completely enclosing
it. Then we arrange for a pole vaulter with an appropriately long pole
to come running into the barn at the same speed as that of the wheel's
rim, with his pole now immensely Lorentz contracted. As he nears the
spinning wheel, he is momentarily at rest with the nearest piece of its
rim, so he locks his pole into conveniently placed hooks on the rim.
His pole barely takes up, say, 50 of the wheel's circumference. He then
hangs on for the ride, goes sailing around the wheel through a good
180o, completely inside the barn, then comes out the other side.

Now of course, we ask what the pole vaulter made of all that. How did
he fit inside the barn when his pole never touched the walls?
Presumably that could not have happened, so this would seem to indicate that
there is something impossible about the setup I've just described.
Perhaps we can conclude that it's impossible to have such a spinning wheel.

Regards,
Don