Talk:Quantum mechanics/Archive 6

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25 Dec 05 is over

24.91.73.141 plopped http://www.nytimes.com/2005/12/27/science/27eins.html in external links. I suppose the travel of enlightenment seekers is apt to be in the other direction: from the there to here. How can something actually be two contradictory things may be the question. Honest-liar, clod-swoosh, correct-incorrect. Here's a quote from that article: "This fall two Nobel laureates, Anthony Leggett of the University of Illinois and Norman Ramsay of Harvard argued in front of several hundred scientists at a conference in Berkeley about whether, in effect, physicists were justified in trying to change quantum theory, the most successful theory in the history of science. Dr. Leggett said yes; Dr. Ramsay said no." Wouldn't it exact if both were right? The Times links the article to some quotes, for instance: " 'I don't like it, and I'm sorry I ever had anything to do with it.' -- Erwin Schrödinger about the probability interpretation of quantum mechanics". If you can bring yourselves to call the eigenwhosis "discrete value" it might help the jargon averse. Is not precision proven to be unobtainable in a reality sure to be uncertain? Unless it both is and isn't, of course. 207.172.134.175 07:05, 28 December 2005 (UTC)

See cat state. --Ancheta Wis 11:13, 28 December 2005 (UTC) Note: |0> |1> are kets, or states. i.e. It is possible to be precise and abstract at the same time. A cat state might be |00...0> + |11...1>. In this notation 0 and 1 are labels like True and False. Or spin Up and Down. etc. Upon re-reading I see that one issue is the existence or nonexistence of precise states without human action. The current experiment which generated a cat state was artificially induced. It will take work to observe a natural 6-atom cat state.

Yes, quantum mechanics wouldn't state that a person was honest and a liar or an object was clod or swoosh at the same time. It would rather state that there's a superposition of the person being honest and of him being a liar or that there's a superposition of the object being clod and being swoosh -- or, for that matter, a superposition of the cat being alive and being dead. Quantum mechanics routinely deals with superpositions of situations, and it is forced to do so by results as seen in the double-slit experiment. Many-worlds theory takes this idea at face value. Ancheta gave the mathematical notation for superpositions. --DenisDiderot 13:18, 28 December 2005 (UTC)

F. Lindner, M. G. Schätzel, H. Walther, A. Baltuska, E. Goulielmakis, F. Krausz, D. B. Milosevic, D. Bauer, W. Becker, G. G. Paulus in Attosecond double-slit experiment Physical Review Letters 95, 040401 (2005) conclude "The observation of interference and its absence at the same time for the same electron (emphasis added) is a beautiful demonstration of the principles of quantum mechanics," and (oh, by the way) attosecond interferometry will have practical applications. The website of Gerhard Paulus explains the experiment. "Superposition" is certainly more firmly established than Jung's Pleroma; note there, "time as relative concept; all historical processes complemented by 'simultaneous' existence in the Bardo or pleroma". Reality is pretty weird. 207.172.134.175 22:38, 28 December 2005 (UTC)

Roger Penrose's omnium appears to be the Bardo or Pleroma, as well. By the way, Penrose, a mathematician who happens to be vitally interested in physics, as evidenced by his new book Road to Reality (I recommend it; it has a very nice discussion of the mathematical concept called a connection as well as a graphic representation for tensor notation; -- his wife illustrated the book) has found a viewpoint that more firmly supports GR than QM. So you might discover that this thread is currently leading to Penrose and GR, as far as I can tell, rather than to QM. --Ancheta Wis 18:02, 29 December 2005 (UTC)

But hold on, this image

Penrose tiling

which resembles the vortex distribution of a bose-einstein condensate shows there is some application of Penrose's ideas to QM. It closely resembles the symmetries in a BEC bose-einstein condensate picture that Eric Cornell recently displayed at a public lecture of his - his picture was blue with each superfluid vortex a dark spot corresponding to a polyhedron in the Penrose tiling, except that the spots followed a hexagonal distribution rather than the pentagonal distribution you see. --Ancheta Wis 20:44, 29 December 2005 (UTC)

Amazon said they'll ship The Road to Reality to me next year. Congrats on your sysopship - don't let them overwork you. GR & QM facets of the same thing? If so, the connection is opaque to the duality mired (i.e. all of us). Happy New Year! Anon user 207.172.134.175 generally also me, Metarhyme 17:52, 30 December 2005 (UTC)

Thank you! Like the old Texas Rangers, who made their star-shaped badges from 5-peso silver coins, I formed an 8-pointed badge out of an Aztec calendar. And a happy J2000+6 to you! --Ancheta Wis 19:46, 30 December 2005 (UTC)

OPERATION to Schrödinger equation

• By the way show given as :

$-{\frac {\hbar ^{2}}{2m}}[({\frac {d^{2}}{dx^{2}}}+{\frac {d^{2}}{dy^{2}}}+{\frac {d^{2}}{dz^{2}}}+{\frac {d^{2}}{dt^{2}}})\Psi (x,y,z,t)]+V\Psi (x,y,z,t)=E\Psi (x,y,z,t)$

Schrödinger equation's coefficient of the extreamly left can be〝operated〞to 2 parts.

One is for Uncertainty Principle exactly well.$\Longrightarrow {\frac {\hbar }{2}}$ which is good for the limited value of the product by $\Delta P$ and $\Delta X$.

The other is for ${\frac {\hbar }{m}}$,recently without any sense in physics well. --HydrogenSu 09:58, 30 January 2006 (UTC)

The left side is just Kinetic + Potential energy. The left half of the left side is Kinetic energy, the V half of the is Potential energy, for a single particle. If you use the heuristic that 'Observables (Kinetic + Potential energies) are Operators', you get the right side of the Schrödinger equation. --Ancheta Wis 10:55, 30 January 2006 (UTC)

Can we take apart by seprated operation on $\hbar \over 2m$ without any reasons of "Observables or not"? (Just in Math to seperate them away?)Thank you,this is my question after reading your reply.--HydrogenSu 18:10, 30 January 2006 (UTC)

This equation confuses me. Why are time and space treated the same way, on the left side in a non-relativistic equation? Why are there time derivatives but a constant energy. David R. Ingham 07:56, 12 February 2006 (UTC)

The Schroedinger equation is non-relativistic. There are relativistic quantum mechanic equations such as the Klein-Gordon Equation. The left side could be seen as the hamiltonian operator on the function and the left side is the scalar energy times the function. This equation therefore is saying that the energy is the eigenvalue. What you also may be confused is that it can also be shown with a time derivative in place of E. This is also correct where the operator corresponding to E is a first order time derivative, this is also seen in classical mechanics but the algebraic structure is different between them. Time and space are not the same, although they appear to be. Time in non-relativistic quantum mechanics is nothing but a parameter, like the affine parameter in general relativity. It has no significance other than being a parameter. The position however is an operator. it is not evident here and in this format since using wave functions is very clumsy in terms of quantum mechanics. the second derivative with respect to space is the momentum operator. its hard to judge what is a parameter and an operator by mearly looking at an equation. i hope that made some sense --Blckavnger 20:55, 17 November 2006 (UTC)

A Question of Linear Operators

I have a question on [1]. Why does

${\mathcal {<}}p^{2}>={\Delta }p^{2}+<p>^{2}$?

--HydrogenSu 09:48, 26 January 2006 (UTC)

I switched it to momentum because thats what the picture said. --Ancheta Wis 11:37, 26 January 2006 (UTC)

My question of that belongs to Quantum mechanics. I hope it be kept.:)

By the way thank you.

To answer your question

$\Delta p^{2}\equiv <(p-<p>)^{2}>$

${\mathcal {=}}<p^{2}-2p<p>+<p>^{2}>$

${\mathcal {=}}<p^{2}>-2<p><p>+<p>^{2}=<p^{2}>-<p>^{2}$

Thanks a lot. By the way I edited some of your Math view for good-browsing. It was too long for looking. Sorry:)--HydrogenSu 18:23, 30 January 2006 (UTC)

Quantum darwinism

I started the article a while back and placed a link here; I'm sure it was removed for a good reason... but couldn't it be linked to somewhere in this article? And or going in the Quantum topic template? - RoyBoy ⁸⁰⁰ 08:15, 30 January 2006 (UTC)

My changes: http://en.wikipedia.org/w/index.php?title=Quantum_mechanics&diff=39241812&oldid=39099331

There is so much discussion here that my edit comments may not be considered sufficient explanation for my changes.

"Quantum mechanics uses complex number" The probabilities are not part of the mathematical formulation. The formulation is in terms of complex wave functions, and so forth.

"These are related to classical physics and ordinary language largely with the use of probability." This is essential to interpretation of classical physics and ordinary language in terms of quantum mechanics. Encyclopedia readers will be looking at it from the other direction, but this wording can be read from the classical point of view also.

"Newton's laws of motion" Gravity has little to do with atoms.

"obeys" qm "arises from" all observations of nature.

"the classical position" in qm, things have wave functions. "position", in the sense of an exact position of a particle is a uniquely classical concept. (Position doesn't seem to have a good link so maybe I will remove the link.)

"instead of describing" This change may not be necessary, but is based on the same argument as above.

"Therefore, quantum mechanics, translated to Newton's equally deterministic description, leads to a probabilistic description of nature." I expect a lot of argument about "equally deterministic", but the time dependent Schrödinger equation is first order in time, which makes it explicitly deterministic. The probabilities do not arise until the classical approximation is first used. The (new) probabilities belong only to the relation between qm on one hand and classical physics and ordinary language on the other.

Perhaps "Newton's equally deterministic description" may be inadequate here, because it is not really his view, it is the view of everyone before Schrödinger and Heisenberg.

David R. Ingham 08:59, 12 February 2006 (UTC)

"probabilistic description of nature" I don't like this phrase, but it is explained now. David R. Ingham 09:09, 12 February 2006 (UTC)

Thank you for the careful writing. As Feynman would have said, good! --Ancheta Wis 12:32, 12 February 2006 (UTC)

Thank your Ancheta Wis, but I hope that a favorable comment by an administrator has not inhibited others from expressing their views. Some of these ideas have been controversial in Wikipedia, and I hope to have a chance to continue to support my points of view. I have found already that mention of Richard Feynman or Julian Schwinger often discourages further argument, like "kings X" in children's games. This is especially useful to me, because I have heard them speak and don't have to cite anything that can be checked. David R. Ingham 08:50, 21 February 2006 (UTC)

High School Student here

Dear Scientists,

I am a 10th grader. I am supposed to do a project on Quantum Mechanics for my school and I really do not have the slightest clue about what any of you are talking about. :( If you really want to make a good page you are going to have to simplify it. Like that guy above said, if you really understand this stuff, then you should be able to explain it to an idiot. So this is a challenge for you guys, please tone the level of scientific facts and words down on here and I think that people will like you more.

I am a big fan of Quantum Mechanics. I think that they are great. However I would really like to learn more about them because I am supposed to write a children's book about them. :(

Well I hope some of you people can take my request to heart and maybe you could try to make

Dear Student. You might want to start with spectroscopy or radioactivity, or even a blackbody (a light bulb). QM doesn't impinge too much in our daily lives, unless you want to count the operation of a transistor or laser. It takes years to understand Quantum physics, although classical mechanics appears on every kid's playground with slides and swings and merry-go-rounds. If you look at the stars you might even wonder why do the stars shine. If you are trying to understand how an atom could exist, you will have just asked a QM question. You should start with the first link at the top of the article. --Ancheta Wis 18:32, 19 February 2006 (UTC)

Thinking about it, your book assignment should be answering what, when, where. How and why are more difficult questions. The physics of the playground answers the first 3 w's only. If you start with why then your level of understanding and and search for answers will take years. 19:03, 19 February 2006 (UTC)

Here is a start at what:

QM can explain the periodic table of the chemical elements.

Now you can start filling in when, where in your book. The illustration for the article shows the first few electron orbitals for chemical element number 1: hydrogen. 19:36, 19 February 2006 (UTC)

But how will you know when you are done with your study for the book? -- When you don't have to click on any link in the Wikipedia article you are studying because you already know what it is going to say. When that is true then you are ready to write. 19:52, 19 February 2006 (UTC)

And what if the words in the articles are foreign to you? Well, you are fortunate enough to still be in school. Ask your teacher about the meanings of those foreign words. I recommend grouping your unknown words or ideas in fewer than seven unknowns at a time. Write each question/ word on a separate index card. When you don't know something, write the unknown down on the card. When you get the answer, write that down on the card as well. Eventually you will have a bunch of cards which you can start sorting into related groups. Use Wikipedia to help you sort the cards. If the words are related, they will be on the same Wikipedia page. Then take the cards with the words on them and construct sentences from the formerly unknown words. If you still can't write a sentence about the words, wait. It takes time to understand anything that is important. That does not mean memorizing everything on the card. If you care about the word, it will remain with you (sometimes for the rest of your life). I hope that you understand that your questions are the most important part of all this research. You can always find answers on the Internet or in a book or article or person you have found. But answers will come to you in their own time, when you are finally ready to understand them. Just wait; I hope you are ready when the answers come.

When the periodic table was invented, it was discovered by a man who also wrote down the elements on index cards. He laid his index cards on the table and grouped like-elements together. When he found a missing element he wrote down a card which predicted the properties of that element.

When Ward Cunningham was inventing the wiki he also used index cards. (Where did the signature go?)

• The signature "23:14, 19 February 2006 Ancheta Wis" seems to have been omitted here.

I am answering a point at a time, without reading everything first.

There is an attempt to simplify called Basics of quantum mechanics, but I disagree with its claim to avoid advanced topics: most of quantum mechanics can be understood without worrying about probabilities.

Writing a children's book about qm is an even more ambitious project than trying to explain it to high-school students. I think it would be of great value if someone could succeed in writing one that would really be read and understood, because I believe that qm, like foreign languages, is best understood if started early.

I told my 11 year old niece "If you keep on looking through more and more powerful microscopes, you don't keep on seeing more detail forever. Eventually matter is composed of units called atoms and motion is composed of units called quanta." I am not sure that helped her more than it confused her, but I can't think of anything better I could have said. Atoms are traditionally taught before quantum mechanics, but are not more fundamental. There would be no explanation of why they form molecules and crystals. David R. Ingham 04:39, 20 February 2006 (UTC)

Classical mechanics does not have a greater effect on in our everyday lives than qm does. It is just more intuitive and closer to direct observation. When you throw a baseball, where it goes is mostly explained by classical mechanics and your thoughts as you catch it are related to Newton's laws. Why it stays together and occupies space and how you can see it are only fully explained with quantum mechanics. But the qm takes too much mathematics to use on the baseball field. It is used to support technology, mostly in chemistry and engineering, to make things that can be used without understanding their design principles. David R. Ingham 05:44, 20 February 2006 (UTC)

Children's book

How about:

Once upon a time there was a particle of yellow light. We call her Goldielocks, though light particles can't really have names. She wandered until she came to an atom that had three bare electrons. One electron was stuck too hard in the atom. One was too loose. The third was just right, so he and Goldielocks became a photoelectron.  ? David R. Ingham 06:20, 20 February 2006 (UTC)

Explanation:

Quantum mechanics explains the fact that light is composed of particles.

If elementary particles like light and electrons could be labeled with names, much of modern physics would not work. Exchanging two identical particles does not change anything.

The term "bare electron" is used a lot, but it doesn't have any justification here beyond resembling the original version of the tale.

A light particle can excite a "loose" electron but that may be less likely than one that is "just right".

One of Einstein's important early discoveries was an explanation of individual light particles knocking individual electrons out of their atoms. The light particle becomes a part of the electron's motion. David R. Ingham 05:59, 21 February 2006 (UTC)

Introducton

• JA: Re:

Quantum mechanics; 03:48 ... David R. Ingham (Talk) (→Description of the theory - I think this is a further improvement, but I don't think we are done. This is a good paragraph technically, but is it simple enough for the introducton?)

• JA: I dunno, it would depend on the charge of the introducton. Jon Awbrey 04:00, 9 March 2006 (UTC)

Schrödinger's QM philosophy

What if the Philosophy section were a separate page, Philosophy of quantum mechanics, currently a redirect. Much could be written on this topic, but separately. For example, Schrödinger, Bohr, Born, Einstein were passionate about their viewpoints; Ernest J. Sternglass' memoir, p. 125, notes that Bohr was influenced by Soren Kierkegaard. --Ancheta Wis 11:00, 9 April 2006 (UTC)

I agree. There is much to right on Philosphical views of Quantum Mechanics.-Holy Ganga 17:21, 9 April 2006 (UTC)

HG's contribution copied here for further discussion.

Regarding mystical philosophical insights on Quantum mechanics, Erwin Schrodinger said, Vedanta teaches that consciousness is singular, all happenings are played out in one universal consciousness and there is no multiplicity of selves. This life of yours which you are living is not merely apiece of this entire existence, but in a certain sense the whole; only this whole is not so constituted that it can be surveyed in one single glance. This, as we know, is what the Brahmins express in that sacred, mystic formula which is yet really so simple and so clear; tat tvam asi, this is you. Or, again, in such words as “I am in the east and the west, I am above and below, I am this entire world". There is no kind of framework within which we can find consciousness in the plural; this is simply something we construct because of the temporal plurality of individuals, but it is a false construction....The only solution to this conflict insofar as any is available to us at all lies in the ancient wisdom of the Upanishad. The multiplicity is only apparent. This is the doctrine of the Upanishads. The mystical experience of the union with God regularly leads to this view, unless strong prejudices stand in the west.

Is there a citation for this? I know a few things about philosophy of physics, and this doesn't ring a bell. --best, kevin [kzollman][talk] 17:38, 9 April 2006 (UTC)

Kevin and HG, I would be grateful for a discussion of the role of the observer in the QM framework. What would be the basis of an observation when the scale of the observer far exceeds the scale of the system under discussion? --Ancheta Wis 17:44, 9 April 2006 (UTC)

I'm not sure what your asking about. Are you worried about the measurement problem? This has received substantial treatment by both physicists and philosophers of physics. We have a very good article on at least one interpretation of quantum mechanics the many-worlds interpretation of quantum mechanics. Is this what you're getting at? --best, kevin [kzollman][talk] 04:49, 10 April 2006 (UTC)

Last I looked, I did not agree that those were very good articles. In my opinion, these questions can only be seriously addressed, after learning the mathematics necessary to understand the basics of qm. Discussing them here in non-mathematical language appears to be endlessly frustrating. David R. Ingham 05:08, 10 April 2006 (UTC)

Inaccuracies in Paragraph 5 of the introduction

I'm very new to editing wikipedia, as in never done it before. :)
I don't want to just delete a line from the article as my first edit, with out a comment about it. The last line in para 5 "It was from this view that the uncertainty principle, the foundation of quantum mechanics, arose." this = wave particle duality
This statement is not true, as far as I know. The uncertainity principle is a mathmatical property of operators, which leads to be the Canonical_commutation_relation. The Heisenburg uncertainity principle is just a specific application of the cannonical commutator.
If I understood how to do math here I would show the derivation of it. Specifically I'd be following the equation 2.50 on page 43 of Introduction to Quantum Mechanics 2nd ed, by Griffiths, as support for it not being from the wave particle duality that gave rise to it.
I'm ignoring the part about the uncertainity principle being the foundation of quantum mechanics when it would be much more proper to say that the Schrödinger Equation is the foundation of Quantum Mechanics.
I'll admit that there may be history where the wave particle duality lead to this that I don't know about, but it doesn't seem a proper statement to have in the article. It makes it seem that because there is the duality it was derived from there to have this result. Which isn't the case as it came from existing mathmatical properties.
Thanks for any patience to this newb as he tries to make articles better.

NijaMunki 07:32, 18 April 2006 (UTC)

Go ahead and change it. Be bold!

By the way, you don't have to type <BR> and you don't have to put underscores in links. For help with math markup, see Help:Formula. —Keenan Pepper 17:02, 18 April 2006 (UTC)

Quantum mechanics and free will discussion - missing

I couldn't find anything on the quantum mechanics pages on the relation between quantum mechanics and free will. I think it's an interesting philosophical discussion, but unfortunately I know next to nothing about it. Anyone who does?

You might try Max Jammer's book, which is listed in [2]. See also the Category:Quantum mechanics for the current articles on the topic. Warning: the topic is currently considered one of the imponderables. We do not seem to know enough yet. That is one reason you may not have found too much. Have you investigated the free will article, as a start? --Ancheta Wis 19:05, 7 May 2006 (UTC)

Needs a longer lead

The current lead at one short paragraph is not enough for a featured article its size. A FA should have a 3, at least 2 paragraph lead that actually says something, rather than the hollow thing currently sitting there that says little more than Quantum Mechanics is a theory of physics. I think the lead needs improvement to meet the ever-increasing FA standards. Loom91 17:52, 9 May 2006 (UTC)

No. The suggested number of paragraphs need not be 2, 3, etc. It depends on the article; a FA can be short, in which case 1 paragraph suffices.

I would be careful about categorical statements like this, as a FARC notation generates a lot of work when each point is not met head-to-head by the single lead-editor of a good article.

Your carefully selected FARC contributions point out a structural difficulty in the popular FAs which have been accreting content by dozens, or even hundreds of editors. --Ancheta Wis 08:24, 12 May 2006 (UTC)

Ancheta makes a good point. The actual criteria at WP:WIAFA only state that an FA should have a concise lead. At WP:FAC, editors have recently been insisting on three paragraphs, but that isn't essential; even if it was, it wouldn't merit demotion (see my comments at the FARC page).

Relation to gravity

At the moment, the paragraph on quantum mechanics and gravity (general relativity) is deeply misleading. On the other hand, a coherent description of the actual problems requires perhaps more technical sophistication than the average reader will have. The article quantum gravity describes the real problems. The actual situation is that gravity can be quantized, but only as a low energy effective theory below the Planck scale. Since we have no means of experimentally probing this scale, the effective theory of quantum mechanics and general relativity is perfectly valid and able to describe all known phenomena. The claim that determinacy is somehow relevant is false; quantum mechanics, in fact, is perfectly deterministic as a theory. It is only when we attempt to apply it to the complicated decohering dynamics of objects that are effectively classical that probabilities arise. In any case, such issues exist for all quantum theories, not just the quantum theory of gravity. I could attempt to explain this in more detail in the entry itself, but I fear it would get too technical, and be revised anyhow by overzealous editors with limited understanding of the issues. So I merely point it out here for now. -- MR

MR, perhaps some discussion might clarify how a theory based on probability amplitudes might be called deterministic. Might not this theory be called stochastic instead? Might it not be more accurate to distinguish an indeterminate form from a deterministic one? --Ancheta Wis 11:02, 27 May 2006 (UTC)

So I guess you're referring to the effective field theory given by perturbative GR as a nonrenormalizable field theory. Does that theory predict any new results? I'm not very familiar with that theory, it seems a lot of particle physicists are loathe to have anything to do with nonrenormalizable field theories (though I guess maybe solid state physicists and string theorists don't mind them as much).

Anyway, I can't figure out which particular part of the article you're complaining about. The paragraph about gravity and quantum mechanics doesn't seem to say anything controversial, and does not mention determinism. But it sounds like you might be referring to this fact: some people questioned the need for a quantum theory of gravity. Perhaps quantum theories of matter could be coupled to classical gravity. This turns out not to be the case, because you can't write a correlation function for fields if you don't know where they become spacelike separated (which depends on the metric). Maybe that's what's meant? Can you point out which text in particular you meant? -lethe ^{talk +} 17:24, 27 May 2006 (UTC)

I mean the paragraph that says:

"It is believed that the theories of general relativity and quantum mechanics, the two great achievements of physics in the 20th century, contradict one another for two main reasons. One is that the former is an essentially deterministic theory and the latter is essentially indeterministic. Secondly, general relativity relies mainly on the force of gravity while quantum mechanics relies mainly on the other three fundamental forces, those being the strong, the weak, and the electromagnetic."

This does mention determinism, and that has nothing to do with the difficulties. Also, the fact that GR deals with gravity and the SM with the other forces is not a "contradiction." The use of this word is strange and misleading. The difficulty, as you say, is that gravity is nonrenormalizable. This does not mean that it "contradicts" quantum mechanics, it simply means that it is at best a low energy effective theory. But that's fine, for the scales we have been able to probe. In other words, there is no contradiction between the theories in the regimes where they make testable predictions about the real world. I think it is important to clarify this.

I am definitely not talking about the idea of coupling quantum mechanics to classical gravity; I think that is manifestly silly.

Also, as far as nonrenormalizable theories go, many particle physicists these days are all too willing to deal with them (extra dimensions), but that's beside the point. The point is that GR is well-tested as a low energy effective theory, and presents no contradictions as such. Of course we would like to have a quantum theory that makes Planck-scale predictions, but the lack thereof doesn't mean our current theories are incompatible. --MR

Put another way: in the days of the Fermi theory of weak interactions, no one said (as far as I know) that it was fundamentally incompatible with quantum theory. It was just a nonrenormalizable theory, which eventually got replaced by the Weinberg-Salam theory, which could make predictions that didn't break down at the weak scale. For some reason with gravity people like to talk as if there's all this extra metaphysical angst associated with the problem. There isn't; it's just that the relevant scale is much farther away and harder to explore. --MR

OK, I'm sorry, I was looking at a different part of the text. Now that we're on the same page, let me respond. OK, so renormalizability of GR is a property of the quantum field theory of perturbative GR, not a property of the classical theory of nonperturbative GR (which is not really a field theory). So when we say that quantum mechanics is incompatible with GR, we really mean just that: GR the classical theory and the quantum mechanics of matter (in any of its guises) contradict each other. It is not at all referring to the nonrenormalizability of the perturbative GR field equations.

Now, as for whether it's silly, well I suppose it is. Isn't it stupid to try to couple a quantum theory of matter to a classical theory of fields? But maybe not as stupid as it first seems. I mean, you do it all the time in quantum mechanics in the presence of an EM field, where it's known as the semiclassical approximation. There is a semiclassical approximation with gravity too. In both cases, the quantum matter couples to a nondynamic field. I guess coupling matter to a nondynamical EM field violates the gauge principle, which dictates that the field be promoted to a dynamical variable and gives you Maxwell's equations. Similarly, coupling matter to a nondynamical background metric violates the equivalence principle, which dictates that the metric be a dynamical variable and gives you Einstein's equations.

One way to conform to the equivalence principle is to make the classical spacetime metric dynamical and set G = <T> where the brackets denote the expectation value of the matter fields. This is what I meant when I said couple classical GR to quantum matter. I totally agree with you that this is just silly. However, it has been investigated in the literature and is mentioned in the first week of any string theory class, where the cited result is that it is inconsistent. This is I think what is meant in the article. So I don't think it says anything wrong, if you interpret it the right way.

But yes, the nonrenormalizability of perturbative GR doesn't indicate anything other than the fact that either quantum gravity isn't a field theory or else that perturbation is inappropriate for gravity (both sides have their proponents). It does not mean that one contradicts the other (as indeed they cannot, or else we live in an inconsistent universe). -lethe ^{talk +} 19:43, 27 May 2006 (UTC)

OK, so renormalizability of GR is a property of the quantum field theory of perturbative GR, not a property of the classical theory of nonperturbative GR (which is not really a field theory).

Classical GR is a field theory. That's why it's in the Landau & Lifshitz book on field theory, for instance. Of course, quantum GR might not be, but it certainly looks like one at long distances.

So when we say that quantum mechanics is incompatible with GR, we really mean just that: GR the classical theory and the quantum mechanics of matter (in any of its guises) contradict each other. It is not at all referring to the nonrenormalizability of the perturbative GR field equations.

Huh? We don't say Maxwell's equations and QED are incompatible, we say one reduces to other in some limit. The same is true of the effective field theory of quantum GR and the classical theory of GR. There's absolutely no incompatibility in sight, and it's misleading for the article to claim that there is.

There is a definite difficulty in quantum gravity, and that's finding a well-defined quantum theory of gravity valid at short distances. I think that's the only claim the article should make along these lines. As you say, it might be solved in field theory (if gravity plus matter turns out to be asymptotically safe), or it might not.

When you say "perturbation is inappropriate for gravity", what do you mean? We certainly ignore nonperturbative gravity effects constantly when doing calculations of, well, pretty much anything. Of course perturbation theory applies to gravity on weakly curved backgrounds, no one disputes this. Unfortunately, we don't really have any strongly curved ones around to study. -- MR

Whether you want to call GR a field theory is a matter of definition I guess, so I won't argue that. My point was simply that when you say say GR is nonrenormalizable, you're not actually talking about GR, you're talking about the field theoretic quantization of perturbative GR. So when the article says that GR and quantum mechanics are contradictory, it does not mean that GR cannot be quantized (presumably it can), it rather means that classical GR and quantum mechanics are incompatible.

Huh? We don't say Maxwell's equations and QED are incompatible. Here is what we would say: the quantum mechanics of charged particles is incompatible with the gauge principle of classical EM fields. In order to have quantum matter and the gauge principle, you must have quantum EM fields. I think you probably aren't even considering this point, because you think it's silly (and it is), but what I'm saying is roughly that classical field theories are incompatible with quantum matter theories (and I might or might not be counting Yang-Mills as a matter theory here).

Listen, let me find some old notes and try to rework that paragraph so that it's not so ... wrong, and word clearly what I think it (and I) am trying to say, so then we can have something much more definite to argue about. -lethe ^{talk +} 22:27, 27 May 2006 (UTC)

Well, MR, I couldn't find the notes which contain the bit which I thought was relevant. Basically, there is some pretty little argument by which you can see that quantum mechanical matter coupled to classical GR leads to a violation of the Heisenberg uncertainty principle. It's a fairly heuristic argument, simple enough for a layman to understand I think, so I'm annoyed that I can't remember it, but I'm sure that it's what the author had in mind when he wrote the paragraph under discussion, and if done right, might make a nice addition to the article. Anyway, the point is that it's not quantized gravity which is incompatible with quantum mechanics, it's GR, which is a classical theory. You can have quantum wood on a classical background, but you can't have a coupled classical background. -lethe ^{talk +} 23:27, 28 May 2006 (UTC)

lethe, perhaps the QFT section gauge covariant derivative#Quantum field theory and the GR section below it pertain to the statements above. --Ancheta Wis 01:49, 29 May 2006 (UTC)

Hmm, despite the article header names, nothing in that article seems to be in any way related to quantum mechanics. Rather, that seems to be a place to list some formulas from differential geometry in a place where the mathematicians can't get to them and make them indecipherable.  :-) -lethe ^{talk +} 01:58, 29 May 2006 (UTC)

No, the idea I'm trying to remember was a cute little gedanken experiment. Something along the lines of: assume you have a quantum particle in a superposition of two quantum states and then you arrange some (classical) gravitational interactions, and then you can perform a measurement to tell you the position and the momentum of the particle. -lethe ^{talk +} 02:02, 29 May 2006 (UTC)

Anville's revision

I just went to the article to see if I could rewrite the paragraph under dispute, and it wasn't there! I see that Anville had already done it. Anville removes the weird sentiment that because GR deals with one fundamental force and quantum mechanics deals with the other three, they are therefore incompatible. Anville also axes the determinism stuff. I had been planning to mention some of the particular difficulties with quantum mechanics and GR, something from what MR and I have been discussing, whereas Anville's simply alludes to "serious problems". Upon further reflection, I'm not sure that this article is the appropriate place to mention, even in a passing summary, what those serious problems are, therefore I think Anville's approach is better than mine (would have been). In short: good work, Anville, and thanks. Have you anything to add, MR? -lethe ^{talk +} 01:54, 29 May 2006 (UTC)

I'm aware of the gedanken experiment you were thinking of (I seem to recall a nice discussion in Wald's book, but I won't have a chance to check until later this week), but in any case I'm not sure it belongs in this article. Anville's rewritten paragraph is much better, in my opinion. I still have some minor misgivings about saying QM works for the very small and GR for the very large, but it's reasonably accurate for an article at this level of technical detail, I think. Referring the reader to the article on quantum gravity is really the right thing to do, so I'm pretty happy with the paragraph as it stands now. -- MR, 29 May 2006

On your suggestion, I'm looking in Wald. He has quite a bit of nice discussion, including the idea that I brought up before of setting G=<T> (classical gravity coupled to the expectation of quantum matter). He doesn't mention the particular gedanken experiment I'm looking for, but that's OK. I agree with you, it doesn't belong in this article. -lethe ^{talk +} 05:18, 29 May 2006 (UTC)

I vaguely recall a gedankenexperiment along those lines in The Feynman Lectures on Gravitation. (Oh, and I'm glad I could help with the rewriting.) Anville 19:23, 2 June 2006 (UTC)