Talk:Hole argument

Neutrality
The second paragraph, "It is incorrectly interpreted by some philosophers ..." seems pretty blatantly non-neutral. There's a serious ongoing scholarly debate about this interpretation. See http://plato.stanford.edu/entries/spacetime-holearg/ for general discussion. I'm new around here, but I hope it's ok to go ahead and tweak it. --Jefelino (talk) 15:21, 28 February 2012 (UTC)

Somehow I missed the neutrality warning below the table of contents before. But I still think the more neutral wording in the second paragraph is an improvement. --Jefelino (talk) 15:36, 28 February 2012 (UTC)

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)

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)

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)

Link to dissertation added. — Preceding unsigned comment added by Ben4wiki (talk • contribs) 11:09, 11 November 2012 (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)

Gordon Belot is a philosopher of physics who teaches at the University of Michigan. That was his doctoral dissertation. (http://philpapers.org/rec/BELWIN) --Jefelino (talk) 15:14, 28 February 2012 (UTC)

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)

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.

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

{dx \over dt} = -x^3 $$ vs.

{3y^2 dy \over dt} = - y^9 $$ 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)

No Problems
Yep, they are not related by a coordinate transformation - that's the whole point!! —Preceding unsigned comment added by Ibayn (talk • contribs) 06:44, 22 June 2008 (UTC)

No Problems 2
I was establishing the underlying gauge transformations of GR, which follows from the principle of general relativity. You must understand that invariance under coordinate transformations is a red herring - all physical theories are invariant under coordinate transformations.

Basically: As is well known, going from newtonian physics to special relativity, following from the principle of special relativity, the position of a particle in space and time only has an objective meaning with respect to an inertial frame. In general relativity, there are no privileged frames of reference with respect to which the position of a particle in space and time has any objective meaning! This is the point of the argument I inserted - Einstein's Hole argument (Hilbert's version of the argument actually). The resolution of this alarming conclusion was given in the article - basically, in GR position and motion has become completely relative and physical obejects are located with respect to one another only and not with respect to the spacetime manifold!!

I did a PhD in theory physics so trust me I have some idea of what I'm talking about. Sadly the argument is'nt well known among the physics community! I'd not seen the Hole argument in any "standard" text book (there are places you can find it but the're a bit obscure - and when you do come accross them they are a bit difficult to decipher, e.g. p 311 of "Physics Meets Philosophy at the Planck Scale") and none of my lecturers had come across it themselves. But it is true and it only took 3 mins to convince me lectures that the argument is valid (I think they felt a bit foolish they hadn't noticed the issue themselves). If you put in the effort to understand the argument then you will be amongst the few people (in the world??!) who get the deepest lesson of GR!!

If you have doubts note that the Hole argument has been given the stamp of approval by all the staff of a leading theory department in the U.K. -

Addressing "Problems With The New Stuff"
The input isn't mathematical, it is completely physical!!! Get it right. The `principle of general relativity' states the the laws of physics are the same for EVERYBODY. This, this, is why we have the same differential equation so solve...

Disputing the above version of Einstein's hole argument
I put up a new section. People really need to understand that, given any solution in one coordinate system, there is another obvious solution associated with any another coordinate system that is NOT obtained by a coordinate transformation on the metric tensor!!! I think the problem people have in accepting this other solution is they are too used to the idea that solutions are only related by coordinate transformations and this is NOT true...And that there is another `distinct' solution is at the root of the Hole argument and people need to get this...


 * That's great. Please provide citations so this can be properly sourced. Paradoctor (talk) 19:19, 10 October 2013 (UTC)


 * Thanks Paradoctor. My sources are mainly from Rovelli's book (and a couple of others) - I've put up references to the pages in his book. I've included a link where you can find a free preliminary version of Rovelli's book. I'm not an expert myself on the exact history and I should look into it more.
 * Can I just mention something else - I keep getting false maths typo errors off wikipedia, this is why I keep saving the same page over again, it seems the only way to stop wikipedia giving me false errors messages. Have other people been experiencing this? IBayn, 11th Oct.


 * Please have a look at TPG. You can easily sign posts by typing four tildes at the end of your post: ~.
 * I don't know what you mean by "maths typo errors", a screenshot might help. You could try Preferences > Appearance > Math > Always render as PNG. For more info on math editing, see WP:MATH.
 * More later. Happy editing. Paradoctor (talk) 04:54, 11 October 2013 (UTC)


 * The math code for wikipedia is basically the same as the math code for Latex. If you type in the wrong thing, make a typo, something it doesn't recognize, it gives you a math error message. Thing is I'm typing in the correct code but it gives me an error message anyway...I dont know why. But if a save the page again the error message goes away and the displayed math formula appear as they should do.Ibayn (talk) 06:07, 11 October 2013 (UTC)


 * Make screenshots before saving, after first save and after second save, please. You can paste the screenshots in MS Paint, if you have nothing else, like XnView or GIMP. Crop as needed, save/export as PNG, upload to Wikimedia Commons, and link them here. Or use one of the many free image hosting services. Paradoctor (talk) 07:46, 11 October 2013 (UTC)

Permission given by Carlo Rovelli to reproduce diagrams
Carlo Rovelli has given me permission to reproduce similar diagrams from his book "Quantum Grtavity" which I will do soon, along with a couple of diagrams of my own and hope this will help illustrate the argument better...

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Substantivalism vs Substantialism
Isn't the stance that spacetime exists independently of the metric defined on it typically referred to as "substantivalism" and not "substantialism"? It looks like some do refer to this is as "substantialism", but most sources use the other term: "substantivilism." This includes Earman's original paper on the hole argument. — Preceding unsigned comment added by MathyPhys (talk • contribs) 10:37, 22 March 2020 (UTC)