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Revision as of 00:46, 29 August 2005

Gosh, I tried to add a comment here an hour so so ago, but apparently it didn't take.

I was trying to say that I just added to the article some citations to print books which I think rather decisively show that the article as it stands mischaracterizes the state of geometrodynamics. First, in two books coauthored by Wheeler and published in 1973, 1995 respectively, he uses Einstein geometrodynamics as a synonym for general relativity, which has certainly never become anabandoned domain of physics! Second, one article in the book edited by Butterfield is on quantum geometrodynamics, which is very much alive.

So I think this article needs to be thoroughly rewritten. If no-one objects (is anyone but me "watching" this page?), I'd like to do that in the next week or so.

I'm watching now, :) --MarSch 13:24, 24 Jun 2005 (UTC)

Thanks, MarSch. I will get some of those books, refresh my memory, and try to rewrite the article in the next few days. --CH (talk) 1 July 2005 03:47 (UTC)

You say "uses Einstein geometrodynamics as a synonym for general relativity". That was my understanding as well, so I was also disconcerted by the article's claim of abandonment. If you do write something to straighten it out, it would be great. GangofOne 20:37, 19 July 2005 (UTC)

Gosh, I'm agreeing with GangofOne! What a strange world. --Pjacobi 20:44, July 19, 2005 (UTC)

Geometrodynamics and GR

MTW's opening scene-setting chapter is called "Geometrodynamics in brief", I think that Wheeler seems to be referring to geometrodynamics as an ongoing research project or concept or "work in progress" rather than a specific finished theory – like the principle of relativity, or the principle of equivalence, individual attempts at implementing the idea can fail without invalidating the basic idea.

Wheeler, A journey into gravity and spacetime (1990) pp.118,

"Einstein's 1915 battle-tested and still-standard law of geometrodynamics, his famous field equation."

But going back to MTW's Gravitation (which calls its introductory chapter, "Geometrodynamics in brief"), we find this:

W.K. Clifford, 1870/1879/1882, quoted in MTW Gravitation, section 44.3 pp1202-1203

“I hold the fact (1) That small portions of space are in fact of a nature analogous to hills on a surface which is on average flat; namely, that ordinary laws of geometry are not valid on them. (2) That this property of being curved or distorted is continually being passed from one portion of space to another after the manner of a wave (3) That this variation in the curvature of space is what really happens in that phenomenon which we call the motion of matter, whether ponderable or etherial. (4) That in the physical world nothing else takes place but this variation, subject (possibly) to the law of continuity.”

MTW continues:

“Ask if there is a sense in which one can speak of a particle constructed out of geometry. Or rephrase the question in updated language: “Is a particle a geometrodynamic exiton?” What else is there out of which to build a particle except geometry itself?

The Clifford-Einstein space theory of matter has not been forgotten in recent years. …

Wheeler (1962, again quoted on pp.1202)

“the vision of Riemann, Clifford and Einstein, of a purely geometric basis for physics, today has come to a higher state of development, and offers richer prospects – and presents deeper problems – than ever before.”

compatibility

Of course, the penalty associated with taking Clifford's approach literally, and applying curvature arguments to conventional mechanics, is that the familiar flat-spacetime physics of special relativity no longer seems to appear anywhere in the description: If all moving-body problems can be described purely in terms of curvature, we have velocity-dependent curvature, and since SR's relationships are a special-case solution for flat spacetime, we no longer have the standard SR equations of motion and Doppler relationships, but … Something Else. Lose the crutch of Euclidean geometry, and we are left looking at a big scary blank page. Its the "total rewrite" option.

So, in that sense GMD does not seem to be the same thing as current GR.

This is good and bad: If a full GMD model is not SR-compliant, it doesn’t fit our usual definition of a "credible" classical theory, which might lead some theorists to decide that the GMD idea is discredited … but since it seems that the current "credibility" criteria only pass theories that are incapable of recreating Hawking radiation effects, perhaps any theory that s going to have to deal with the black hole information paradox needs to fail these criteria to have a chance of working. ErkDemon 00:46, 29 August 2005 (UTC)