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Why is angular momentum quantized?

  1. Oct 30, 2007 #1
    Hello Everybody.

    I wanted to find a good explanation for "Why is angular momentum quantized?" but I found a lot of explanations most of them includes math.
    Could you help me about the question Why is angular momentum quantized? philosophically.

    thank you form now.
     
  2. jcsd
  3. Oct 30, 2007 #2

    clem

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    Welcome to physics. A lot of explanations need math.
     
  4. Oct 30, 2007 #3
    Hmm...angular momentum quantization without math. Well, from the perspective of a wavefunction, angular momentum is the "generator" of rotations. However, if you rotate an object by 2*pi, it should be as if you did nothing to it at all. Quantization ensures this. (Actually, it's more general than this, but you said not to use math.)
     
  5. Oct 30, 2007 #4

    malawi_glenn

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    The language / tool in physics is math, not philosophy. Sorry to dissapoint you.

    Also, angular momentum is a physical concept defined by math..
     
  6. Oct 30, 2007 #5
    thank you for your answers. but I meant why it is quantized what is the reason for that. of course basic math must be in there. philosophically in my question is by words, like you are telling it to your father. There is an expressin from a big physicsists who I dont remember the name, If you are not able to express a phenomena in physics to your grand father that means you dodnt understand it. it was something like that. :)

    thank you.
     
  7. Oct 30, 2007 #6

    malawi_glenn

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    Try to explain lattice gauge theories to a 80year old man! ;)

    If we ask you this: what sources have you considered?
     
  8. Oct 31, 2007 #7
    is not there a good explenation for this consept? OK: math can be in this explanation.

    :(
     
  9. Oct 31, 2007 #8

    ZapperZ

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    Is there a reason why you are asking about the "angular momentum" in particular? Does this mean that you already have a satisfactory explanation on why other parameters such as energy, spin, magnetic flux, etc. are quantized and that they no longer are puzzling to you?

    Zz.
     
  10. Oct 31, 2007 #9

    nrqed

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    I had no problem talking exlaining some work I was doing related to lattice gauge theory to Hans Bethe when he was still alive and way passed 80 years old :wink:
     
  11. Oct 31, 2007 #10
    because it is fundamentally generated by a digital algorithm- as are all features of the cosmos- continuous mathematical models are only approximations of what are in actuality logical operations on the discrete quantized states of a bit register
     
    Last edited: Oct 31, 2007
  12. Oct 31, 2007 #11

    OOO

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    I think, at least part of the reason why angular momentum is quantized can be explained without math.

    If you imagine angular momentum as something that runs on a circle, and then add quantum mechanics as causing some "spirals" around this circle, then you are only able to close the spiral if it winds an integer times around the circle.

    Closing the spiral corresponds to a stationary quantum state. Of course this doesn't directly explain half integer spin, but I'm sure someone more clever than me can extend this explanation to spinors (however I can hardly believe that this can be done without math...).
     
  13. Oct 31, 2007 #12

    malawi_glenn

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    =) Of course not.. but i meant the average 80y old..
     
  14. Oct 31, 2007 #13
    Given some finite amount of energy you can only store a finite amount of information in a finite volume. Clearly, if angular momentum or any other local degree of freedom were not quantized, this principle would be violated and an infinite amount of information could be stored in a finite volume. The entropy of any system would be infinite...
     
  15. Oct 31, 2007 #14

    you have struck upon the fundamental reasons why continuous/classical systems are unphysical- any truly continuous element of a system would lead to infinite instability- it would have infinite degrees of freedom and be expressed as pure entropy- it could never interact with the rest of the universe-

    the only kinds of things that can have the quality of existence are the discrete quantized states produced by algorithmic processes
     
    Last edited: Oct 31, 2007
  16. Oct 31, 2007 #15

    OOO

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    You're saying this as if it was a mathematical fact. But then classical electrodynamics would be impossible mathematically. The classical field does in fact have an infinite number of degrees of freedom in a finite volume and yet the classical field has finite energy density. So I feel the information thing doesn't explain quantization.
     
  17. Oct 31, 2007 #16
    Well, you need to quantize the field. Impose some boundary conditions on the field and solve for the eigenstates. The energy eigenvalues are of the form [tex]\sum_{k, \sigma}\left(n_{k,\sigma} + 1/2) \hbar\omega_{k}[/tex], the quantum numbers [tex]n_{k,\sigma}[/tex].

    In the classical limit you get the ultraviolet catastrophe, which is caused by the fact that you can let the frequencies of the occupied modes go to infinity while keeping the energy bounded.
     
    Last edited: Oct 31, 2007
  18. Oct 31, 2007 #17
    I agree with SetAi.

    Note that Classical Mechanics, perhaps also classical electromagnetism, allows one to build an apparatus that can solve the Halting problem by brute force. One can make a so-called "rapidly accelerating computer". The clock cycle of this computer will accelerate so fast that an infinite number of computations can be performed in a finite time.

    Classical physics is thus not reconcilable with computability.
     
  19. Oct 31, 2007 #18

    OOO

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    Who says that nature must conform to our limited ability to compute something ? Probably you see more clearly than me that this leads to unavoidable mathematical inconsistencies. But in the meantime I tend to think that nature is quantized because it's quantized and we have designed mathematical tools that reflect this fact.
     
  20. Nov 1, 2007 #19

    clem

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    A lot of explanations need math.
     
  21. Nov 2, 2007 #20
    ?

    actually thers is no specific reason about angular momentum. But in quantum mechanics as known to all quantization of angular momentum is a main body I think. Of course I know some about the quantization of energy or via bohr model about the quantization of angular momentum. However I would be more satisfy if I heard more about this fact.

    thank you.
     
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