Pauli Exclusion Principle

Discussion in 'Physics & Math' started by Harmony, Dec 27, 2011.

1. TrooperSecular SanityValued Senior Member

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I don't know, CptBork. Maybe he didn’t fall into the same logical trap as the woo woos, after all. This paper suggests that they were able to entangle macroscopic diamonds. Well anyhow, what is the wave function for a particle in an infinite square well potential? :shrug:

"Oxford and NUS physicist Vlatko Vedral, who was not involved in the new research, says it can't be that entanglement exists at the micro level (say of photons) but not at the macro level (say of diamonds)," because those worlds interact."

Quantum Entanglement Links 2 Diamonds

http://www.sciencemag.org/content/334/6060/1213.summary

Last edited: Jan 6, 2012
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3. brucepValued Senior Member

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It doesn't either. The quote I referenced was Farsight not you. This is what he said:

"In essence a mathematical conjuring trick is employed to do a hop skip and a jump over the end of time, by pretending that a stopped clock is still ticking away, when it isn't."

You agree with what he said? Hopefully not since that comment proofs Farsight doesn't understand the difference between a remote analysis and a local analysis. The Rain observers wristwatch time doesn't stop when falling through the event horizon.

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5. RJBeeryNatural PhilosopherValued Senior Member

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While it wouldn't normally be that big of a deal, this particular issue is directly related to a topic under discussion, therefore I must insist on some pedantry here. It doesn't read like you are attributing the quote to me? Read it again.
I agree with what he said TO THE EXTENT that that Kruskal coordinates were brought in to make the mathematical singularity at the EH vanish...that's it. That's what "to the extent" means, just as I wrote in my last post.
I don't know you brucep, and misattributing a quote is a very minor offense, but so far I'm not impressed with your ability to read what I'm writing. :shrug:

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7. CptBorkRobbing the Shalebridge CradleValued Senior Member

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But this isn't what Dr. Cox was talking about. Dr. Cox was talking about all particles in the universe being instantaneously connected in a causal fashion at all times (while somehow not violating causality). I read more on the double square well potential example, and it doesn't even seem to account for the localization of various particles, i.e. a quantum state with a particle localized to a well-defined region would exist in a superposition of the energy eigenstates, which is not the situation he considers when invoking the exclusion principle. In Dr. Cox's example, the electrons don't interact with anything, aren't localized to a narrow region, and their wavefunctions would never change or move around since they already correspond to well-defined energies, and that's totally unrealistic even in the simplest of real world laboratory examples.

Firstly we must note that "square well potential" refers to a hypothetical, unrealistic 1-dimensional simplification ("particle in a box" is somewhat more realistic, try Googling it). Secondly, there are an infinite number of possible wave functions a particle can have in such a potential. In the position basis they would be normalized linear combinations of sine and cosine waves whose frequencies are chosen so that the amplitudes are zero at the boundaries of the potential.

Edit: That's for inside the infinite potential well. Outside the well, for finite energies the wavefunction is always zero, so the total wave function is a linear combination of truncated sines and cosines.

Last edited: Jan 6, 2012
8. brucepValued Senior Member

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You're right of course. I wasn't thinking. RJ is your initial. I was thinking the RJ was a reference to the Rain metric which doesn't make much sense either since that would be Gullstrand-Painleve. Sorry.

9. TrooperSecular SanityValued Senior Member

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That makes sense. Thanks, CptBork.

While we’re on the subject of counterintuitive consequences of quantum weirdness, can I ask you something about superposition? There’s this quantum physicist, Aaron O’Connell, who created the world's first quantum machine. His measurements of the quantum machine constitute the first direct observations of quantized behavior in the motion of a visible object. “The experiment showed that a large object (made of about 10 trillion atoms) can display just as much quantum weirdness as single atoms do.”

Well, how in hell can you actually see something move and not move at the same time with the naked eye?

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Making Sense of a Visible Quantum Object

"Quantum Microphone" Puts Visible Object in Two Places at Once

10. brucepValued Senior Member

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Thanks that was interesting. Seems we read this paper, http://www.ncbi.nlm.nih.gov/pubmed/20237473, awhile back. Didn't have to buy it then.

Another possible macroscopic quantum object is a Bose-Einstein Condensate.

11. RJBeeryNatural PhilosopherValued Senior Member

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Well, brucep, you went from me being skeptical of you to me being impressed! A straightforward admission of error and apology is a rare-find on this forum (unfortunately). Well done, brother

12. TrooperSecular SanityValued Senior Member

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Was there a discussion about it, as well?
Yes, of course.

A while back, I was reading about sorting superfluidity from Bose-Einstein condensation in atomic gases. I asked AN and prometheus, if the flux pinning that takes place in superconductors could also take place in superfluids. They explained the two different effects very well. Although, they have a few qualitatively similar properties and BSC descriptions exist for both. However, Lunar was able to find an example of flux pinning in superfluids and some interesting stuff on the dynamics of the vortex, if you’re interested.

13. FarsightValued Senior Member

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Check out rotons.

brucep: I do understand the difference between a remote analysis and a local analysis. The thing is, where the coordinate speed of light is zero, light has stopped, your light clock has stopped, and you have stopped. It takes you forever to measure that the local speed of light is 299,792,458 m/s. You never actually measure it. A reference frame is an artefact of measurement, and if you can't measure anything, you haven't got one. And you never ever will.

14. TrooperSecular SanityValued Senior Member

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Cool! Thanks, Fairsight. I’ve came across most of the quasiparticles but never the roton. Darn, I wish I could read this paper by Feynman.

Superfluidity and Superconductivity

15. przyksquishyValued Senior Member

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The problem isn't you using the term "branching". The problem is you making superficial deductions from the name Everett called the process instead of the actual mechanism behind it.

No, before the measurement, the world was described by a single non-entangled wavefunction. Then it evolved to a single entangled state while the measurement was being performed. That's the branching process: the evolution of the wavefunction from one that isn't entangled to one that is very strongly entangled. And that's a continuous process.

Well done. You've just proved that, all this time you've been judging the MWI, you never understood even the most basic ideas behind it.

False analogy. While you can instantly tell whether you like a dish or not, you are only in a position to criticise the chef because you've tasted better dishes in your life, and thus know that better dishes are not only possible but commonly prepared by better chefs. Where's your equivalent when you get to criticising the way physicists explain QM? What evidence do you have that these physicists are doing something wrong and that they could reasonably do things better?

Strawman. How did "all the most fundamental processes we'd known about over the last century or so of dramatically improving measurements" get changed to "all well-behaved so-called random processes"? The situation with QM is analogous to the outcomes of all the processes anyone has ever studied consistently occuring with a 1 in [number of possible outcomes] chance.

Given that we've been probing nature with dramatically improving precision over the last century or so, that's a pretty major difference. We've already ruled out that it's a matter of looking just a bit deeper into things.

No, my argument is that believing "the mechanism" exists, without evidence and just because you want it to be that way, is a profoundly unscientific attitude. Do you understand the difference?

Nope. I picked two different examples proving two rather different things that happened to be in two different threads. You denied ever phrasing anything in a declarative manner, and I showed you where you did just that. You wanted examples of where someone's perfectly relevant response went over your head? I produced those too.

Another thread entirely... where you chose to [POST=2626370]re-post[/POST] exactly the same thing again.

You're moving the goalposts. [POST=2882637]Here[/POST]'s where they were originally:
The two threads I linked to just happen to be the one I first participated in and the one after which you stopped asking questions. Furthermore, in your [POST=2883065]subsequent[/POST] post, you brought up this:
which I remember from [POST=2684731]here[/POST]. Whatever you want to call them, these are certainly among the threads we're talking about.

No, your summary doesn't even make any sense. Guest was pointing out that your home-made definition of a coordinate system was inadequate. As he explains in the very text you quoted.

I don't think that's a rational argument. I also don't remember Guest ever using it. He certainly did not in any of the three posts I linked to in the coordinate thread, so well done for proving my point: Guest's posts went over your head.

No, I'm mostly pointing that thread out as an example of where you totally misjudged a post by Guest.

Last edited: Jan 9, 2012
16. przyksquishyValued Senior Member

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This is disgusting RJ. You were clearly caught out putting words in Guest's mouth that he never uttered, and you try to deflect that with your previous attempt to redefine the discussion? That thread certainly was one of your black hole discussion threads. Your motivations for starting it were clear, and the discussion explicitly returned to black holes soon enough. You didn't just take a sudden independent interest in coordinate systems. Also, if it were really so clear to you that the thread was not about black holes, where did your false attribution of "Guest's reply was that this is wrong because BH's exist...a priori" come from?

No, I already told you how I picked those particular posts: I remembered them. (And do you really find it implausible that the first example I'd remember is from a thread I actually participated in?) That was the first place in the first thread I looked in. It is also from that same thread that I originally found this comment, by the way:
I originally saw that [POST=2626370]here[/POST]. Notice that's on the same page as two of Guest's posts that I linked to. The posts I linked to were all either more-or-less where I remembered them, or in that one case, visible on the same page. I never needed to go scouring for anything.

So as usual your assessment of things is completely wrong.

Last edited: Jan 9, 2012
17. RJBeeryNatural PhilosopherValued Senior Member

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So when I measure z+ spin up on a particle, my world is now strongly entangled to the world in which the measurement was z+ spin down? And, in EPR, the system is described by a non-entangled wavefunction until it is measured??

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It doesn't matter either way; MWI continues to suffer the same problem that I've pointed out 3 times now (as highlighted in red in your text): determining "when" these events occur in the theoretical, ontologically physical wavefunction.
It's not a false analogy. I've had 10,000 dishes in my life and I'm currently being served, say, borscht; while it's possible that there is no better way to prepare it than the way it is currently being served, there is also that chance that the chef could use a better recipe. I'm holding out hope for the latter. That's it. The chef is revered enough that he doesn't need your defense of him (or the dish!).
This is not right and I can't believe you continue to hold this attitude. Searching for a "better" description of what we observe is the very heart of science. We shouldn't need to wait until the math "doesn't quite work" to continue searching. If that were the case, why the hell did we spend so much time pursuing String Theory? Did you consider that to be a gigantic exercise in folly?

18. przyksquishyValued Senior Member

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If you meant "spin up" rather than "spin down" at the end, then yes, something like that.

No, my earlier description was admittedly oversimplified. The key point in both cases is that the observer becomes entangled with the system being measured. So in EPR you start with two particles that are entangled with one another but otherwise uncorrelated with anything else, then that evolves to a state where one or more observers become part of the entanglement.

And 3 times your problem has had no basis in the MWI. I think the problem is that you're assuming MWI substitutes wavefunction collapse with just a single transformation to the global quantum state. But that's not what happens. In MWI, if multiple observers make different measurements on the same system, eg. as in the case with two observers each measuring their half of an EPR pair, each observer separately becomes part of the entangled quantum state at the time and place they make their own measurement. In each case that only involves a purely local transformation of the global quantum state.

That's not what you said originally. Before you were criticising the way physicists explain QM.

If you're just "hoping for better", then you're free to do that of course, but then the question turns to why you're even posting about that here. What's the point of yet another random person on the internet saying they hope someone will find a better/more complete/more intuitive/whatever way of explaining quantum physics for only the millionth time?

Obviously. But "better" only in an objective sense I explained earlier: more accurate predictions, fewer postulates and adjustable parameters, better unification, less logical inconsistencies. The scientific idea of "better" gives no weight whatsoever to "I find this more intuitive" or "I'd like the world to have this property".

See above. People pursuing string theory, or working toward unification or the "theory of everything" in general are expecting that the end result will be an improvement on what we currently have in the sense I just described above. There are indications that there is plently of room for improvement: only two of the four forces have been unified, there's the heirarchy problem, we don't have a consistent quantum theory of gravity, the Standard Model has something like 19 adjustable parameters (more if you add neutrino masses), and we don't yet definitively know the nature of dark matter, just to name a few examples.

Last edited: Jan 10, 2012
19. FarsightValued Senior Member

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You can, see http://www.4shared.com/office/q9wKDbHt/feynman_rp_-_superfluidity_and.html

Click on download now, it takes about 20 seconds, then click on download now again. Note the mention of the "elastic jelly". The electron is a kind of roton, but of stress flow rather than fluid flow.

20. Guest254Valued Senior Member

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Errrm, no. We've been talking about spheres, which in mathematics refers to a two dimensional object. This is patently obvious from the previous threads, and if it wasnt obvious, this is yet another indication that you don't understand the material at hand. I expect this is your attempt to shift the goal posts, but given the hole you've found yourself in, I'm willing to forgive you.

No, and this is yet another indication that you don't understand this stuff at all. There is no such thing as an "observer at infinity". Period. Full stop. I will once again explain: in the Schwarzschild spacetime the proper time experienced by an observer for which $\mathrm{d} r=\mathrm{d}\theta = \mathrm{d}\phi =0$ is

$\mathrm{d} \tau = \left( 1- \frac{2M}{r}\right)^{1/2} \mathrm{d} t$

We can see that as the r-coordinate gets large the proper time for this observer approaches with the coordinate time t. When physcists use the phrase "observer at infinity" they are pretending that r is so big that they really do coincide, simply because it makes subsequent calculations easier. Informally, they pretend $r=\infty"$ -- but obviously that point doesn't exist. This doesn't cause any problems -- it simply means all computations done under this regime will actually have a small error term in them (depending on the r-coordinate) which we can make as small as we please by choosing r larger and larger.

Your comments aptly demonstrate more of your misunderstandings of this topic. Clearly what I've outlined above is not difficult, or even technical, but you still didn't grasp it. Even after explanations, you still didn't get it! But here you are insisting that you do know what you're talking about.

Look, it's not a big deal that you don't follow a lot of this stuff, lots of people don't get these things -- general relativity is hard. As I said, you should learn a little humility. Pull your socks up, untwist your knickers and start reading an introductory book on relativity.

21. RJBeeryNatural PhilosopherValued Senior Member

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Hah! Talk about moving goal posts and digging holes! Only because I tire of your side comments I'm going to start treating you equivalently:
So, here you're attempting to make the claim that because spheres exist (e.g. I believe the Earth was discussed at one point) in reality, the idea that a proper coordinate system being required to describe all of reality has been falsified. Once again you clearly demonstrate your lack of distinction between reality and idealized mathematical concepts. [NOTE: Annoying to read that kind of tripe isn't it? It reminds me of Tach. In the future, just stick to your point and I'll do the same.] A 2D sphere only exists in your mind, while what you're actually describing is a 3D sphere (aka a ball). A 3D sphere can be trivially, continuously (and bijectively) mapped with Cartesian coordinates. My point stands, as does my original one that coordinate systems are continuous both by definition and in my understanding and usage because I was using the bijective term, which implies both continuity and inversed continuity. Your claims that I "actually meant something else" even though I used the proper terms are a futile attempt at misdirection. Tell you what, throw me your shovel and I'll drop a rope down for you. [NOTE: Can you sense my condescending tone? Despite what you may think, it's not cutesy when you do it, either.]

I'm tiring of this...

22. RJBeeryNatural PhilosopherValued Senior Member

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Criticizing inconsistent or even non-existent explanations. How is this different from saying a dish is unpalatable? As I said, I'm getting tired of this topic.
You already know that I'm not just passively complaining; I think about this every single day. Wouldn't it be hypocritical not to? A more palatable description of reality (however that may be defined) is not unattainable just because przyk declares it to be. Also (and I know this is really going to bug you) but if a solution appears not be be attainable by exhaustively learning the current explanations (not to be confused with exhaustively studying the currently observable data that lead others to those explanations), then maybe a relaxation of presumptions is in order.
I'm not aware of string theory even theoretically providing more accurate predictions in QM. Also, Occam's Razor (i.e. "fewer postulates and adjustable parameters") has philosophical value precisely due to its aesthetic -- it's an appeal to our longing to describe things as simply as possible, which in itself has no objective merit. In other words, we already do filter our descriptions with our biased preferences.

23. CptBorkRobbing the Shalebridge CradleValued Senior Member

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Well ok, so an overwhelming majority of scientists appreciate searching for the simplest possible way of accurately describing measurable phenomena- that's made clear to laymen on a regular basis. You can come up with any explanation you want for things to work out the way they do, but unless it actually makes accurate testable predictions that aren't made by other models, no one doing actual research in the field is likely to give a hoot. Is there a reason anyone out there should appreciate the preferences of your own palate over something simpler and more directly measurable?