Discussion in 'Physics & Math' started by Harmony, Dec 27, 2011.
Benzene and Dioxygen (among others) say you're wrong.
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Not neccessarily (unless I'm misunderstanding your point) - we can observe the presence of electron degeneracy (and therefore the Pauli Exclusion principle) in atoms and molecules. It's predicted regardless of whether we treat the electron wave function as an actual wave, or a probability distribution.
Nope, I'm just "some guy".
But if one could eliminate wave-particle duality, for example, without touching the predictive power behind the stochastic process of QM I suspect it would be more palatable to many.
Well sure, and to many a theological explanation is even more palatable still. In the case of the rolling dice you frequently refer to, we have good reasons to believe there's more predictability in the dice than probability allows for, and that a detailed mechanical analysis could in principle do a better job. The onus would be on you to establish that there's evidence for a deterministic description when it comes to QM behaviour. You'd also have to do it in a way which doesn't violate Relativistic causality when dealing with Bell-type experiments, as we've discussed in the past.
Postulate #1: God did it.
I dare you to get simpler! Please Register or Log in to view the hidden image! Not horribly predictive, I suppose...
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Er, no, the issue isn't with 2-spheres existing or not existing. The issue is whether you're considering them unphysical, which doesn't sound like exactly the same thing (it doesn't help that this judgmenent of unphysicalness of yours is something you've never actually defined). Is there something a priori unphysical about 2-spheres?
No. You're abusing terminology here and effectively changing the debate. Normally when we talk about coordinate mappings in GR we mean mapping spacetime with the same number of coordinates as there are spacetime dimensions. The analogous thing to do with the 2-sphere is to map it with just two coordinates. (This is important because when we say that it's not necessarily possible to map all of spacetime with a single coordinate system, we're saying it for the same reasons we're saying it's not possible to map the 2-sphere with a single coordinate system.)
The "trivial" mapping you're describing is actually what mathematicians would call an embedding, where you view a manifold as a structure embedded in a higher dimensional Euclidean space. There's a theorem to the effect that you can always do this with any Riemannian manifold as long as it is sufficiently differentiable. In GR things are a little different because spacetimes are modeled as Lorentzian manifolds rather than Riemannian ones, but a little Googling turns up a reference to an analogous result for the type of manifold we use in GR.
So apparently it's generally possible to globally "map" any Lorentzian manifold (a.k.a. 3+1 dimensional GR spacetime), in the sense of an embedding, but in the worst case you could need as many as 87 spacelike coordinates and 3 timelike ones to do it.
Er, what? Bijectivity doesn't imply continuity. That's why it is normally explicitly included in the definition of a coordinate system.
Aha! So you admit my debate points are effective! Please Register or Log in to view the hidden image!Please Register or Log in to view the hidden image!Please Register or Log in to view the hidden image!
I was going to go into Guest's meaning of "believing in" 2-spheres and how that relates to the subject of mathematics describing Reality (which was the original topic in the bijective coordinates thread)...but then...no.
Seriously, przyk, don't take this the wrong way but I'm checking out of this thread. The topic has morphed into a completely unrecognizable beast, hashing over an old subject that's marginally relevant at best. If I'm going to juggle multiple fronts it has to be interesting banter to me. If this was a war of attrition, then I concede.
Now, if you'd like to start a thread on aspects/ambiguities/inconsistencies of current physical theories that you would like to see eliminated via a T.O.E...kind of like a Physicist's wishlist...THAT would be interesting to me.
I said in one atom. Benzene and O2 aren't atoms.
Thanks for the link to the freebie. I owe you one. Please Register or Log in to view the hidden image!
That's my point - the Pauli Exclusion Principle doesn't just apply to single atoms, as you stated. It applies to whole molecules. It applies to \(\beta\)-carotene just as readily as it applies to atomic hyrdogen.
To put it another way, when we apply your statement "No two electrons in a single atom can be in the same quantum state. But an electron in one atom can be in the same quantum state as an electron in the the atom next door" to benzene, dioxygen, and \(\beta\)-carotene, we find it to be precisely false, because there are quantum states that apply to an atom and its neighbour, or across all of the atoms in the molecule, that are still only capable of containing two spin paired electrons. Which leads us to my second point which is that it's not neccessarily true that "an electron in one atom can be in the same quantum state as an electron in the the atom next door".
It should also be noted, I suppose, that the Pauli exclusion principle also does not apply exclusively to electrons. It applies to all fermions including fermionic nuclei (for example Carbon-13) - although loosely bound pairs of fermions can behave as Bosons.
Except that here you're talking about electrons in a shared molecular orbital, and in that case it's true that there can only be one for every allowed set of quantum numbers and position/momentum wavefunction amplitudes. But when we're talking about atoms lightyears apart, there's nothing in principle to stop the electrons in each atom from having the same quantum numbers and energies, since their position wavefunctions would still be different.
I know, that's the point that I'm making.
It doesn't just apply to electrons.
It doesn't just apply to single atoms.
A quantum state can apply to multiple atoms.
It [Pauli's Exclusion Principle] applies to any Fermion, and any quantum state.
I get that as well, but that wasn't what I was replying to, the post that I was refering to was explicitly and specificaly addressing electrons on neighbouring atoms, and the poster made the same wrong statement twice.
"Criticising" carries the implication that physicists are doing something wrong and that they could reasonably do better. For which you have no support. Also, you haven't even fully done the equivalent of tasting the dish yet, which makes your criticism to a large extent prejudice.
Then what are you doing? You don't appear to be solving anything either. Any time I ask you how you recover the predictions of quantum theory from any of your ideas, you seem to shy away from the idea of having to do any actual work.
I am not declaring anything is unattainable. I don't need to. You're misplacing the burden of proof here. You want to go around telling people you have ideas that you think can fix problems with or restore features to quantum physics? It's your job to support that, and not mine or anyone else's to refute it.
I don't see the point you're trying to make. Quantum physics is something you need to learn whether you agree with it or not. In an ideal world you could look up all the experimental results supporting quantum physics and formulate your own opinion about it. But realistically that's impossible. There's just far too many results. There's already more experimental data than you could possibly hope to analyse in a single human lifetime, with more results coming in at a rate faster than you could analyse them.
That's half the point of quantum physics even if you don't like it: it's the standard experimenters have been comparing their results to since the theory's infancy. You need to learn quantum physics because it is a summary of all the experimental results you will have to be able to explain.
It isn't intended to. Existing theories are already so successful at making predictions that our best chance of experimentally breaking them is a 27 kilometre long collider that took a decade to build, cost billions, and consumes as much power as a small city when in operation.
No, Occam's razor also has very real practical value. The idea behind it is that extra postulates and parameters will show up when a model is going in the wrong direction or someone is trying to shoehorn a theory into something it's not. More parameters is also in a sense "cheating" since it is generally possible to fit a model more closely to known data points if it can be optimised over more parameters. So if two models both fit known data to within experimental error, Occam's razor recognises the one that needs the least postulates and parameters as the more impressive accomplishment. Finally there are also ways in which more postulates and parameters can degrade the "quality" of a model itself. The most obvious one is that more complexity gives a model more opportunities to contain internal inconsistencies. Another is that more parameters will typically reduce a model's predictive power. The reason for that is that optimising too many adjustable parameters over data points - with inevitable experimental errors - is more likely to result in a model that's over-tuned on the noise and statistical fluctuations rather than the underlying pattern.
Occam's razor is not arbitrary.
Stop nitpicking Trippy. I gave a fair response to the OP, which included this:
"The presenter had an uncut diamond and explained that when he warmed it up some of the electrons changed energy levels and as a result all of the electrons in all of the atoms in the universe had to adjust their energy levels because no two could be the same".
It's total trash. It's moonshine. It's garbage. It's woo, presented as bona-fide physics. Address that instead of muddying the waters and starting an argument.
Trooper: my pleasure.
Nitpicking... Yeah, sure, okay...
I've muddied nothing.
"Honest misunderstanding of the Pauli exclusion principle in a popular science lecture" doesn't cut it?
I don't think it even has to be that - what's the maximum distance an electron can be from its parent atom again?
There isn't a maximum distance. But the point is that the reasoning behind Brian Cox's assertion is wrong. The Pauli exclusion principle says that two electrons can't be in the same quantum state. But as has already been pointed out, there is more to an electron's quantum state than just its energy level. The whole spatial wavefunction (as well as the spin state) matters. That's why Pauli exclusion matters for electrons in the same atom or molecule (because their spatial wavefunctions can completely overlap and Pauli exclusion is the only thing preventing that) but is largely a non issue for electrons in separated atoms.
Of course that doesn't mean Pauli exclusion completely switches off just because two electrons are bound to different atoms. But in that case Pauli exclusion shows up as a repulsive force between the atoms that (if I recall correctly) drops off exponentially with distance, so very soon it's no longer the dominant force between nearby atoms. So there's an effect due to Pauli exclusion between electrons even in different atoms, but it's nothing like what Brian Cox says it is.
That was bugging me. You guys explained it well. Thanks! :worship:
What he said led everyone to the conclusion that atoms could not be isolated. Personally, I think it was intentional, to push his new book.
“When they are far apart and isolated, the atoms have identical energy levels. However, as the spacing between the two atoms becomes smaller, the electron wave functions begin to overlap. Antibonding orbital are repulsive and act to destabilize the molecule as a whole.”
Lec 14 | MIT 5.111 Principles of Chemical Science
Double Twit Experiment – What Brian Cox Gets Wrong
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