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foam" as well, and many other approaches to quantum gravity. The reason being that the argument produces a "minimal length" under which spacetime cannot be probed. This CANNOT be reproduced by a framework of selfadjoint non commuting coordinates, since selfadjoint operators have eigenstates (of finite or infinte length), which can be measured with arbitrarily high precision: think of quantum mechanics, where the
Heisenberg uncertainty does not cast any absolute limitation on the ABSOLUTE precision of the position OR speed of an electron; the limitation is only on the JOINT precisions of position AND velocity.
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all have continuous spectra, which are fully
Lorentz covariant in the strongest sense (Lorentz symmetries are unitarily implemented, including translations). It is clear that Snyder's and the DFR model have nothing to do with each other, already as mathematical objects. As far as motivations are concerned, they also are completely different: Snyder wanted to regularise quantum field Lagrangeans, DFR wanted to implement a gravity induced physical principle of stability of spacetime under localisation. This makes thee section "Heisenberg model spacetimes" completely wrong.
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far as I know, this is the first model of this kind, and should not be presented as a "revival of Snyder's model"; I think it is the oldest physically motivated model of quantum spacetime available in the literature, and should be presented as such. By the way, the models with C-number commutator (erratically referred as "Moyal spaces", "Heisenberg models" and such) are nothing but irreducible components of the DFR model, and only were considered in the literature after the DFR paper.
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A more refined argument was discussed by DFR, where uncertainty relations were obtained from assuming a reasonable physical principle, AND commutation relations implementing those uncertainty relations were found (there, the implicitly assumed spherical symmetry of Mead's experiment is dismissed). As
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It should be stressed that the possibility of deformations of the symmetries is one point of disagreement among the specialists, and should be represented as such. The DFR model being a mathematically well defined model with undeformed symmetries shows that the POSSIBILITY of deforming symmetries is
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I run by chance in this page. I think the page contains some errors which should be corrected, including misrepresenting some contributions. Since however I was involved in the field (I later became a coauthor of D and F of DFR), I would prefer to discuss with you some problems, and implement the
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The subject "quantized spacetime" is a speculative subject and there exist not any commonly approved theory about this. I collected here a summary of some mathematical concepts, which are mainly based on discrete geometry and quadratic algebra. Use of the terminology is not established in physics.
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Usually the argument of the time-energy uncertainty is realised as a variant of the "Heisenberg microscope" argument, the first was probably Chris Alden Mead, early '60s. However it does not lead at all to the necessity of non commutative coordinates: in fact it is cited by people doing "spacetime
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This is related with a second problem of the article: Snyder's model has three space coordinates with discrete spectra and one continuous time coordinate. Of course, only discrete space translations are possibile. The DFR model describes four non commuting selfadjoint operators (coordinates) which
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Firstly, as you already discussed, there is some confusion with the term "quantised". The
Schroedinger position and momenta of quantum mechanics are the major (and most succesful) example of quantised quantities, which are not discrete (they have continuous spectra). "Quantised" as a synonim of
170:"discrete" is a remnant of the early days of quantum theory, and should be used very carefully, to avoid confusing the reader (who, reading wikipedia, is probably not an expert) and make him think that quantising is the same as discretising.
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I agree that this article could be more useful if it were written in layman's terms. Although I have a basic understanding of quantized space, I do not understand the author's terms well enough to convert this to simpler language.
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I hope you're able to participate in the delete discussion: as the main contributor your views on why the article is here, whether it could be improved or merged will be valuable. --
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Now, we may discuss which level of detail is appropriate for a
Knowledge page, but if we wish to mantain the level it has now, these things should be represented correctly.
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I've declined the speedy request because you have proposed that this article is merged, therefore we'll be needing this talk page for any discussion to take place.
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Of course the first problem is the lack of a Layman presentation, but should be written after the definition of the main content at the technical level.
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has to be explained. As it is now, it is not very useful to a reader who (like myself) knows only little of theoretical physics.
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The word "quantized" is not used in math. Instead the words "discrete" or its synonym "non-continuous" are used there. Pekka.
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are different concepts, but this is not clear for the average reader interested in physics and will have to be explained.
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Thanks, I just wanted to remove the speedy template for the same reason. It appears to me that quantized spacetime and
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Quantum gravity does however not belong under this subject. Its math has a quite different base. / Pekka
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I've found the first two references on Google books,
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