jlg@lanl.ARPA (Jim Giles) (03/14/86)
In article <446@3comvax.UUCP> michaelm@3comvax.UUCP (Michael McNeil) writes: >Returning to Ken's original point, which started off this whole series >of articles, in the above reference Bertrand Russell writes as follows: > > But in the modern theory the question between Copernicus and > his predecessors is merely one of convenience; all motion > is relative, and there is no difference between the two > statements: `the earth rotates once a day' and `the heavens > revolve about the earth once a day.' The two mean exactly the > same thing, just as it means the same thing if I say a certain > length is six feet or two yards. Astronomy is easier if we > take the sun as fixed than if we take the earth, just as > accounts are easier in decimal coinage. {Signet, pp. 13-14} Whatever Bertrand Russell's qualifications in mathematics are, no one would ever accuse him of being a great physicist. One of the paramount features of General Relativity is that the laws of physics should appear the same in ALL reference frames. In a reference frame which is fixed with respect to the average motion of the nearby stars, those stars all appear to be traveling with low (relatively) velocities. In a 'reference frame' which is fixed to the spinning Earth, the nearby stars appear to be traveling MUCH FASTER than the speed of light. (Consider A- Centauri: radius of 'orbit' around Earth is 4.2 light years, it 'orbits' once per day, total distance traveled per day is 2*4.2*PI light years or about 26 light years per day.) The consequences of stars being tachyons in one 'frame' and not being tachyons in the other would cause the observers in the two frames to come to different conclusions about the laws of physics in Earth local space (that is, the only way to reconcile the two observations is to assume that there is a space-time singularity between the two observers, but when they go to look they won't find one). The bottom line is that rotation is LOCALLY discernable and is therefore NOT a property of Einstein's reference frames (whether they are lorentz frames or not). One way of locally measuring rotation is with a foucault pendulum (which you even mentioned). Meanwhile ALL Einstein frames are LOCALLY indistinguishable from lorentz frames. For the definition of 'frame' and 'local' I suggest you read the first few chapters of MTW ('Gravitation') again. I just did - fascinating stuff! J. Giles Los Alamos
gwyn@brl-smoke.UUCP (03/15/86)
In article <446@3comvax.UUCP> michaelm@3comvax.UUCP (Michael McNeil) writes: >Come on, people! It isn't just the misspelling, it isn't just the >strong language (whether you call it name-calling or not) -- Karl's >argument is completely wrong! Einstein's theory of general relativity >was published more than seventy years ago (1915) -- and it certainly >*does* allow non-inertial reference frames! Only Einstein's *special* >relativity (1905) is restricted in its application to inertial frames. The idea that centrifugal force can be explained by the inductive effect of all matter in the universe is known as Mach's principle. This principle appears to be necessary for any theory that claims that there is no absolute motion. Einstein originally supported Mach's principle and tried to deduce it from general relativity, but in later years he became less convinced of its necessity. The concepts of "absolute", "relative", and "motion" are more subtle than they appear, it turns out. Because of the emphasis on teaching the special theory of relativity, far too much emphasis is placed on so-called "inertial frames" of reference. From a more general viewpoint, one has an inertial frame (locally) whenever the metric is diagonal. It is not always possible to diagonalize the metric by a differentiable change of coordinates, let alone one corresponding to a "motion"; this observation has led to attempts to extend general relativity using a more general notion of metric. > 39.2. Metric Theories of Gravity > > Two lines of argument narrow attention to a restricted class > of gravitation theories, called *metric theories*. It should be noted that Einstein and other early workers in relativity theory determined that the general theory was incomplete, and attempted to extend it in various ways. Some of these attempts generalized the idea of metric, but the most successful theories were formulated in terms of the affine connection of the tangent bundle, with metric introduced only comparatively late in the formal development of the theories, as a derived notion or as an independent-but-related notion. My favorite formulation of the general theory, Schr"odinger's, introduces the metric purely as shorthand for an entity that can be produced from the affinity field. The emphasis on metric has its origins in the Gauss/Riemann development of differential geometry; related concepts have spread throughout linear mathematics. The main complaint I have against Misner/Thorne/ Wheeler is that the book does not adequately prepare one for understanding or investigating the more general theory, which does not track the usual development of differential geometry. The "pure affine" field theory yields a number of interesting symmetries beyond those of general relativity. These are expected to correspond to physical laws other than the gravitational field equations. This was the motivating idea behind the "unified field theory" program pursued by Einstein and others, which has almost universally been called a failure by textbooks. If one compares the structure of theories such as Einstein/Straus/Kaufman with present-day non-Abelian gauge field theories, it becomes apparent that Einstein as usual knew what he was doing and was simply ahead of his time.
gsmith@brahms.BERKELEY.EDU (Gene Ward Smith) (03/15/86)
In article <424@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >In article <446@3comvax.UUCP> michaelm@3comvax.UUCP (Michael McNeil) writes: >>Returning to Ken's original point, which started off this whole series >>of articles, in the above reference Bertrand Russell writes as follows: >> >> But in the modern theory the question between Copernicus and >> his predecessors is merely one of convenience; all motion >> is relative, and there is no difference between the two >> statements: `the earth rotates once a day' and `the heavens >> revolve about the earth once a day.' The two mean exactly the >> same thing, just as it means the same thing if I say a certain >> length is six feet or two yards. Astronomy is easier if we >> take the sun as fixed than if we take the earth, just as >> accounts are easier in decimal coinage. {Signet, pp. 13-14} > >Whatever Bertrand Russell's qualifications in mathematics are, no one >would ever accuse him of being a great physicist. One of the paramount >features of General Relativity is that the laws of physics should >appear the same in ALL reference frames. In a reference frame which >is fixed with respect to the average motion of the nearby stars, those >stars all appear to be traveling with low (relatively) velocities. In a >'reference frame' which is fixed to the spinning Earth, the nearby stars >appear to be traveling MUCH FASTER than the speed of light. (Consider A- This "faster than light" motion is merely conventional. It has NOTHING WHATEVER to do with tachyons or real faster than light motion. Russell is correct (almost) in his quote above. You are dead wrong. Try writing a rotating coordinate frame in GR (not hard) and you will see. >For the definition of 'frame' and 'local' I suggest you read the first few >chapters of MTW ('Gravitation') again. I just did - fascinating stuff! You need to do more than read it (we both have, apparently). You need to understand it. Read it again, using your noggin. ucbvax!brahms!gsmith Gene Ward Smith/UCB Math Dept/Berkeley CA 94720 Fifty flippant frogs / Walked by on flippered feet And with their slime they made the time / Unnaturally fleet.
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/15/86)
In article <424@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >In article <446@3comvax.UUCP> michaelm@3comvax.UUCP (Michael McNeil) writes: >>Returning to Ken's original point, which started off this whole series >>of articles, in the above reference Bertrand Russell writes as follows: >> >> But in the modern theory the question between Copernicus and >> his predecessors is merely one of convenience; all motion >> is relative, and there is no difference between the two >> statements: `the earth rotates once a day' and `the heavens >> revolve about the earth once a day.' The two mean exactly the >> same thing, just as it means the same thing if I say a certain >> length is six feet or two yards. Astronomy is easier if we >> take the sun as fixed than if we take the earth, just as >> accounts are easier in decimal coinage. {Signet, pp. 13-14} > >Whatever Bertrand Russell's qualifications in mathematics are, no one >would ever accuse him of being a great physicist. So? BR's statements were essentially correct. The only possible point to challenge is his assertion that there is 'no difference', but that is a matter of semantics, not physics. > One of the paramount >features of General Relativity is that the laws of physics should >appear the same in ALL reference frames. The laws that are invariant are the ones in covariant form, which is essentially a circular definition. The essence of General Relativity is that space-time is a four-dimensional manifold with a Lorentzian metric, that the laws of physics hold on the manifold in an invariant way, and that local observers can put local frames on the manifold and make measurements that way. The local observers can put ANY coordinate frame they want on it, "rotating" or not. > In a reference frame which >is fixed with respect to the average motion of the nearby stars, those >stars all appear to be traveling with low (relatively) velocities. In a >'reference frame' which is fixed to the spinning Earth, the nearby stars >appear to be traveling MUCH FASTER than the speed of light. (Consider A- >Centauri: radius of 'orbit' around Earth is 4.2 light years, it 'orbits' >once per day, total distance traveled per day is 2*4.2*PI light years or >about 26 light years per day.) This is complete nonsense. The nearby stars in the rotating frame are travelling at a NUMBER which is much larger than the number obtained by measuring light in an inertial rectangular coordinate frame. The fact that the one number in the one frame is bigger than another number in another number is meaningless. Is Alpha Centauri suddenly whipping 9490 times faster than the photons it is omitting in the (apparent) direction of motion? Of course not. The fact that Alpha Centauri is seen moving slower than light in ONE frame means it moves slower than light in ALL frames. > The consequences of stars being tachyons in >one 'frame' and not being tachyons in the other would cause the observers >in the two frames to come to different conclusions about the laws of >physics in Earth local space (that is, the only way to reconcile the two >observations is to assume that there is a space-time singularity between >the two observers, but when they go to look they won't find one). It also leads to natural explanations of the Bermuda triangle, I'm sure. >The bottom line is that rotation is LOCALLY discernable and is therefore >NOT a property of Einstein's reference frames (whether they are lorentz >frames or not). One way of locally measuring rotation is with a foucault >pendulum (which you even mentioned). Meanwhile ALL Einstein frames are >LOCALLY indistinguishable from lorentz frames. The first two sentences are correct. The last one is completely wrong. Frames locally indistinguishable from Lorentz frames are called inertial. In such frames, special relativity as standardly presented is valid. SR can be done in accelerated frames, but care must be taken. But rotation can be detected more generally. For example, in a universe with just one rotating black hole, ie, a Kerr metric, the local geometry is a Kerr geometry, no matter WHERE in the universe you measure. And given enough local information (a Cauchy surface), the entire metric is determined uniquely. >For the definition of 'frame' and 'local' I suggest you read the first few >chapters of MTW ('Gravitation') again. I just did - fascinating stuff! I suggest YOU read the first few chapters again. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
desj@brahms.BERKELEY.EDU (David desJardins) (03/16/86)
In article <1825@brl-smoke.ARPA> gwyn@brl.ARPA writes: > >The idea that centrifugal force can be explained by the inductive >effect of all matter in the universe is known as Mach's principle. >This principle appears to be necessary for any theory that claims >that there is no absolute motion. Am I stupid? I have reread the first sentence above many many times and can't make any sense out of it. In an empty (flat) universe some frames are accelerated and some are not. This is in the absence of any matter. What does "the inductive effect of all matter in the universe" have to do with centrifugal force?? This is not an attack, just a request for explanation... -- David desJardins
jlg@lanl.ARPA (Jim Giles) (03/17/86)
In article <12398@ucbvax.BERKELEY.EDU> gsmith@brahms.UUCP (Gene Ward Smith) writes: >In article <424@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: > >>In article <446@3comvax.UUCP> michaelm@3comvax.UUCP (Michael McNeil) writes: >>>Returning to Ken's original point, which started off this whole series >>>of articles, in the above reference Bertrand Russell writes as follows: >>> >>> But in the modern theory the question between Copernicus and >>> his predecessors is merely one of convenience; all motion >>> is relative, and there is no difference between the two >>> statements: `the earth rotates once a day' and `the heavens >>> revolve about the earth once a day.' The two mean exactly the >>> same thing, just as it means the same thing if I say a certain >>> length is six feet or two yards. Astronomy is easier if we >>> take the sun as fixed than if we take the earth, just as >>> accounts are easier in decimal coinage. {Signet, pp. 13-14} >> >... Russell is >correct (almost) in his quote above. You are dead wrong. Try writing a rotating >coordinate frame in GR (not hard) and you will see. > >>For the definition of 'frame' and 'local' I suggest you read the first few >>chapters of MTW ('Gravitation') again. I just did - fascinating stuff! > > You need to do more than read it (we both have, apparently). You need >to understand it. Read it again, using your noggin. Russell is not even CLOSE to being right. I suspect he was mislead by Mach's principle which explains the origin of momentum as being relative to the distribution of mass throughout space. The fact that momentum is relative in no way implies that the choice between Copernicus and Ptolemy is merely one of convenience. Consider a pendulum swinging freely at the north pole (disregard precession effects that are classical). In classical theory, the plane through which the pendulum swings will rotate once per day when measured relative to the Earth, and it will appear fixed relative to the distant stars (this seems to imply that it is the Earth that is turning). Now according to Mach's principle as applied in GR, the pendulum will be seen to turn relative to the Earth - but not EXACTLY once per day, and it will seem to rotate SLIGHTLY relative to the fixed stars (this is even after ALL classical causes of precession have been eliminated). The emphasized words point out that this is a VERY SMALL (read: unmeasurable with today's technology) effect for the Earth: for practical purposes Copernicus was right. Now, to a small extent, Copernicus was wrong as well: the universe IS rotating around the Earth (at least around a coordinate system with zero measured angular momentum) - but VERY slowly. In either case, a particle attached to a local reference frame in GR would have NO angular momentum (and would, therefore, imply that the reference frame was fixed relative to the distant stars - properly modified by Mach's principle to include the effect of nearby rotating masses). Nothing which is fixed relative to the Earth fits this requirement. Note: I have always said 'local reference frame', which in GR is ALWAYS a Lorentz frame. See box 1.3 in "Gravitation". End of Note. The part of "Gravitation" relevant to Mach's principle starts about page 450. Small flame: Some people on the net seem to think that it is the origin of knowledge or the accuracy of spelling that constitutes a valid argument. This is NOT true: I always have to look up 'Lorentz' when I put it into text - it just doesn't look right to me. Perhaps the difference with me is that I DO bother to look it up so that my contributions to the net are at least spelled right whatever other merits they may have. But, don't tell me something is bogus just because the spelling is wrong. Let the argument stand or fall on its own merit. (Maybe it should be spelled 'Larry' :-) End of small flame. J. Giles Los Alamos
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/22/86)
Follow ups are to net.physics only. In article <556@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >>In article <424@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >>>For the definition of 'frame' and 'local' I suggest you read the first few >>>chapters of MTW ('Gravitation') again. I just did - fascinating stuff! Actually, the definitions are not in the book. >> You need to do more than read it (we both have, apparently). You need >>to understand it. Read it again, using your noggin. >Note: I have always said 'local reference frame', which in GR is ALWAYS >a Lorentz frame. It is? Do you make this up as you go along? Is it congenital? As a matter of fact, all GR frames are Lorentzian, which is totally different than saying all frames are Lorentz frames, which, as you admit is what YOU'VE been saying all along. The preference for Lorentz frames IS a mathematical convenience: "Physics is simple only when analyzed locally." There is nothing physical about coordinate systems per se. That is the whole point of emphasizing the geometry of space-time in the first place. And if you do not realize that, then you just do not understand GR at all. A rotating frame is still a frame. It is not a Lorentz frame, but it is still Lorentzian. Why do you think Einstein called it the GENERAL theory? Since it holds under ALL frames, not just the special relativity Lorentz frames. Bertrand Russell IS correct, and I wish you'd stop spewing your nonsense. You are worse than Ted Holden actually: even the non-experts can tell that he spouts gibber, but your misreadings of MTW might confuse a lot of people. > See box 1.3 in "Gravitation". End of Note. Try READING the box, not just looking at it. And the surrounding text: These theorems lend themselves to empirical test in the appropriate, very special coordinate systems: ... local Lorentz coordinates ... in the local Lorentz geometry of physics. However, the theorems rise above all coordinate systems in their content. [pp 19,23] ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
vis@mit-trillian.MIT.EDU (Tom Courtney) (03/25/86)
Hmm, the way a foucalt pendumlum behaves proves that the earth is rotating? I was taught that in school too, but then I read an article claiming that if the universe rotated around the earth, the pendulum would do the same thing. Sorry, I don't remember the article or justifications. Does anyone have a proof, one way or the other?
desj@brahms.BERKELEY.EDU (David desJardins) (03/27/86)
In article <133@mit-trillian.MIT.EDU> vis@trillian.UUCP (Tom Courtney) writes: >Hmm, the way a foucalt pendumlum behaves proves that the earth is rotating? >I was taught that in school too, but then I read an article claiming that >if the universe rotated around the earth, the pendulum would do the same >thing. Sorry, I don't remember the article or justifications. Does anyone >have a proof, one way or the other? Yes, exactly. This is the point that Matt Wiener and others have been trying to make (I hope I can speak for him). From the fact that these two descriptions lead to the same result, we conclude that it is meaningless to say that the universe is rotating about the Earth (since it is equivalent to the simpler assumption that the Earth is rotating). Meaningless but definitely not wrong. For an intuitive (mathematically non-rigorous) derivation of this see MTW pp. 547-49. -- David desJardins
kay@warwick.UUCP (04/24/86)
[Tom Courtney] >>Hmm, the way a foucalt pendumlum behaves proves that the earth is rotating? >>I was taught that in school too, but then I read an article claiming that >>if the universe rotated around the earth, the pendulum would do the same >>thing. [David desJardins] > Yes, exactly. This is the point that Matt Wiener and others have been >trying to make (I hope I can speak for him). From the fact that these two >descriptions lead to the same result, we conclude that it is meaningless >to say that the universe is rotating about the Earth (since it is equivalent >to the simpler assumption that the Earth is rotating). Meaningless but >definitely not wrong. If the two descriptions lead to the same result (I don't disagree with this) then how can one be considered "meaningless" unless we also consider the other to be identically "meaningless"? Surely all we may say is that the two descriptions are restatements of "the Earth and the Universe have relative rotation"? The principle of parsimony may indeed lead us to prefer the first description on grounds of local utility, but it does not allow us to affirm that the second is meaningless. Kay. -- "I AM; YOU ARE; HELLO: all else is poetry" ... mcvax!ukc!warwick!kay