tag:blogger.com,1999:blog-22973357.post2236597761458717023..comments2014-10-22T04:52:38.169-04:00Comments on Backreaction: The Equivalence PrincipleSabine Hossenfelderhttps://plus.google.com/111136225362929878171noreply@blogger.comBlogger104125tag:blogger.com,1999:blog-22973357.post-80089189655621265392008-09-08T21:09:00.000-04:002008-09-08T21:09:00.000-04:00A closed timelike loop allows you to go back to a ...A closed timelike loop allows you to go back to a point in space <I>and time</I>. That means it is a curve of non-zero length on which you'd have your own eigentime, but you could re-visit a time in the past. It causes the usual time-travel conundrums and is generally considered to be something you better avoid in your theory. Best,<BR/><BR/>B.Beehttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-90179317839465732132008-09-08T21:05:00.000-04:002008-09-08T21:05:00.000-04:00Hi Bee,You said: unless your spacetime allows clos...Hi Bee,<BR/>You said: <I>unless your spacetime allows closed timelike loops you will have to accelerate one of the twins to get them to meet again which breaks the symmetry</I><BR/><BR/>What do closed timelike loops do? I am trying to figure out the Magellan variation of the paradox, the one with cylindrical universe. Can you please help? <BR/>Thanks!<BR/>AditiStargazerhttp://www.blogger.com/profile/16482382083784806186noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-59280710888792683052008-08-28T20:48:00.000-04:002008-08-28T20:48:00.000-04:00http://www.blogodoom.com/images/girls_with_math_on...http://www.blogodoom.com/images/girls_with_math_on_backs.jpg<BR/><BR/>My choice of general relativity continues to be correct.eric gissehttp://www.blogger.com/profile/10598878490537720448noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-84613760524950455762008-08-22T21:30:00.000-04:002008-08-22T21:30:00.000-04:00HiBee,very nice explanation.Btw since you write ex...Hi<BR/>Bee,<BR/>very nice explanation.<BR/>Btw since you write excellent articles you should<BR/>blog on the speed of gravity controversy <BR/><A HREF="http://physics.wustl.edu/cmw/SpeedofGravity.html" REL="nofollow">in 2003 </A> I'd like to know your take on it.Shantanunoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-42318759043217851742008-08-22T12:35:00.001-04:002008-08-22T12:35:00.001-04:00No time to read all these comments, but an excelle...No time to read all these comments, but an excellent place to learn about the twin paradox is in Schutz's <A HREF="http://www.amazon.com/First-Course-General-Relativity/dp/0521277035/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1219422652&sr=8-2" REL="nofollow">book</A>.<BR/><BR/>Also, take a look at the nice front cover (and explanation inside) of Koks' <A HREF="http://www.amazon.com/Explorations-Mathematical-Physics-Concepts-Language/dp/0387309438/ref=sr_1_1?ie=UTF8&s=books&qid=1219422812&sr=1-1" REL="nofollow">book</A>.Christinehttp://egregium.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-69916951243477377922008-08-22T12:35:00.000-04:002008-08-22T12:35:00.000-04:00No time to read all these comments, but an excelle...No time to read all these comments, but an excellent place to learn about the twin paradox is in Schutz's <A HREF="http://www.amazon.com/First-Course-General-Relativity/dp/0521277035/ref=pd_bbs_sr_2?ie=UTF8&s=books&qid=1219422652&sr=8-2" REL="nofollow">book</A>.<BR/><BR/>Also, take a look at the nice front cover (and explanation inside) of Koks' <A HREF="http://www.amazon.com/Explorations-Mathematical-Physics-Concepts-Language/dp/0387309438/ref=sr_1_1?ie=UTF8&s=books&qid=1219422812&sr=1-1" REL="nofollow">book</A>.Christinehttp://egregium.wordpress.com/noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-10977954613683219062008-08-19T11:05:00.000-04:002008-08-19T11:05:00.000-04:00Reductionism paved the way for Emergence. Emergenc...Reductionism paved the way for Emergence. Emergence from reductionism, is creatively free.<BR/><BR/>A proposition then:These two avenues exist in the idea of "The Equivalence Principle?" At the "same time."Platohttp://www.blogger.com/profile/00849253658526056393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-25543522980036966602008-08-18T14:41:00.000-04:002008-08-18T14:41:00.000-04:00Dr Who.Please write down a prediction of General R...Dr Who.<BR/><BR/>Please write down a prediction of General Relativity that cannot be derived from the Spin 2 propagating in a flat background formalism.<BR/><BR/>You cannot of course, because the two are equivalent, as they must be. In fact, entire textbooks written by Nobel Laureates treat the subject.<BR/><BR/>Which language you choose to express physics in, is inconsequential. Sometimes geometrical langauge is more useful (for instance to look at horizons), and other times pure field theory is more useful (gravitational waves, numerical solutions etc)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-69513297112443010642008-08-18T13:44:00.000-04:002008-08-18T13:44:00.000-04:00“Orin, all of us who take Quantum Mechanics to be ...“Orin, all of us who take Quantum Mechanics to be a complete theory condescend to Einstein.”<BR/><BR/>I don’t know what you have in mind, but if you claim “non-relativistic” QM at that time (without Principle of Local Gauge Invariance) was complete and that QT is complete today you are hopelessly naïve.<BR/><BR/>“That is at the essence of science and mathematics.”<BR/>I guess you condescend to D.Hilbert too.<BR/><BR/>Robert Lauglin:”Physicists have always argued about which kind of law is more important - fundamental or emergent - but they should stop. The evidence is mounting that ALL physical law is emergent, notably and especially behavior associated with the quantum mechanics of the vacuum.”<BR/><BR/>A. Einstein started his “Note about QT” (Electrons et photons, 5-th Solvay) with the statement that he didn’t contribute essentially to QM. Obviously it is self requirement rank 1א physicist (L.D. classification). One should contribute at least on level M. Gell-Mann or/and R.P. Feynman to understand that he is not self appointed God.<BR/><BR/>Hi Orin,<BR/><BR/>“We are not talking about QM here. We are talking about SR.”<BR/><BR/>No. E. Schrödinger: “Matter stands much the same with another system, the electromagnetic field. Its laws are "relativity personified", a non-relativistic treatment being in general impossible.” See also F.J. Dyson “Feynman’s proof of the Maxwell equations”, Am. J. Phys., 58, 209 (1990).<BR/><BR/>P.S. I am not anonymous at 9:13 AM, August 18, 2008.<BR/><BR/>D.Hilbert:” On the contrary I think that wherever, from the side of the theory of knowledge or in geometry, or from the theories of natural or physical science, mathematical ideas come up, the problem arises for mathematical science to investigate the principles underlying these ideas and so to establish them upon a simple and complete system of axioms, that the exactness of the new ideas and their applicability to deduction shall be in no respect inferior to those of the old arithmetical concepts”.<BR/><BR/>In other words it is the famous question of A.Einstein:”What really interests me is whether God had any choice in the creation of the world.”<BR/><BR/>Both are talking about what is known in Geometry as the set of the Principal Postulates. I consider their analog in Physics the following:<BR/><BR/>1) Postulate of Unitarity: determination of the Physics as the general theory of fields-W.R.Hamilton and E. Schrödinger wave mechanics;<BR/><BR/>2) Postulate of Communication/Causality: physical determination of geometry;<BR/><BR/>3) Postulate of Relativity: definition of the action and the inertial systems, determination of the connection between the physics and geometry;<BR/><BR/>4) Postulate of Local Gauge Invariance: determination of the fundamental interactions (mutually interacting physical systems);<BR/><BR/>5) Postulate of Least Action: determination of the dynamical behavior of the physical system (physical analog of the Fifth Postulate).<BR/><BR/>Thus the answer to A. Einstein question is Yes. EP is the empirical fact and must <BR/>be derived deductively within the adequate theory of gravitational interaction.<BR/><BR/>I claim that the presented set is a complete set. The completeness will be verified by the actual realization the unification of all fundamental interactions program. The Postulate of Relativity is an origin, cradle of modern physics. The completeness will be proved through the attempts to reduce it.<BR/><BR/>Thank you all.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-21599235656026037102008-08-18T13:41:00.000-04:002008-08-18T13:41:00.000-04:00Proper time to quote John Archibald Wheeler. Well,...Proper time to quote John Archibald Wheeler. Well, somebody's got to.<BR/><BR/>"Matter tells spacetime how to curve; spacetime tells matter how to move."<BR/><BR/>As to Poe and Dodgson, I'll add that Jonathan Swift wrote that Mars had two small moons, one so close that it rises in the West and sets in the East, many years befor Asaph Hall discovered Phobos and Deimos.<BR/><BR/>Finally, I'm biased because I've loved my wife since I met her about 24 years ago, but perhaps the sexiest thing about her is that she is a Physics professor.<BR/><BR/>-- Prof. Jonathan Vos Post<BR/><BR><BR><BR/>http://magicdragon.comAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-7560084377248904702008-08-18T12:57:00.000-04:002008-08-18T12:57:00.000-04:00Arun: "Sigh, I'll try one last time."I don't know ...Arun: "Sigh, I'll try one last time."<BR/><BR/>I don't know Arun, this seemed pretty intentional to me, to say the least.Giotisnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-14086139559729720012008-08-18T12:45:00.000-04:002008-08-18T12:45:00.000-04:00There was no intent to be condescending and I only...There was no intent to be condescending and I only apologize for where I added to the confusion.<BR/><BR/>-ArunArunhttp://www.blogger.com/profile/03451666670728177970noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-91572900938803667192008-08-18T12:39:00.000-04:002008-08-18T12:39:00.000-04:00Orin: "This interpretation goes hand in hand with ...Orin: "This interpretation goes hand in hand with Einstein's original 'Machian' ideas and motivation for SR, and one of the reasons I have always found SR beautiful. In other words, reality is defined by the motion of objects relative to each other, not relative to some 'objective' coordinate system."<BR/><BR/><BR/>Orin, this is GR you are talking about not SR. In GR this is formulated with the principle of general covariance i.e. GR is invariant under active diffeomorphisms. This means that it doesn't need a background or a frame if you like. You could say that the Gravitational field is the background. BUT SR still needs an inertial frame extended throughout all space time to work. During the turnaround of the twin he changes inertial frame. That's the whole point. <BR/><BR/>I think that is cause of all the misunderstandings.<BR/><BR/><BR/>Bee: Could you please clarify the thing about the Wiki calculation. Do you find it wrong? To me it looks fine.<BR/><BR/>BRGiotisnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-16117727157315301462008-08-18T12:31:00.000-04:002008-08-18T12:31:00.000-04:00OK, better worded: Why is the field from an extend...OK, better worded: Why is the field from an extended planar mass curved (if it is, and in space-time in the net since of course it is still a parallel field) rather than the flat field of the Rindler elevator? txNeil'http://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-69803102155258800132008-08-18T12:27:00.000-04:002008-08-18T12:27:00.000-04:00OK thanks Bee. For anyone who wants to try, this i...OK thanks Bee. For anyone who wants to try, this is perhaps the more cogent question: <I>why</I> is the allegedly curved g-field (if G. Egan was right ...) of an extended planar mass not like the elevator flat field?<BR/><BR/>PS: thanks andrew for excerpt from Lewis Caroll about the EP. Perhaps even more "amazing", Edgar Allen Poe first came up with the modern-like explanation of how to avoid the Olbers' paradox in 1848.<BR/><BR/>From http://en.wikipedia.org/wiki/Olbers%27_paradox<BR/><BR/><I>Edgar Allan Poe was the first to solve Olbers' paradox when he observed in his essay Eureka: A Prose Poem (1848):</I><BR/><BR/> "Were the succession of stars endless, then the background of the sky would present us a uniform luminosity, like that displayed by the Galaxy – since there could be absolutely no point, in all that background, at which would not exist a star. The only mode, therefore, in which, under such a state of affairs, we could comprehend the voids which our telescopes find in innumerable directions, would be by supposing the distance of the invisible background so immense that no ray from it has yet been able to reach us at all."[1]<BR/><BR/>However, IIRC there is an odd mathematical paradox in which one can evade the Olbers paradox by having ever more attenuated "hierarchies" of stars and galaxies, so the integral of star surface interception going out to infinity actually converges - true?Neil'http://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-71624180048176411412008-08-18T12:18:00.000-04:002008-08-18T12:18:00.000-04:00Hi Orin,Well, I am genuinely sorry if I misunderst...Hi Orin,<BR/><BR/>Well, I am genuinely sorry if I misunderstood you. It seemed to me you were trying to say there's something funny with the explanation we've been trying to give you. If not, then I think the issue is settled anyway. Thanks for your interesting comments. Best,<BR/><BR/>B.Beehttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-15411077865734453442008-08-18T12:07:00.000-04:002008-08-18T12:07:00.000-04:00Hi Bee,The connection of both lines in that point ...Hi Bee,<BR/><BR/><I>The connection of both lines in that point you dislike does matter. As I said already above though I don't know why you're hanging yourself up on this unphysical limit with infinite acceleration in one point - just because the limit looks unintuitive? There is nothing 'hand-wavy' here, there are no 'subleties' and there is no paradox.</I><BR/><BR/>Wow. No. This is exactly what I meant earlier when I said that if one tries to press some of these points they end up being condescended to with dismissive blanket statements like "there are no subtleties". Also, as I have repeatedly said, I don't in the slightest think there is a paradox at all. I'm pressing a point about an explanation for the paradox, not the paradox itself. Finally, no I'm not pressing the point about the infinite acceleration because the limit looks unintuitive -- it doesn't look unintuitive to me -- I am doing it for simplicity, so as to remove the mathematical contribution due to the accelerating leg of the trip.<BR/><BR/><I>Your 'argument' that sweeping away an apparent paradox that was interesting a century ago is 'condescending' to the founder of the theory is ridiculous. For one, you use it to make your 'worries' more serious, a tactic that's called 'appeal to authority' which doesn't have any scientific merit, so please omit it.</I><BR/><BR/>I disagree. First of all, did you read Arun's posts? They seemed condescending to me (of course you're not a good person to be appealing to given that I think your last post was rather condescending), just from anyone's perspective. I brought Einstein into my statement to be diplomatic -- I was basically saying, "if I were Einstein, would you really formulate your arguments so flippantly?" Perhaps I was appealing to authority, but more to make a personal point about discourse rather than content.<BR/><BR/>Anyways, this is frustrating, and the conversation should probably be dropped. I can only say that it is unfortunate given that I simply have a genuine curiosity about this matter that I would like to satiate as best I can.<BR/><BR/>Cheers,<BR/>Orinorinhttp://www.blogger.com/profile/13399554077097548978noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-12268523392999632012008-08-18T11:51:00.000-04:002008-08-18T11:51:00.000-04:00hmm, though maybe it should have been 'proper time...hmm, though maybe it should have been 'proper time of the curve' and not 'on the curve'? Sorry if that was confusingly formulated.Beehttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-13687313444801645542008-08-18T11:48:00.000-04:002008-08-18T11:48:00.000-04:00Hi Orin,What Arun and Dr. Who patiently told you i...Hi Orin,<BR/><BR/>What Arun and Dr. Who patiently told you is correct. You apparently also did not quite understand what I initially said. I said the proper time on the curve is continuous in the limit when you squeeze all the acceleration into one point, not about the limit of the point itself. This limiting situation is not identical to having one twin moving away from Earth and somebody else who never was accelerated moving back towards Earth again in some triangle. <BR/><BR/>Dr Who actually said it much better actually than I did: the one curve is a geodesic, the other one isn't. Period. They are not equivalent and can't be made such. The one observer is inertial, the other one isn't. The connection of both lines in that point you dislike does matter. As I said already above though I don't know why you're hanging yourself up on this unphysical limit with infinite acceleration in one point - just because the limit looks unintuitive? There is nothing 'hand-wavy' here, there are no 'subleties' and there is no paradox. <BR/><BR/>Your 'argument' that sweeping away an apparent paradox that was interesting a century ago is 'condescending' to the founder of the theory is ridiculous. For one, you use it to make your 'worries' more serious, a tactic that's called 'appeal to authority' which doesn't have any scientific merit, so please omit it. Second, if we were to argue with the worries and misunderstandings of deceased people we'd never make any progress. <BR/><BR/>Best,<BR/><BR/>B.Beehttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-73954189515335539162008-08-18T11:34:00.000-04:002008-08-18T11:34:00.000-04:00Anonymous,I believe this is responding to your poi...Anonymous,<BR/><BR/><I>I believe this is responding to your point - just as in the Euclidean plane, the lack of a preferred coordinate system doesn't mean we can't draw a triangle.</I><BR/><BR/>Ah, yes. I now realize I misinterpreted Arun's statement. What I am saying: <BR/><BR/>My interpretation of SR was that 'lack of a prefered coordinate system' went beyond what that of the Euclidean plane, in the sense that you <I>can't</I> draw a triangle. I guess the property of not being able to draw a triangle could itself be taken as a the expression of my interpretation of space-time in SR. This interpretation goes hand in hand with Einstein's original 'Machian' ideas and motivation for SR, and one of the reasons I have always found SR beautiful. In other words, reality is defined by the motion of objects relative to each other, not relative to some 'objective' coordinate system. Apparently, as Arun points out, this view may be dated and now naive. I don't know better, as every textbook on SR I have read seems to indicate that the interpretation of SR has not improved since its inception and does nothing to dispel the notion that Einstein was right about the motivations for his theory.<BR/><BR/>Cheers,<BR/>Orinorinhttp://www.blogger.com/profile/13399554077097548978noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-84979338615456721362008-08-18T11:31:00.000-04:002008-08-18T11:31:00.000-04:00Hi Cecil,For one, the way I have stated the EP it ...Hi Cecil,<BR/><BR/>For one, the way I have stated the EP it doesn't speak about inertial and gravitational masses. As to your question about the definition of gravitational mass, for that you'd need the field equations. To begin with please note it is generally not only a mass that gravitates but the stress-energy tensor, it is just for testparticles in the appropriate limit that one has this simple case. If you couple something to gravity, the field equations will tell you how it couples, and that then how tells you what the gravitational mass (energy) is. Roughly speaking you'd have to compare the graviational to the kinetic energy tensor (which is usually the same due to the EP). I don't see how the definition of gravitational mass would have any consequences except for gravity. Best,<BR/><BR/>B.Beehttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-10422174560012667942008-08-18T11:24:00.000-04:002008-08-18T11:24:00.000-04:00Hi Neil,Well, I think you've answered your own que...Hi Neil,<BR/><BR/>Well, I think you've answered your own question. A spacetime either has a curvature or it hasn't. I don't know how you want to 'model' a spacetime with curvature by one without. As to the differences, I don't know, I'd compute the geodesics and see what they do. Best,<BR/><BR/>B.Beehttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-75953646643317834422008-08-18T11:17:00.000-04:002008-08-18T11:17:00.000-04:00Bee, your outline of the Equivalence Principle fit...Bee, your outline of the Equivalence Principle fits in with my understanding (based on middle-brow explanations) that a "uniform" and parallel gravity field is just like the environment in an elevator with constant (proper) acceleration. Even then I came to appreciate the need to adjust for "Rindler coordinates" arising from the Lorentz contraction of the accelerating framework. That led to hyperbolic motion of the frame and position-dependent proper acceleration:<BR/>a_0 = X/c^2. The question I'm developing to is whether the field around an extended planar mass is like that of the "elevator" in EP explanations.<BR/><BR/>Hence I liked to play with various scenarios in Rindler "elevators" to see if odd things happened in g-fields. One thing I came up with (original? - in 1979) was that a gyroscope being moved rapidly across the floor of a RE would precess (due to the gyroscope orientation being "Thomas precessed" relative to the standard of floor orientation.) Has anyone heard about that?<BR/><BR/>I always assumed (makes an ASS out of U and ME!) that RE field would also define g-field environment above a very extended (not infinite!) planar mass distribution. But I got into a big argument in the Cosmic Variance thread at http://cosmicvariance.com/2007/11/13/arxiv-find-universal-quantum-mechanics/#comments about issues like gravitomagnetism and the manner which objects, starting out very past and parallel to the planar mass, fall to the floor. I thought I could use the intuitive EP/RE understanding, but was told by Greg Egan there that I could not (if you can skim that thread it would help to get the point.) Significant "money quote" from Greg:<BR/><BR/>><BR/>The metric I get from the weak-field approximation described in Misner, Thorne & Wheeler’s Chapter 18, applied to a planar mass distribution of area mass density sigma, for a square mass of half-side-length H, is:<BR/><BR/>ds^2 = (-1+h) dt^2 + (1+h) (dx^2 + dy^2 + dz^2)<BR/><BR/>where h = ...<BR/>...<BR/><BR/>This space-time is not flat. It has a Riemann curvature tensor with components that are first-order in sigma (as opposed to the Einstein and Ricci tensors, which are second-order in sigma, i.e. zero in the linearised approximation — as they must be in order to be vacuum solutions).<BR/>> [end quote since I don't have time for HTML games]<BR/><BR/>OK, quick scoop and challenge: Is it really true that the g-field above an extended planar mass (intuitively expected to be like the elevator field to the extent we don't move vertically enough to get the hyperbolic variations in "g") really can't be modeled by the Einstein/Rindler elevator field of common understanding, after all? If so, what implications and notable exceptions and outcomes? Thanks, and for your patience also.Neil'http://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-53051728510856076932008-08-18T09:56:00.000-04:002008-08-18T09:56:00.000-04:00Descendants?Reflections on RelativityIn any case, ...Descendants?<BR/><BR/><A HREF="http://www.mathpages.com/rr/s8-06/8-06.htm" REL="nofollow" TITLE="On Gauss's Mountains">Reflections on Relativity</A><BR/><BR/><I>In any case, it seems reasonable to agree with Buhler, who concludes in his biography of Gauss that "the oft-told story according to which Gauss wanted to decide the question [of whether space is perfectly Euclidean] by measuring a particularly large triangle is, as far as we know, a myth."</I>Platohttp://www.blogger.com/profile/00849253658526056393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-46563098383767778772008-08-18T09:54:00.000-04:002008-08-18T09:54:00.000-04:00Cecil Kirksey: Even though my involvement in that ...Cecil Kirksey: Even though my involvement in that question about EP operating on different 'types' of matter was about 15 yrs ago (I've not kept up with the latest research), I don't think the answer is clear yet. See my <A HREF="http://cosmicvariance.com/2006/05/18/dark-energy-task-force-report/#comment-23337" REL="nofollow">old comment</A> on cosmicvariance and a more recent <A HREF="http://cosmicvariance.com/2008/07/24/matter-v-antimatter-i-the-baryon-asymmetry/" REL="nofollow">post by Mark</A> at the same blog.amaragrapshttp://www.blogger.com/profile/15769062084934190681noreply@blogger.com