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QM and GOD - and also what is

  1. Dec 2, 2003 #1
    Hi,

    this is my second post, so I start with a warm hello to all.

    Now has the Subject thread, asks (and I know this has been asked many a times)

    the world of the Quantum, is indeed "random" (or maybe is largely random) - but does this in itself argue or rid the existence of a theistic God?

    My second question is even more suited to this forum, can anyone explain to me what is Hamiltian space, and just what is an "inner product"??


    Thanks!


    Ps: Please note I am dyslexic.
     
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  3. Dec 2, 2003 #2

    selfAdjoint

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    QM says nothing about any gods, your our anyone else's. Discussion of God and <your topic here> should be put on the religion board.

    Instead of Hamilton space, I think you mean Hilbert space. This is an "algebra" (the simplest one is the complex numbers), and an algebra is by definition a vector space with with a product that distributes.

    So a vector space is a collection of things called vectors that you can add a + b = c and multiply by constanst ka = b so that it's linear k(a + b) = ka + kb.

    And the inner product of two vectors gives a constant {b]ab[/b] = k.

    In addition to the inner product we have the algebra product where the product of the two vectors gives another vector: a*b = v.

    In quantum mechanics the states of a quantum system are in one to one correspondence with vectors (actually rays of vectors) in some Hilbert space. And observable properties are Hermitian operators from the Hilbert space to itself. I'll define Hermitian some other time.
     
  4. Dec 2, 2003 #3
    re

    Hi selfAdjoint

    “QM says nothing about any gods, you’re our anyone else's. Discussion of God and <your topic here> should be put on the religion board.”

    I never claimed that QM does, nor am I discussing the existence of God, rather does the randomness that the QM, hold that the concept of theistic God, is thrown out of the window? I am not asking for a theological debate of Gods existence or no existence!

    Thus issues such has
    And just what does this randomness or random entail? – Would be an excellent start.
    And of primary focus, e.g. is the universe thus RANDOM, or is it random from OUR perspective?

    Secondly, while I do agree that for the most part, this part of my question could be better suited in the religion board.

    BUT I also feel the issue will be and should be very accurate (and more so on the scientific parts. that is QM. Has God existence or nonexistence can not really be answered scientifically, it is clear that the discussion was not geared to “) within here “QM says nothing about any gods, your our anyone else's”. Rather we are dealing with this random issue…. And from that we can make some “answers”

    Now for my second part of my post:


    “Instead of Hamilton space, I think you mean Hilbert space”

    Indeed, my error – I apologize.

    “and an algebra is by definition a vector space with with a product that distributes.”

    Sorry I am not mathematical so please use layman terms – or more layman style.

    I take this to mean – if I am incorrect please correct it – has a vector can be defined as - to me means direction of some sort, if we had lots or points linked up, they in turn will generate an“object”???

    “So a vector space is a collection of things called vectors that you can add a + b = c

    Like a straight line?

    “and multiply by constanst ka = b so that it's linear k(a + b) = ka + kb.”

    Sorry, but my background is not mathematical, from what I can have a very very crude guess and highly probably wrong: you incorporating the constant into the vector?

    Is Ka = b the same a and b’s has in a+b=c?

    Anyway can you please explain this!


    What does K mean? – you do say…

    And the inner product of two vectors gives a constant {b]ab[/b] = k.

    But that is utterly worthless to me! To me your saying that K is the constant generated by the inner products of two vectors, yet there is no explanation has to what they really are!…. Which I am assuming by guesswork, an inner product is when you bring the constant together with the vector space? – like a “meeting place”???
     
  5. Dec 2, 2003 #4

    chroot

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    QM is a scientific theory. Quantum mechanics textbooks do not include the word God, nor do students studying the theory ever hear the word God mentioned in class. Quantum mechanics has nothing to do with God (though I suppose if God exists, then he has something to do with quantum mechanics ).

    This is not really the place to begin learning the theory -- at least not with the formalism in selfAdjoint's post. If you'd like to learn it, I suggest you purchase a book.

    You're not likely to get an argument about God going here on physicsforums, as we do not allow religious discussion here. If this thread wanders off into theological debate, it will be locked.

    - Warren
     
  6. Dec 2, 2003 #5

    chroot

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    Re: re

    Consider a concrete example. In Euclidean three-space ([itex]\mathbb{R}^3[/itex]), the inner product of two vectors [itex]a_1 \mathbf{i} + a_2 \mathbf{j} + a_3 \mathbf {k}[/itex] and [itex]b_1 \mathbf{i} + b_2 \mathbf{j} + b_3 \mathbf {k}[/itex] is [itex]a_1 \cdot b_1 + a_2 \cdot b_2 + a_3 \cdot b_3[/itex].

    In general, the inner product is simply an operation on two vectors that produces a scalar. In other words, the inner product is a map [itex][\cdot , \cdot] \mapsto \mathbb{R}[/itex].

    - Warren
     
  7. Dec 3, 2003 #6

    selfAdjoint

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    I didn't introduce the method of doing the inner product because it requires defining basis vectors, just as I didn't define Hermitian because it requires the involution. If you just want to have images in your head when you see the words, this level is OK, but you seem to actually want to do things with the concepts. That requires learning the math. Try the introduction to Linear Algebra down in the math sectioon of PF. That has some links you can use too.
     
  8. Dec 3, 2003 #7
    re

    Hello warren

     
  9. Dec 3, 2003 #8
    re

    ops sorry didnt mean to send it twice!
     
    Last edited: Dec 3, 2003
  10. Dec 3, 2003 #9

    chroot

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    Re: re

    If you don't know what an inner product is, you obviously don't know quantum mechanics. If you are not willing to learn quantum mechanics, then there is little point in discussing anything about it with you. You must learn a subject before you can be competent to debate about it.
    It does not have anything to do with God. Your belief in your God has nothing to do with the scientific study of quantum mechanics. It is irrelevant to the study of quantum mechanics.
    The universe is truly random. A particle truly has no specific value of property until that property is measured. It is not a matter of poor technology, or poor measurement technique. An electron with a precisely defined position can have any momentum at all, and no measurement technology will ever be able to make this not so. An electron whose position has not been measured yet has no defined position yet.
    Determinism does not seem to be the correct theory of the microscopic world. Probabilism seems to be.
    Yes.
    No. Deterministic systems cannot ever be truly random. As you said, chaotic systems and pseudorandom number generators can provide the "illusion" of randomness, but they cannot be truly random (since they're deterministic). Determinism and randomness are mutually exclusive properties.
    Could be. This question has nothing to do with quantum mechanics.
    No, it doesn't say that. Popularizers of quantum theory -- the people who write paperback books -- say that. Quantum mechanics does not deal with the philosophical meaning of measurement at all. Measurements, whether made by eye or by photodetector, result in the same effects.
    The phrase 'degree of freedom' already has another meaning in the context of physical theory. Please don't attempt to redefine it.
    There can certainly be such thing as an isolated electron. The so-called free particle propagator describes what happens to the wavefunction of just such a particle.
    I read this paragraph several times. I can only conclude it is gibberish. Photons do not have perspectives.
    I don't know what this means, either.
    I think we scientists have every intention of getting the science right.

    - Warren
     
  11. Dec 3, 2003 #10
    I think you are trying to understand why photons obey different rules
    to everyday objects? Putting yourself in the shoes of a photon doesn't really work terribly well though.

    I think you are saying that you can not easily get a direct experience of quantum mechanics. People get confused by trying to understand quantum mechanics using classical physics.
     
  12. Dec 3, 2003 #11
    Re: Re: re

    "No, it doesn't say that. Popularizers of quantum theory -- the people who write paperback books -- say that. Quantum mechanics does not deal with the philosophical meaning of measurement at all. Measurements, whether made by eye or by photodetector, result in the same effects."

    back this up, I never talked about the philosophical meanings here:


    "The phrase 'degree of freedom' already has another meaning in the context of physical theory. Please don't attempt to redefine it."

    How can I redefine something, if i made no attempt to define it in the frist place?

    i didnt dissuss quantity that can vary, eg componet of velocity

    "There can certainly be such thing as an isolated electron. The so-called free particle propagator describes what happens to the wavefunction of just such a particle."

    please explain!... and does this "isolation" mean that the obervers obervsation wont effect its "properties"?

    "I read this paragraph several times. I can only conclude it is gibberish. Photons do not have perspectives."

    Really? so if a time to a photon has no meaning it doesnt count has a perspective?

    I never claimed I know QM, you missed my point totaly, I took issue with the fact that you almost assert, I have beguin QM... how do you propose I did my degree in chemistry, without some Knowlege of Quantum physics, thats not to say I KNOW ALL OF IT, or most.

    I ask questions to learn, correct myself and debate - not because I already know the answers - unless I am very unsure of them.



    No it doesnt - not always, one whom as little knowelege STILL can make at times important comments, on the other hand they run the risk of drawing up strawman arguments.


    I never actually disagreed with this, and in fact allot of what I wrote argees with this, my point was discussing "random".


    I am sorry, but I spent time wriing the HUP, i never claimed that this is a result of poor results, or apparatus! I stated that what we use... the apparatus are bulit with within a classical framework, we see from a classical point of veiw, a quantum world, and that trying to bring classical though will arise contradictions!

    so why do you say that the universe is thus RANDOM, instead of the universe has is randomness?

    sure on the small probablity rules, but this does not mean everything is thus random or uncertain, it does mean that we cant know, the precise measurments of an electron (both postion and momentum)...and QM will tell us there is none. (but this is already colored with our pre-concepts in the macro-world!)
     
  13. Dec 3, 2003 #12

    chroot

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    Of course you did. You said "my other point is that has QM says that the oberver is very much apart of the system". This is a philosophical viewpoint, on the level of an interpretation of quantum mechanics. It is not actually part of quantum mechanics. Quantum mechanics does not concern itself with what an observer is or is not.
    The wavefunction begins having one form. As the particle moves, its wavefunction changes to another form (somewhat gradually, of course). The "function" that describes how the free particle's wavefunction changes is called the "free particle propagator." If the particle is free, then there are no observers, rather by definition.
    I still have no idea what you meant with the original paragraph.
    I do assert that you don't know quantum mechanics, based both on the questions you ask, and the wacky things you claim the theory says. If you got a degree in Chemistry but don't know what an inner product of two vectors is, you should really demand a refund from your university.
    You seem to be rather sure that you know things about quantum mechanics in this thread.
    The chances are slim -- very slim.
    Of course you did. You said " but to some extent, it does not mean for certain a lack of causation", rather a lack of measuring it... its a kind of semi-ignorance thing?". This indicates you'd rather believe the particles have complementary properties, but we lack the sophistication to precisely measure those properties. That is incorrect.
    What is a "classical framework," and how does one build an apparatus within it?
    I'm not sure I understand the disctinction between "has" and "is" in this context. I mean that, when you measure the spin of an electron along some axis, you get either +1/2 or -1/2, randomly.
    Are you suggesting it's possible to build a deterministic system from probabilistic parts? Perhaps you need to think about that some more -- it can't be done.
    Our preconceptions from the macroscopic world would have us believe the electron does have both its complementary properties at the same time. It seems this is not so, so we have abandoned those preconceptions, and embraced a new set of rules for the microscopic world.

    - Warren
     
  14. Dec 3, 2003 #13
    Re: Re: Re: Re: re

    "Of course you did. You said "my other point is that has QM says that the oberver is very much apart of the system". This is a philosophical viewpoint, on the level of an interpretation of quantum mechanics. It is not actually part of quantum mechanics. Quantum mechanics does not concern itself with what an observer is or is not."

    Just what do you mean by "what an observer is or is not? that is very vague - it could mean is, in the sense "conscience" or something else - please explain yourself!

    i never said what or who, this observer is, rather the act of observation...effects what is being observed, i went on to ask you to back up what you said before, you have not.



    "The wavefunction begins having one form. As the particle moves, its wavefunction changes to another form (somewhat gradually, of course). The "function" that describes how the free particle's wavefunction changes is called the "free particle propagator." If the particle is free, then there are no observers, rather by definition."

    are you reffering to the wavefunction changes over time? -or is that something different?, when I said isolated, i meant that any obervers looking at it, wont in some way effect it!

    you say they are no observers, why? - I though that separteness or locality is not allowed (at last in the CHI)

    "I do assert that you don't know quantum mechanics, based both on the questions you ask, and the wacky things you claim the theory says."

    with respect, half the things you assert I said are simply what you think I meant by it!

    "If you got a degree in Chemistry but don't know what an inner product of two vectors is, you should really demand a refund from your university."

    it was a degree in chemistry, not physicis.. why QM was needed we dont cover all topics, and unless you know the topics covered, you comment is pretty offbeat.

    "You seem to be rather sure that you know things about quantum mechanics in this thread. "

    you of course are allowed to think..and asserrt what you think i "seeming" - think i know of QM.


    "Of course you did. You said " but to some extent, it does not mean for certain a lack of causation", rather a lack of measuring it... its a kind of semi-ignorance thing?". This indicates you'd rather believe the particles have complementary properties, but we lack the sophistication to precisely measure those properties. That is incorrect."

    Why, why cant it mean from our prespective? within the universe, while we many have no right to dissuss..from a transcdent point of view, it would be wrong thus to assert, that our prespective is the ONLY One!

    "What is a "classical framework," and how does one build an apparatus within it?"

    we bulid experiments and measure, with from OUR PRESPECTIVE into the quantum!

    "I'm not sure I understand the disctinction between "has" and "is" in this context. I mean that, when you measure the spin of an electron along some axis, you get either +1/2 or -1/2, randomly."

    in this case then the random only extends to which where the spin..is either + or - not that there is total random.

    "Are you suggesting it's possible to build a deterministic system from probabilistic parts? Perhaps you need to think about that some more -- it can't be done."

    no, i am saying it may seem to be probabilistic... within certian context.
     
  15. Dec 3, 2003 #14

    chroot

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    Bah, I'm done. I'm not going to beat it into your head. Buy a book. Or don't.

    - Warren
     
  16. Dec 4, 2003 #15
    re

    odd that for example:

    " An electron does not exist in isolation, because it can borrow energy from the uncertaninty relation, for a short enought time, and use it to create a photon" : In search of scrodingers cat By John Gribbin p196

    yet you seem to disagree with my shorten version of this:


    ...while atomic systems can NOT be seperated, and there is NO such thing has say an isolated electron...

    you state:

    "There can certainly be such thing as an isolated electron. The so-called free particle propagator describes what happens to the wavefunction of just such a particle."

    No, John was quite clear that there was no such thing, unless this was one of those paperback books your talking about, hence why (and with other comments you make) I asked you to support your "claims"... did you not really.
     
  17. Dec 4, 2003 #16

    chroot

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    I assume Gribbin is talking about vacuum fluctuations and virtual photons. It comes down to your definition of "isolated." My definition, the one followed in most treatises on QM, is simply that an isolated particle experiences uniformly zero potential. If you'd like to choose a different definition, that's fine.

    And yes, this is one of the problems I have with paperback books -- they don't really teach the reader everything -- they teach the reader little bits and pieces, enough to whet the apetite. The reader then automatically does what humans do -- he amalgamates those bits and pieces into a cohesive world-view. Unfortunately, when you only have bits and pieces, that world-view you create is not likely to be correct. That's why the world is full of cocktail-party physicists who are so sure they're right, when they just aren't. I generally like the idea of teaching physics to the public, and I know people like Gribbin mean well. Unfortunately, many people seem to think a paperback by Gribbin is equivalent to an education is physics -- and it just isn't.

    - Warren
     
  18. Dec 4, 2003 #17
    you assume correct, and that photons can be formed has a result of electrons not existing in isolation (Which is why i menitioned a atomic system.

    Ok fair enough, people do have different difintions, and different concepts and ideas, and situtions... lead to different difintions, but lets make this clear - if you are aware of this, then its your duty to ask for clairfication, or to insure no cross wires!


    I asked you before what i beleived to be fair questions they were:

    are you reffering to the wavefunction changes over time? -or is that something different?, when I said isolated, i meant that any obervers looking at it, wont in some way effect it!

    you say they are no observers, why? - I though that separteness or locality is not allowed (at last in the CHI)


    this is true, however some people dont know or have access to all the info, so they tend to ask questions or basis the arguements on what they "known": and this are not assertions has such rather not proper statements of some sort (are you aware of Carnaps, schlicks - logical postivism - explinations of science ? ) which are open for correction, and addition.



    PS: one obervation, which is not really IF CORRECT QM: when i said isolated electron.. that does not mean particles does it, yes an electron is a "particle" - when oberved that way - but electron is a form of particle, particles are not forms of electrons! it appears you might of confused the two, but that might be a result of me being misslead my the name "isolated particle experiences uniformly zero potential." on the other hand it does not nesscerly exlulde an electron.- in which case please explain my error.


    also i would like to ask you something else:

    how can it be a particle...and not be oberved? when "things" are not oberved, i though at last in the commman interpration of QM... it doesnt narrow down its options?
     
  19. Dec 4, 2003 #18

    chroot

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    How am I supposed to know what you think the word 'isolated' means?
    If it's isolated, there are no observers -- rather by definition. All observations affect the system. There are no kinds of observations that do not. Observation of an observable quantity leaves the system in an eigenstate of that observable. This is a postulate of the theory.
    Who doesn't have access to library?
    It does not matter.
    What narrows down what options? What are you talking about?

    - Warren
     
  20. Dec 5, 2003 #19

    Stingray

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    Re: Re: re

    I don't agree with this. Quantum mechanics must deal with the meaning (in some sense) of measurement, but it does so poorly. This is a shortcoming of the theory.

    It is irrelevant to define the behavior of a field (wavefunction or density matrix) without precisely defining how that field can be observed. A "measurement" in quantum mechanics is an ambiguous concept. Considering the massive effect that it has on the dynamics of a system, it shouldn't be this way. I don't think anyone truly believes that human consciousness is required to collapse a state, so what is? To give a more specific example, Schrodinger's cat type effects are clearly wrong on the scale of a cat.

    Further, if QM is a fundamental theory (which we have no reason to doubt), it applies to the measurement device as well as the system being measured. So the entire thing may be taken as a closed, unmeasured system evolving as states usually do. The second formulation has to give the same answer as the usual one that is used in quantum mechanics (probabilities). Mathematically, this is impossible (since the Hamiltonian is unitary), but the results could be arbitrarily close, which is good enough I think. In my opinion, this is one of the most remarkable results of quantum theory, yet I don't think it has ever been shown rigorously.
     
  21. Dec 5, 2003 #20
    “How am I supposed to know what you think the word 'isolated' means?”

    A question, which is pretty irrelevant, the issue is not about what you know or don’t know,
    What I think I mean, rather if you don’t know, yet still comment – despite the fact your unaware of what I mean by a term, yet you still claim one to be wrong, or right… how do you know. In short you don’t you just said so.

    That’s why I added the point that one seeks to know what definition being used – you didn’t!

    “If it's isolated, there are no observers -- rather by definition”

    Ok so why would it be called a particle? “Electron” maybe, (has they have wave/particle duality ) but your system does not have an oberver, at all!! –

    “All observations affect the system. There are no kinds of observations that do not”

    yes I agree

    “Observation of an observable quantity leaves the system in an eigenstate of that observable. This is a postulate of the theory.”

    And that eigenstate, in part forms the basis for the next set of wavefunctions… but when “we” are not looking at it… remember you said there are no observers – how the hell can you call it a particle, QM DOES not tell us what a system is like when we are NOT looking at it, you seem to assert, that it does!

    Also you asserted before the universe IS random, why such a strong assertation?

    The Schrödinger equation is determinsic in the sense that, given a wavefunction at an initial time, it makes a definite prediction of what the wavefunction will be at any later time. During a measurement, the eigenstate to which the wavefunction collapses is probabilistic, not deterministic. (Has we cant say which values we get with certainty) The probabilistic nature of quantum mechanics thus stems from the act of measurement.

    Did I not say that the random could be a result or our observation?

    And yes, here is where interpretations fit in, but I would say they should be addressed. – while the correct context stated

    “Who doesn't have access to library?”

    nice try, but somewhat ignorant, A library does not always contain valid information in fact, neither do all “textbooks” and the way in which some subjects are teach, Libraries tend to holds lots of those paperbacks you so much tend have a problem with, not to mention the scope and quality and quantity of info, did you ever wonder why I said:

    access to all the info

    rather than… to info
     
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