[General] research papers
Adam K
afokay at gmail.com
Wed Oct 21 18:20:49 PDT 2015
Martin,
So the story of Einstein vs Bohr at Solvay is exceedingly interesting, as
is de Broglie's attempt there to interpret quantum physics in a non-crazy
way.
This book
http://www.amazon.com/Quantum-Theory-Crossroads-Reconsidering-Conference/dp/1107698316
is pretty interesting on the subject.
It is specifically cast as a revisitation of de Broglie's pilot wave
hypothesis, and why it gained no traction at the time. Pauli is made into
something of a villain.
This review http://arxiv.org/pdf/1409.5956.pdf is not particularly
sympathetic to the authors' thesis, but is an interesting quick read and
contains some great quotes by de Broglie.
I am not sure what you mean about people thinking QM cannot be reconciled
with special relativity. Are you talking about entanglement and spooky
action at a distance? (EPR).
Adam
On Wed, Oct 21, 2015 at 3:51 PM, Mark, Martin van der <
martin.van.der.mark at philips.com> wrote:
> Dear Adam,
>
> thank you for that, I do agree. Contrary to popular believes, I think
> Einstein was more right about almost anything than he perhaps believed
> himself. But this is just my personal opinion.
>
> But that does not mean I disagree very much with Richard. In fact Einstein
> and the rest of physicists were not yet ready for the next thing after
> relativity: quantum mechanics. Planck was there, but he had his own
> opinion. Einstein did actually get the photon concept, of course.
> Rutherford added an important piece of the puzzle.
>
>
>
> And then came Bohr with his model of the atom. And then the other famous
> quantum people.
>
> There is one that got famous, but not quite as famous as he should have
> been. At one Solvay conference Bohr’s PR and style of arguing apparently
> won at the cost of the point of view of Louis de Broglie’s.
>
> As a consequence, we still suffer and the masses believe that quantum
> mechanics cannot be reconciled with special relativity. The opposite is
> true: Louis de Broglie DERIVED quantum mechanics from special relativity.
> Even better, EPR experiments are in accordance with special relativity, see
> Feynman, Wheeler, Tetrode and Carver Mead.
>
> All that is left from de Broglie is his wavelength, and his Harmony of
> Phases, which he derived from special relativity, is hardly known by the
> physics community.
>
>
>
> Cheers, Martin
>
>
>
>
>
> *From:* Adam K [mailto:afokay at gmail.com]
> *Sent:* donderdag 22 oktober 2015 0:06
> *To:* Nature of Light and Particles - General Discussion <
> general at lists.natureoflightandparticles.org>
> *Cc:* Mark, Martin van der <martin.van.der.mark at philips.com>; Joakim
> Pettersson <joakimbits at gmail.com>; ARNOLD BENN <arniebenn at mac.com>;
> Anthony Booth <abooth at ieee.org>; Ariane Mandray <ariane.mandray at wanadoo.fr
> >
>
> *Subject:* Re: [General] research papers
>
>
>
> "If he had been more clever and intuitive,"
>
>
>
> My own beliefs impel me point out that this is a hugely presumptuous thing
> to say about Einstein, even as a joke. Einstein was arguably the
> paradigm of intuition. All of the below quotes on intuition are by him:
>
> “Indeed, it is not intellect, but intuition which advances humanity.
> Intuition tells man his purpose in this life.”
>
> “The mind can proceed only so far upon what it knows and can prove. There
> comes a point where the mind takes a leap—call it intuition or what you
> will—and comes out upon a higher plane of knowledge, but can never prove
> how it got there. All great discoveries have involved such a leap.”
>
> *“*I believe in intuition and inspiration. At times I feel certain I am
> right while not knowing the reason. When the eclipse of 1919 confirmed my
> intuition, I was not in the least surprised. In fact I would have been
> astonished had it turned out otherwise. “
>
> “The supreme task of the physicist is the discovery of the most general
> elementary laws from which the world-picture can be deduced logically. But
> there is no logical way to the discovery of these elemental laws. There is
> only the way of intuition, which is helped by a feeling for the order lying
> behind the appearance, and this *Einfühlung *(feeling-one’s-way-in) is
> developed by experience.”
>
> L. de Broglie referred to Einstein's theory of relativity as "un effort
> intellectuel peut-être sans exemple." His own investigations were a
> matter of passion for him, "une difficulté qui m'a longtemps intrigué" and
> he would not have thought Einstein should have been more clever or
> intuitive. Finally, it was Einstein's intuition that led him to recognize
> immediately that de Broglie was onto something serious with his thesis,
> when it was passed to him from de Broglie's examiners, who had no clue what
> to make of it.
>
>
>
> Adam
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> On Wed, Oct 21, 2015 at 1:20 PM, Richard Gauthier <richgauthier at gmail.com>
> wrote:
>
> Hi Martin,
>
> Right you are. As I remember Einstein's 1905 article “Is the inertia of
> matter a measure of its energy content?" (it’s been a while), Einstein
> imagined two emitted rays of light of equal frequency moving in opposite
> directions coming from a stationary mass. When the rest frame of the mass
> and the two oppositely moving rays of light is shifted to a moving frame
> and the mass is moving in the same direction as one of the light rays, the
> light ray moving in the direction of the mass’ velocity gains more energy
> from the relativistic Doppler shift than the light ray moving in the other
> direction loses, leaving a net gain in the energy of the two light rays
> from the moving mass, as measured in this moving frame. Einstein equated
> this net gain in energy of the two oppositely moving light rays with the
> energy lost by the mass when it emitted the two light rays, and from this
> he derived E= mc^2 (modern terms). If he had been more clever and
> intuitive, he would have also in 1905 derived the de Broglie wavelength for
> a moving electron, which comes from setting his two energy formulas — E =
> hf for a photon’s energy and E = gamma mc^2 for an electron's total energy
> — equal to each other: hf = gamma mc^2 , which together imply (not
> logically but intuitively) that an electron is a circulating charged photon
> generating the de Broglie wavelength. But he unfortunately didn’t do this,
> and missed out on a second Nobel. If he had done this we would
> unfortunately never have heard of M. Louis de Broglie and "la comedie
> francaise". Instead it would have been "la comedie suisse". With these two
> “errors” (photons and matter waves) on his scientific resume, instead of
> just one, Einstein probably would never have received Planck’s
> recommendation for a job in Berlin.
>
> all the best,
>
> Richard
>
>
>
> On Oct 21, 2015, at 10:18 AM, Mark, Martin van der <
> martin.van.der.mark at philips.com> wrote:
>
>
>
> Hi Richard, just for the record, E=mc^2 came before de Broglie and he in
> turn came before schroedinger and quantummechanics,
>
> Cheers, Martin
>
>
>
> Verstuurd vanaf mijn iPhone
>
>
> Op 21 okt. 2015 om 18:40 heeft Richard Gauthier <richgauthier at gmail.com>
> het volgende geschreven:
>
> Hello John and Albrecht and all,
>
> Yes, I’m very much aware that the de Broglie wavelength can be
> generated from the relativistic Doppler interference of two Compton
> wavelength waves moving in opposite directions. This is the
> light-in-a-box-standing-wave-transferred-into-another-relativistic-frame
> explanation and I used it also in a previous circulating-photon electron
> model to generate the de Broglie wavelength, just as Martin did in 1991 and
> you and Martin did in your 1997 paper and John M also did. I think
> Einstein used it in his 1905 paper to derive E=mc^2. My derivation was
> independent of your paper, which I hadn’t read when I gave my derivation,
> which was borrowed from the derivation of an electron modeler with a “space
> resonance” model of the electron. He though my approach to the electron was
> “clever, but wrong”. I refrained from returning the compliment. All these
> derivations requires that there are waves moving in opposite directions and
> interfering to generate the de Broglie wavelength. In my spin-1/2 charged
> photon model however, the de Broglie wavelength is generated, without wave
> interference, from a helically circulating charged photon moving in a
> longitudinally forward direction and emitting plane waves along the
> direction the charged photon is moving along the helix. This derivation
> generates along the helical z-axis the de Broglie relativistic matter-wave
> equation PHI = A e^i(kz-wt) for a moving electron having the relativistic
> de Broglie wavelength h/(gamma mv).
>
> Albrecht, a reply for your "fundamental objection” to my model is in
> process. Don’t worry, I can answer it.
>
> with best wishes,
>
> Richard
>
>
>
>
>
> On Oct 21, 2015, at 7:34 AM, John Williamson <
> John.Williamson at glasgow.ac.uk> wrote:
>
>
>
> Dear all,
>
> The de Broglie wavelength is best understood, in my view, in one of two
> ways. Either read de Broglies thesis for his derivation (if you do not read
> french, Al has translated it and it is available online). Alternatively
> derive it yourself. All you need to do is consider the interference between
> a standing wave in one (proper frame) as it transforms to other
> relativistic frames. That is standing-wave light-in-a-box. This has been
> done by may folk, many times. Martin did it back in 1991. It is in our 1997
> paper. One of the nicest illustrations I have seen is that of John M -
> circulated to all of you earlier in this series.
>
> It is real, and quite simple.
>
> Regards, John.
> ------------------------------
>
> *From:* General [
> general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticles.org]
> on behalf of Dr. Albrecht Giese [genmail at a-giese.de]
> *Sent:* Wednesday, October 21, 2015 3:14 PM
> *To:* Richard Gauthier
> *Cc:* Nature of Light and Particles - General Discussion; David Mathes
> *Subject:* Re: [General] research papers
>
> Hello Richard,
>
> thanks for your detailed explanation. But I have a fundamental objection.
>
> Your figure 2 is unfortunately (but unavoidably) 2-dimensional, and that
> makes a difference to the reality as I understand it.
>
> In your model the charged electron moves on a helix around the axis of the
> electron (or equivalently the axis of the helix). That means that the
> electron has a constant distance to this axis. Correct? But in the view of
> your figure 2 the photon seems to start on the axis and moves away from it
> forever. In this latter case the wave front would behave as you write it.
>
> Now, in the case of a constant distance, the wave front as well intersects
> the axis, that is true. But this intersection point moves along the axis at
> the projected speed of the photon to this axis. - You can consider this
> also in another way. If the electron moves during a time, say T1, in the
> direction of the axis, then the photon will during this time T1 move a
> longer distance, as the length of the helical path (call it L) is of
> course longer than the length of the path of the electron during this time
> (call it Z). Now you will during the time T1 have a number of waves (call
> this N) on the helical path L. On the other hand, the number of waves on
> the length Z has also to be N. Because otherwise after an arbitrary time
> the whole situation would diverge. As now Z is smaller than L, the waves on
> the axis have to be shorter. So, not the de Broglie wave length. That is my
> understanding.
>
> In my present view, the de Broglie wave length has no immediate
> correspondence in the physical reality. I guess that the success of de
> Broglie in using this wave length may be understandable if we understand in
> more detail, what happens in the process of scattering of an electron at
> the double (or multiple) slits.
>
> Best wishes
> Albrecht
>
> Am 21.10.2015 um 06:28 schrieb
> Richard Gauthier:
>
> Hello Albrecht,
>
>
>
> Thank you for your effort to understand the physical process described
> geometrically in my Figure 2. You have indeed misunderstood the Figure as
> you suspected. The LEFT upper side of the big 90-degree triangle is one
> wavelength h/(gamma mc) of the charged photon, mathematically unrolled from
> its two-turned helical shape (because of the double-loop model of the
> electron) so that its full length h/(gamma mc) along the helical trajectory
> can be easily visualized. The emitted wave fronts described in my article
> are perpendicular to this mathematically unrolled upper LEFT side of the
> triangle (because the plane waves emitted by the charged photon are
> directed along the direction of the helix when it is coiled (or
> mathematically uncoiled), and the plane wave fronts are perpendicular to
> this direction). The upper RIGHT side of the big 90-degree triangle
> corresponds to one of the plane wave fronts (of constant phase along the
> wave front) emitted at one wavelength lambda = h/(gamma mc) of the
> helically circulating charged photon. The length of the horizontal base of
> the big 90-degree triangle, defined by where this upper RIGHT side of the
> triangle (the generated plane wave front from the charged photon)
> intersects the horizontal axis of the helically-moving charged photon, is
> the de Broglie wavelength h/(gamma mv) of the electron model (labeled in
> the diagram). By geometry the length (the de Broglie wavelength) of this
> horizontal base of the big right triangle in the Figure is equal to the top
> left side of the triangle (the photon wavelength h/(gamma mc) divided (not
> multiplied) by cos(theta) = v/c because we are calculating the hypotenuse
> of the big right triangle starting from the upper LEFT side of this big
> right triangle, which is the adjacent side of the big right triangle making
> an angle theta with the hypotenuse.
>
>
>
> What you called the projection of the charged photon’s wavelength
> h/(gamma mc) onto the horizontal axis is actually just the distance D that
> the electron has moved with velocity v along the x-axis in one period T of
> the circulating charged photon. That period T equals 1/f = 1/(gamma mc^2/h)
> = h/(gamma mc^2). By the geometry in the Figure, that distance D is the
> adjacent side of the smaller 90-degree triangle in the left side of the
> Figure, making an angle theta with cT, the hypotenuse of that smaller
> triangle, and so D = cT cos (theta) = cT x v/c = vT , the distance the
> electron has moved to the right with velocity v in the time T. In that same
> time T one de Broglie wavelength has been generated along the horizontal
> axis of the circulating charged photon.
>
>
>
> I will answer your question about the double slit in a separate e-mail.
>
>
>
> all the best,
>
> Richard
>
>
>
> On Oct 20, 2015, at 10:06 AM, Dr. Albrecht Giese <genmail at a-giese.de>
> wrote:
>
>
>
> Hello Richard,
>
> thank you for your explanations. I would like to ask further questions and
> will place them into the text below.
>
> Am 19.10.2015 um 20:08 schrieb Richard Gauthier:
>
> Hello Albrecht,
>
>
>
> Thank your for your detailed questions about my electron model, which
> I will answer as best as I can.
>
>
>
> My approach of using the formula e^i(k*r-wt) = e^i (k dot r minus
> omega t) for a plane wave emitted by charged photons is also used for
> example in the analysis of x-ray diffraction from crystals when you have
> many incoming parallel photons in free space moving in phase in a plane
> wave. Please see for example
> http://www.pa.uky.edu/~kwng/phy525/lec/lecture_2.pdf . When Max Born
> studied electron scattering using quantum mechanics (where he used PHI*PHI
> of the quantum wave functions to predict the electron scattering
> amplitudes), he also described the incoming electrons as a plane wave
> moving forward with the de Broglie wavelength towards the target. I think
> this is the general analytical procedure used in scattering experiments.
> In my charged photon model the helically circulating charged photon,
> corresponding to a moving electron, is emitting a plane wave of wavelength
> lambda = h/(gamma mc) and frequency f=(gamma mc^2)/h along the direction
> of its helical trajectory, which makes a forward angle theta with the
> helical axis given by cos (theta)=v/c. Planes of constant phase emitted
> from the charged photon in this way intersect the helical axis of the
> charged photon. When a charged photon has traveled one relativistic
> wavelength lambda = h/(gamma mc) along the helical axis, the intersection
> point of this wave front with the helical axis has traveled (as seen from
> the geometry of Figure 2 in my charged photon article) a distance
> lambda/cos(theta) = lambda / (v/c) = h/(gamma mv) i.e the relativistic de
> Broglie wavelength along the helical axis.
>
> Here I have a question with respect to your Figure 2. The circling charged
> photon is accompanied by a wave which moves at any moment in the direction
> of the photon on its helical path. This wave has its normal wavelength in
> the direction along this helical path. But if now this wave is projected
> onto the axis of the helix, which is the axis of the moving electron, then
> the projected wave will be shorter than the original one. So the equation
> will not be lambdadeBroglie = lambdaphoton / cos theta , but: lambda
> deBroglie = lambdaphoton * cos theta . The result will not be the
> (extended) de Broglie wave but a shortened wave. Or do I completely
> misunderstand the situation here?
>
> Or let's use another view to the process. Lets imagine a scattering
> process of the electron at a double slit. This was the experiment where the
> de Broglie wavelength turned out to be helpful.
> So, when now the electron, and that means the cycling photon, approaches
> the slits, it will approach at a slant angle theta at the layer which has
> the slits. Now assume the momentary phase such that the wave front reaches
> two slits at the same time (which means that the photon at this moment
> moves downwards or upwards, but else straight with respect to the azimuth).
> This situation is similar to the front wave of a *single* normal photon
> which moves upwards or downwards by an angle theta. There is now no phase
> difference between the right and the left slit. Now the question is whether
> this coming-down (or -up) will change the temporal sequence of the phases
> (say: of the maxima of the wave). This distance (by time or by length)
> determines at which angle the next interference maxima to the right or to
> the left will occur behind the slits.
>
> To my understanding the temporal distance will be the same distance as of
> wave maxima on the helical path of the photon, where the latter is lambda
> 1 = c / frequency; frequency = (gamma*mc2) / h. So, the geometric
> distance of the wave maxima passing the slits is lambda1 = c*h /
> (gamma*mc2). Also here the result is a shortened wavelength rather than
> an extended one, so not the de Broglie wavelength.
>
> Again my question: What do I misunderstand?
>
> For the other topics of your answer I essentially agree, so I shall stop
> here.
>
> Best regards
> Albrecht
>
>
>
>
> Now as seen from this geometry, the slower the electron’s velocity v,
> the longer is the electron’s de Broglie wavelength — also as seen from the
> relativistic de Broglie wavelength formula Ldb = h/(gamma mv). For a
> resting electron (v=0) the de Broglie wavelength is undefined in this
> formula as also in my model for v = 0. Here, for stationary electron, the
> charged photon’s emitted wave fronts (for waves of wavelength equal to the
> Compton wavelength h/mc) intersect the axis of the circulating photon
> along its whole length rather than at a single point along the helical
> axis. This condition corresponds to the condition where de Broglie said
> (something like) that the electron oscillates with the frequency given by f
> = mc^2/h for the stationary electron, and that the phase of the wave of
> this oscillating electron is the same at all points in space. But when the
> electron is moving slowly, long de Broglie waves are formed along the axis
> of the moving electron.
>
>
>
> In this basic plane wave model there is no limitation on how far to
> the sides of the charged photon the plane wave fronts extend. In a more
> detailed model a finite side-spreading of the plane wave would correspond
> to a pulse of many forward moving electrons that is limited in both
> longitudinal and lateral extent (here a Fourier description of the wave
> front for a pulse of electrons of a particular spatial extent would
> probably come into play), which is beyond the present description.
>
>
>
> You asked what an observer standing beside the resting electron, but
> not in the plane of the charged photon's internal circular motion) would
> observe as the circulating charged photon emits a plane wave long its
> trajectory. The plane wave’s wavelength emitted by the circling charged
> photon would be the Compton wavelength h/mc. So when the charged photon is
> moving more towards (but an an angle to) the stationary observer, he would
> observe a wave of wavelength h/mc (which you call c/ny where ny is the
> frequency of charged photon’s orbital motion) coming towards and past him.
> This is not the de Broglie wavelength (which is undefined here and is only
> defined on the helical axis of the circulating photon for a moving
> electron) but is the Compton wavelength h/mc of the circulating photon of a
> resting electron. As the charged photon moves more away from the observer,
> he would observe a plane wave of wavelength h/mc moving away from him in
> the direction of the receding charged photon. But it is more complicated
> than this, because the observer at the side of the stationary electron
> (circulating charged photon) will also be receiving all the other plane
> waves with different phases emitted at other angles from the circulating
> charged photon during its whole circular trajectory. In fact all of these
> waves from the charged photon away from the circular axis or helical axis
> will interfere and may actually cancel out or partially cancel out (I don’t
> know), leaving a net result only along the axis of the electron, which if
> the electron is moving, corresponds to the de Broglie wavelength along this
> axis. This is hard to visualize in 3-D and this is why I think a 3-D
> computer graphic model of this plane-wave emitting process for a moving or
> stationary electron would be very helpful and informative.
>
>
>
> You asked about the electric charge of the charged photon and how it
> affects this process. Clearly the plane waves emitted by the circulating
> charged photon have to be different from the plane waves emitted by an
> uncharged photon, because these plane waves generate the quantum wave
> functions PHI that predict the probabilities of finding electrons or
> photons respectively in the future from their PHI*PHI functions. Plus the
> charged photon has to be emitting an additional electric field (not emitted
> by a regular uncharged photon), for example caused by virtual uncharged
> photons as described in QED, that produces the electrostatic field of a
> stationary electron or the electro-magnetic field around a moving electron.
>
>
>
> I hope this helps. Thanks again for your excellent questions.
>
>
>
> with best regards,
>
> Richard
>
>
>
>
>
> On Oct 19, 2015, at 8:13 AM, Dr. Albrecht Giese <genmail at a-giese.de>
> wrote:
>
>
>
> Richard:
>
> I am still busy to understand the de Broglie wavelength from your model. I
> think that I understand your general idea, but I would like to also
> understand the details.
>
> If a photon moves straight in the free space, how does the wave look like?
> You say that the photon emits a plane wave. If the photon is alone and
> moves straight, then the wave goes with the photon. No problem. And the
> wave front is in the forward direction. Correct? How far to the sides is
> the wave extended? That may be important in case of the photon in the
> electron.
>
> With the following I refer to the figures 1 and 2 in your paper referred
> in your preceding mail.
>
> In the electron, the photon moves according to your model on a circuit. It
> moves on a helix when the electron is in motion. But let take us first the
> case of the electron at rest, so that the photon moves on this circuit. In
> any moment the plane wave accompanied with the photon will momentarily move
> in the tangential direction of the circuit. But the direction will
> permanently change to follow the path of the photon on the circuit. What is
> then about the motion of the wave? The front of the wave should follow this
> circuit. Would an observer next to the electron at rest (but not in the
> plane of the internal motion) notice the wave? This can only happen, I
> think, if the wave does not only propagate on a straight path forward but
> has an extension to the sides. Only if this is the case, there will be a
> wave along the axis of the electron. Now an observer next to the electron
> will see a modulated wave coming from the photon, which will be modulated
> with the frequency of the rotation, because the photon will in one moment
> be closer to the observer and in the next moment be farer from him. Which
> wavelength will be noticed by the observer? It should be lambda = c / ny,
> where c is the speed of the propagation and ny the frequency of the orbital
> motion. But this lambda is by my understanding not be the de Broglie wave
> length.
>
> For an electron at rest your model expects a wave with a momentarily
> similar phase for all points in space. How can this orbiting photon cause
> this? And else, if the electron is not at rest but moves at a very small
> speed, then the situation will not be very different from that of the
> electron at rest.
>
> Further: What is the influence of the charge in the photon? There should
> be a modulated electric field around the electron with a frequency ny which
> follows also from E = h*ny, with E the dynamical energy of the photon. Does
> this modulated field have any influence to how the electron interacts with
> others?
>
> Some questions, perhaps you can help me for a better understanding.
>
> With best regards and thanks in advance
> Albrecht
>
> PS: I shall answer you mail from last night tomorrow.
>
> Am 14.10.2015 um 22:32 schrieb Richard Gauthier:
>
> Hello Albrecht,
>
>
>
> I second David’s question. The last I heard authoritatively, from
> cosmologist Sean Carroll - "The Particle at the End of the Universe”
> (2012), is that fermions are not affected by the strong nuclear force. If
> they were, I think it would be common scientific knowledge by now.
>
>
>
> You wrote: "I see it as a valuable goal for the further development to
> find an answer (a *physical *answer!) to the question of the de Broglie
> wavelength."
>
> My spin 1/2 charged photon model DOES give a simple physical explanation
> for the origin of the de Broglie wavelength. The helically-circulating
> charged photon is proposed to emit a plane wave directed along its helical
> path based on its relativistic wavelength lambda = h/(gamma mc) and
> relativistic frequency f=(gamma mc^2)/h. The wave fronts of this plane wave
> intersect the axis of the charged photon’s helical trajectory, which is the
> path of the electron being modeled by the charged photon, creating a de
> Broglie wave pattern of wavelength h/(gamma mv) which travels along the
> charged photon’s helical axis at speed c^2/v. For a moving electron, the
> wave fronts emitted by the charged photon do not intersect the helical axis
> perpendicularly but at an angle (see Figure 2 of my SPIE paper at
> https://www.academia.edu/15686831/Electrons_are_spin_1_2_charged_photons_generating_the_de_Broglie_wavelength )
> that is simply related to the speed of the electron being modeled. This
> physical origin of the electron’s de Broglie wave is similar to when a
> series of parallel and evenly-spaced ocean waves hits a straight beach at
> an angle greater than zero degrees to the beach — a wave pattern is
> produced at the beach that travels in one direction along the beach at a
> speed faster than the speed of the waves coming in from the ocean. But that
> beach wave pattern can't transmit “information” along the beach faster than
> the speed of the ocean waves, just as the de Broglie matter-wave can’t
> (according to special relativity) transmit information faster than light,
> as de Broglie recognized. As far as I know this geometric interpretation
> for the generation of the relativistic electron's de Broglie wavelength,
> phase velocity, and matter-wave equation is unique.
>
>
>
> For a resting (v=0) electron, the de Broglie wavelength lambda =
> h/(gamma mv) is not defined since one can’t divide by zero. It corresponds
> to the ocean wave fronts in the above example hitting the beach at a zero
> degree angle, where no velocity of the wave pattern along the beach can be
> defined.
>
>
>
> Schrödinger took de Broglie’s matter-wave and used it
> non-relativistically with a potential V to generate the Schrödinger equation
> and wave mechanics, which is mathematically identical in its predictions to
> Heisenberg’s matrix mechanics. Born interpreted Psi*Psi of the Schrödinger equation
> as the probability density for the result of an experimental measurement
> and this worked well for statistical predictions. Quantum mechanics was
> built on this de Broglie wave foundation and Born's probabilistic
> interpretation (using Hilbert space math.)
>
>
>
> The charged photon model of the electron might be used to derive the
> Schrödinger equation, considering the electron to be a circulating
> charged photon that generates the electron’s matter-wave, which depends on
> the electron’s variable kinetic energy in a potential field. This needs to
> be explored further, which I began in
> https://www.academia.edu/10235164/The_Charged-Photon_Model_of_the_Electron_Fits_the_Schrödinger_Equation .
> Of course, to treat the electron relativistically requires the Dirac
> equation. But the spin 1/2 charged photon model of the relativistic
> electron has a number of features of the Dirac electron, by design.
>
>
>
> As to why the charged photon circulates helically rather than moving in
> a straight line (in the absence of diffraction, etc) like an uncharged
> photon, this could be the effect of the charged photon moving in the Higgs
> field, which turns a speed-of-light particle with electric charge into a
> less-than-speed-of-light particle with a rest mass, which in this case is
> the electron’s rest mass 0.511 MeV/c^2 (this value is not predicted by the
> Higgs field theory however.) So the electron’s inertia may also be caused
> by the Higgs field. I would not say that an unconfined photon has inertia,
> although it has energy and momentum but no rest mass, but opinions differ
> on this point. “Inertia” is a vague term and perhaps should be dropped— it
> literally means "inactive, unskilled”.
>
>
>
> You said that a faster-than-light phase wave can only be caused by a
> superposition of waves. I’m not sure this is correct, since in my charged
> photon model a single plane wave pattern emitted by the circulating charged
> photon generates the electron’s faster-than-light phase wave of speed c^2/v
> . A group velocity of an electron model may be generated by a superposition
> of waves to produce a wave packet whose group velocity equals the
> slower-than-light speed of an electron modeled by such an wave-packet
> approach.
>
>
>
> with best regards,
>
> Richard
>
>
>
>
>
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