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Author Topic: Why do we ignore the Quantum Harmonic Oscillator?  (Read 2918 times)

Offline Arthur Geddes

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The current dogma asserts that things are quantized.  It seems people don't generally realize that things are quantized for a reason; in order to sustain an harmonic dynamic in a closed loop, there has to be some form of resonance.  It's this requirement, i call it a coherence requirement, coupled with the wave property of things that quantizes the energy of 'things around things.'  It's fine to think of things as in pieces but; along with those pieces goes a coherence requirement.

Why do we ignore the coherence requirement?  Is it because the particle aspect gives us rights &; the coherence aspect gives us responsibilities?


 

Offline PmbPhy

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Re: Why do we ignore the Quantum Harmonic Oscillator?
« Reply #1 on: 01/05/2016 22:39:54 »
Quote from: Arthur Geddes
The current dogma asserts that things are quantized.  It seems people don't generally realize that things are quantized for a reason; in order to sustain an harmonic dynamic in a closed loop, there has to be some form of resonance.
That makes no sense to me. Can you clarify it for me? I.e. what do you mean by "harmonic dynamic in a closed loop" and why should here be some form of resonance? Do you know what the term resonance means? See: https://en.wikipedia.org/wiki/Resonance

Quote from: Arthur Geddes
  It's this requirement, i call it a coherence requirement, ...
From what you described above its far from clear what "coherence requirement" means. Please describe.

The title of this thread is Why do we ignore the Quantum Harmonic Oscillator?  The fact of the matter is that all quantum mechanics textbooks discuss the simple harmonic oscillator in detail.
 

Offline alancalverd

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Re: Why do we ignore the Quantum Harmonic Oscillator?
« Reply #2 on: 01/05/2016 23:11:41 »
Please don't confuse experimental evidence (for quantisation) with dogma (coherence requirement).

And far from being ignored, to quote Wikipedia

Quote
it is one of the most important model systems in quantum mechanics.
 

Offline Arthur Geddes

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Re: Why do we ignore the Quantum Harmonic Oscillator?
« Reply #3 on: 02/05/2016 02:23:46 »
Please don't confuse experimental evidence (for quantisation)

It's the graph of black body radiation that gives us the fundamentals of experimental foundation for quantization of photons.  I appreciate that.

Quote
with dogma (coherence requirement).

I don't appreciate that.  The graviton is more dogmatic; that's the point of "current dogma."  There is a QHO at the root the photon; the one at the root of the graviton would have to be the de Broglie wavelength of the massive bodies in some orbit or other ... maybe, i guess; like two black holes spinning into each other... sure.  There would be discrete states prior to impact?  Where's the math?

Quote

And far from being ignored, to quote Wikipedia

Quote
it is one of the most important model systems in quantum mechanics.
Then it should be mentioned more often.
 

Offline Arthur Geddes

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Re: Why do we ignore the Quantum Harmonic Oscillator?
« Reply #4 on: 02/05/2016 03:08:04 »
Lemme check my terminology...
 

Offline evan_au

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Re: Why do we ignore the Quantum Harmonic Oscillator?
« Reply #5 on: 03/05/2016 04:29:52 »
    Quote from: Arthur Geddes
    The graviton is more dogmatic; that's the point of "current dogma."
    At present, the graviton is considered a hypothesis; I don't think anyone would be dogmatic about its existence until we get some more solid experimental evidence for their existence (or, considering their incredibly small energy, more likely theoretical evidence).

    Quote
    the one at the root of the graviton would have to be the de Broglie wavelength of the massive bodies in some orbit or other ... maybe, i guess; like two black holes spinning into each other... sure.
    The de Broglie wavelength of a black hole of (say) 30 Solar masses would be miniscule.

    However, we can work out the wavelength of the gravitons recently discovered. Early in the event, the gravitational waves had a frequency around 50Hz, which I understand is due to the black holes rotating around each other 25 times per second.

    From the observed fact that the gravitational waves travel at pretty much the speed of light, we can calculate their wavelength:
    c≈v=fλ
    Where:
    • f is the frequency, say 50Hz (observed range: 40Hz - 400Hz)
    • v is the velocity of the gravitational waves, which is roughly c (the speed of light)
    • λ is the wavelength

    So we get λ= 6000km (range: 750-7500km)

    Quantum effects of electromagnetism (light & electrons) prevent electrons collapsing into the nucleus (the "ultraviolet catastrophe"). This is because of the Plank constant in E=ħf.

    The quantum effects of gravity do not prevent solar-mass black holes from collapsing into each other. If gravity is quantized, I am sure that the equivalent constant for gravity is a lot smaller than ħ (by perhaps 40 orders of magnitude?).[/list]
     

    Offline alancalverd

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #6 on: 03/05/2016 08:09:23 »
    Then it should be mentioned more often.
    It turns up in every first-year quantum physics course, just as breathing is mentioned when you learn to swim. Thenceforward it's almost instinctive. 
     

    Offline Arthur Geddes

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #7 on: 03/05/2016 16:55:01 »
    It turns up in every first-year quantum physics course, just as breathing is mentioned when you learn to swim. Thenceforward it's almost instinctive.
    Or, just forgotten...; when i did engineering there were a lot of people just trying to pass; different motive, i suppose.  I gotta check this out more.  Thanks for the feedback.
     

    Offline Arthur Geddes

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #8 on: 03/05/2016 16:57:41 »
    If gravity is quantized, I am sure that the equivalent constant for gravity is a lot smaller than ħ (by perhaps 40 orders of magnitude?).
    But, there is no theoretical quantized harmonic oscillator for mass?  I don't suppose there is: if not then, what ground for the graviton?
     

    Offline PmbPhy

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #9 on: 04/05/2016 02:02:34 »
    Quote from: Arthur Geddes
    The current dogma asserts that things are quantized.
    I disagree with this assertion. Quantization is most definitely not dogma. The term dogma is defined as a belief or set of beliefs that is accepted by the members of a group without being questioned or doubted. That's not how physics works.
     

    Offline Arthur Geddes

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #10 on: 04/05/2016 06:19:46 »
    I disagree with this assertion. Quantization is most definitely not dogma. The term dogma is defined as a belief or set of beliefs that is accepted by the members of a group without being questioned or doubted. That's not how physics works.
    I appreciate your objection & am compelled to clarify my meaning.  Science is as you say &, some aspire to be good scientists & do good science.  Sadly; proprietary knowledge being as it is &, people being as they are, there are dogmas of the day provided by popular culture.

    The wave nature of matter was a dogmatic assertion that survived it's test; General Relativity was less dogmatic owing to the success of Special Relativity.  The Graviton seems as dogmatic an assertion as the wave nature of matter but, yet to be tested.
     

    Offline alancalverd

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #11 on: 04/05/2016 20:19:07 »
    Don't confuse a useful mathematical model with dogma, or even truth. Professionals recognise the difference. The deBroglie wavelength has some useful applications as an approximation to solutions to the Schrodinger equations, which are more accurately descriptive.
     

    Offline evan_au

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #12 on: 04/05/2016 22:25:07 »
    Quote from: Arthur Geddes
    It seems people don't generally realize that things are quantized for a reason
    If you are measuring events that are orders of magnitude larger than the quantization level, some applications can get away with ignoring any underlying quantization.

    So for AM radio stations, we can ignore the quantization of photons, because the individual photons have far less energy than the thermal noise that we deal with all the time.

    And there are no known lower limits to the energy of photons (except maybe the size of the universe) - one of the biggest radio transmitters in our Solar system is the Sun, transmitting on a wavelength of around 22 light-years. This somewhat chaotic oscillator is not really quantized.

    Quote
    there is no theoretical quantized harmonic oscillator for mass?  I don't suppose there is: if not then, what ground for the graviton?
    We know that non-quantized gravity is incompatible with general relativity, so we don't actually have a fully-working theory of gravitation at present.

    Quantized gravity claims to be making significant progress in alignment with general relativity, so this might become a working theory.

    If non-quantized gravity is broken, it is worth exploring quantized gravity.

    Quote from: George Bernard Shaw
    You see things; and you say 'Why?' But I dream things that never were; and I say 'Why not?'
     

    Offline Arthur Geddes

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #13 on: 09/05/2016 03:27:53 »
    We know that non-quantized gravity is incompatible with general relativity,...

    ?? news to me; how do we know this?
     

    Offline Arthur Geddes

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #14 on: 09/05/2016 03:34:38 »
    The deBroglie wavelength has some useful applications as an approximation to solutions to the Schrodinger equations, which are more accurately descriptive.

    So the statistics of finding it... Something that animations often get wrong is the variation of electric & magnetic field with respect to each other; the animations tend to represent zero crossings at the same time, the waves in phase.  The waves are 90 degrees out of phase & i wonder, the statistics of knowing about an electron, its location & momentum as aspects of the probability wave: are they 90 degrees out of phase?
     

    Offline evan_au

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #15 on: 09/05/2016 12:20:45 »
    We know that non-quantized gravity is incompatible with general relativity,...

    ?? news to me; how do we know this?
    I was referring to the fact that quantum gravity is not renormalizable (using current techniques).
    So I should have said something like "quantum theory is incompatible with gravity".


    Sorry about that.
     

    Offline PmbPhy

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #16 on: 09/05/2016 17:24:58 »
    Quote from: Arthur Geddes
    I appreciate your objection & am compelled to clarify my meaning.  Science is as you say &, some aspire to be good scientists & do good science.  Sadly; proprietary knowledge being as it is &, people being as they are, there are dogmas of the day provided by popular culture.
    Proprietary knowledge has nothing to do with quantum mechanics. In fact there is no proprietary knowledge in any science since proprietary knowledge is defined as follows: from http://www.businessdictionary.com/definition/proprietary-information.html
    Quote
    Proprietary Knowledge: Information that is not public knowledge (such as certain financial data, test results or trade secrets) and that is viewed as the property of the holder. The recipient of proprietary information, such as a contractor in the procurement process, is generally duty bound tom refrain from making unauthorized use of the information.
    I can't even imagine how you used such a term in a discussion of science.

    Quote from: Arthur Geddes
    The wave nature of matter was a dogmatic assertion that survived it's test; General Relativity was less dogmatic owing to the success of Special Relativity.  The Graviton seems as dogmatic an assertion as the wave nature of matter but, yet to be tested.
    You are quite wrong in all of that. The wave nature of matter was always public knowledge because the research was always published in  scientific journals which are accessible to those who were interested in the subject.

    By the way. The graviton hypothesis is just that, i.e. an hypothesis. They've never been observed up until now so they can't be said to exist. However the day may come when they move from hypothesis to observational fact.
    « Last Edit: 09/05/2016 17:35:05 by PmbPhy »
     

    Offline PmbPhy

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #17 on: 09/05/2016 17:37:58 »
    We know that non-quantized gravity is incompatible with general relativity,...

    ?? news to me; how do we know this?
    I was referring to the fact that quantum gravity is not renormalizable (using current techniques).
    So I should have said something like "quantum theory is incompatible with gravity".


    Sorry about that.
    Hi Evan. Can you please help me understand what you mean here? E.g. why would you assert

    (1) We know that non-quantized gravity is incompatible with general relativity
    (2) quantum theory is incompatible with gravity".

    Thanks.
     

    Offline Arthur Geddes

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #18 on: 09/05/2016 19:39:16 »
    I can't even imagine how you used such a term in a discussion of science.

    It helps me understand other's preference to confuse the issue.

    Quote

    Quote from: Arthur Geddes
    The wave nature of matter was a dogmatic assertion that survived it's test; General Relativity was less dogmatic owing to the success of Special Relativity.  The Graviton seems as dogmatic an assertion as the wave nature of matter but, yet to be tested.
    You are quite wrong in all of that. The wave nature of matter was always public knowledge because the research was always published in  scientific journals which are accessible to those who were interested in the subject.

    You seem to be confusing the issue.  I've not suggested the wave nature of matter was at any time proprietary; i'm in no position to suggest such a thing.
     

    Offline evan_au

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #19 on: 09/05/2016 22:35:07 »
    Quote from: PmbPhy
    Can you please help me understand what you mean here? E.g. why would you assert
    (2) quantum theory is incompatible with gravity".

    Conventional quantum theory suffers from infinities in the maths. But these can be made to disappear by "Renormalization".

    However, all attempts to include gravity in quantum theory has resulted in infinities that don't go away (using currently known mathematical tricks).

    See: https://en.wikipedia.org/wiki/Renormalization#Renormalizability
     

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    Re: Why do we ignore the Quantum Harmonic Oscillator?
    « Reply #19 on: 09/05/2016 22:35:07 »

     

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