[General] Quantisation of classical electromagnetism

[Andrew Meulenberg]

Dear Martin,

It is great communicating with someone who has also thought about the
issue. My comments are sometimes too cryptic because I assume that you
would have come to the same conclusions. Let me try (in brown) to identify
some of the differences below.

On Thu, May 7, 2015 at 3:50 AM, Mark, Martin van der <
martin.van.der.mark at philips.com> wrote:

>  Andrew, thanks, please see below, in green
>
>
>
> Dr. Martin B. van der Mark
>
> Principal Scientist, Minimally Invasive Healthcare
>
>
>
> *From:* General [mailto:general-bounces+martin.van.der.mark=
> philips.com at lists.natureoflightandparticles.org] *On Behalf Of *Andrew
> Meulenberg
> *Sent:* woensdag 6 mei 2015 19:46
> *To:* Nature of Light and Particles - General Discussion
> *Subject:* Re: [General] Quantisation of classical electromagnetism
>
>
>
> Dear John W,  Martin, et al.,
>
> I don't think that a week together in San Diego would be enough to
> transfer the information that we all need to share. And, I will probably
> miss even that. I am already learning so much and have so much to
> contribute that I feel frustrated that I have to divide my time.
>
> Just this morning (my time), I changed my idea of the electron radius.
> After seeing it expressed many times by various members of this group as
> 1/2 the Compton radius (and considering that to be wrong), it finally hit
> me, when reading it again, that, even within my own model, *I *had been
> wrong and this smaller radius is probably correct.
>
> some comments below:
>
>
>
>
>
> On Wed, May 6, 2015 at 3:28 PM, Mark, Martin van der <
> martin.van.der.mark at philips.com> wrote:
>
>
>
> Andrew, John, all
>
>
>
> John W is quite right as well, just a small remark on the hydrogen atom.
>
> By the virial theorem, for a 1/r potential, potential energy is minus two
> times the kinetic energy and kinetic energy is equal to the binding energy
> (13.6 eV in the ground state).
>
> For the structure of the atom there are three conditions, one of
> electromagnetic, and two of inertial nature.
>
> 1) The coulomb potential runs to minus infinity, that is very deep. It
> comes from the charge of proton and electron.
>
> 2) Then the centrifugal force (depends on mass of proton and electron)
>  must balance the Coulomb force, this could have been in a continuum of
> orbits if the electron and proton were just particles (without a wave
> nature) (see gravitation and solar system for an exact analogy),
>
> 3) The mass of proton and electron set the scale of the de Broglie
> wavelength (which, incidentally, is exactly the same for proton and
> electron in the bound state), and hence the bound state has a finite size,
> 0.1 nm diameter for the ground state. The particle's waves must interfere
> constructively within the boundary conditions: quantized energy levels
> appear.
>
> Cheers, Martin
>
>
>
> I also have three basic conditions:
>
>    - The QM description of the mechanical resonance of a body confined in
>    a potential well. The reason for this resonance is not the interference
>    with the nucleus (which does not appear in the fundamental equations).
>    There is a simple physical and mathematical basis that is taught in 1st
>    year calculus.
>    - The classical description of the orbiting electron creates an EM
>    field that is evolving into a photon as the electron decays to a deeper
>    level. The resonance between the electron and emitted-photon frequencies,
>    along with the virial theorem and conservation of energy and ang. mom.,
>    determine the allowed energy levels. The fact that these levels agree with
>    the mechanical levels gives a double resonance.
>
> I do not really understand what you mean by the double resonance.
>

 The levels identified with the classical description agree with those of
the mechanical (QM) system.

>
>    - the ground state is established by the requirement of a photon to
>    have an angular momentum of hbar.
>
> Why is this fundamental?  It depends on the system you are looking at.
> Circular orbits are a confusing thing o look at too, if you want to look at
> angular momentum. The real hydrogen atom has NO angular momentum (spin=0)
> in the ground state, contrary to the Bohr model of it!!!!!
>

[Exactly, therefore it cannot radiate a photon except to a system w ang.
mom. = hbar. No levels below gnd state have that value.]


> The groundstate of the atom is the groundstate because it is the lowest
> energy state, with just the fundamental tone (one wavelength) fitting to
> the boundary conditions.
>

There is no reason *given* that the wavelength cannot fit 2 cycles rather
than one. Is it more difficult than having n wavelengths in a single cycle?
(ref Lissajou figures) This is the basis of Mill's hydrino states. The
limiting factor is the photon.


>  The one wavelength holds for the complete atom, electron and proton: the
> electron is light and moving fast, the proton id heavy and slow, but both
> have the same momentum! Hence they have the same de Broglie wavelength...
>

The solution assuming an infinite mass nucleus (hence no deBroglie
wavelength & no resonance) still produces discrete levels. Therefore that
issue cannot be causal.


>   Looking at your conditions produced other thoughts.
>
>    1. The statement that "the coulomb potential runs to minus infinity"
>    is a mathematician, not a physicist talking.
>
> True. The Coulomb potential is a mathematical concept that models reality
> quite perfectly. Mathematics is the language of physics. Further, the
> electron has an almost 1/r dependent potential still at TeV collision
> energies, this is why people say it has point-like behavior.
>

And, it will be considered valid until experimental evidence show
otherwise. Then, 60 years of mathematical 'proofs' will immediately
disappear. Do you know of any nuclear physicist who would consider the
nuclear Coulomb potential to be a singularity? Even before the quark model
became popular? What is reality, a singular potential that contains all of
the energy in the universe, or a presently measured finite charge density
of the proton and neutron? Feynman jested that the whole universe consisted
of a single electron oscillating back and forth in time. If it was singular
and contained all of the energy in the universe, maybe Feynman's jest was
correct.


>  Further your remark is irrelevant because the binding energy of the
> ground state of hydrogen (or any atom) is alpha^2 times smaller than the
> electron's classical radius (which incidentally is close to the charge
> radius of the proton)
>

Do you consider the proton charge radius to be its field-energy density or
the major extent of its *Coulomb potential* (e.g., the electron Compton
radius)? We haven't defined charge yet have we? [Am I being the
mathematician now for insisting on a valid definition?]


>  The potential energy PE must come from the energies, as expressed by the
> mass and charge, of proton and electron. Since the largest energy is the
> mass, the PE is limited to a GeV. Therefore, the electrical potential
> cannot exceed this value.
>
> Yes it can exceed its RESTmass , and will be precisely gamma m0, see
> above, not exceeding its relativistic mass, of course.
>

In some frame of reference, the relativistic mass is infinite. However, the
charge field changes in that frame also. In the rest frame, PE is finite
and 1/r must be limited.

 This, like relativity, makes a big difference in some fields of physics.
>
>    1. The source of the wave nature of the electron is never defined in
>    QM. Is it the 'hidden variable"?
>
> No it is not,  but almost, what the real structure is, well we have our
> ideas,,,, The hidden variable has to do with phase coherence in the
> measurement process. Will explain that over a glass of beer, it is worth a
> good set of papers.
>
> It can be defined classically, if spin is a real angular momentum, not
> just a Q#, and relativity is more than just a mind game.
>
> Quantum spin is angular momentum, but not that of a rigid body. For spin 1/2
> you need something like a fluid  that is circulating in 2 directions at the
> same time, like a spinning, rotating , twisting torus. Think of a smoke
> ring with a twist and rotating like a wheel
>
> More beer required here too
>

I think of the surface of a ball of yarn! Only photons can pass thru each
other (or itself), thus the electron is more than a fluid. It is
circulating in *all* directions. Uniquely, it can have an infinity of
angular momenta. That is why it can have spin 1/2 in *any* direction you
wish to chose. That question puzzled since college days; but, I was too
'young' to properly question the 'cant' being fed us. I don't think that
the professors, bright as they were, could have understood my question,
much less answered it. (What about a spin axis along the time direction?)

>
>    1. I do not believe that looking at the system in center-of-mass
>    (momentum) coordinates introduces quantized levels in two dimensions. Can
>    only adding 1 or 2 more dimensions produce the fixed levels? Can you
>    describe how such levels might occur? If you define a bell as quantized,
>    then the levels can be quantized. However, they still can have a continuum
>    of values unless the structure is fixed. I have to admit that this is like
>    my condition 1 and both are weak w/o a better reason for discrete values.
>    The 'standing wave' concept is attractive, but misleading.
>
> More below:
>
>   *From:* General [mailto:general-bounces+martin.van.der.mark=
> philips.com at lists.natureoflightandparticles.org] *On Behalf Of *John
> Williamson
> *Sent:* woensdag 6 mei 2015 11:12
>
>
> *To:* Nature of Light and Particles - General Discussion
> *Cc:* Nick Bailey; Kyran Williamson; Michael Wright; Manohar .; Ariane
> Mandray
> *Subject:* Re: [General] Quantisation of classical electromagnetism
>
>
>
> Hihi,
>
> A lot of questions there Andrew.
>
> All quantised means is "countable".
>
>
>
> QM is certainly putting a lot more weight to the word than that. Pointing
> out resonances has a physical meaning that can be useful.
>
>
> Yes there are exceptions. Mostly exceptions! The quantised electron charge
> comes, for me, from an interaction rate. Hence the reason all charges in
> contact have the same value.
>
>
>
> I would say that this looks at effect, not cause or definition.
>
>
>
>    Other quantum numbers may just be an intrinsic sign- such as the
> lepton number difference between the positron and the electron. Quantised
> states in atoms and quantum wells are resonant states, indeed. In the FQHE
> these are bound quasi-particle-flux-quantum states. These are more musical
> ratios, than integer numbers. Quantised conductance, for example, is simply
> a rate-per-single-electron. The popular press and Wikipedia tends to sweep
> all the unknowns into one big unknown. That thing which cannot be known -
> the great UNCERTAINTY! Assigning a quantum number to something is
> tantamount to putting all your lack of understanding into a single number.
> Too much of this kind of shit passes as understanding!
>
>
>
> Agreed!
>
>
> The ground state of the Hydrogen atom is that energy where potential=
> kinetic, and the de Broglie wavelength of the electron equals the de
> Broglie wavelength of the proton. A single wavelength with periodic
> boundary conditions - for both! What a beautiful resonance! Simple, singing
> resonance - with no dissipation. Physics tries indeed to mystify this, but
> it is really a simple congruence. Engineers know better!
>
>
>
> For a 1/r potential the virial thm states that KE = PE/2. You and Martin
> agree about the relationship between proton and electron as being
> important. Is this a claim of QM or something that you both simply agreed
> on? The basic Schrodinger equation assumes an infinite proton mass.
>
>
>
> This has nothing to do with the Schroedinger equation but with the Born
> approximation, which is not necessary to make, the proton mass is finite,
> and it can be taken into account by introducing the reduced mass: m_p x
> m_e/(m_p + m_e)
>
> Oh and KE = -PE/2, PE is negative!!!
>

Introducing the reduced mass (and a nuclear deBroglie wavelength for
'resonance') changes the values, but not the nature, of the discrete energy
levels. The nucleus travels~2000 orbits before it completes a single
deBroglie wavelength. How come the electron is only allowed a maximum of a
single cycle?

>
>
> There is no nuclear wavelength, yet the solution has discrete levels. You
> are correct about a resonance between two wavelengths (frequencies). But I
> think that they are between the electron and EM wave becoming a photon.
>
>
> Indeed the Coulomb potential goes way down (as you argue so beautifully in
> your paper). Shorter lengths, however, are less than one wavelength and
> hence, though they could be resonant, actually at a higher energy, through
> interference. The one wavelength state is the ground state. For this state
> the Coulomb field, cancelled outside the Bohr radius corresponds exactly to
> the 13.6 eV binding energy of the Hydrogen atom. All very simple and very
> beautiful!
>
>
>
> What prevents the 1/2 wavelength state from existing and being occupied?
> (Or for 1/n, with a single wavelength being completed in n orbits.)
>
>
>
> If you do that, it simply interferes away, then that energy has to go
> somewhere, it cannot be destroyed, so it will be radiated. This is why
> atoms radiate while an electron changes "orbit" : temporarily there is no
> fit, but energy must be conserved.
>

Are you assuming that the electron is a wave and not localized? That its
wave function, distributed around the atom and extended to 2 orbits per
cycle, would cancel because of phase reversal? Then what about 3 (or any
odd integer) orbits?

>
> More below:
>
>
> Martin is, as usual, right in (pretty much) everything he says. Especially
> in that it is very important!
>
> Regards, John W.
>  ------------------------------
>
> *From:* General [general-bounces+john.williamson=
> glasgow.ac.uk at lists.natureoflightandparticles.org] on behalf of Mark,
> Martin van der [martin.van.der.mark at philips.com]
> *Sent:* Wednesday, May 06, 2015 8:48 AM
> *To:* Nature of Light and Particles - General Discussion
> *Cc:* Nick Bailey; Kyran Williamson; Michael Wright; Manohar .; Ariane
> Mandray
> *Subject:* Re: [General] Quantisation of classical electromagnetism
>
> Dear Andrew,
>
> I have good answers to most of your questions, but have no time right now
> to write them down,
> we must come back to this, it is very important indeed.
>
> In any case it comes down to the following:
>
> ·         Quantization comes from any wave equation with imposed boundary
> conditions. [if you can establish standing waves?] stationary waves may
> do already
>
> ·         Uncertainty is no more than what the Fourier limit tells you.
> [agreed]
>
> ·         Copenhagen interpretation is Copenhagen mystification: although
> it is not very wrong at the simple level, it takes away any possibility for
> improvement by dogma.[agreed]
>
> ·         Wave/particle dualism is the consequence of special relativity,
> see Louis de Broglie. [do you have a particular reference? I have not
> seen this statement before.] Thesis of Louis de Broglie, more beer would
> also help. Niels Bohr and his gang were successful enough to make people
> forget about this or so, it is a mystery why it has not become common
> knowledge among physicists.
>
> I think that I had heard that before, but not really registered on it. I
had thought of relativity as applied to the deBroglie wavelength rather
than being fundamental to it. I'm finding that my youthful disinterest in
the history of physics is extracting a penalty now.

I don't have his Thesis handy; but, in his "Theory of Quanta," he does
provide support for your earlier statement about resonance between the
nucleus and electron.

"This is exactly BOHR's formula that he deduced from the theorem mentioned
above
and which again can be regarded as a phase wave resonance condition for an
electron in
orbit about a proton."

If this is also considered resonance, rather than just strict mechanics,
then the energy levels have 3 resonances in coincidence.

Andrew

>
>
>
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