michaelm@3comvax.UUCP (Michael McNeil) (03/12/86)
In article <2874@sjuvax.UUCP> bhuber@sjuvax.UUCP (B. Huber) writes: >In article <2057@jhunix.UUCP> ins_adsf@jhunix.UUCP writes: >>In article <368@ihnet.UUCP> eklhad@ihnet.UUCP (K. A. Dahlke) writes: >>>> 1) According to Einstein, it's relative--there _is_no_such_thing_ as >>>> absolute rest. You _can_ say that the sun goes around the earth; >>>> the math is just easier the other way. >>>> Kenneth Arromdee >>>Oh come on folks!!! The sun (universe) does not twirl around the earth!!! >>>Einstein never even implied such a thing. >>>Motion is relative *only* when considering inertial reference frames, >>>as determined by Lawrence transformations. >>>Rotation is definitely not an inertial reference frame. >>>It is not a matter of mathematical complexity, >>>the earth really does rotate. >>>Put simplistically (as we must when posting to this newsgroup), >>>if the universe spun around the earth, it would fly apart, >>>and even nearby galaxies would be traveling faster than light. >>>Similarly, the earth revolves around the sun, >>>and the solar system revolves within our galaxy. >>>These are not arbitrary conventions, they are facts. >>>The amount of bogus physics in this newsgroup is astonishing. >>> Karl Dahlke >> I don't intend to get involved in the evolution argument, but if the >>universe would fly apart when rotating about the earth, it will just as >>surely disintegrate when rotating about the sun. So that reasoning falls >>apart. Nothing really rotates strictly about anything. >> It is correct that Einstein spoke about inertial reference frames, but >>a note to Mr. Dahlke: name calling begins at home. Refering to Lorentz >>transformations as "Lawrence transformations" shows that your knowledge >>in this field is also "bogus". >> David Fry >What reasoning falls apart? I fail to comprehend the (apparently) >extraordinary leap of logic that is required to reason from the specific >proposition, 'the universe does not rotate around the sun' to the general >proposition, 'nothing ... rotates ... about anything'. Fry owes us, at >least, an elaboration of this argument. > >I cannot see either that misspelling 'Lorentz' nullifies any of Dahlke's >argument, which should be judged on its own merits. {...} > >As to name-calling, I read none of that in Dahlke's article. It is only >natural that someone who is even modestly acquainted with modern physics >would become upset at the plethora of unsupported assertions that appear >in this newsgroup. There is nothing the matter, per se, with being wrong: >having the opportunity to make mistakes is what learning and investigation >are all about. Making an assertion without any support is to maintain >a position solely on one's personal authority. Such a stance is rarely >illuminating. > Bill Huber 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. It's a shame knowledge of Einstein's theory isn't more widespread (especially in net.physics!) so many years after it was published. Though, I suppose, like they say of churches, net.physics isn't a temple for saints, but a hospital for sinners. I imagine it must be the memories of all those undergraduate physics classes, where inertial reference frames were ground into our flesh, never to be forgotten, while terms like "special" (applied to what one knew) and "general" (applied to what one did not know) gradually slip away. I *highly* recommend that people learn *more* about relativity! An excellent up-to-date reference for those with a modicum of college- level physics background is *Gravitation*, by Charles W. Misner, Kip S. Thorne, and John Archibald Wheeler, published in 1973 by W. H. Freeman and Co., San Francisco. This 1,310-page tome declares itself to be "a textbook on gravitation physics (Einstein's `general relativity' or `geometrodynamics')." The book is designed to provide a full-year, rigorous, graduate-level course in gravitation physics -- intending, as it says, "to give a competence in gravitation physics comparable to that which the average Ph.D. {in physics} has in electromagnetism." There is also an alternative route through the text ("Track 1") which is less thorough. "It is suitable for a one-semester course at the junior or senior level or in graduate school; and it constitutes -- in the opinion of the authors -- the indispensable core of gravitation theory that every advanced student of physics should learn." Mathematical prerequisites for Track 1 are "only vector analysis and simple partial-differential equations." I highly recommend the book. Additional references in relativity theory and gravitation physics: Albert Einstein, *The Meaning of Relativity*, Fifth Edition, Princeton University Press, Princeton, 1956. A mathematical introduction to both the special and general theories. Albert Einstein, *Relativity: The Special and General Theory*, Crown Publishers, Inc., New York, 1961. An elementary exposition of the relativity theories; only algebra is needed. Bertrand Russell, *The ABC of Relativity*, Revised Edition, George Allen and Unwin, Ltd., or Signet Science Library, 1958. Another elementary introduction -- but no algebra is required. 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} I would think this would finish the debate over what Einstein "never even implied." However, it is still relevant to ask, what is the status of Einstein's theory of general relativity in modern physics? The following two sections from Misner, Thorne, and Wheeler's *Gravitation* explore this question of alternative theories of gravity. 39.1. Other Theories Among all bodies of physical law none has ever been found that is simpler or more beautiful than Einstein's geometric theory of gravity {...}; nor has any theory of gravity ever been discovered that is more compelling. As experiment after experiment has been performed, and one theory of gravity after another has fallen by the wayside a victim of the observations, Einstein's theory has stood firm. No purported inconsistency between experiment and Einstein's laws of gravity has ever surmounted the test of time. *Query*: Why then bother to examine alternative theories of gravity? *Reply*: To have "foils" against which to test Einstein's theory. To say that Einstein's geometrodynamics is "battle-tested" is to say it has won every time it has been tried against a theory which makes a different prediction. How then does one select new antagonists for decisive new trials by combat? Not all theories of gravity are created equal. Very few, among the multitude in the literature, are sufficiently viable to be worth comparison with general relativity or with future experiments. The "worthy" theories are those which satisfy *three criteria for viability: self-consistency, completeness, and agreement with past experiment*. *Self-consistency* is best illustrated by describing several theories that fail this test. The classic example of an internally inconsistent theory is the spin-two field theory of gravity [Fierz and Pauli (1939) {...}], which is equivalent to linearized general relativity {...}. The field equations of the spin-two theory imply that all gravitating bodies move along straight lines in global Lorentz reference frames, whereas the equations of motion of the theory insist that gravity deflects bodies away from straight-line motion. (When one tries to remedy this inconsistency, one finds oneself being "bootstrapped" up to general relativity {...}.) Another self-inconsistent theory is that of Kustaanheimo (1966). It predicts zero gravitational redshift when the wave version of light (Maxwell theory) is used, and nonzero redshift when the particle version (photon) is used. *Completeness*: To be complete a theory of gravity must be capable of analyzing from "first principles" the outcome of every experiment of interest. It must therefore mesh with and incorporate a consistent set of laws for electromagnetism, quantum mechanics, and all other physics. No theory is complete if it *postulates* that atomic clocks measure the "interval" dTau {...} constructed from a particular metric. Atomic clocks are complex systems whose behavior must be calculated from fundamental laws of quantum theory and electromagnetism. No theory is complete if is *postulates* that planets move on geodesics. Planets are complex systems whose motion must be calculated from fundamental laws for the response of stressed matter to gravity. {...} *Agreement with past experiment*: The necessity that a theory agree, to within several standard deviations, with the "four standard tests" (gravitational redshift, perihelion shift, electromagnetic-wave deflection, and radar time-delay) is obvious. Equally obvious but often forgotten is the need to agree with the expansion of the universe (historically the ace among all aces of general relativity) and with observations at the more everyday, Newtonian level. Example: Birkhoff's (1943) theory predicts the same redshift, perihelion shift, deflection, and time-delay as general relativity. But it requires that the pressure inside gravitating bodies equal the total density of mass-energy, p = rho; and, as a consequence, it demands that sound waves travel with the speed of light. Of course, this prediction disagrees violently with experiment. Therefore, Birkhoff's theory is not viable. Another example: Whitehead's (1922) theory of gravity was long considered a viable alternative to Einstein's theory, because it makes exactly the same prediction as Einstein for the "four standard tests." Not until the work of Will (1971b) was it discovered that Whitehead's theory predicts a time-dependence for the ebb and flow of ocean tides that is completely contradicted by everyday experience {...}. 39.2. Metric Theories of Gravity Two lines of argument narrow attention to a restricted class of gravitation theories, called *metric theories*. The first line of argument constitutes the theme of the preceding chapter {i.e. Chapter 38 -- "Testing the Foundations of Relativity"}. It examined experiment after experiment, and reached two conclusions: (1) *spacetime possesses a metric; and* (2) *that metric satisfies the equivalence principle* (the standard special relativistic laws of physics are valid in each local Lorentz frame). *Theories of gravity that incorporate these two principles are called metric theories*. In brief, Chapter 38 says, "For any adequate description of gravity, look to a metric theory." *Exception*: Cartan's (1922b, 1923) theory ["general relativity plus torsion"; see Trautman (1972)] is nonmetric, but agrees with experiment and is experimentally indistinguishable from general relativity with the technology of the 1970's. The second line of argument pointing to metric theories begins with the issue of completeness (preceding section). To be complete, a theory must incorporate a self-consistent version of all the nongravitational laws of physics. No one has found a way to incorporate the rest of physics with ease except to introduce a metric, and then invoke the principle of equivalence. Other approaches lead to dismaying complexity, and usually to failure of the theory on one of the three counts of self-consistency, completeness, and agreement with past experiment. *All the theories known to be viable in 1973 are metric*, except Cartan's. [See Ni (1972b); Will (1972).] In only one significant way do metric theories of gravity differ from each other: their laws for the generation of the metric. In general relativity theory, the metric is generated directly by the stress-energy of matter and of nongravitational fields. In Dicke-Brans-Jordan theory {...} {Brans and Dicke (1961); Jordan (1959); Dicke (1962)}, matter and nongravita- tional fields generate a scalar field phi; then phi acts together with the matter and other fields to generate the metric. Expressed in the language of section 38.7, phi is a "new long-range field" that couples indirectly to matter. As another example, a theory devised by Ni (1970, 1972) {...} possesses a flat-space metric eta and a universal time coordinate t ("prior geometry" {...}); eta acts together with matter and nongravitational fields to generate a scalar field phi; and then eta, t, and phi combine to create the physical metric g that enters into the equivalence principle. All three of the above theories -- Einstein, Dicke-Brans- Jordan, Ni -- were viable in the summer of 1971, when this section was written. But in autumn 1971 Ni's theory, and many other theories that had been regarded as viable, were proved by Nordtvedt and Will (1972) to disagree with experiment. This is an example of the rapidity of current progress in experimental tests of gravitation theory! {pp. 1066-1068.} -- Michael McNeil 3Com Corporation "All disclaimers including this one apply" (415) 960-9367 ..!ucbvax!hplabs!oliveb!3comvax!michaelm Rather than have one global frame with gravitational forces we have many local frames without gravitational forces. Stephen Schutz, statement in January 1966 final examination in course in relativity, Princeton University [To Ernst Mach, regarding confirmation at a forthcoming eclipse] ... If so, then your happy investigations on the foundations of mechanics, Planck's unjustified criticism notwithstanding, will receive brilliant confirmation. For it necessarily turns out that inertia originates in a kind of interaction between bodies, quite in the sense of your considerations on Newton's pail experiment. The first consequence is on p. 6 of my paper. The following additional points emerge: (1) If one accelerates a heavy shell of matter S, then a mass enclosed by that shell experiences an accelerative force. (2) If one rotates the shell relative to the fixed stars about an axis going through its center, a Coriolis force arises in the interior of the shell; that is, the plane of a Foucault pendulum is dragged around (with a practically unmeasurably small angular velocity). Albert Einstein's appreciation to Ernst Mach, written on June 25, 1913, while working hard at arriving at his November 1915 formulation of standard general relativity
ian@sdcsma.UUCP (Ian Ferris) (03/12/86)
In article <446@3comvax.UUCP> michaelm@3comvax.UUCP (Michael McNeil) gives
a short list of good books on relativity theory. Here's another:
*Einstein's Theory of Relativity* by Max Born, available from Dover
This is another book "for the general reader" but it's much more
detailed than most such books and also goes into the historical
background more thoroughly than any other book at this level I
know of. If you understand the physics but wonder how
Einstein ever thought of it, try
*'Subtle is the Lord ... ': The Science and the Life of Albert Einstein*,
by Abraham Pais, Oxford University Press (Hardback 1982, Paperback 1983)
Supposedly the reader can skip the mathematical and physical details
in this book, but I doubt the validity of this claim -- I regard
working it all out as a sort of lifetime homework assignment.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
jlg@lanl.ARPA (Jim Giles) (03/23/86)
>In article <556@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >>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? The reference is: "Gravitation", Misner, Thorne, and Wheeler, 1973: W.H. Freeman and Co., p.21: "STATEMENTS OF FACT ... The geometry of spacetime is locally Lorentzian everywhere." The emphasis is theirs. There is, therefore a local Lorentzian frame everywhere (actually, an infinity of them). On page 23 the text goes on "... these theorems [about spacetime] rise above all coordinate systems in their content. They refer to intervals or distances." "All coordinate systems" here refers to the infinity of available Lorentzian frames which you might select for computational purposes. Any non-Lorentzian coordinate system causes the theorems in question to be completely reformulated for that system (mainly because the metric (a word which actually doesn't appear yet) is no longer valid - intervals don't behave properly in a non-Lorentzian coordinate system). There seems little point in continuing a discussion with someone who can only spout rhetoric and resort to ad hominem attacks. If you can give references, information, or understandable explanations which support your view, then do so. But quit playing meaningless word games with terminology that does no more than muddy the waters of understanding. And, certainly, if all you can do is resort to name calling, you shouldn't even post your article. >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. Bertrand Russell's remark implied that there was no difference between a rotating and a non-rotating coordinate system. Since this is NOT true, I don't see how you can hold that he is correct. But, on the off chance that you have any EVIDENCE, I wish you would present it. I, on the other hand, have presented several ways to distinguish a rotating coordinate system from a non-rotating one; I have given references; and I have refrained from the use of jargon and terminology which would confuse the lay readership on the net. I have also (until now) refrained from ad hominem attacks. Now, if you have ANY evidence which shows a rotating coordinate system is indistinguishable from a non-rotating one - PRESENT IT. Any other garbage you put on the net I (for one) will ignore. J. Giles Los Alamos
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?
weemba@brahms.BERKELEY.EDU (Matthew P. Wiener) (03/27/86)
In article <854@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >>In article <556@lanl.ARPA> jlg@a.UUCP (Jim Giles) writes: >>>Note: I have always said 'local reference frame', which in GR is ALWAYS >>>a Lorentz frame. ^^^^^^^ ^^^^^ > "... The geometry of spacetime is locally Lorentzian everywhere." ^^^^^^^^^^ Lorentz frame is not the same as Lorentzian geometry. And your assertion is completely false as stated. >The emphasis is theirs. There is, therefore a local Lorentzian frame >everywhere (actually, an infinity of them). On page 23 the text goes on >"... these theorems [about spacetime] rise above all coordinate systems in >their content. They refer to intervals or distances." "All coordinate >systems" here refers to the infinity of available Lorentzian frames which >you might select for computational purposes. Any non-Lorentzian coordinate >system causes the theorems in question to be completely reformulated for >that system (mainly because the metric (a word which actually doesn't >appear yet) is no longer valid - intervals don't behave properly in a >non-Lorentzian coordinate system). Read what you just quoted. There are no non-Lorentzian coordinate systems in a Lorentzian geometry. But whatever you are talking about, the theorems in question rise above coordinate systems, just like MTW said in your quote, and unlike your last sentence. If a law or theorem is expressed in covariant form, ie with tensors, it is true in all coordinate frames. That is why we use tensors in the first place: to identify the underlying geometric meaning behind the coordinate systems. ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
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
jlg@lanl.UUCP (03/28/86)
In article <12702@ucbvax.BERKELEY.EDU> weemba@brahms.UUCP (Matthew P. Wiener) writes: >[...] There are no non-Lorentzian coordinate systems >in a Lorentzian geometry. I'm surprised to see you admit this! You have been talking all along about rotating 'frames' (which aren't Lorentzian). Now, you have finally admitted this to be inappropriate. Bravo! J. Giles Los Alamos
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