Talk:Hole argument

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To-do list for Hole argument:

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Tasks for expert: Following model of recent preprint in citations (and perhaps earlier papers by Stachel), write a proper article Rewrite according to comments received (if any). If possible add figures illustrating the argument. Note that Einstein's original drawing is available at Hebrew University, but unfortunately copyright probably precludes adding it here. But an external link would be good! Tasks for anyone: Correct spelling, diction, grammar, etc. Query obscure points in talk page

Contents 1 Fer gosh sakes, don't plagiarize! 2 New version by User:Ian Beynon 3 Odd Citation 4 Students beware 5 Some Historical Comments of Uncertain Accuracy 6 Problems With The New Stuff

[edit] Fer gosh sakes, don't plagiarize!

User:129.10.210.52, I just noticed that the paragraphs you inserted into the tiny stuby I wrote were lifted verbatim from one of the articles by Norton which I cited. In future, please don't do that. We gave the citation so that interested readers could go read what Norton has to say, not so that someone could plagiarize from the article! Sheesh.---CH 03:37, 2 February 2006 (UTC)

[edit] New version by User:Ian Beynon

I was planning to expland this stub in a very different way (focusing on explicit to illustrate the idea of the hole problem more concretely, and relating this to the fundamental local isometry problem solved by Ricci and later more elegaantly by Élie Cartan). Haven't had a chance to read Ian's version, but just noticed that he used figures he grabbed from a paper Rovelli--- this would be an image copyright violation so they were autoremoved. Ian, can you draw your own figures and upload these? ---CH 04:35, 16 May 2006 (UTC)

[edit] Odd Citation

"WHATEVER IS NEVER AND NOWHERE IS NOT:. SPACE, TIME, AND ONTOLOGY IN CLASSICAL AND QUANTUM GRAVITY. by. Gordon Belot. B.Sc., University of Toronto, 1991" Is this published? We don't want to cite an undergraduate class essay or something like that! ---CH 10:05, 19 May 2006 (UTC)

See WP:RS. I have removed this since my question has gone unanswered. If anyone knows more, perhaps the citation can be fixed and readded (if it is published work by a reputable scholar who someone chose to describe oddly as Gordon Belot. B.Sc., University of Toronto, 1991). ---CH 06:41, 17 June 2006 (UTC)

[edit] Students beware

I had been monitoring this for bad edits (although I never did get around to trying to fact check the extensive rewrite by another user), but I am leaving the WP and am now abandoning this article to its fate.

I emphatically do not vouch for anything you might see in more recent versions, although I hope for the best.

Good luck to all students in your search for information, regardless!---CH 00:48, 1 July 2006 (UTC)

[edit] Some Historical Comments of Uncertain Accuracy

Having edited this article, I wanted to clarify some historical points which I do not have the patience to substantiate with references and write about properly, but which explain the context. Einstein's hole argument sounds completely absurd to a modern geometer, since it confuses the form that the metric takes in different coordinate systems with the actual physical situation described by the metric. The question then arises, how did Einstein come to make such a blunder?

I believe that the reason is that Einstein always had a physical interpretation in mind when he talked about a coordinate system. A system of coordinates for him is a collection of observers on a grid of points making measurements. The coordinate system, as Einstein tends to interpret it, is then part of the physical description of a situation--- it is the location of all the metersticks and clocks which are performing the measurments. It is not just a contrivance for giving a mathematical form to a metric.

Taking this perspective, it is natural that one could get confused about the fact that different coordinate systems, interpreted as "different" configurations of clocks and metersticks, could give different answers as to the form of the metric. The resolution would require that the different configurations of clocks and metersticks give the same answer as to the nature of all the relations between the physical objects whose positions they measure. This point of view explains why Einstein uses the language of relational space-time--- that the relations between objects is all that is important--- when resolving this paradox. The modern point of view, which does not give the coordinate system any physical significance at all, makes the resolution of the paradox apparent. Indeed, it is hard to even clearly state the paradox in a modern language. This is why I think it is best to stick with Einstein's original examples.

I can give some evidence for this point of view regarding Einstein's perspective toward coordinate systems from his other work on the general theory. When Einstein discusses the conservation of energy and momentum in General Relativity in 1917 or thereabouts, he constructs an explicitly coordinate dependent Pseudo-tensor. Everyone else who was active in relativity (Weyl and Schroedinger among others) criticized Einstein on the grounds that the coordinate system could not possibly take part in defining such a physical quantity as the energy, but Einstein felt that the dependence on coordinates was only natural, given that the gravitational field was localized at different places depending on the state of motion of the observers. This is again a physical point of view which interprets the coordinate system as a collection of observers.

It is also possible, in my view, although again I have no substantiation, that the absurd confusion between coordinate systems evident in the "hole paradox" paper is what led Hilbert to say that "Every Kindergardener knows more about four dimensional geometry than Einstein, yet it is Einstein who is doing the work (of constructing General Relativity)".

This observation is likely false, because Hilbert makes a variant of the same hole argument in an early draft of his paper on General Relativity. Looks like he's aping Einstein.Likebox (talk) 06:58, 27 December 2007 (UTC)

The reason I am going to great lengths to talk about the history in the discussion section is because the paradox is really so trivial from a modern perspective that a deep discussion of its philosophical ramifications is completely out of place. The notion of a relational space time might be a deep and important philosophical idea, but to fabricate this notion from such an unfortunate blunder is like trying to make jewelry out of horse manure.

Nevertheless, there is a current fashion in some philosophical circles to do just that. But I think that this should not change the article content. I think the article should explain Einstein's original, erronious, reasoning, not the nebulous reasoning of the modern philosophers who misunderstand the confusion and write about it.

[edit] Problems With The New Stuff

There are problems with the new stuff--- the example which starts everything off is severely misleading. The two equations mentioned are not coordinate transformations of each other, they are textual transformations of each other. They are the same equation.

For a good example, use

vs.

which are equivalent by a change of variables.

The discussion of passive/active transformations is one of those things that authors introduce to clarify, but which bugs me personally. I think Einstein's way of stating things is better, but best of all is to clarify everything with gauge theory first.Likebox (talk) 08:45, 6 January 2008 (UTC)