[General] Quantisation of classical electromagnetism

[Andrew Meulenberg]

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.
   - the ground state is established by the requirement of a photon to have
   an angular momentum of hbar.

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. 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. This, like
   relativity, makes a big difference in some fields of physics.
   2. The source of the wave nature of the electron is never defined in QM.
   Is it the 'hidden variable"? 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.
   3. 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. 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.)

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?]
>
> ·         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.]
>
> ·         The measurement problem  for the smallest things has to with 3
> things: (in)coherence (=phase information of the wavefunction), intrinsic
> disturbance: the probe is non negligible, and the Fourier limit. [agreed]
>
> ·         There is only one crucial difference with classical mechanics:
> non-local action in EPR-like experiments. [? Relativity predicts
> wormholes? This could couple events.]
>
No more comments below

Andrew

> The latter is wider spread than quantum mechanics. Understanding
> space-time, non-locality and the connection/blend of fields with space-time
> is the least understood bit of physics.
>
> I have to go!
>
> Cheers, Martin
>
____________________________________________________

> *From:* General [
> mailto:general-bounces+martin.van.der.mark=philips.com at lists.natureoflightandparticles.org
> <general-bounces+martin.van.der.mark=philips.com at lists.natureoflightandparticles.org>]
> *On Behalf Of *Andrew Meulenberg
> *Sent:* woensdag 6 mei 2015 8:26
> *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 John W,
>
> Since you say that the bell's resonance makes its sounds quantized, then
> are all quantized states just resonances? Are there exceptions? If not,
> then why does QM not use the classical, understandable, concept of
> resonance. I have assumed that it is just the priesthood's way of assuring
> that its 'flock' does not revert to the 'ol time religion'.
>
> So, if a bell is quantized because of its mass and structure, then I
> suppose that a photon can be similarly 'quantized' because of its energy
> and structure. The classical concept of the soliton is no longer acceptable
> notation for a physical phenomenon.
>
> On the same basis, is a black hole quantized? Because it has a specific
> 'size' for a given mass, and 'rings' when excited (is this an incorrect
> conclusion from some of the recent galactic density distributions
> attributed to the big bang/), it should be classed as a quantum bell.
>
> A deeper question (not just one of semantics) is how can one represent
> resonances on a potential-energy diagram? The 1/r coulomb potential is a
> straight line on a log-log plot of potential energy vs radius. Is there any
> way of correctly representing (e.g. by 'dips') the total energy minima
> associated with resonant states of the electron orbitals? In other words,
> how does one relate energy and resonances? This issue is one that I have
> occasionally been thinking about related to both electrons and photons. I
> assume that it is necessary to plot total energy (or some other form)
> rather than just potential energy. Or, is it sufficient to include all
> forms of potential energy?
>
> QM often states that the atomic ground state is the minimum energy level.
> Yet, obviously, the Coulomb potential of the nucleus goes much deeper. QM
> claims that, by this statement, it overcomes the classical dilemma of the
> electron spiraling into the nucleus. Classical physics can easily solve the
> problem by use of conservation of energy and momentum and inclusion of
> photons with their specific characteristics. QM, by not including the
> photon in the Schrodinger equation, must solve the problem by mathematics
> and fiat, not by physics.
>
> We have to be careful that we do not fall into the same trap as QM did
> with the atom, when we try to define the photon and the electron.
>
> Andrew
>    ______________________________________________
>
>
>
> On Wed, May 6, 2015 at 9:56 AM, John Williamson <
> John.Williamson at glasgow.ac.uk> wrote:
>
> Hello Andrew,
>
> You ask such good questions!
>
> Yes of course it is - to the fundamental frequency and to its harmonics.
> Quantisation comes down to something that simple. In the paper I circulated
> the quantisation is not put in (as it is not for the bell), but comes out
> (as it does for the church bell) as a consequence of the nature of the
> object/ objects concerned (emitter and absorber for the photon resonance).
>
> Everything in quantisation comes down, fundamentally, to coherence,
> resonance and harmony. [agreed]
> I gave a talk entitled "How the universe listens to itself:spherical
> music" at a conference back in 2009 - in which I used the analogy of a
> spherical bell (and its inverse) to explain the photon inter-action. I've
> attached a pdf of the slides for the talk.
>
> This will become part of the "interaction with the absorber" paper - if I
> ever get round to it.
>
> Cheers, John.
>  ------------------------------
>
> *From:* General [general-bounces+john.williamson=
> glasgow.ac.uk at lists.natureoflightandparticles.org] on behalf of Andrew
> Meulenberg [mules333 at gmail.com]
> *Sent:* Tuesday, May 05, 2015 1:57 PM
> *To:* Nature of Light and Particles - General Discussion
> *Subject:* Re: [General] Quantisation of classical electromagnetism
>
> Dear John W.
>
> Your paper looks very interesting. However, I am going to force myself to
> put off reading it until I after I catch up on my other obligations.
> Nevertheless, a quick question. Is a church bell quantized?
>
> Andrew
>
> _____________________________________________
>
>
>
> On Tue, May 5, 2015 at 1:24 PM, John Williamson <
> John.Williamson at glasgow.ac.uk> wrote:
>
> Good morning everyone,
>
> None of us gets the whole picture- yet. We, however, may each understand
> some aspects of science, which need to be resolved within the group (and
> the rest of the science community for that matter) as a whole. I think
> that, if we want to make progress, as a group, to making a collective
> effort to eventually solve Hilbert's sixth problem and understand how
> everything works, we need a proper theoretical basis with which to
> calculate and with which to model. Maxwell theory is good to a point, but
> is not quantized and does not have a mechanism to confine light to go round
> and round in circles in our models. We need a better theory.
>
> By a theory here I do not mean some loose idea with some nice consequences
> and able to calculate a number or two (like the WvdM model for example!).
> To properly understand how things work it is not good enough to just
> flag-up the problems of this or that model - all models have problems (the
> standard model more than most!)- we need to put-up and develop a real
> theories and then try to knock them down with experiment. If they fail-
> just make up a new theory. That is the scientific method.
>
> First problem in creating any new theory is where to start? On which basis?
>
> Some of you may not have yet come across Hilbert's sixth. It is one of the
> famous set of problems he posed at the turn of the century before last
> which remains unsolved. Briefly it is finding an axiomatic, logical and
> complete mathematical system that precisely parallels reality - just and no
> more.  In other words finding a mathematics which precisely describes all
> of physics.
>
> Coming back to the task in hand. Physics is now so vast that there are
> many possible starting bases. All may give some insight into the truth, but
> none yet solves Hilbert's sixth. I will not bother with theories set up, by
> design, to be outwith the boundaries of that which is measureable
> experimentally as I see no point in starting from somewhere where one is
> already lost. Others may play that game if they wish.
>
> Lets just list a few of the possible starting candidate frameworks (some
> within the umbrella of the "standard model"):
>
> 1.     Shroedinger quantum mechanics
>
> 2.     Dirac relativistic quantum mechanics
>
> 3.     Quantum electrodynamics
>
> 4.     General relativity
>
> 5.     Special relativity
>
> 6.     Maxwell electromagnetism
>
> These all stand on their own - of course. Any final theory should also be
> manifestly consistent- at some level of simplification - with all of the
> above.
>
> Now comes my personal view of each as a candidate starting frameworks on
> which to make further progress. The conclusions at the end of each are not
> definitive - just my personal opinion at present. Each sentence starting
> "Conclusion" contains a pun, which is intended.
>
> The first, while it has many practical applications, is too simple as it
> is is non-relativistic. Conclusion-too uncertain.
>
> The second is a good possibility, however I think it is too complicated in
> one respect and too simple in another. Too complicated in that it contains
> BOTH a non-commutative (Dirac) algebra AND yet uses the far simpler complex
> algebra in solutions. I think its starting point has already passed the
> proper basis point and has implicitly added something which is just not
> there in reality. I think it contains a great deal of truth but that the
> added complexity (pun) makes for confusion. It confused Dirac himself (as
> stated in his famous textbook by himself). If he was confused then what
> chance have any of the rest of us got. This stand-point is backed up by the
> fact that, despite being a corner-stone of the "Standard Model", it has not
> yet been used in any practical engineering application at all (delighted if
> anyone can pose a counter-example by the way). Conclusion-too complex.
>
> Now the third, quantum electrodynamics, looks good. It is not (yet) in
> conflict with any known experiment within its realm of validity.  Indeed
> this is the starting point for many. Personally, having worked with it back
> in the eighties in develping (parts of) big monte-carlo programmes
> (incorporating both QED and QCD) - I do not think this is the right answer.
> The problem is that it has neither a detailed, microscopic dynamics of the
> charges which are its sources, nor of the photon which is, for it the
> exchange particle responsible for electromagnetism. For it, the photon is
> that thing that carries the electromagnetic interaction more than a
> particle in its own right. I do not see how to make it work starting from
> its starting points. Lots of other folk (much smarter than me) have been
> trying just that for many years without success. Good luck folk!
> Conclusion-I think folk just do not get the point.
>
> On to the fourth. This is also good, also consistent with all of
> experiment (within its realm of validity). Could be made to work. Again,
> many have tried. Wheeler made a good attempt with Geometro-dynamics. Any
> new theory had better be consistent with it in the weak limit. I think it
> is still missing its heart and foundation though. Conclusion- it is just
> too weak.
>
> Now to the fifth. All good. Not much in it though - per se. Conclusion:
> not special enough.
>
> Now to the sixth. This is often neglected as being old-hat, but (as
> Chandra has said) it is also consistent with all of experiment within its
> realm of validity. It is, and always was fully (special) relativistic. This
> is at least more special then than the preceding candidate. There is just
> more in it. The main deficiency -up till now - is that it has been missing
> a proper means of quantizing it and a proper wave-function for the photon.
> Conclusion: the area seems a good field from which to start - just need to
> properly investigate its boundaries and find a proper means to quantize it.
>
> On this theme, I have attached a paper, containing a few speculations of
> my own, to set myself up to be knocked down on anything which is too
> speculative, ill-informed or downright wrong! It explains and expands on
> the theory presented at FFP14 last year and outlined in the paper I
> circulated earlier. The paper as it stands can be shortened as it contains
> some repetition and a quite a lot of background analogy (such as pretty
> much all of the discussion on page 7, for example). I've decided to leave
> this in for the moment as it may help understanding. There are also other
> things that should probably go in if I have the time - such as a
> wavefunction separating the polarization and rotation-horizon parts of the
> wave function. Am still working on that.
>
> This was intended as a draft paper for the upcoming conference in San
> Diego, even though it is more about the photon itself than the electron or
> its inter-actions, so I was thinking of withdrawing it and replacing it
> with one on the problems of causality in absorber interaction theory (to
> address the problems raised by, amongst others, Chip). I'm re-considering
> this, as I think it provides some of the background theory for the other
> paper on the electron nature. An alternative may be to place it elsewhere
> within the conference as it is more relevant to the photon itself than to
> the electron. What do you think, Chandra and Andrew?
>
>
>
>
>
>  I think it is correct that it has limited value to try to understand one
> thing (the electron) in terms of another thing which is, perhaps, even more
> poorly understood (the photon). I agree as well that we need to address the
> underlying root-cause of quantisation if we are really to understand what
> is going on. Understanding the photon is what the paper aims to do
>
> I'm a bit shy, in the present company, of jumping in with both feet here.
> This is not really my field. I know more about (and have published widely
> in) elementary particle physics and solid state physics (and I think this
> helps in some respects) but am by no means an optics or a photonics guy. I
> am relying on you all (especially people such as Chandra, Robert and Tim)
> to put me straight on this. I do not want to step on everyones toes! The
> paper attached contains a development of the Maxwell equations to include
> dynamical mass, dual mass and angular momentum terms. The development here
> looks pretty simple to me. Has it been done before? Please, all of you,
> fill me in here. It would be very embarrassing to miss an important
> reference to this.
>
> There is also an argument in the paper as to why classical
> electromagnetism must be quantized in its travelling-wave solutions. I
> think this must be new as I'm sure I should have heard of it otherwise. Am
> I wrong? There is also a fully relativistic, quantized, Schroedinger-like,
> first-order electromagnetic wave-function. Again- have such things ever
> been studied elsewhere?
>
> The paper, as it stands, does not yet contain a calculation of  hbar from
> first principles - though I am working on this as well as with a more
> advanced 4D wave-function and in conjunction with the polarization
> discussion and have what I think may be an answer - though that lies also
> within the realms of physical chemistry where I am even less at home. If I
> cannot sort it out before August it could, possibly, become a topic for
> discussion.
>
> I will circulate the draft paper to other people in other groups as well
> (some on the mailing above). Another thing I would be grateful for is
> suggestions as to which peer-reviewed journal would be an appropriate place
> to submit this work for a more general circulation.
>
> Regards, John W.
> </a>
>
>
>
>
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