• What is ''quantum dualism'' ?

    From 44socrat@gmail.com@21:1/5 to All on Thu Dec 27 03:49:09 2018
    What is ''quantum dualism'' ?
    Planck / Einstein described ''quantum'' as ''quantum of action'': E=hf
    where ( h)  is a ''quantum of action''- particle and (f) its frequency.
    (wave / particle duality - simultaneously )
    Uhlenbeck and Goudsmit described how this action is possible: E=h*f
    ( h bar = h/2pi )
    / My opinion./
    ===

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  • From Thomas 'PointedEars' Lahn@21:1/5 to 44socrat@gmail.com on Fri Jan 11 18:58:41 2019
    [This follow-up has become rather long since eventually it also served as
    exam preparation. Hope it helps, and CMIIW.]

    44socrat@gmail.com wrote:
    What is ''quantum dualism'' ?

    A term you invented.

    BTW, in English one uses the quotation mark ("), not two straight
    apostrophes, and one does not write space before a question mark (“?”).

    Planck / Einstein described ''quantum'' as ''quantum of action'':

    No.

    E=hf where ( h) is a ''quantum of action''- particle and (f) its frequency.

    No. ℎ is NOT a particle, it is a _quantity_: the quantum of action (“action” in physics does not mean the same as “activity” in colloquial speech), or simply Planck(’s) constant.

    The particle of which E = ℎ f is the total end kinetic energy is the photon (formerly, Planck: „Lichtquant“ “quantum of light”), of monochrome electromagnetic radiation of frequency f. Actually, from

    E² = m²c⁴ + p²c²

    with m = 0 it is

    E = p c = (ℏ × |k⃗|) × c = ℎ/2π × 2π∕λ × c = ℎ∕λ × c = ℎ c∕λ = ℎ f

    (Planck–Einstein relation).

    The photon is also the quantum of the electromagnetic field.

    It turned out to be necessary to introduce the idea that the energy of light could only be available in portions (quanta) in order to avoid and solve the *ultraviolet catastrophe*:

    ---------------------------------------------------------------------------- One can think of a closed, opaque box with a little hole in it as a good approximation of a *black body*, i.e. an ideal, theoretical physical body
    that absorbs all incoming radiation (and reflects none, therefore appears black):

    _____________
    : _________ :
    : : .`. : :
    : : .' `._:
    : : .' . `.
    : :'. .' : :`.
    : :__`.'____: : `.__ __
    :_____________: :'. |PE

    Such a black body is a perfect absorber, but therefore also a perfect
    emitter: It emits absorbed radiation again as infrared (thermal) radiation.

    But since there is only a little hole in the box, the emitted thermal
    radiation is unlikely to get out of the box. So as long as radiation is
    going into the box, the temperature of the box’s walls increases. When no more radiation is going into the box, the box will develop into a state
    where the walls of the box and its inside space have the same temperature (thermal equilibrium).

    But there is one major problem: Classically, the spectral energy density (energy density for a certain frequency/wavelength) in the box is described by

    u(f, T) = 8π/c³ k T f² Rayleigh–Jeans (radiation) Law,

    where c is the speed of light, k is Boltzmann’s constant, T is the temperature of the box, and f is the frequency of the radiation.

    To determine the total energy density in the box, we would have to calculate the integral over all frequencies that are absorbed by the box. But we have defined that it is a perfect absorber, so it absorbs *all* frequencies, and
    we would have to calculate the integral over *all* frequencies:

    ∞ ∞
    u_tot = ∫ u(f, T) df = 8π k T/c³ ∫ f² df.
    0 0

    But this integral (the area under the curve of the function) is infinite as
    the function value grows towards infinity; in particular, when frequencies
    are high (as is the case with ultraviolet radiation, around 10¹⁵ Hz):

    <https://www.wolframalpha.com/input/?i=plot+8*pi%2F(299792458)%5E3+*+1.38e-23+*+3000+*+f%5E2+for+f+%3D+0+to+1e15>

    (plotted for T = 3000 K)

    So *classically* (under the assumption that light is an electromagnetic
    wave) the energy density in the box should be infinite. But such an energy density is unphysical and it is NOT what is being observed. Thus, the Rayleigh–Jeans Law fails to describe black body radiation completely correctly (it is still a good approximation for long wavelengths).

    Max Planck found in 1900 that, to solve this problem, one must assume that
    the thermal radiation is the result of the oscillations of charge carriers
    in the box’ walls, each one a little harmonic oscillator, that can only
    have an energy, and therefore can only absorb energy, that is portioned (*quantized*) into integer multiples of a constant,

    ℎ ≈ 6.625 × 10⁻³⁴ J s

    [now it occurs to me that maybe he called it “h” for „harmonischer
    Oszillator“ – German for “harmonic oscillator”; I have read one
    other account, I do not remember where, that claims it was “h”
    for „Hilfsvariable“ “helper variable”].

    If you do that, then the spectral energy density in the box is described instead by

    u(f, T) = 8π ℎ f³/c³ × 1/(exp(ℎ f/(k T)) − 1) Planck’s (radiation) law.

    Thus the ultraviolet catastrophe is avoided: If the frequency becomes large, then the first factor is still large, but the second factor is small. So
    the function value approaches zero for large frequencies, and the integral
    over the function over all frequencies f never becomes infinite:

    <https://www.wolframalpha.com/input/?i=plot+8*pi+*+6.625e-34+*+f%5E3%2F(299792458)%5E3+*+1%2Fexp(6.625e-34+*+f%2F(1.38e-23+*+3000)+-+1)+for+f+%3D+0+to+1e15>

    (again plotted for T = 3000 K)

    And this is what is actually being observed.

    There are several applications for this law. In astrophysics, where the effective temperature of a star corresponds to its color, because depending
    on that temperature its light has a maximum intensity at a certain frequency/wavelength and it can be modeled as a black body.

    A planet or moon can be modeled as a black body as well, and its surface temperature can be estimated when its distance from its star is known.
    This leads to the concept of a habitable zone around a star, important for finding habitable exoplanets.

    For example, one can use it to show that if there were no natural greenhouse effect, the mean surface temperature on Terra (Earth) would be −18.5 °C instead of 14 °C (liquid water unlikely, like on Mars), and that it is human influence that increased that to 15 °C within the past century. (More than
    16 °C mean surface temperature will be catastrophic, hence the globally
    agreed “2-degrees-target” until 2100; less would be better, of course.)

    1. Terra reflects 30 % of incoming radiation (albedo; so absorbs only
    70 %);

    2. the irradiated area is equivalent to that of a circle with the radius
    of Terra (only the day side);

    3. the emitting area is the surface area of a sphere with the radius
    of Terra (day and night side)

    0.7 F☉ π r² = 4π r² T⁴ σ

    T = ∜(0.7 F☉/(4 σ)) ≈ 254.6 K ≈ −18.58 °C.

    F☉ – solar constant: flux density of solar radiation at 1 AU
    (solar luminosity L☉ = 4π R☉² T☉⁴ σ = 4π (1 AU)² F☉)
    r – radius of Terra
    T – mean surface temperature of Terra (if there were no atmosphere)
    σ – Stefan–Boltzmann constant

    The concept is carried over to *color temperature* in everyday life, e.g.
    for light bulbs and computer displays. Presently, it is way past midnight
    here and the Redshift software has automatically gradually adjusted the
    color temperature of my laptop’s display to 3700 K because our biorhythm is tuned to the apparent color of our star, which is more reddish closer to
    sunset (due to Rayleigh scattering), to which this color temperature corresponds; it will let me sleep better after writing this than if I had
    been exposed to the bluish light of 6500 K that corresponds to sunlight in a blue day sky (to which it will automatically revert if I use my laptop
    during the day). In ambient lighting, color temperature makes the
    difference between “soft”, “warm”, “natural”/“daylight”, and “cool” lights.
    ----------------------------------------------------------------------------

    In 1905, Einstein showed that Planck’s assumption that the energy of electromagnetic radiation/light is quantized in this way can explain also
    the classically inexplicable photoelectric effect; therefore, that Planck’s “quantum of light”, later called “photon”, and quantization of energy, was
    more than the result of a mathematical trick to avoid infinities:

    <http://hyperphysics.phy-astr.gsu.edu/hbase/mod1.html#c2>

    This realization spawned the field of quantum mechanics (QM), which is at
    the core of all modern physics and technology (even computers, and I am not even talking about quantum computers).

    (wave / particle duality - simultaneously )

    Yes. But later in the development of QM it was realized that there is
    actually no duality: all objects, including those who were previously
    thought to be point-like particles (e.g., electrons), exhibit wave-like behavior: they are properly described by a wave function that solves the Schrödinger equation. It just does not show on larger-than-microscopic scales.

    Uhlenbeck and Goudsmit described how this action is possible: E=h*f

    That is not a description of anything.

    ( h bar = h/2pi )

    Yes. So what? (You have not used hbar. I did.)

    --
    PointedEars
    Git: <https://github.com/PointedEars> | SVN: <http://PointedEars.de/wsvn/> Twitter: @PointedEars2
    Please do not cc me. / Bitte keine Kopien per E-Mail.
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    PointedEars

    Twitter: @PointedEars2
    Please do not cc me. / Bitte keine Kopien per E-Mail.

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  • From Thomas 'PointedEars' Lahn@21:1/5 to Thomas 'PointedEars' Lahn on Fri Jan 11 19:56:29 2019
    Supplemental and correction:

    Thomas 'PointedEars' Lahn wrote:
    ℎ is NOT a particle, it is a _quantity_: the quantum of action (“action” in physics does not mean the same as “activity” in colloquial
    speech), or simply Planck(’s) constant.

    In German it is also called „Plancksches Wirkungsquantum“ which translates to “Planck’s quantum of action”.

    The particle of which E = ℎ f is the total end kinetic energy is the photon
    ^^^
    _and_, not “end”

    (formerly, Planck: „Lichtquant“ “quantum of light”), of monochrome electromagnetic radiation of frequency f. […]

    ---------------------------------------------------------------------------- […]
    If you [assume quantization], then the spectral energy density in the box
    is described instead by

    u(f, T) = 8π ℎ f³/c³ × 1/(exp(ℎ f/(k T)) − 1) Planck’s (radiation) law.

    Thus the ultraviolet catastrophe is avoided: If the frequency becomes large, then the first factor is still large, but the second factor is small. So
    the function value approaches zero for large frequencies, and the integral over the function over all frequencies f never becomes infinite:

    <https://www.wolframalpha.com/input/?i=plot+8*pi+*+6.625e-34+*+f%5E3%2F(299792458)%5E3+*+1%2Fexp(6.625e-34+*+f%2F(1.38e-23+*+3000)+-+1)+for+f+%3D+0+to+1e15>

    <https://www.wolframalpha.com/input/?i=plot+8*pi+*+6.625e-34+*+f%5E3%2F(299792458)%5E3+*+1%2F(exp(6.625e-34+*+f%2F(1.38e-23+*+3000))+-+1)+for+f+%3D+0+to+1e15>

    (somehow the parentheses disappeared)

    (again plotted for T = 3000 K)

    And this is what is actually being observed.

    […]

    --
    PointedEars

    Twitter: @PointedEars2
    Please do not cc me. / Bitte keine Kopien per E-Mail.

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