## Uniform gravitational Field

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I\'m been always interested in the Equivalence Principle beauty,\nand got the opinion that we have to try to deeply understand it.\nBefore formulating General Relativity, Einstein tried to derive his\nresults directly from this principle, but he could not get all of them.\n\nFor a uniform gravitational field I think should be possible to derive\nall the correct result only using an uniform accelerated observer\nand the Equivalence Principle.\nI read many Books and papers on this subject and found that Rindler\nin his book Essential Relativity states (around page 120 of my edition)\nthat it is not possible to do that. On the same subject I found a paper\n(E. Fabbri, European Journal of Physics 1994 pag 197) that states\nthat this is possible and some calculation are done.\nThere are few paper on this subject, but recently I found this one in\nthe electronic archivie. http://uk.arxiv.org/abs/gr-qc/0409033\nI found this article rather interesting for both pedagogical and conceptual\nanalysis. Did someone else read it?\n\nKarl Poessl\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>I'm been always interested in the Equivalence Principle beauty,
and got the opinion that we have to try to deeply understand it.
Before formulating General Relativity, Einstein tried to derive his
results directly from this principle, but he could not get all of them.

For a uniform gravitational field I think should be possible to derive
all the correct result only using an uniform accelerated observer
and the Equivalence Principle.
I read many Books and papers on this subject and found that Rindler
in his book Essential Relativity states (around page 120 of my edition)
that it is not possible to do that. On the same subject I found a paper
(E. Fabbri, European Journal of Physics 1994 pag 197) that states
that this is possible and some calculation are done.
There are few paper on this subject, but recently I found this one in
the electronic archivie. http://uk.arxiv.org/abs/http://www.a.../gr-qc/0409033
analysis. Did someone else read it?

Karl Poessl



Karl Poessl wrote: > > I'm been always interested in the Equivalence Principle beauty, > and got the opinion that we have to try to deeply understand it. Note that postulating the EP to model gravitation is entirely unnecessary. Weitzenboek's affine gravitation (autoparallel paths) contains the exact whole of metric gravitation General Relativity (geodesic paths) - qualitative and quantitative - down to the last decimal place. Affine gravitation is much harder to calculate. Affine gravitation is much richer for allowing EP violation in several circumstances. Only one of them can be correct. Affine gravitation allows EP violation by 1) Physically spinning test masses. Alas, they must be relativistically spinning to have measurable violation ampltiude. The two pairs of antiparallel spin 10,000 rpm fused silica gyro balls in Gravity Probe-B show no hint of free falling along non-parallel paths in hard vacuum vs. each other or their essentially non-spinning fused silica housing. 2) Electomagnetically polarized test masses (magnets). Alas, the active spin mass fractions are sub-ppm and gravitation only affects mass. Spin Eotvos experiments by Eric Adleberger, Wei-Tou Ni, and others give experimental null outputs to fractional parts-per-trillion difference/average. 3) Opposite geometric parity test masses. No alas at all $- 99$.$97+%$ active mass and calculated theoretical extremal cases are trivial to obtain. Three seminal parity Eotovs experiments are serially proceeding in PR China using enantiomorphic single crystal quartz test masses against each other (full parity experiment) and each against amorphous fused silica (hemiparity experiments). See qz.pdf below. > Before formulating General Relativity, Einstein tried to derive his > results directly from this principle, but he could not get all of them. > > For a uniform gravitational field I think should be possible to derive > all the correct result only using an uniform accelerated observer > and the Equivalence Principle. GR directly derives from the EP. Quadrupole tidal forces come later. > I read many Books and papers on this subject and found that Rindler > in his book Essential Relativity states (around page 120 of my edition) > that it is not possible to do that. On the same subject I found a paper > (E. Fabbri, European Journal of Physics 1994 pag 197) that states > that this is possible and some calculation are done. > There are few paper on this subject, but recently I found this one in > the electronic archivie. http://uk.arxiv.org/abs/http://www.a.../gr-qc/0409033 > I found this article rather interesting for both pedagogical and conceptual > analysis. Did someone else read it? Any treatment that derives metric gravitation from the EP must respect affine gravitaton that wholly ignores the EP and neverhtheless arrives at the same destinations. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf



Uncle Al wrote: > Note that postulating the EP to model gravitation is entirely > unnecessary. Weitzenboek's affine gravitation (autoparallel paths) > contains the exact whole of metric gravitation General Relativity > (geodesic paths) - qualitative and quantitative - down to the last > decimal place. Affine gravitation is much harder to calculate. > Affine gravitation is much richer for allowing EP violation in several > circumstances. Where can I read about W's ideas? $$-drl$$

## Uniform gravitational Field

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>"Karl Poessl" &lt;karl.poessl@libero.it&gt; wrote in message\nnews:cP3xd.33116\\$Zk.606505@twister2.libero.it...\n\n&gt; I\'m been always interested in the Equivalence Principle beauty,\n&gt; and got the opinion that we have to try to deeply understand it.\n&gt; Before formulating General Relativity, Einstein tried to derive his\n&gt; results directly from this principle, but he could not get all of\n&gt; them.\n&gt;\n&gt; For a uniform gravitational field I think should be possible to\n&gt; derive all the correct result only using an uniform accelerated\n&gt; observer and the Equivalence Principle.\n\nKarl,\n\nThe Equivalence Principle is limited to one spatial dimension. In\nspite of that, the EP is a wonderful teaching device. I know of no\nphysics question involving photons or clocks in motion, in gravity, in\na radial direction, where it won\'t give you a correct answer for short\ndistances. The problem is that a uniformly accelerated observer\nimitates a unidirectional gravitational field with the force of\n"gravity" varying in strength as 1/r not 1/r^2.\n\nHow do you propose accelerating an observer so as to create an\nartificial gravity with a field strength that varies as 1/r^2 or, even\nbetter, as an arbitrary time-independent function of some radial\ncoordinate r?\n\nEugene Shubert\nhttp://www.everythingimportant.org/relativity/special.pdf\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Karl Poessl" <karl.poessl@libero.it> wrote in message news:cP3xd.33116$Zk.606505@twister2.libero.it...

> I'm been always interested in the Equivalence Principle beauty,
> and got the opinion that we have to try to deeply understand it.
> Before formulating General Relativity, Einstein tried to derive his
> results directly from this principle, but he could not get all of
> them.
>
> For a uniform gravitational field I think should be possible to
> derive all the correct result only using an uniform accelerated
> observer and the Equivalence Principle.

Karl,

The Equivalence Principle is limited to one spatial dimension. In
spite of that, the EP is a wonderful teaching device. I know of no
physics question involving photons or clocks in motion, in gravity, in
a radial direction, where it won't give you a correct answer for short
distances. The problem is that a uniformly accelerated observer
imitates a unidirectional gravitational field with the force of
"gravity" varying in strength as 1/r not $1/r^2$.

How do you propose accelerating an observer so as to create an
artificial gravity with a field strength that varies as $1/r^2$ or, even
better, as an arbitrary time-independent function of some radial
coordinate r?

Eugene Shubert
http://www.everythingimportant.org/r...ty/special.pdf



Karl Poessl wrote in message news:cP3xd.33116$Zk.606505@twister2.libero.it... > I'm been always interested in the Equivalence Principle beauty, > and got the opinion that we have to try to deeply understand it. > Before formulating General Relativity, Einstein tried to derive his > results directly from this principle, but he could not get all of them. The equivalence principle is not contained anywhere in the mathematics of GR. Several people have tried to derive GR from the EP, but no one has succeeded. IIRC, the closest anyone got was Whitehead's theory $and/or$ the Entwurf. > For a uniform gravitational field I think should be possible to derive > all the correct result only using an uniform accelerated observer > and the Equivalence Principle. The problem lies in the fact that there is no such thing as a uniform gravitational field. > I read many Books and papers on this subject and found that Rindler > in his book Essential Relativity states (around page 120 of my edition) > that it is not possible to do that. I have not read Rindler. But no other source claims that it is not possible to do the derivation. Only that the EP is not contained within the current derivation of GR. And that no one has yet managed it. > On the same subject I found a paper > (E. Fabbri, European Journal of Physics 1994 pag 197) that states > that this is possible and some calculation are done. > There are few paper on this subject, but recently I found this one in > the electronic archivie. http://uk.arxiv.org/abs/http://www.a.../gr-qc/0409033 > I found this article rather interesting for both pedagogical and > conceptual analysis. Did someone else read it? -- greywolf42 ubi dubium ibi libertas {remove planet for return e-mail}  greywolf42 wrote: > > Karl Poessl wrote in message > news:cP3xd.33116$Zk.606505@twister2.libero.it... > > I'm been always interested in the Equivalence Principle beauty, > > and got the opinion that we have to try to deeply understand it. > > Before formulating General Relativity, Einstein tried to derive his > > results directly from this principle, but he could not get all of them. > > The equivalence principle is not contained anywhere in the mathematics of > GR. Several people have tried to derive GR from the EP, but no one has > succeeded. IIRC, the closest anyone got was Whitehead's theory $and/or$ the GR *postulates* the EP. The EP is wholly unnecessary. Weitzenboeck's affine gravitation, without the EP, is indistinguishable from GR's predictions in all cases. Affine gravitation is a richer theory than GR. All ya gotta do is identify two local lumps that reproducibly fall along non-parallel paths in vacuum and GR is falsified. All mathematically allowed divergent possiblities have been examined, except for one http://www.mazepath.com/uncleal/qz.pdf that is in progress. The hemiparity Eotvos experiment, P3(2)21 quartz vs. fused silica, nulls within experimental error. The full parity Eotvos experiment, P3(1)21 quartz vs. P3(2)21 quartz, is next. > > For a uniform gravitational field I think should be possible to derive > > all the correct result only using an uniform accelerated observer > > and the Equivalence Principle. > > The problem lies in the fact that there is no such thing as a uniform > gravitational field. "Local" test masses sample a sufficiently small volume of spacetime taht quadrupolar tidal effects are below detection level. > > I read many Books and papers on this subject and found that Rindler > > in his book Essential Relativity states (around page 120 of my edition) > > that it is not possible to do that. > > I have not read Rindler. But no other source claims that it is not possible > to do the derivation. Only that the EP is not contained within the current > derivation of GR. And that no one has yet managed it. GR *postulates the EP. You cannot derive a postulate from the theory it founds. You cannot defend a postulate, either. Euclid's Fifth (Parallel) Postulate is a special case. Elliptic and hyperbolic geometries violate it. GR is wholly validated by observation, http://arXiv.org/abs/http://www.arxi...tro-ph/0401086 http://arxiv.org/abs/http://www.arxi...tro-ph/0312071 and GR is wholly at the mercy of two lumps that fall differently. We'll know by end of 2005. > > On the same subject I found a paper > > (E. Fabbri, European Journal of Physics 1994 pag 197) that states > > that this is possible and some calculation are done. > > There are few paper on this subject, but recently I found this one in > > the electronic archivie. http://uk.arxiv.org/abs/http://www.a.../gr-qc/0409033 > > I found this article rather interesting for both pedagogical and > > conceptual analysis. Did someone else read it? "A partially alternative derivation of the expression for the time dilation effect in a uniform static gravitational field is obtained by means of a thought experiment in which rates of clocks at rest at different heights are compared using as reference a clock bound to a free falling reference system (FFRS)." It ASSUMES the EP. Suppose I fabricate two Swatch wristwatches, one from right-handed quartz and the other from left-handed quartz. If we ASSUME the Equivalence Principle, then the Gedankenexperiment is OK. If the EP has parity violation, the two clocks will not fall identically and no conclusions at all are forthcoming from the Gedankenexperiment. In the more general sense the FFRS can be left-handed or right-handed, defined by the vector crossproduct of two of its axes vs. the direction of the third (and more generally, the coordinate-invariant vector triple product). Einstein ASSUMES (x,y,z) and $(-x,-y,-z)$ are indistinguishable. Weitzenboeck is compatible with them being non-equivalent (no EP). -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf



Uncle Al wrote in message news:41EADD26.360A3273@hate.spam.net... > greywolf42 wrote: > > Karl Poessl wrote in message > > news:cP3xd.33116$Zk.606505@twister2.libero.it... > > > I'm been always interested in the Equivalence Principle beauty, > > > and got the opinion that we have to try to deeply understand it. > > > Before formulating General Relativity, Einstein tried to derive his > > > results directly from this principle, but he could not get all of > > > them. > > > > The equivalence principle is not contained anywhere in the mathematics > > of GR. Several people have tried to derive GR from the EP, but no one > > has succeeded. IIRC, the closest anyone got was Whitehead's theory > > $and/or$ the > > GR *postulates* the EP. The EP is wholly unnecessary. GR discuss the EP. But GR equations are not based on it. So, I think we agree here. > Weitzenboeck's > affine gravitation, without the EP, is indistinguishable from GR's > predictions in all cases. Affine gravitation is a richer theory than > GR. > > All ya gotta do is identify two local lumps that reproducibly fall > along non-parallel paths in vacuum and GR is falsified. All > mathematically allowed divergent possiblities have been examined, > except for one > > http://www.mazepath.com/uncleal/qz.pdf > > that is in progress. The hemiparity Eotvos experiment, P3(2)21 quartz > vs. fused silica, nulls within experimental error. The full parity > Eotvos experiment, P3(1)21 quartz vs. P3(2)21 quartz, is next. > > > > For a uniform gravitational field I think should be possible to derive > > > all the correct result only using an uniform accelerated observer > > > and the Equivalence Principle. > > > > The problem lies in the fact that there is no such thing as a uniform > > gravitational field. > > "Local" test masses sample a sufficiently small volume of spacetime > taht quadrupolar tidal effects are below detection level. The point is, that GR does not work outside of arbitrarily small scale regions. A 'true' theory of gravity should be able to be used at any scale. > > > I read many Books and papers on this subject and found that Rindler > > > in his book Essential Relativity states (around page 120 of my > > > edition) that it is not possible to do that. > > > > I have not read Rindler. But no other source claims that it is not > > possible to do the derivation. Only that the EP is not contained > > within the current derivation of GR. And that no one has yet > > managed it. > > GR *postulates the EP. You cannot derive a postulate from the theory > it founds. True, but irrelevant. The EP is not used in the derivation of GR at all. > You cannot defend a postulate, either. Euclid's Fifth > (Parallel) Postulate is a special case. Elliptic and hyperbolic > geometries violate it. You cannot defend a mathematical postulate -- but then, there is no need to. However, physical assumptions (postulates) must be defended in scientific theory. > GR is wholly validated by observation, > > > > http://arXiv.org/abs/http://www.arxi...tro-ph/0401086 > http://arxiv.org/abs/http://www.arxi...tro-ph/0312071 > > > and GR is wholly at the mercy of two lumps that fall differently. > We'll know by end of 2005. I'm not attacking the validity of GR in this post. I am merely noting that the EP is not part of the weak field approximations of GR that are used in the above links. {snip} -- greywolf42 ubi dubium ibi libertas {remove planet for return e-mail}  greywolf42 says... > > The equivalence principle is not contained anywhere in the mathematics > > of GR. Several people have tried to derive GR from the EP, but no one > > has succeeded. Is the EP enough to derive GR? Definitely not. Roughly speaking, GR consists of two parts (1) How gravity affects matter and nongravitational fields, and (2) how matter and nongravitational fields affect gravity. As far as I know, there is no way at all to derive part 2, how matter affects gravity, from the EP alone, but part 1 is *almost* completely derivable from the EP. If you know what physics is like in flat spacetime, then the EP allows you to figure out what physics is like in the presence of gravity. You just piece together solutions in little regions of spacetime to get a solution in an extended region. This works as long as you are dealing with weak fields and small particles that don't make much change to the gravitational field by their motion. >> "Local" test masses sample a sufficiently small volume of spacetime >> taht quadrupolar tidal effects are below detection level. > >The point is, that GR does not work outside of arbitrarily small scale >regions. A 'true' theory of gravity should be able to be used at any >scale. I don't understand that point$. *Most* (if$ not all) theories of physics are expressed in the form of differential equations, which basically amount to describing how things behave in an infinitesimal region of spacetime. GR is no different from other theories in this respect. Differential geometry allows us to patch together descriptions of all the small regions into a description of the universe. As long as all interactions are local and (therefore) there are no fundamental extended particles, it is enough to have a theory that works in a small enough patch. >I'm not attacking the validity of GR in this post. I am merely noting that >the EP is not part of the weak field approximations of GR that are used in >the above links. Yes, it is. If gravity only interacts with matter and other fields through the metric tensor, then the equivalence principle is automatically valid. On the other hand, something I'm not sure about is whether particles with intrinsic spin violate the equivalence principle. I would think that a massive spinning object would produce different effects on particles depending on their spin, which would violate the equivalence principle, in the sense that no matter how small a spacetime region one looks at, particles would not behave the same as in flat spacetime. -- Daryl McCullough Ithaca, NY  greywolf42 wrote: > The equivalence principle is not contained anywhere in the mathematics of > GR. Several people have tried to derive GR from the EP, but no one has > succeeded. This is largely incorrect. Einstein, Infeld, and Hoffmann showed in 1937 that the Einstein field equations imply that sources move along geodesics, which in turn implies the equivalence principle. Of course, the proof is only an approximation, although a very good one. But the equivalence principle itself is only a very good approximation -- if you drop a feather and a brick in a vacuum, they will emit slightly different amounts of gravitational radiation as they fall, and the radiation reaction will make affect their accelerations. There has been $a *huge*$ amount of work on tis since 1937, in part because this kind of calculation, carried to high enough order, is a good way to predict gravitational wave forms. There's a nice summary in Damour's article in the book $_300$ Years of $Gravitation_,$ edited by Hawking and Israel; see especially section 6.14, "The effacement of internal structure in the external problem (Einsteinian case)." Steve Carlip  greywolf42 wrote: $>=20$ > Uncle Al wrote in message > news:41EADD26.360A3273@hate.spam.net... > > greywolf42 wrote: > > > Karl Poessl wrote in message > > > news:cP3xd.33116$Zk.606505@twister2.libero.it... [snip] > > GR *postulates the EP. You cannot derive a postulate from the theory > > it founds. $>=20$ > True, but irrelevant. The EP is not used in the derivation of GR $at al=$ l. Jahrbuch der Radioaktivit=E4t Elect. 4 411 (1907) The EP is a *founding postulate* of GR as are Lorentz invariance, invariant lightspeed for all inertial observers... > > You cannot defend a postulate, either. Euclid's Fifth > > (Parallel) Postulate is a special case. Elliptic and hyperbolic > > geometries violate it. $>=20$ > You cannot defend a mathematical postulate -- but then, there is $no nee=$ d to. > However, physical assumptions (postulates) must be defended in scientif= ic > theory. Euclid is wrong as Newton is wrong. You cannot navigate or survey with Euclid. Euclid is a special case of more general geometry (first Riemann and Bolyai/Lobechevsky, then Thurston) as Newton is a special case of Einstein. If two local test masses in vacuum that do not fall along parallel geodesics are discovered, GR is fundamentally wrong for being founded upon an empirically falsified hypothesis. Mass is a tensor in metic gravitation (GR); (x,y,z) and $(-x,-y,-z)$ transform identically. Mass can be a pseudotensor in affine gravitation; (x,y,z) and $(-x,-y,-z) *do not*$ transform identically.=20 Only one of them can be correct. The only operative falsifying tests would be based upon angular momentum or geometric parity. Only the latter can deliver high amplitude divergences - unless you can deliver a test mass composed of ~100 mass-% relativistic spins, aligned particles or literal physical mass. The former would be magnets that trivially cannot be more than 50 parts-per-million polarized spin mass. The latter is limited by binding energy and cannot do better than millisecond pulsars. Not good enough and sloppy to play with. =20 > > GR is wholly validated by observation, > > > > > > > > http://arXiv.org/abs/http://www.arxi...tro-ph/0401086 > > http://arxiv.org/abs/http://www.arxi...tro-ph/0312071 > > > > > > and GR is wholly at the mercy of two lumps that fall differently. > > We'll know by end of 2005. $>=20$ > I'm not attacking the validity of GR in this post. I am merely noting = that > the EP is not part of the weak field approximations of GR that are $used=$ in > the above links. The EP is the *founding postulate* of $GR -$ Einstein's elevator Gedankenexperiment. Spacetime curvature immediately follows. Affine gravitation has spacetime torsionn not curvature. Gravitation forces in affine theory looks like Lorentz force in EM. It is a tremendous jump toward unification if it is demonstrable. GR makes no detectably bad predictions either in kind or quantitatively. Affine gravitation makes no detectably bad predictions either in kind or quantitatively. Metric gravitation is wholly contained within affine gravitation, plus more. Both theories cannot be correct. The place to look is *not* where they agree. The place ito look is where they *disagree.* It's a no-brainer. --=20 Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz.pdf



I think the EP is embodied in the covariant derivative of the metric tensor, $g_{uv};w =0,$ (Weinberg's "Grav and Cosmo", Eq. 4.6.16). The late Prof. Greub advised me that $g_{uv};w=0$ is an imposed condition and is not generally true in all geometries, but we take it for granted when we use association in GR. H. Weyl, in his 1918 paper, "Gravitation and Electricity", ((it's in Dover's PoR)), appears to have used something other than $g_{uv};w=0$ in his Eq, following #7, in an unsuccessful attempt at a unified field. The $g_{uv}$ are regarded as the potentials in GR, as the way they vary in the geodesic, form the basis of the equation of motion, the geodesic equation, given by the absolute derivative of the 4-velocity, $DU^u=0,$ which essentially vanishes absolute acceleration, but based on $g_{uv};w=0$. The EP requires the equation of motion be independant of the substance as $DU^u=0$ is. Regards Ken S. Tucker



Daryl McCullough wrote in message news:cstr530315g@drn.newsguy.com... > greywolf42 says... Please try to get the attribution marks correct, if you are going to snip within the post. (Attributions fixed). > > Uncle Al wrote in message > > news:41EADD26.360A3273@hate.spam.net... > > > greywolf42 says... > > > > The equivalence principle is not contained anywhere in the > > > > mathematics of GR. Several people have tried to derive GR from the EP, but no > > > > one has succeeded. > > > > > > GR *postulates* the EP. The EP is wholly unnecessary. > > > > GR discuss the EP. But GR equations are not based on it. So, I think > > we agree here. > > Is the EP enough to derive GR? Definitely not. Roughly speaking, > GR consists of two parts (1) How gravity affects matter and > nongravitational fields, and (2) how matter and nongravitational > fields affect gravity. As far as I know, there is no way at all > to derive part 2, how matter affects gravity, from the EP alone, > but part 1 is *almost* completely derivable from the EP. If you > know what physics is like in flat spacetime, then the EP allows > you to figure out what physics is like in the presence of gravity. > You just piece together solutions in little regions of spacetime > to get a solution in an extended region. This works as long as > you are dealing with weak fields and small particles that don't > make much change to the gravitational field by their motion. To discuss whether something is derivable, or not, in a theory requires actual math. I'll simply note that it has not been done. To claim something is not possible is easy. To show it, requires a mathematical proof. > >> "Local" test masses sample a sufficiently small volume of spacetime > >> taht quadrupolar tidal effects are below detection level. > > > >The point is, that GR does not work outside of arbitrarily small scale > >regions. A 'true' theory of gravity should be able to be used at any > >scale. > > I don't understand that point$. *Most* (if$ not all) theories of > physics are expressed in the form of differential equations, > which basically amount to describing how things behave in an > infinitesimal region of spacetime. A true, physical theory is not dependent upon the form of the mathematics in which it is expressed. And as soon as you limit yourself to 'spacetime' you are discussing GR. > GR is no different from > other theories in this respect. Why not provide an example of what you are talking about. Maxwell's equations can easily be written in non-differential form. > Differential geometry allows > us to patch together descriptions of all the small regions > into a description of the universe. But you have to arbitrarily adjust all your values to make this work. This simply hides any mistakes under the interface "smoothing". > As long as all > interactions are local and (therefore) there are no fundamental > extended particles, But if fundamental particles *are* extended, then this won't work. This is called assuming your conclusion. > it is enough to have a theory that works in a > small enough patch. It may be enough for you ... and for some others. > >I'm not attacking the validity of GR in this post. I am merely noting > >that the EP is not part of the weak field approximations of GR that > >are used in the above links. > > Yes, it is. If gravity only interacts with matter and other fields > through the metric tensor, then the equivalence principle is automatically > valid. That is hardly self-evident. Perhaps you have some more detailed support for your assertion? > On the other hand, something I'm not sure about is whether particles > with intrinsic spin violate the equivalence principle. I would think > that a massive spinning object would produce different effects on > particles depending on their spin, which would violate the equivalence > principle, in the sense that no matter how small a spacetime region > one looks at, particles would not behave the same as in flat spacetime. Then you have just shown that the EP is not part of the math of GR. -- greywolf42 ubi dubium ibi libertas {remove planet for return e-mail}



I think the EP is embodied in the covariant derivative of the metric tensor, $g_{uv};w =0,$ (Weinberg's "Grav and Cosmo", Eq. 4.6.16). The late Prof. Greub advised me that $g_{uv};w=0$ is an imposed condition and is not generally true in all geometries, but we take it for granted when we use association in GR. H. Weyl, in his 1918 paper, "Gravitation and Electricity", ((it's in Dover's PoR)), appears to have used something other than $g_{uv};w=0$ in his Eq, following #7, in an unsuccessful attempt at a unified field. The $g_{uv}$ are regarded as the potentials in GR, as the way they vary in the geodesic, form the basis of the equation of motion, the geodesic equation, given by the absolute derivative of the 4-velocity, $DU^u=0,$ which essentially vanishes absolute acceleration, but based on $g_{uv};w=0$. The EP requires the equation of motion be independant of the substance as $DU^u=0$ is. Regards Ken S. Tucker



"Daryl McCullough" schrieb > Is the EP enough to derive GR? Definitely not. Roughly speaking, > GR consists of two parts (1) How gravity affects matter and > nongravitational fields, and (2) how matter and nongravitational > fields affect gravity. As far as I know, there is no way at all > to derive part 2, how matter affects gravity, from the EP alone, Indeed, and this simply follows from the existence of other metric theories of gravity. Ilja



greywolf42 says... >To discuss whether something is derivable, or not, in a theory requires >actual math. I'll simply note that it has not been done. Yes, it has. That's the standard approach taken by texts such as Misner, Thorne, and Wheeler's _Gravitation_. >> I don't understand that point$. *Most* (if$ not all) theories of >> physics are expressed in the form of differential equations, >> which basically amount to describing how things behave in an >> infinitesimal region of spacetime. > >A true, physical theory is not dependent upon the form of the mathematics >in which it is expressed. And as soon as you limit yourself to 'spacetime' >you are discussing GR. I thought that *was* what we were discussing. GR describes gravity as curved spacetime. >> GR is no different from >> other theories in this respect. > >Why not provide an example of what you are talking about. Newton's equations, Maxwell's equations, the Schrodinger equation, the heat equation, the propagation of sound. They are all written (or can be written) in the form of differential equations. >Maxwell's equations can easily be written in non-differential form. Yes, there is an integral form for Maxwell's equations, as well. But what's wrong with the differential form? >> Differential geometry allows >> us to patch together descriptions of all the small regions >> into a description of the universe. > >But you have to arbitrarily adjust all your values to make this work. This >simply hides any mistakes under the interface "smoothing". I don't know what you mean by that. >> As long as all >> interactions are local and (therefore) there are no fundamental >> extended particles, > >But if fundamental particles *are* extended, then this won't work. That's right. If there are extended particles held together by nonlocal forces, then GR (and SR, for that matter) are probably wrong. >> it is enough to have a theory that works in a >> small enough patch. > >It may be enough for you ... and for some others. In what sense is $it *not*$ enough? >> Yes, it is. If gravity only interacts with matter and other fields >> through the metric tensor, then the equivalence principle is automatically >> valid. > >That is hardly self-evident. Perhaps you have some more detailed support >for your assertion? In a small enough region of spacetime, it is always possible to choose a coordinate system in which the metric tensor has its flat spacetime form. Therefore, the equations describing the motions of particles and the evolution of fields are identical to those in flat spacetime. So freefall in a gravitational field is equivalent to inertial motion in the absence of a gravitational field. Of course, this is only true in the limit as the dimensions of the region go to zero, but the equivalence principle is only true in that limit. >> On the other hand, something I'm not sure about is whether particles >> with intrinsic spin violate the equivalence principle. I would think >> that a massive spinning object would produce different effects on >> particles depending on their spin, which would violate the equivalence >> principle, in the sense that no matter how small a spacetime region >> one looks at, particles would not behave the same as in flat spacetime. > >Then you have just shown that the EP is not part of the math of GR. Maybe. -- Daryl McCullough Ithaca, NY



Uncle Al wrote in message news:41F27D60.75463716@hate.spam.net... > > greywolf42 wrote: > $>=20$ > > Uncle Al wrote in message > > news:41EADD26.360A3273@hate.spam.net... > > > greywolf42 wrote: > > > > Karl Poessl wrote in message > > > > news:cP3xd.33116Zk.606505@twister2.libero.it... > [snip] > > > > GR *postulates the EP. You cannot derive a postulate from the theory > > > it founds. > $>=20$ > > True, but irrelevant. The EP is not used in the derivation of GR $at al=$ > l. > > Jahrbuch der Radioaktivit=E4t Elect. 4 411 (1907) That isn't GR. GR was 1915. GR was 1913, if you include the Entwurf. > The EP is a *founding postulate* of GR as are Lorentz invariance, > invariant lightspeed for all inertial observers... The EP is not used within the mathematics of GR at all. So, it is not a "founding postulate" of the math of GR. And the math of GR is the only thing that is testable. > > > You cannot defend a postulate, either. Euclid's Fifth > > > (Parallel) Postulate is a special case. Elliptic and hyperbolic > > > geometries violate it. > > > > You cannot defend a mathematical postulate -- but then, there is no need > > to. However, physical assumptions (postulates) must be defended in > > scientific theory. > > Euclid is wrong as Newton is wrong. You cannot navigate or survey > with Euclid. Euclid is a special case of more general geometry (first > Riemann and Bolyai/Lobechevsky, then Thurston) as Newton is a special > case of Einstein. If two local test masses in vacuum that do not fall > along parallel geodesics are discovered, GR is fundamentally wrong for > being founded upon an empirically falsified hypothesis. By your logic, GR is fundamentally wrong. For it is well known that two masses will never fall precisely along parallel paths. GR requires an arbitrary limitation to "local" regions. > Mass is a tensor in metic gravitation (GR); (x,y,z) and $(-x,-y,-z)$ > transform identically. Mass can be a pseudotensor in affine > gravitation; (x,y,z) and $(-x,-y,-z) *do not*$ transform identically.=20 > Only one of them can be correct. The only operative falsifying tests > would be based upon angular momentum or geometric parity. Only the > latter can deliver high amplitude divergences - unless you can deliver > a test mass composed of ~100 mass-% relativistic spins, aligned > particles or literal physical mass. The former would be magnets that > trivially cannot be more than 50 parts-per-million polarized spin > mass. The latter is limited by binding energy and cannot do better > than millisecond pulsars. Not good enough and sloppy to play with. > > > GR is wholly validated by observation, > > > > > > > > > > > > http://arXiv.org/abs/http://www.arxi...tro-ph/0401086 > > > http://arxiv.org/abs/http://www.arxi...tro-ph/0312071 > > > > > > > > > and GR is wholly at the mercy of two lumps that fall differently. > > > We'll know by end of 2005. > $>=20$ > > I'm not attacking the validity of GR in this post. I am merely noting = > that > > the EP is not part of the weak field approximations of GR that are $used=$ > in > > the above links. > > The EP is the *founding postulate* of $GR -$ Einstein's elevator > Gedankenexperiment. It doesn't matter how often you make the claim. It doesn't change the fact that the EP has never been successfully used within the maths modern GR. The elevator has been shown to be flawed. One must limit the elevator to arbitrarily small, "local" regions. {snip more repetition of the claims} -- greywolf42 ubi dubium ibi libertas {remove planet for return e-mail}  wrote in message news:csul4u8l7\$1@skeeter.ucdavis.edu... > greywolf42 wrote: > > > The equivalence principle is not contained anywhere in the mathematics of > > GR. Several people have tried to derive GR from the EP, but no one has > > succeeded. > > This is largely incorrect. Einstein, Infeld, and Hoffmann showed in 1937 > that the Einstein field equations imply that sources move along geodesics, > which in turn implies the equivalence principle. Which does not contradict my statement. "Implication" (after the fact) is not sufficient. > Of course, the proof > is only an approximation, although a very good one. I believe that that's a contradiction in terms. If something is an approximation, then it cannot be a proofs. > But the equivalence > principle itself is only a very good approximation -- if you drop a feather > and a brick in a vacuum, they will emit slightly different amounts of > gravitational radiation as they fall, and the radiation reaction will > make affect their accelerations. Interesting ... but not relevant to the discussion of the EP in GR. > There has been $a *huge*$ amount of work on tis since 1937, in part because > this kind of calculation, carried to high enough order, is a good way > to predict gravitational wave forms. There's a nice summary in Damour's > article in the book $_300$ Years of $Gravitation_,$ edited by Hawking and > Israel; see especially section 6.14, "The effacement of internal structure > in the external problem (Einsteinian case)." And yet, despite the "huge" effort, no one has succeeded. Which is not too surprising, since the EP is not needed within the actual calculations of GR. That doesn't mean that it is not a useful concept. -- greywolf42 ubi dubium ibi libertas {remove planet for return e-mail}