[General] Quantisation of classical electromagnetism

[Andrew Meulenberg]

Dear Martin,

Unless we are willing and able to argue constructively, we don't really
have a 'critical mass' needed to carry a project forward. We need to be
able to hone our ideas and their presentation. We might even be able to
change our minds.

response below (in black):

On Tue, May 12, 2015 at 2:00 AM, Mark, Martin van der <
martin.van.der.mark at philips.com> wrote:

>  Dear Andrew, I have been away for a few days.
>
> In your previous replies you tried to challenge me to be precise, and have
> questioned the correctness of my statements. That is very good.
>
>
>
> But unfortunately you have put me in a position where I, in turn, have to
> correct you on all the things you say that are half baked or wrong. It is
> difficult to remain very polite since most of your brown replies, need
> "attention". So brace, but remember that I only put in the effort because I
> respect you and because I think that your opinion matters.
>
>
>
> I hope no one is color blind, yet another color will be used: purple!
> (just in case some haze troubles the mind...)
>
>
>
> So: purple (Martin) responds to brown (Andrew) responds to green (Martin)
> responds to red (Andrew)
>
>
>
>
>
> Dr. Martin B. van der Mark
>
>
>
>
>
> *From:* General [mailto:general-bounces+martin.van.der.mark=
> philips.com at lists.natureoflightandparticles.org] *On Behalf Of *Andrew
> Meulenberg
> *Sent:* donderdag 7 mei 2015 7:40
>
> *To:* Nature of Light and Particles - General Discussion
> *Subject:* Re: [General] Quantisation of classical electromagnetism
>
>
>
> 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.
>
> To be precise: the mechanical part equals the mechanical part. No
> information in that at all, it is not a coincidence it is an incidence.
>

The classical description, based on conservation of energy and momentum,
should include the photon energy, E(gamma).

   -  TE = KE + PE + E(gamma)

E(gamma) is not included in the standard QM derivation of the H atom. (It
should be in the time-dependent Schrodinger equation. However, that is not
what is generally taught for the H atom. I'm sure that it is at some level.
Did you have it taught to you? )

>
>    - 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.]
>


> Wrong answer to the given question. The ground state has IN THE FIRST
> PLACE nothing to do with the emitted energy part, but with what remains.
> What remains must be a mode of the system, a quantum state they call this
> in quantum mechanics. It means that a single wavelength, 3D resonance must
> be maintained. For the hydrogen atom (or for that matter any spherical
> system) must have simultaneous solutions for r, theta and phi, such that at
> least one has a single wave in it. It appears to be the radial solution, a
> breather (not the Bohr type phi solution with one wavelength on the
> circumference).
>
> To get from a higher state into this state the right combination of
> energy, momentum and angular momentum must be emitted, hence the selection
> rules as the are, and that is what your answer is about.
>

We may be talking at crossed purposes here. Let me try to straighten it
out. (We still may have to talk, but this will help me to focus and
remember.) Forgive me if I, for brevity, make flat statements as if they
are known facts. And please correct me when I am wrong.

   1. To go below the 'ground state', by photonic emission, it is necessary
   for this 'final' (ground) state to become an emitter.
   2. To get to the ground state, an electron must radiate a photon (which
   has ang mom of hbar). The final state of the system includes that photon.
   If we renormalize the H + photon system by subtracting the photon to get
   the bare atom, in the ground state, then the final state has zero ang mom
   and any lower state, if one existed, would also have zero ang mom.
   3. To go to any lower state (by the same process) requires a second
   photon. If neither the 'final' nor any lower state has sufficient ang mom
   to form a 2nd photon, no photonic transition can occur (unless we have
   other electrons or atoms close enough for longitudinal photons to exchange
   energy - the Mill's process?). Zero-zero photonic transitions are highly
   forbidden. [Note that my original comment (in red) stated "... the
   requirement of a photon to have an angular momentum of hbar." The
   photon, *not* the bare ground state, has ang mom of hbar.
   4. The ground state has an isotropic electron distribution. The H gnd
   state angular momentum of zero (to +/- hbar/2, from the HUP) allows its
   electron to have a linear orbit, through the nucleus, and the full range of
   elliptical orbits (including all circular orbits of +/- hbar/2) with
   different axes. QM provides the probability distribution of an electron in
   all of those orbits.
   5. The radial orbit and the circular orbit are both (extreme) solutions
   and have the same conditions of the eigenvalue.
   6. My statement was about the transition from the ground state to a
   lower state, not the transition to the ground state.


       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.
>
> See previous answer and understand that the reason is implicitly given
> there already. A mode of a resonator or waveguide, a quantum state, these
> are the same sort of things. They have Q or quality factor that tells you
> how broad or narrow the resonance is and how long it lives. For a very long
> live time such as the ground state hydrogen atom, the Q is very very high,
> and the level is very precisely defined. The wave must therefore fit very
> very very very precisely on the mode. Not a factor of two difference, no,
> minus dozens of orders of magnitude precise!
>
>
>
I may like that resonance answer. However, in the atomic system there are
only losses by photonic emission (true?), so *any* orbit that cannot
radiate has an infinite Q value. The HUP indicates that the resonance may
be very broad. The precision of the energy level (which is an average
value?) is extremely high because it is a value determined from an infinite
number of 'measurements' (the time independent solution). What is the
standard deviation of individual orbit measurements?

>        The one wavelength holds for the complete atom, electron and
> proton: the electron is light and moving fast, the proton is 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.
>
> Bullshit, sorry, but here you should really know better since:
>
> 1)      I have told you already you are referring to the BORN
> APPROXIMATION
>
> 2)      It is in every basic textbook, second year physics
>
> 3)      The so-called reduced mass gives a slightly different set of
> levels, the correct levels. Remember the Rydberg constant? And its slightly
> different numbers?
>
> Just do your homework, and go to Wikipedia, that will be good enough.
>
>
>
> Here another remark regarding your earlier question, whether I was talking
> physics or mathematics. (see next question below)
>
> Here you see I get the physics right because I think physics. Then I get
> the numbers right because I understand the approximations, the calculus and
> the details. That can only be if you know how to the mathematics right.
>
> Sorry I just hate mediocrity.
>

I think that you missed my point. I was objecting to your assumption of a
resonance between the nuclear and electron deBroglie wavelengths. The
mathematical levels and deBroglie wavelengths exist whether the nuclear
mass is finite or infinite. The values do change, but not much.

However, the basis of my objection was ill-founded and you naturally
responded to a different thought. I should have thought about the
conservation laws as being resonances, rather than assuming that they were
not.

>
>
>      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.
>
> I am responding to 60 years of mathematical physicists rejecting the
anomalous solution of the Dirac equations because of the consequences of a
'singularity' at r = 0. Physicists should never go there because there is
no such thing as a point charge. I do not believe that having point-like
behavior includes the singularity.

>
>
> 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.
>
>
>
> The Coulomb potential is BY DEFINITION a 1/r potential associated with a
> POINT CHARGE.
>
> It therefore runs, by definition, to minus infinity.
>

The Coulomb potential, including r=0, is a non-physical entity. It is a
mathematical model - with limitations.

>
>
> Real charges, like the proton or a charged party balloon, rubbed-up on a
> cat, have a cut-off at their respective charge radii of 0.87 fm and 10 cm:
> at smaller size the potential may be or is quite constant. There is always
> a reason in the physics of things that will avoid infinities naturally.
>
> I know you want to make that point, and I fully agree. But please do not
> misuse the argument or definition of things.
>

If the Coulomb 'law' were supplemented with an r > 0 statement, perhaps it
would not be mistaken and misused by the mathematical physicists. I have to
be careful not to misuse existing definitions - even if they are flawed.

>       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?]
>
>
>
> It is the proton's START of the Coulomb potential! Look it Up in a book on
> high energy physics if you really want to know exactly what they mean by it.
>
>
>
I find it interesting that the electron radius is defined on a theoretical
basis; while the proton charge radius is based on an experimental process.

>        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?)
>
>
>
> Who are you trying to convince here? Surely not me. Look at the 1997
> Williamson van der Mark paper and find all you try to say. Incidentally the
> word fluid refers to something you apparently do not know: It is well known
> that electromagnetic fields behave like a so-called INVISCID FLUID.
>
> Other fluids are useful too: more beer required ;-) I do agree that spin 1/2
> is not easy, I know the problems and the salient details. It is one of the
> key things in physics to understand!
>

I thought that I had gotten that '97 paper and at least looked it over.
However, I can't find it on my computer now. I'll have to download it again
tomorrow. I'll also have to examine the EM fields as an inviscid fluid. Can
such fluid waves then pass thru each other? EM waves can (but not always).

>
>    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?
>
>
>
>      I have given you all the clues, now please do the work! The nucleus
> is slow and heavy, the electron light and fast, oscillating about their
> common centre of mass with EXACTLY the same momentum and hence the same de
> Broglie wavelength.
>
> 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?
>
>
> The electron is a  wave and a particle at the same time, right?
>

I consider an electron to be a particle consisting of a self-wrapped photon
and with an 'external' wave intimately associated with it. The wave is not
extended (although there are associated evanescent waves that are); I
believe it to be one of orientation.

A photon is the reverse, it is a wave that is confined (limited in extent,
but not wrapped) to act as a (sometimes long) particle.

A photon could be multiply 'wrapped' about a proton, an electron cannot be
wrapped about a proton.

Best regards;

Andrew

>
> 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.
>
> It is not your fault, it is mentioned rarely. But since I have, now you
> know.
>
> 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
>
>                  Dear Andrew I hope to have cleared up a few things,
> surely we should talk about them some more,
>
> Very best regards, Martin
>
>
>
>
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