The Knowable and The Unknowable in quantum mechanics

Discussion in 'Physics & Math' started by lethe, Nov 12, 2002.

  1. James R Just this guy, you know? Staff Member

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    34,678
    Tom,

    Your 6-dimensional theory sounds to me like what is known as an <b>ad-hoc hypothesis</b>. i.e. one which is postulated only to solve a specific problem.

    My question again is: what are the observational consequences of this theory? How can we test it?

    How can we tell, say, a 5-dimensional universe from your 6-dimensional model experimentally and/or observationally?

    In short, how can we distinguish your 6-dimensional universe model from the accepted 4-dimension model of standard quantum mechanics?
     
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  3. James R Just this guy, you know? Staff Member

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    Tom,

    On another point: your claim that relativity is wrong is an unsupported assertion. If you want to make that kind of statement in a physics forum, you would do better if you supported the claim with some reasoning. You might like to start a new thread.

    Please remember all the previous conversations we've had about relativity if you do choose to debate this point. I don't want to have to re-cover old ground again.
     
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  5. overdoze human Registered Senior Member

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    Hrrrm... Please pardon my random incursion. I still periodically lurk here (though I won't be contributing much.) But I found this topic (and lethe's posts) quite interesting, so on to the point:

    That last line (in bold) is where you lost me. It seems to me that the right-hand side should read 1-P(b,c), not 1+P(b,c). After all, it's the outcome of integrating \rho(x) - \rho(x)A(b,x)A(c,x). So why did the '-' change into a '+'?

    If I take the inequality

    |P(a,b)-P(a,c)| <= 1-P(b,c)

    and substitute the values you give later on (P(a,b)=0, P(a,c) = P(b,c) = -0.707), then we have

    0.707 <= 1.707

    Which is no contradiction at all. (?!)

    Sorry if I'm missing something obvious. It's been a long day and it's kind of late and everything... Thanks for your posts!
     
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  7. Crisp Gone 4ever Registered Senior Member

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    Hi Tom,

    "If you read the fourth post on this thread, you will find my explanation for the EPR paradox. This explanation would also allow for nonlocal hidden variables. What do you think about it??"

    If your explanation allows non-local hidden variables, then it is in contradiction with Bell's statements, which immediatelly follow from the quantum mechanical postulates. Can you indicate where the differences between your and Bell's reasoning are ? I.e. why exactly your result is different ?

    It clearly must be one of the two explanations, so now I am wondering where the fundamental difference resides.

    Bye!

    Crisp
     
  8. lethe Registered Senior Member

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    2,009
    overdoze, that is my mistake. i filled in some steps from the book, but i messed it up a little there. the mistake is this: Int[\rho(x)A(b,x)A(c,x)]=P(b,c). the total probability of measuring the b and c vectors is the B measurement times the C measurement, times \rho, the number of states with each value.

    i have written at the top of that post this: P(a,b)=Int[\rho(x)A(a,x)B(b,x)]. switching b for a and c for b, and then using the fact that A(c,x)=-B(c,x) will get the required result.

    i will go back and fix it. also i have noticed that the angle brackets that i used to indicate an inner product got eaten up as html, so that is missing too. i will fix it as well.
     
  9. lethe Registered Senior Member

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    2,009
    thanks for pointing out that oversight. i believe i have fixed it, so let me know if you think it checks out now. also, i changed my unit vectors from a,b,c to u,v,w, just because i want it to be clear that there is no relationship between a and A, and b and B. A and B are the measurable values of electrons one and two, respectively. u,v,w are arbitrary directions that i can choose to measure either electron 1 or electron 2 or both, along.

    because of this thread, i have been rereading some of bell s work, and i think i have some more things to tell you about what bell says about the possibility of nonlocal theories.
     
  10. Prosoothus Registered Senior Member

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    1,973
    James, lethe, and Crisp,

    I will attempt to answer all your questions regarding my multi-dimensional theory in the new thread called "The Lego Theory" I just posted.

    Tom
     
  11. Prosoothus Registered Senior Member

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    lethe,

    I just want to ask you about something that you said before that confused me. You stated that a particle has no unique location until it's measured.

    My question is what do you mean by "measured". If particle A comes within particle B's electric field, isn't particle A measuring particle B?? In a hydrogen atom, doesn't the proton "measure" the electron, and vice versa? Shouldn't they both have unique locations to each other since they are both being "measured" by each other??

    Crisp, James, and chroot: Feel free to answer these questions as well.

    Tom
     
  12. chroot Crackpot killer Registered Senior Member

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    2,350
    No, the proton and electron are not "measuring" each other. The exact location of the electron has no bearing on the proton's behavior. The electron can be said to exist over a locus of points, and it behaves as if it is present at all of those points simultaneously. The proton experiences the net effect of the electron's spread in position, not a point-like effect.

    This brings up a very valid point, Prosoothus: you're so indefatigably sure that you're right and physics is wrong -- but you haven't even taken the time or made the effort to even understand what is it physics is saying.

    How can you denounce, or hope to improve, a theory you don't even understand?

    - Warren
     
  13. (Q) Encephaloid Martini Valued Senior Member

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    20,535
    Schroedinger, Erwin! Professor of physics!
    Wrote daring equations! Confounded his critics!
    (Not bad, eh? Don't worry. This part of the verse
    Starts off pretty good, but it gets a lot worse.)
    Win saw that the theory that Newton'd invented
    By Einstein's discov'ries had been badly dented.
    What now? wailed his colleagues. Said Erwin, "Don't panic,
    No grease monkey I, but a quantum mechanic.
    Consider electrons. Now, these teeny articles
    Are sometimes like waves, and then sometimes like particles.
    If that's not confusing, the nuclear dance
    Of electrons and suchlike is governed by chance!
    No sweat, though--my theory permits us to judge
    Where some of 'em is and the rest of 'em was."
    Not everyone bought this. It threatened to wreck
    The comforting linkage of cause and effect.
    E'en Einstein had doubts, and so Schroedinger tried
    To tell him what quantum mechanics implied.
    Said Win to Al, "Brother, suppose we've a cat,
    And inside a tube we have put that cat at--
    Along with a solitaire deck and some Fritos,
    A bottle of Night Train, a couple mosquitoes
    (Or something else rhyming) and, oh, if you got 'em,
    One vial prussic acid, one decaying ottom
    Or atom--whatever--but when it emits,
    A trigger device blasts the vial into bits
    Which snuffs our poor kitty. The odds of this crime
    Are 50 to 50 per hour each time.
    The cylinder's sealed. The hour's passed away. Is
    Our pussy still purring--or pushing up daisies?
    Now, you'd say the cat either lives or it don't
    But quantum mechanics is stubborn and won't.
    Statistically speaking, the cat (goes the joke),
    Is half a cat breathing and half a cat croaked.
    To some this may seem a ridiculous split,
    But quantum mechanics must answer, "Tough @#&!
    We may not know much, but one thing's fo' sho':
    There's things in the cosmos that we cannot know.
    Shine light on electrons--you'll cause them to swerve.
    The act of observing disturbs the observed--
    Which ruins your test. But then if there's no testing
    To see if a particle's moving or resting
    Why try to conjecture? Pure useless endeavor!
    We know probability--certainty, never.'
    The effect of this notion? I very much fear
    'Twill make doubtful all things that were formerly clear.
    Till soon the cat doctors will say in reports,
    "We've just flipped a coin and we've learned he's a corpse."'
    So saith Herr Erwin. Quoth Albert, "You're nuts.
    God doesn't play dice with the universe, putz.
    I'll prove it!" he said, and the Lord knows he tried--
    In vain--until fin'ly he more or less died.
    Win spoke at the funeral: "Listen, dear friends,
    Sweet Al was my buddy. I must make amends.
    Though he doubted my theory, I'll say of this saint:
    Ten-to-one he's in heaven--but five bucks says he ain't."

    --CECIL ADAMS
     
  14. Prosoothus Registered Senior Member

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    chroot,

    Here is a quote from you:

    You say that when you measure an electron and find that it is at an exact point, what do you mean by "measuring". Does the measuring have to be done by a human, or can it be done by a dog or a cat? Can it be done by a computer?? How big does the "measuring" device have to be?? Can the "measuring" device be the size of molecule?? How about the size of an atom, or even a subatomic particle?? Does there have to be an observer present with the measuring device, or is it sufficient for the measuring device to be alone? Since a proton can sense an electron as a result of its field, isn't a proton a crude measuring device???

    Tom
     
  15. Prosoothus Registered Senior Member

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    Q,

    Funny poem! I had a good laugh.

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    Tom
     
  16. chroot Crackpot killer Registered Senior Member

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    If you want to get an exact number for the position of electron, you must devise a situation where the exact position is important. In other words, if you design an experiment that depends on the exact position of an electron, you will find that the electron has an exact position. A proton interacts with an electron as if the electron exists at a locus of points. You could say that the proton "measures" the electron, but does not request an exact position. The only criterion that the proton-electron system mandates is that the wavelength of the electron should fit an integral number of times in its orbit. A scattering event, such as the bouncing of a very high-frequency photon off the electron, would be a measurement that demands the electron appear at a more precise position. Making the electron pass through a very narrow slit is another way of forcing the electron to take on a more precise position.

    - Warren
     
  17. Prosoothus Registered Senior Member

    Messages:
    1,973
    Chroot,

    What about other electrons?? In a lead atom there are 86 electrons. Wouldn't all these electrons force any single electron in the lead atom to give its exact position?? From what you say, it appears that the more electrons that are present in an atom, the greater the force on each of the electrons to reveal their exact locations. Is this correct??

    Tom
     
  18. chroot Crackpot killer Registered Senior Member

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    2,350
    No, there are 82.
    No.
    No.

    - Warren
     
  19. lethe Registered Senior Member

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    prosoothus, at the risk of giving you impetus to go trumpeting off again about how physics has a theoretical roadblock because of incorrect thinking, i am going to admit that i think this is a rather insightful question, and difficult to answer.

    after all, how do you measure a particle? A:by letting it interact with other particles. so exactly what sorts of interactions are sufficient to collapse a wavefunction? my detector is made of protons, is it not? are these protons different from the single protons in the nucleus? sometimes it does look as though the axioms of quantum mechanics require the presence of an intelligent observer, and i think that is a deficiency of the theory.

    in practice, it is usually clear what comprises a measurement: an interaction with a macroscopic detector, as opposed to other microscopic particles. but from a rigorous viewpoint, this is circular logic: "Q: what makes a measurement? A:something that makes a measurement." since a detector is by definition something that measures, and macroscopicness is just a point of view.

    one way that the philosophical physicists explain the notion of measurement, is with the "many-worlds" theory. simply put, the many worlds interpretation is a slight modification of the orthodox position of quantum mechanics, in which the collapse of the wavefunction, that happens with each measurement, is abandoned. instead, wavefunction superposition propogates to every particle that the quantum particle interacts with, including, but not limited to, conscious observers. thus: when i measure the spin of the electron, i become a superposition of two people, one person that measured spin up, and one that measured spin down. there is never any wavefunction collapse.

    i mentioned this theory already, as a way of resolving schrödinger s paradox. it is not too well accepted by the scientific community, but i think it is probably valid. i don t know too much about this theory, but i do know one or two people in my department who subscribe to the theory. i imagine if you think that schrödinger s paradox is proof that quantum mechanics is false, then you will not like the many-worlds interpretation.

    personally, i don t like the many-worlds interpretation. it doesn t seem any more axiomatically grounded than the notion of an intelligent observer with her macroscopic detector. but i must confess a bit of ignorance on the matter. perhaps i will look into it a bit and post some about it, but no promises.
     
  20. lethe Registered Senior Member

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    2,009
    actually crisp, let me clarify what bell s theorem tells us a bit, since i think the way i said it may have been a bit unclear.
    a) a quantum mechanical treatment with local hidden information implies bells theorem.

    b) bells theorem is incompatible with orthodox quantum mechanics, which predicts that the inequality will not hold.

    c) measurements have shown that the orthodox position is true, and bells theorem is false.

    d) thus there can be no local hidden information in a quantum mechanical treatment.

    since i did my initial post on this thread, i have been reading more of bells work, and it seems to me that bell himself said that his theorem should apply to non-hidden variable systems, i.e. the orthodox theory. in other words, he claimed that it proved that any quantum mechanical treatment must necessarily be nonlocal. it is not obvious to me at this point exactly how the hidden variables and nonlocality are related.

    so while the entire scientific community used his theorem as a basis to claim that there is no possible hidden variable theory, it was really intended to disprove locality.

    i will post some more about bell s work.
     
  21. chroot Crackpot killer Registered Senior Member

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    2,350
    I've never been a believer of "complete wavefunction collapse." I'm believe that every particle is always in some superposition of states, and always has at least indeterminacy in any two non-commuting observables, like position and momentum. A particle is localised by travelling through an aperture -- but it's not localised to one exact position, since the aperture is not infinitesimally thin. The wavefunction isn't "collapsed," it's just squeezed.

    The answer to the measurement paradox, to me at least, is that "measurement" is any situation which "squeezes" the particle's wavefunction. It doesn't require any sort of intelligence.

    - Warren
     
  22. Prosoothus Registered Senior Member

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    chroot,


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    Let me ask you again: Wouldn't the electrons in a lead atom "squeeze" each others wavelengths thereby giving them (relative) positions?? And if your answer is still no, than why not??

    Tom
     
  23. chroot Crackpot killer Registered Senior Member

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    2,350
    Yes, as been said. The electron in an atom does not have an equal probability of being anywhere in the universe, as an electron with exactly known momentum would be. The electron exists in the atom in a distinct probability distribution. This would be the "squeezing."

    - Warren
     

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