玻恩–奥本海默近似 boa the kinetic energy of the nuclei in a molecule is usually much smaller than the kinetic energy of the electrons,

This step is often justified by stating that "the heavy nuclei move more slowly than the light electrons." Classically this statement makes sense only if the momentum p of electrons and nuclei is of the same order of magnitude. In that case m_nuc >> m_elec implies p²/(2m_nuc) << p²/(2m_elec). It is easy to show that for two bodies in circular orbits around their center of mass (regardless of individual masses), the momentum of the two bodies is equal and opposite, and that for any collection of particles in the center of mass frame, the net momentum is zero. Given that the center of mass frame is the lab frame (where the molecule is stationary), the momentum of the nuclei must be equal and opposite to that of the electrons. A hand waving justification can be derived from quantum mechanics as well. Recall that the corresponding operators do not contain mass and think of the molecule as a box containing the electrons and nuclei and see particle in a box. Since the kinetic energy is p²/(2m), it follows that, indeed, the kinetic energy of the nuclei in a molecule is usually much smaller than the kinetic energy of the electrons, the mass ratio being on the order of 10⁴).^{[citation needed]}


玻恩–奥本海默近似



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I take the question being asked to be:- "If gravity doesn't exist, what are the implications ?" Ergo, anything to do with Erik Verlinde is irrelevant to the question. Gravity is one of the two infinite range forces; the other being the Coulomb force between electric charges. Unlike electric charges, eg proton and electron, if they meet, effectively cancel as far as external fields are concerned. Like electric charges mutually repel, and can only be compressed together by Coulombic forces, outside of them; which in turn requires more outer charges. Earnshaw's theorem tells us that no stable configuration of electric charges exists, so large amounts of matter cannot be compressed to high density by any static Coulomb field. Gravity, is the only long range force that pulls instead of pushes (between like objects). So gravity sucks. Without gravity there would be no stars; and no ground or apples to fall on it. Doesn't matter a jot why gravity does or does not exist; without it there would be nothing that we would recognize. share|improve this answer edited Sep 18 '13 at 18:50 answered Sep 16 '13 at 17:38 user26165

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You have a few misconceptions here. General Relativity does NOT say that there is no gravity I know you didn't state that but just in case... On the other hand, it says that it is a manifestation of the curvature of spacetime;. This can be summarised by deriving the EFE from the EH action, and then do the appropriate considerations to be consistent with Newtonian Gravity (c.f. here, this answer of mine, if you want the technical details). Similarly, in QFT, the other fundamental forces are curvatures of certain bundles. Verlinde's theory does not really say that there is no gravity Instead, it gives a "mechanical" explanation for (Newtonian) gravity, through some sort of entropy differences, which I do not fully understand. Verlinde's theory is not likely to be true, anyway Verlinde's theory only derives Newtonian Gravity, and it is unlikely that it will be ever consistent with General Relativity, for example,. While it has been pointed out in the comments by Danu & Jerry Schrimer (and I think I had a very bad memory of what Verlinde's paper was about, looking at the abstract...), the above argument is wrong, I still think the Verlinde paper cannot be right. See for example, these articles by Lubos and this paper by Kobhakidze (whom I initially thought to be Verlinde himself). Finally, to your question.... Ok, now what about your question? As I said, Verlinde's theory does not agree with even General Relativity, and it's probably not going to be quantised either, so it will never agree with string theory, most likely. Also, if it were true that gravity didn't exist, apples would stop falling. share|improve this answer edited Sep 16 '13 at 15:14 answered Sep 16 '13 at 14:28 Dimensio1n0 3,60341537

2   A few notes: 1) Verlinde's paper basically assumes the Hawking entropy and spherical symmetry, and then derives the Newtonian force--this is, by happenstance, identical to the GR geodesic equation for radial observers 2) Other entropic approaches have been able to derive the Hilbert action 3) I've always looked at these as arguments that GR is "generic" rather than emergent, anyway. –  Jerry Schirmer Sep 16 '13 at 14:32 1   Verlinde did actually derive GR using his approach, in the original paper in fact (although I'm entirely ignorant of the details). –  Danu Sep 16 '13 at 14:39 @DImension10 Maybe i posted the question in the wrong way..For what i understood from Verlinde's theory gravity is not a foundamental force but it just derive from the other ones and it's a form of entropy of the space time..As you saying,if this theory doesn't fit with general relativity,string theory or other models im trying to understand what Verlinde is trying to explain with this assumption –  user27494 Sep 16 '13 at 14:48 @JerrySchirmer Are you saying that Verlinde's approach doesn't change nothing in current theories but it's just a way to explain gravity ? –  user27494 Sep 16 '13 at 15:03 @Danu: Hm... Seems you're right. I'll probably fix my answer. –  Dimensio1n0 Sep 16 '13 at 15:05 @JerrySchirmer: Ok, let me correct my answer. One minute. –  Dimensio1n0 Sep 16 '13 at 15:06 @user27494: No; see the links (Specifically, the first.) in the updated answer. It seems that the theory of entropic gravity doesn't really agree with experiments. –  Dimensio1n0 Sep 16 '13 at 15:15 @DImension10AbhimanyuPS Ok,just for understand a little bit..Verlinde's entropic gravity doesn't seem to work right? –  user27494 Sep 16 '13 at 15:21 add a comment |