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Quantum effects caused by our mathematics?

  1. Nov 30, 2015 #1
    Forgive me if I sound ignorant, but is it possible that quantum affects (value of h, why physical dimensions appear to come in discreet chuncks, etc) all stem from our mathematics (which originated as counting numbers -quantum steps). I do understand that calculus was invented to help remedy this, but it still bothers me that at the heart of calculus we take limits that approach zero in a denominator but never can actually be zero. Thus an infinitely small nonzero number which is at the heart of calculus is also at the heart of quantum physics. Please don't beat me up too badly for asking ☺
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  3. Nov 30, 2015 #2

    Vanadium 50

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    Effects. And no, since quantum behavior predates human mathematics by about 13.7 billion years.
  4. Dec 1, 2015 #3


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    And we know that by the method of science, which is based on mathematics invented by humans. :wink:

    More seriously, are you suggesting that mathematics is a human construct, and that physics is not? (I know mathematicians who would claim the opposite.)

    In any case, this is an interesting variant of the chicken-or-egg dilemma. What is first, physics or mathematics?
    Last edited: Dec 1, 2015
  5. Dec 1, 2015 #4


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    Physics obviously came first. Math is used to describe what is already there.
  6. Dec 1, 2015 #5
    I am suggesting that mathematics and physics are both human constructs and that the limit we have with mathematics (infinities tat we get when we try and divide by zero), are showing up as a physical phenomenon in physics as we try and understand smaller and smaller time frames, energy levels, etc. Thus I ponder if there is a new means (similar to today's mathematics) that is still in need of discovering / inventing that could help us better understand the world we live in.
  7. Dec 1, 2015 #6
    I've been thinking about the nature of light, recently, and it ties in to what you are proposing.

    What if light actually is a "wave", and its just that we can only detect it in certain energy levels? What if much of what we attribute to "quantum mechanics" is merely a result of our detection equipment (on a fundamental level)?
  8. Dec 1, 2015 #7


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    Mathematics is a human invention, but due to the interplay between pure and applied mathematics is not just pure thought - it too is influenced by applications to the world out there.

    Physics on the other hand is entirely constrained by correspondence with experiment.

    As to QM we have a much better idea these days what its basis is:

    It seems we have two choices - usual probability theory or QM - nature chose QM. Such is dictated by experiment - not mathematics.

  9. Dec 1, 2015 #8


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    People have considered such things - none of them work.

    We now know pretty well why QM is as it is - see my post above.

    What it means - that is another matter - but the why of the QM formalism is much better understood these days. And even finding an alternative is severely constrained:

    Last edited: Dec 1, 2015
  10. Dec 1, 2015 #9


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  11. Dec 1, 2015 #10
    Thanks for the feed back. Those 2 links will keep me busy.
  12. Dec 1, 2015 #11


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    But also atoms only react to it at certain energy levels.
  13. Dec 2, 2015 #12


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    It is a wave.

    It's harder to detect light at some energy levels than others, but the energy is related to the frequency and there are no frequencies at which we cannot detect light so there are no missing levels.
  14. Dec 2, 2015 #13


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    (There's nothing in quantum mechanics that says that physical dimensions come in discrete chunks)

    Consider a beam of silver ions passing through a Stern-Gerlach device.
    If we start with the postulates of classical physics and then apply math, we will conclude that a single diffuse beam will come out. If we start with the postulates of quantum physics and then apply math, we will conclude that two distinct beams will come out. Thus it can't be that the quantum mechanical effect is caused by some limitation of our mathematics; the math works just fine either way.

    Instead, the quantum mechanical model is forced on on us by the results of the experiment. We try it and we find two distinct beams coming out.
  15. Dec 2, 2015 #14
    I am not trained in maths very much. Nevertheless I find that mathematics is a means to describe phenomena or abstract notions. The kind of mathematics used may vary, and, in my eyes, that influences the power, accuracy range and descriptive range of it depending on the subjects it is applied to. So no, not an ignorant notion of you in my eyes (at all). :smile:
    Last edited: Dec 2, 2015
  16. Dec 2, 2015 #15
    As I understand it (coming only from an engineering background), light (including all radio frequencies outside of our visible spectrum) come in discreet chunks called photos from E =hf equation. Does quantum mechanics dispute photon chunks of energy?
  17. Dec 2, 2015 #16


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    Of course not.

    But what's going on is far from simple. Its described by Quantum Field Theory where even the number of particles is not fixed:

    That however has nothing to do with physical dimensions - a Quantum Field is continuous.

    How particles emerge is complicated - but its similar to a quantum harmonic oscillator with its creation and annihilation operators:

  18. Dec 2, 2015 #17


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    You are right that when light interacts with matter, it always deposits its energy and momentum in discrete chunks whose size is given by E=hf.

    Usually when someone says that physical "dimensions" come in discrete chunks, they're using the word to refer to time and space. If that's not what you meant, we're good.
  19. Dec 3, 2015 #18
    Photons may deposit energy in discrete chunks, but the energy free photons can take (equivalently, frequency) is not discretized as far as we know. In quantum mechanics there are discrete and continuous aspects in a mix, both discrete and continuous mathematics is used. Both kinds of mathematics are mathematics.

    If you contend that mathematics originated in counting, and only later continuous models were devised which you find "suspicious" (like infinity never actually being reached) consider this. Maths originated also as geometry, which was initially separate from algebra. But geometry has already aspects of continuity of the 1600's calculus, namely irrational numbers, which expose the "existence" of real numbers, an uncountably infinite set. So continuous maths is necessarily there as much as triangles, it's not "more fictitious" than discrete algebra.

    And then there's the fact that continuous maths has effectively solved Zeno's paradox, infinity is actually reached, though you may be skeptical about it if you haven't seen the proof.
  20. Dec 4, 2015 #19
    I guess I struggle with an infinity being reached as that seems like a contradiction. By definition i expect that an infinity cannot be reached. Also I am intrigued by that fact that calculus has at its roots a "quantum" nature (since it is a limit of a ratio's denominator that is infinitesimal but not zero in size). I understand that this point of view is possibly just my lack of adequate training in much higher mathematics but I was interested in hearing what others thought on this.
  21. Dec 4, 2015 #20
    I approve your reasoning regardless of what number base or type of math that's used "as a best fit model to describe said phenomenom" the phenomenon had to be present to be modeled after in the first place.
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