Pauli Exclusion Principle

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

  1. Farsight

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    3,492
    Some interesting stuff there Harmony. I saw a few things that I think aren't quite right, but even so I think the general picture you present is the right picture. Mind you, this is perhaps not the best place to discuss it.
     
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  3. przyk squishy Valued Senior Member

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    But you don't yet know quantum physics or the MWI. All you've done is built up prejudices about both that, for some reason, you insist on being vocal about.

    Are you saying you can't look beyond what word someone uses? Because whatever Everett or DeWitt might have called it, the point is that the measurement process in the MWI is modeled in terms of entanglement and decoherence, which are already a standard part of quantum theory. The whole point of the MWI is that its what you get if you take quantum physics, throw out the measurement/wavefunction collapse rule, and then approach modeling the observer and the system they're observing in exactly the same way you'd approach modeling any interacting quantum system. And generally that's a continuous process.

    First of all, which physicists? It doesn't make sense to lump them all into one category because different physicists aren't all going to explain quantum mechanics the same way. Even among texts and lecture notes the presentation isn't uniform: a "standard" introductory text like Cohen-Tannoudji's doesn't present QM the same way as Feynman does in volume 3 of his Lectures, or as Preskill does in his notes on quantum computation.

    Or are you specifically talking about the mainstream, lowest-common-denominator presentation of QM, e.g. as given in standard introductory texts, which focuses on explaining a simple set of rules that are generally well accepted to work by everyone?

    Either way, are you saying you think you can do better?

    But I'm not criticising your personal interpretation of QM here (though I've done that in other threads). Right now I'm criticising your criticisms of QM and approaches to interpreting it. In short, they're largely uninformed. Which is really something you should fix before developing your own interpretation of QM anyway.

    No, what I was saying was that if the probabilistic rules of dice throwing didn't just apply to dice, but consistently and uniformly applied to all the most fundamental processes we'd known about over the last century or so of dramatically improving measurements, then you'd have a situation more comparable to the one we have now with QM.

    [POST=2604287]This[/POST]:
    is your idea of a question? Is well established physics supposed to get put on trial like this every time an inexperienced layman who doesn't even know the theory forms a knee-jerk impression of it?

    So I have to waste ridiculous amounts of time going back linking to every single post everyone made and justifying my impression of them, when I'm in a far better position to judge their validity and relevance than you are to begin with? And we're talking about me digging up posts that went over your head the first time you saw them. Why should I believe they wouldn't just go over your head a second time?

    So I'll decline from being exhaustive. That said, here's a couple of examples that stick out in my mind where you completely misjudged Guest's replies. The first concerns [THREAD=104296]this thread[/THREAD] where Guest's posts [POST=2625930]here[/POST], [POST=2626254]here[/POST], and [POST=2626667]here[/POST] really hit the nail on the head. Each of these posts contains both a direct, literal answer to the question you asked in the OP, as well as an explanation that you were asking the wrong question: every possible pseudo-Riemannian manifold could be mapped bijectively to \(\mathbb{R}^{4}\) and was therefore physical by your definition, but mathematicians require more than bijectivity from coordinate mappings. At that point it was up to you to take that information and either accept that your question had been resolved (if you still stood by bijectivity as a sufficient condition for physicality) or revise your question (if you'd learned something about the way mathematicians define things that lead you to want you to change your question accordingly). Instead, you did what amounted to insulting Guest.

    For the second, take [THREAD=106221]this thread[/THREAD]. You asked a question, and early on I gave you a perfectly correct, logical answer. Yet for a long time you were hesitant to accept it because, for all you like to believe about yourself, you basically didn't find my response authoritative enough. That might pass on its own, but what was worse was that Guest showed up and gave you [POST=2689035]exactly what you needed[/POST]: an authoritative answer, from a forum member much more senior than I or even AlphaNumeric, confirming to you among other things that the response I'd given you was perfectly correct. All you could do was berate him for that, and yet the only reason his post was necessary at all was that your attitude made it necessary.

    Note that I'm in no way trying to be exhaustive here. These are just two examples I happened to specifically remember, and it doesn't help your case that Guest was probably the contributor you criticised the most, when he really gave you some of the most relevant and informative replies you received. You're really not as good at "separating the wheat from the chaff" as you think you are.

    The first obviously. But I don't agree with you painting the whole discussion that way. Complaining about the quality of other's posts doesn't mean yours were any better. You're assuming another false dichotomy in all this, in that someone either had to be an expert at the topic in GR you were criticising and see the complete resolution, or that they should agree with your problem. But that's absolutely not the case. It was obvious to everyone that your impression there was a problem was based on an extremely naive impression of GR's account of a black hole. What was irritating was that you engaged in a hell of a lot of bullshit reasoning yourself, and everyone could see it was bullshit, all the while having to read you arrogantly judge everyone's level of competence and understanding. The other posters were perfectly correct to identify your problem as a lack of understanding of certain prerequisites, such as your almost nonexistant grasp of coordinate systems. I think you also dragged up some GR math like the Schwarzschild metric a couple of times and started playing around with it without really understanding what you were doing. You doggedly insisted everyone should see your problem your way even as others pointed out that your way was founded on ignorance and misconceptions.
     
    Last edited: Jan 5, 2012
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  5. przyk squishy Valued Senior Member

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    RJ: by the way, in all this I'm referring to the whole discussion that arose about the physicality of black holes given that the Schwarzschild coordinates were "bad". But looking back that wasn't the [POST=2598968]original[/POST] question you asked, which in the end I don't think anyone answered. In my opinion that's not really surprising because evaporating black holes aren't part of the "standard" general relativity we all learned as undergraduates. Black hole evaporation is in a grey area where different theories that usually don't talk to each other (GR, QFT, and thermodynamics) are forced to cooperate. That makes it a rather specialist topic and you were unlikely to come across an expert on it on a forum like this who could give you a definitive answer. All anyone could do for you here was guess at why things might be more subtle than you were picturing (and for anyone with any experience with GR, that's not difficult to imagine), which is what started to happen before the discussion mutated into one about the Schwarzschild metric (which describes an eternal, non-evaporating black hole).

    But anyway, the reason I'm posting again: apparently your original question is one with a standard answer. Or at least standard enough to show up in some FAQ lists:

    http://cosmology.berkeley.edu/Education/BHfaq.html#q9
    http://apod.nasa.gov/htmltest/gifcity/bh_pub_faq.html#evaporate
     
    Last edited: Jan 5, 2012
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  7. Harmony Harmony Registered Senior Member

    Messages:
    84
    Wave description

    Thank you for taking the time to look at the web site:

    I would very much appreciate your comments on the points that you thought were not quite right. The best place to discuss it will be in the thread titled Wave Description which is located at:

    http://www.sciforums.com/showthread.php?p=2861276#post2861276

    in the Alternative theories section.

    Harmony
     
  8. RJBeery Natural Philosopher Valued Senior Member

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    So when I use the term branching it deserves "condescension quotes", but when I point out that the theory's authors used the term it's my problem for not being able to overlook it? If I measure a particle as having +z spin, how exactly does my world and the world in which I measured that particle as having -z spin NOT branch? It DOES branch. Both "worlds" were capable of being described by the same entangled, continuous wavefunction, and now they are not, and, because of this, an advocate of the ontological wavefunction in MWI would still have to be able to account for "when" those worlds branched along the wavefunction's existence. It's trivial to assign this point as being that of the time of measurement, but not when EPR-type experiments are involved. In other words, as I said, you do not escape the problem by positing that the ontological wavefunction "never" collapses.
    Perhaps, perhaps not. I have my own ideas, but you don't have to be a chef in order to declare a dish unpalatable.
    The probabilistic rules of dice DO apply consistently and uniformly to all well-behaved so-called random processes (e.g. coin flipping). The only difference is that we can see coins and dice (I'm speaking specifically of the apparent randomness of QM, not entanglement). What your argument boils down to is that, because we cannot see the mechanism, it doesn't exist, therefore if we could not see coins and dice then they would be completely described by their probabilistic descriptions. My point is that this would only be acceptable if those coins and dice were fundamentally unseeable and impervious to any theoretical modelling.
    You're playing some sleight-of-hand here. You posted a quote from deep within my second battle-scarred BH thread, but then linking to posts from Guest in another thread entirely. Here's the OP of the bi/sur/in-jective coordinate thread which you claim Guest provided answers to:
    You really think this is posed in an authoritative, arrogant manner? It's not even directly related to BH's btw, it was simply a thread which spawned out of a prior discussion of them. Of your many links, NONE of them were to responses in the BH threads!

    Also, Guest's reply was this:
    Guest made the presumption that I was wrong because the math required multiple manifolds rather than a single coordinate system. In other words, I posited that reality should be describable by a single, continuous coordinate system. Guest's reply was that this is wrong because BH's exist...a priori. On its own, this is not a rational argument and if you think it is I am disappointed. This is CHAFF, not WHEAT.
    You're pointing to a supposed example of me not wanting to accept what is told to me, when all you've done is link to a thread which proves that I will accept an answer as soon as *I* understand it. What you see as being stubborn is actually just tenacity to understand. (Plus I would point out that I recognized this as an issue that I needed and wanted to understand...I had identified the "wheat"...therefore I started a thread devoted to the subject.)
     
  9. CptBork Valued Senior Member

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    6,460
    Is there an a priori reason we should trust your intuition here? 'Cuz when it came to describing things more than \(10^{23}\) times too small for my eyes to see, I found that my own intuition wasn't worth bollocks. Would have been great if my intuition had worked, then I wouldn't have needed to study for any exams and I could've skipped ahead a couple of years.
     
  10. Guest254 Valued Senior Member

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    1,056
    My (Internet) ears are burning! Bold bits added for your convenience, and I've inserted the bit of my response you conveniently missed out (red text).
    Unfortunately, you once again demonstrate that you don't understand answers even when they're given to you. Let's try to make some meaning out of your comments.

    The math required multiple manifolds??? What?

    No, you didn't mention continuity at all, hence my reference to homeomorphisms and the rest of the red text. This demonstrates that, even now, you still don't understand the answers that were given to you!

    What? Seriously, what? Where in my response is there any mention of black holes?!?!
     
  11. RJBeery Natural Philosopher Valued Senior Member

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    4,222
    Drama much, Guest? Anyway, this is moving off track, but here we go...
    Now, you can critique my fumbling syntax all day (I wasn't the one that brought up manifolds) but when I try to express a concept in layman's terms it's a waste of time if you're not capable of or not going to be intellectually sincere in your effort to understand my point. If I describe the location x of an object with some function f(t) = t^2 + 5t, with the added stipulation that at t=4 the value of x="banana", it would be difficult for this description to intuitively satisfy a mapping to anything resembling reality. Agreed?

    That was my point. I was suggesting that reality should be expressible by a single coordinate system (and, by this, I meant continuous with a continuous inverse, etc). You flatly said I "see it" wrong but then you dive into semantics. Perhaps you could clarify what you meant by "seeing it wrong", because I interpret that to mean that you don't think reality is or should be expressible by a single coordinate system. Is that what you meant, or not?

    Regardless of the wording in my OP, I was searching for more than simply a method of labeling discrete points, and from what I'm reading in your response(s) my original terminology of using "coordinate system" was correct.
    If coordinate systems are continuous by definition then why isn't it implied??
    Yes, I agree, it's quite confusing why przyk would point to that particular thread when we were discussing black holes. I suspect it's because he searched in vain for elucidating responses in the proper thread, and then claimed that it would be a waste of time to do so.
     
  12. Guest254 Valued Senior Member

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    1,056
    No, you're now inserting the caveat of continuity. At no point in your "this is how I see it" was continuity mentioned. This was the salient point, but it still seems that it's gone over your head. We even went through the whole bijection between (0,1) and [0,1) thing in a hope to help you construct a bijection from a sphere to a plane!

    And this just cements the fact you still don't understand any of the material at hand! If you're given one coordinate system then you immediately have infinitely many coordinate systems, since there are obviously infinitely many homemorphisms from R^n to itself.

    You already know your use of the terminology was incorrect, you were happy to admit it only a few posts later here. This also serves to falsify your story of "I meant continuous but didn't say it". Nice work.

    That in no way answers my question. You claimed "Guest's reply was that this is wrong because BH's exist...a priori" -- there is no mention of black holes in my reply, so what on Earth do you mean? If you just said something silly and don't want to admit it, that's ok -- I forgive you! Same goes for the multiple manifolds boob.
     
  13. RJBeery Natural Philosopher Valued Senior Member

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    If I used the phrase "coordinate system", and then you said coordinate systems are continuous by definition, why is it that you're now claiming I even needed to qualify it with "continuous"? The absurdity of my t=4 mapping to x="banana" should be proof enough that continuity was implied in my original intent.

    Also, you didn't answer my question. What did you mean by "seeing it wrong"? Do you disagree with the idea that Reality should be describable by a single coordinate system?
     
  14. Guest254 Valued Senior Member

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    1,056
    Come now -- work with me here, or this all gets a little same-y
    So did you or didn't you know the definition? Your seemed fairly proud of the fact you didn't know what you were talking about before, but now you want to claim you did! Make up your mind.
    But this is even more worrying! Your statement says nothing about continuity, which now indicates you don't even know what that means! This isn't looking good.
    And again, you clearly demonstrate that you don't even understand what a coordinate system is. If there exists one coordinate system then there are infinitely many coordinate systems, because there are infinitely many homeomorphisms from R^n to itself.

    Would you like to dig your hole any deeper, or are you close enough to the Earth's core now?
     
  15. RJBeery Natural Philosopher Valued Senior Member

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    "Same-y" is right, I've asked the same question 3 times and you avoid answering it. My ORIGINAL point (18 months ago, or whenever that thread was started) was that the idea does not sit well with me that we must use different coordinate systems to get around inconvenient areas of space when trying to model reality. My memory is sketchy, but I mentioned the sphere the sphere as an analogy; you or AN pointed out that polar coordinates are not bijective and so my criteria for reality failed, lest I deny the existence of a sphere. But we can use Cartesian coordinates bijectively with a sphere...
    I've already answered this:
    So, please stop muddying the waters with semantics and suppositions about what I 'really knew and when I knew it'. Rereading my last post I see you're getting confused by my phrase "single coordinate system". I meant "single" in terms of using a particular one to model the infinite observer and then switching to another (e.g. Kruskal) to describe the areas near the EH (i.e. they are nonhomeomorphic, or what I would term bijective). A proper coordinate system should be capable of describing all of reality; do you agree with this?

    Now, maybe there's a way around this involving the addition of another dimension or something, I don't know, and this entire conversation was a mere philosophical musing from the past, but you keep picking at it without actually answering my question.
     
  16. Guest254 Valued Senior Member

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    1,056
    No we can't! How can you not get this after all this time? We can create a bijection between the sphere and the plane (you were actually walked through this!), but not a homemorphism (i.e. a continuous bijection with continuous inverse).

    For someone who insists he always knew about the continuity condition, you're not very good at invoking it!

    The Kruskal coordinates are a global coordinate system for the Schwarzschild spacetime. There is no such thing as an "observer at infinity", and I have explained this to you before, but as with most things you're told, you don't seem to have understood it. Go back and read it again. For the love of God: please, please learn!

    Obviously not, because I believe in spheres.

    I don't want to be the eternal meanie, but you do yourself no favours. You've been given countless explanations of these things and they all seem to go over your head. You tell us you're a real critical thinker with a genuine passion for physics, but you're unwilling (or unable, I don't know) to go away and learn the most rudimentary parts of the theory you want to wax lyrical about.

    Take the case in point -- you've clearly not even taken the time out to understand the notion of a coordinate chart. We all said you should do this. We all said it was a fundamental part of GR. We all said you'd benefit from doing it. And here we are, over a year and a half later and you haven't even taken the time out to digest a wikipedia page or two.

    Learn a little humility. You seem to think you understand lots of things people tell you (e.g. you thought you understood all this coordinate stuff here), but more often than not it transpires you completely mis-understand. Man up, buy an introductory text book and start reading.
     
  17. RJBeery Natural Philosopher Valued Senior Member

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    I'm not talking about a plane. I'm talking about a 3-dimensional cartesian coordinate system. The "spheres" you claim to believe in, such as the Earth, are 3-dimensional. Please describe a point on the sphere which is not uniquely identified by a single set of cartesian coordinates. This is why I suggested that maybe we can always get around the problem of indeterminability by adding more dimensions. I really haven't thought about this issue for quite a while...
    Not quite. There is no such thing as an "observer at infinity in the Kruskal coordinate system".
    And stop with your dramatic peanut gallery commentary.
     
  18. Farsight

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    3,492
    I see mention of Kruskal-Szekeres, RJ. That's an interesting one, to do with the proper time of an observer falling into a black hole. Let's say that Guest is falling into a black hole, and he's holding a clock. You and I are in our spaceships at a safe distance watching him through telescopes. We have all the necessary apparatus to compensate for redshift and doppler effects. We see his clock running slower and slower as it approaches the event horizon. Then at the event horizon, we that it stops. Oh, and I forgot to mention, his clock is a light clock. It's stopped, so the coordinate speed of light is zero at the event horizon. That means that you, me and everybody else in the real world will agree that nothing else happens. Forever. Until the end of time. Light has stopped, and so has Guest. He doesn't see anything any more, and he doesn't measure any proper time on his stopped clock.

    Now take a look at this page from Misner/Thorne/Wheeler's Gravitation posted by a guy called Jesse. On the diagram on the left, the curve peaks to infinity at the event horizon. That's the gravitational time dilation tending to infinity, and coordinate time tending to forever. At the top of the peak, is the end of time, so there is no top to it. But it's "transformed away" using Kruskal-Szekeres coordinates. 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.
     
  19. RJBeery Natural Philosopher Valued Senior Member

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    That's right FS. Kruskal coordinates were brought in to deal with mathematical singularities. Had we not been forced to do this, Guest would acknowledge that the infinite observer is perfectly legitimate, but now that he sees my point he's going to simply claim the infinite observer is an invalid concept...perhaps Guest could explain to me "where" gravitational potential energy is zero relative to a mass at the origin, in Kruskal coordinates?
     
  20. brucep Valued Senior Member

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    There's no event horizon coordinate singularity associated with Kruskal-Szekeres, RJ. The Schwarzschild metric has the coordinate singularity at the event horizon for the remote bookkeeper frame. Your mixing up metrics so your conclusions are wrong. Especially this comment you made

    "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."

    Complete nonsense to anybody who understands how to use metric solutions and what the analysis means.
     
  21. RJBeery Natural Philosopher Valued Senior Member

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    I didn't make that comment, and I understand that Kruskal coordinates contain no singularity at the EH. That's why they're used!
     
  22. brucep Valued Senior Member

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    I wasn't referring to your comments. I was referring to the Farsight post [#115]. I quoted a portion of it.

    "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."
     
  23. RJBeery Natural Philosopher Valued Senior Member

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    This reads like you attribute the quote to me. I agreed with Farsight to the extent that Kruskal coordinates were brought in to make the mathematical singularity at the EH vanish.
     

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