[General] De Broglie Wave

Richard Gauthier richgauthier at gmail.com
Wed Feb 10 11:25:11 PST 2016


Hello Albrecht,

    The reason your formula m=hbar/Rc works so well to derive the electron’s mass m is that if you solve it for R you get R= hbar/mc  = 1/2pi   h/mc   .   This radius R is the radius of a circle whose circumference is one Compton wavelength h/mc (the wavelength of a photon having the energy E=mc^2 of a resting electron.)  If the electron’s charge magnitude e moves at light-speed in a single loop circle of this circumference h/mc (corresponding to a photon momentum of mc), the magnetic moment that is generated by this circulating light-speed electric charge is EXACTLY the  Bohr magneton  ehbar/2m  . Check this using M = I A  if you don’t believe me.   So when you find that 2 pi R = lambda in your Powerpoint slide , this is just saying that lambda is the circumference of a circle which has R as its radius.  This calculation has no bearing on the size or inertial mass of a photon. Plus, there is no experimental evidence that a photon consists of either 2 or 4 particles, just one (same as for the electron).   Your derivation of the electron's inertia seems to ignore that your two massless light-speed particles move in an orbit of circumference one Compton wavelength h/mc which generates the Bohr magneton ehbar/2m . So it’s no surprise at all (and no genuine derivation of the electron’s mass) to derive the electron’s mass m from the Bohr magneton ehbar/2m in your electron model.  You have no photon model and no derivation of a photon’s inertial mass. And your 2-particle electron model, though it has given you much satisfaction over the years, and rightly so as it is your original mental creation, is unfortunately a non-starter in serious physics.
 
      Richard

> On Feb 10, 2016, at 9:57 AM, Albrecht Giese <genmail at a-giese.de> wrote:
> 
> Sorry! I have forgotten the attachment. Now included.
> 
> Hello Richard,
> 
> good question!
> 
> My model works originally for leptons and for quarks. The photon is somewhat different visible through the different spin. So, I am not sure that the photon can be described by two sub-particles, maybe the description needs four sub-particles. But this means only a limited correction factor.
> 
> For the determination of the mass, the model needs the size of the particle. For the electron I have determined the size from the magnetic moment. In case of the photon the wavelength can be taken as a measure for the size. If the wavelength is inserted into the equation for mass, then the dynamical mass (equivalently the energy) is the result. And that fits well.
> 
> I have attached two pages of my power-point presentation in San Diego. There you can see the calculation. The calculation is done there the other way around. I start with the energy, convert it to the mass and show that the resulting size of the photon corresponds to its wavelength.  - In case of any questions, please ask.
> 
> Albrecht
> 
> Am 10.02.2016 um 17:41 schrieb Richard Gauthier:
>> Hello Albrecht,
>>      If you have solved the problem of inertia, then the inertial mass of a photon should also be explainable by your two-particle electron model. Is it?
>>          Richard
>> 
>>> On Feb 10, 2016, at 5:13 AM, Albrecht Giese < <mailto:genmail at a-giese.de>genmail at a-giese.de <mailto:genmail at a-giese.de>> wrote:
>>> 
>>> Hi Wolf,
>>> 
>>> why do you think that I am frustrated? Why should I? Since I found 17 years ago the mechanism of inertia, which functions so straight and logical with precise results, I am continuously happy. And the appreciation by interested physicists is great. Since 14 years my site about mass in internationally #1 in the internet. Only sometimes the mass site of Nobel Prize winner Frank Wilzcek is one step higher. But that is good companionship.
>>> 
>>> True that it is a problem with Main Stream. They do not object but just do not care. They love the Higgs model even though it is proven not to work. - It just need patience. I still have it.
>>> 
>>> Yes, quantum numbers work fine, but they are physically little or not founded. It is similar to the known Pauli Principle. That also works, but nobody knows why. And the bad thing is that nobody from Main Stream concerned about this non-understanding. That is the biggest weakness in today's physics in my view.
>>> 
>>> Albrecht
>>> 
>>> 
>>> Am 09.02.2016 um 20:35 schrieb Wolfgang Baer:
>>>> I can feel your frustration, Albrecht, 
>>>> The oldies are probably all wrong, but it's important to remember that right or wrong they give us the platform from which to see farther.
>>>> "standing on the shoulders of others", and right or wrong they give us something tangible to argue about
>>>> and what quantum numbers have done for us to organize chemistry is amazing.
>>>> 
>>>> wolf
>>>>  
>>>> Dr. Wolfgang Baer
>>>> Research Director
>>>> Nascent Systems Inc.
>>>> tel/fax 831-659-3120/0432
>>>> E-mail wolf at NascentInc.com <mailto:wolf at NascentInc.com>
>>>> On 2/9/2016 10:18 AM, Albrecht Giese wrote:
>>>>> Hi Al,
>>>>> 
>>>>> the choice of de Broglie is not suboptimal, it is clearly wrong. Badly wrong. The wave he has introduced does not exist, and if it would exist its behaviour would cause a physical behaviour which is in conflict with measurements (if those are comprehensively done).
>>>>> 
>>>>> I agree with you that the main object now is to move forward. But we will not move successfully forward if we carry millstones with us. De Broglie's wave is a millstone. I just had a look into a new textbook about QM, which was highly recommended by our university. It makes full use of de Broglie's relation between momentum and wavelength, so this is unfortunately not just history. 
>>>>> 
>>>>> But looking into the history: Bohr, Sommerfeld and others have used the result of de Broglie to explain quantum numbers. Particularly the quantisation of the angular momentum on atomic shells is explained by "standing waves" where the wavelength is the one defined by dB. This obviously hides the true reason of this quantisation, but as anyone believes that the Ansatz using de Broglie is right, nobody is looking for the correct cause. - This is one of the reasons for our sticking physics.
>>>>> 
>>>>> Tschüss back
>>>>> Albrecht
>>>>> 
>>>>> 
>>>>> Am 09.02.2016 um 14:57 schrieb af.kracklauer at web.de <mailto:af.kracklauer at web.de>:
>>>>>> Hi Albrecht:
>>>>>>  
>>>>>> As you fully know, the very same idea can be expressed in various languages.  This is true of physics also. The very same structure can be attached to variuos words and images.  I do not defend deBroglie's choice of words and images. I too find his choice suboptimal and somewhat contrdictory.  So what?  He was playing his hand at that time with the hand he was delt at that time.  Since then, other ideas have been found in the deck, as it were.  I find that, without changing any of his math, one can tell a story that is vastly less etherial and mysterious and, depending on the reader's depth of analysis, less self-contradictory.  I think my story is the one DeBrogle would have told if he had been inspired by some facits of SED.  And, some people have a greater affinty and interest in abstract structures, in particular when their mathematical redintion seems to work, that for the stories told for their explication.  This is particularly true of all things QM. 
>>>>>>  
>>>>>> Anyway, the main object now (2016) is to move forward, not critique historical personalitites.  So, I'm trying to contribute to this discussion by adding what I know now, and what I have found to be useful.  We are "doing" physics, not history.  Let's make new errors, not just grind away on the old ones!
>>>>>>  
>>>>>> BTW, to my info, both Dirac and Schrödinger would agree that deBroglie proposed some not too cogent arguments regarding the nature of QM-wave functions. Still, the best there at that time. All the same, they too went to their graves without having found a satisfactory interpretation.  SED throws some new ingredients into the mix.  
>>>>>>  
>>>>>> Tschuss, Al 
>>>>>>  
>>>>>> Gesendet: Dienstag, 09. Februar 2016 um 13:41 Uhr
>>>>>> Von: "Albrecht Giese"  <mailto:genmail at a-giese.de><genmail at a-giese.de> <mailto:genmail at a-giese.de>
>>>>>> An:  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>
>>>>>> Cc:  <mailto:general at lists.natureoflightandparticles.org>general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>, "Richard Gauthier"  <mailto:richgauthier at gmail.com><richgauthier at gmail.com> <mailto:richgauthier at gmail.com>
>>>>>> Betreff: Re: [General] De Broglie Wave
>>>>>> Hi Al,
>>>>>> 
>>>>>> I have the impression that you have a solution for particle scattering which is in some way related to the idea of de Broglie. (I also have of course a solution). But was this the goal of our discussion and of my original contribution? It was not! My objection was de Broglie's original idea as stated in his thesis and as taken over by Schrödinger and Dirac.
>>>>>> 
>>>>>> You have a lot of elements in your argumentation which I do not find in the thesis of de Broglie. (There is e.g. nothing at dB about SED ore background.)
>>>>>> 
>>>>>> The essential point of our discussion is the meaning of his wave - and his wavelength. I think it is very obvious from his thesis (which you clearly know) that his "fictitious wave" accompanies a particle like the electron all of the time. There is no interaction mentioned except that there is an observer at rest who measures the frequency of the particle. But without influencing the particle.
>>>>>> 
>>>>>> Now it is normal knowledge that a frequency and as well a wavelength appears changed for an observer who is in motion. This is caused by the Doppler effect. But the Doppler effect will never cause that a finite wavelength changes to Infinite if an observer moves at some speed unequal to c. But just that happens to the wave invented by de Broglie. It follows the equation
>>>>>> 
>>>>>> lambda = h/(m*v)    where v is the speed difference between the particle and the observer (to say it this time this way). And this is in conflict to any physics we know.
>>>>>> 
>>>>>> Best, Albrecht
>>>>>> 
>>>>>>  
>>>>>> Am 08.02.2016 um 17:20 schrieb  <x-msg://106/af.kracklauer@web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>:
>>>>>> Hi Albrecht:
>>>>>>  
>>>>>> Your challenge is easy!  In fact my last responce covered it.   The RELEVANT velocity is the relative velocity between the particle and the slit; not that between the observer-particle or observer-slit.   An observer will see all kinds of distortions of the events, starting with simple persepctive due to being at some distance from the slit and its registration screen.  In additon this observer will see those deB waves affecting the particle (NOT from the particle, nor from the slit, but from the universal background there before either the particle or slit came into being)  as perspectively-relativistically distorted (twin-clock type distortion).  BUT, the observer will still see the same over-all background because the totality of background signals (not just those to which this particle is tuned), i.e., its spectral energy density, is itself Lorentz invariant.  That is, the observer's  motion does not  enable it to empirically distinguish between the background in the various frames, nor does the background engender friction forces.
>>>>>>  
>>>>>> You have got to get your head around the idea that deB waves are independant of particles whatever their frame.
>>>>>>  
>>>>>> Schrördinger did toy with some aspects that deBroglie used, but never did succeed in rationalizing his eq. in those or any other terms.  For him, when died, wave functions were ontologically completely mysterious.  From SED proponents, I'm told, my thoughts in #7 on  <http://www.nonloco-physics.0catch.com/>www.nonloco-physics.0catch.com <http://www.nonloco-physics.0catch.com/>, are unique in formulating S's eq. in terms of deB concepts.  Try it, maybe you'll like it.  
>>>>>>  
>>>>>> There are other SED-type stories too, but as they are based on diffusion (parabolic, not hyperbolic) precesses, I find them self contradictory.
>>>>>>  
>>>>>> ciao, Al
>>>>>>  
>>>>>> Gesendet: Montag, 08. Februar 2016 um 141 Uhr
>>>>>> Von: "Albrecht Giese"  <mailto:genmail at a-giese.de><genmail at a-giese.de> <mailto:genmail at a-giese.de>
>>>>>> An:  <x-msg://106/af.kracklauer@web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>
>>>>>> Cc:  <x-msg://106/general@lists.natureoflightandparticles.org>general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>, "Richard Gauthier"  <mailto:richgauthier at gmail.com><richgauthier at gmail.com> <mailto:richgauthier at gmail.com>
>>>>>> Betreff: Re: [General] De Broglie Wave
>>>>>> Hi Al,
>>>>>> 
>>>>>> if you follow de Broglie, you should have an explanation for the following experiment (here again):
>>>>>> 
>>>>>> Electrons move at 0.1 c towards the double slit. Behind the double slit there is an interference pattern generated, which in the frame of the slit follows the rule of de Broglie. But now there is an observer also moving at 0.1 c parallel to the beam of electrons. In his frame the electrons have momentum=0 and so wavelength=infinite. That means: No interference pattern. But there is in fact a pattern which does not disappear just because there is another observer. And the moving observer will see the pattern. - This is a falsification of de Broglie's rule. What else?
>>>>>> 
>>>>>> The understanding that the de Broglie wave is a property of the particle (even though depending on their speed, but not on an interaction) was not my idea but the one of Schrödinger and Dirac and many others. Also by de Broglie himself.
>>>>>> 
>>>>>> Ciao Albrecht
>>>>>> 
>>>>>>  
>>>>>> Am 08.02.2016 um 03:30 schrieb  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>:
>>>>>> Hi Albrecht:
>>>>>>  
>>>>>> BUT, the laws of Physics for "being" in a frame are not the laws for interacting between frames!  The deB. wave is not a feature of a particle in its own frame, but a feature of the interaction of such a particle with at least one other particle in another frame.  When the two frames are moving with respect to each other, then the features of the interaction cannot be Lorentz invariants.  When one particle is interacting with another particle (or ensemble---slit say) the relevant physics is determined by the deB wave in that sitation, whatever it looks like to an observer in a third frame with yet different relative velocities.  It is a perspective effect: a tree is the same ontological size in fact no matter how small it appears to distant observers.  Observed diminished size(s) cannot be "invriant."  Appearances =/= ,,so sein''.
>>>>>>  
>>>>>> You have gotten your head stuck on the idea that deB. waves are characteristics intrinsic to particles in an of themselves.  Recalibrate!  DeB waves are                                                       charactteristics of the mutual interaction of particles.
>>>>>>  
>>>>>> Best, Al
>>>>>>  
>>>>>> Gesendet: Sonntag, 07. Februar 2016 um 22:10 Uhr
>>>>>> Von: "Albrecht Giese"  <mailto:genmail at a-giese.de><genmail at a-giese.de> <mailto:genmail at a-giese.de>
>>>>>> An:  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>
>>>>>> Cc:  <mailto:general at lists.natureoflightandparticles.org>general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>, "Richard Gauthier"  <mailto:richgauthier at gmail.com><richgauthier at gmail.com> <mailto:richgauthier at gmail.com>
>>>>>> Betreff: Re: [General] De Broglie Wave
>>>>>> Hi Al,
>>>>>> 
>>>>>> at one of your points I really disagree. The physical laws have to be fulfilled in every frame. That means that all physical processes have to obey the same laws in all frames. So also the process at the double slit. But the rule given by de Broglie looks correct in only one frame, that is the frame where the double slit is at rest. For an observer in motion the diffraction pattern looks very similar as for the observer at rest, but for the observer in motion the results according to de Broglie are completely different, because the momentum of the particle is different in a wide range in the frame of a moving observer and so is the wavelength assigned to the particle.
>>>>>> 
>>>>>> The specific case: At electron scattering, the observer co-moving with the electron will see a similar pattern as the observer at rest, but de Broglie says that for this observer there does not exist any pattern. That is strongly incorrect.
>>>>>> 
>>>>>> The Schrödinger equation and also the Dirac function should have correct results in different frames, at least at non-relativistic speeds. This requirement is clearly violated through their use of de Broglie's rule.
>>>>>> 
>>>>>> Grüße
>>>>>> Albrecht
>>>>>> 
>>>>>> PS: Your article refers to "Stochastic Electrodynamics". That is in my knowledge not standard physics and so a new assumption.
>>>>>> 
>>>>>>  
>>>>>> Am 07.02.2016 um 19:03 schrieb  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>:
>>>>>> Hi Albrecht:
>>>>>>  
>>>>>> In my view the story in my paper has no new assunptions, rather new words for old assumptions.  As I, along with most others, see it, there is no conflict with experiment, but a less than fully transparent explantion for experimental observations (particle beam diffrction) otherwise unexplained.  At the time of writing, and nowadays too (although I'd to think that my paper rationalizes DeB's story) it was the most widely accepted story for this phenomna.  
>>>>>>  
>>>>>> The only entities that logically need to be Lorentz invariant are the particle.  I the deB wave is not a 'Bestandteil' of the particle, but of its relations with its envionment, then invariance is not defined nor useful.
>>>>>>  
>>>>>> M.f.G.  Al
>>>>>>  
>>>>>> Gesendet: Sonntag, 07. Februar 2016 um 14:39 Uhr
>>>>>> Von: "Albrecht Giese"  <mailto:genmail at a-giese.de><genmail at a-giese.de> <mailto:genmail at a-giese.de>
>>>>>> An:  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>
>>>>>> Cc:  <mailto:general at lists.natureoflightandparticles.org>general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>, "Richard Gauthier"  <mailto:richgauthier at gmail.com><richgauthier at gmail.com> <mailto:richgauthier at gmail.com>
>>>>>> Betreff: Re: [General] De Broglie Wave
>>>>>> Hi Al,
>>>>>> 
>>>>>> thank you for your reference. Your paper has a lot of intelligent thoughts but also a lot of additional assumptions. With reference                                                           to the de Broglie wave, I think, is the situation much simpler on the level of conservative knowledge. De Broglie has misunderstood relativity (particularly dilation) and so seen a conflict which does in fact not exist. He has solved the conflict by inventing an additional "fictitious" wave which has no other foundation in physics, and also his "theorem of harmonic phases" which as well is an invention without need. And his result is in conflict with the experiment if we ask for Lorentz invariance or even for Galilean invariance. -  If we follow the basic idea of de Broglie by, however, avoiding his logical error about relativity, we                                                           come easily to a description of matter waves without logical conflicts. This does not need new philosophy or other effort at this level.
>>>>>> 
>>>>>> Best, Albrecht
>>>>>> 
>>>>>>  
>>>>>> Am 06.02.2016 um 03:15 schrieb  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>:
>>>>>> Hi Albrecht:
>>>>>>  
>>>>>> DeBroglie's verbage is indeed quite rococo!  Nonetheless, his machinations, although verbalized, in the true tradtion of quantum mechanics, mysteriously, can be reinterpreted (i.e., alternate verbage found without changing any of the math) so as to tell a fully, if (somewhat) hetrodoxical, story.  See #11 on  <http://www.nonloco-physics.0catch.com/>www.Nonloco-Physics.0catch.com <http://www.nonloco-physics.0catch.com/>.
>>>>>>  
>>>>>> cc:  Waves are never a characteristic of a single, point-like entity, but colletive motion of a medium.  IF they exist at all.  My view is that E&M waves are a fiction wrought by Fourier analysis.  The only real physical part is an "interaction", which mnight as well be thought of an absract string between charges.  Also, neutrons have electric multipole moments; i.e., they are totally neutral but not charge-free. 
>>>>>>  
>>>>>> Best,  Al 
>>>>>>  
>>>>>> Gesendet: Freitag, 05. Februar 2016 um 21:43 Uhr
>>>>>> Von: "Albrecht Giese"  <mailto:genmail at a-giese.de><genmail at a-giese.de> <mailto:genmail at a-giese.de>
>>>>>> An:  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>,  <mailto:general at lists.natureoflightandparticles.org>general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>
>>>>>> Cc: "Richard Gauthier"  <mailto:richgauthier at gmail.com><richgauthier at gmail.com> <mailto:richgauthier at gmail.com>
>>>>>> Betreff: Re: [General] De Broglie Wave
>>>>>> Hi Al,
>>>>>> 
>>>>>> true, in the frame of the particle the dB wavelength is infinite. Because in its own frame the momentum of the particle is 0. The particle oscillates with the frequency of the particle's Zitterbewegung (which background fields do you have in mind? De Brogie does not mention them). This oscillation is in no contradiction with this wavelength as the phase speed is also infinite. For the imagination, the latter means that all points of that wave oscillate with the same phase at any point.
>>>>>> 
>>>>>> Which  background waves do you have in mind? What is the CNONOICAL momentum? And what about E&M interactions? De Broglie has not related his wave to a specific field. An E&M field would anyway have no effect in the case of neutron scattering for which the same de Broglie formalism is used. And into which frame do you see the wave Lorentz-transformed?
>>>>>> 
>>>>>> So, an electron in his frame has an infinite wavelength and in his frame has the double slit moving towards the                                                           particle. How can an interference at the slits occur? No interference can happen under these conditions. But, as I have explained in the paper, the normal wave which accompanies the electron by normal rules (i.e. phase speed = c) will have an interference with its own reflection, which has then a wavelength which fits to the expectation of de Broglie. But that is a very local event (in a range of approx. 10^-12 m for the electron) and it is not at all a property of the electron as de Broglie has thought.
>>>>>> 
>>>>>> To say it again: The de Broglie wavelength cannot be a steady property of the particle. But Schrödinger and Dirac have incorporated it into their QM equations with this understanding.
>>>>>> 
>>>>>> If I should have misunderstood you, please show the mathematical calculations which you mean.
>>>>>> 
>>>>>> Ciao, Albrecht
>>>>>> 
>>>>>>  
>>>>>> Am 05.02.2016 um 19:20 schrieb  <mailto:af.kracklauer at web.de>af.kracklauer at web.de <mailto:af.kracklauer at web.de>:
>>>>>> Hi: Albrecht:
>>>>>>  
>>>>>> Your arguments don't resonate with me.  The deB' wave length is infinite in the particles frame: it is the standing wave formed by the inpinging background waves having a freq. = the particle's Zitterbewegung.  If these TWO waves are each Lorentz x-formed to another frame and added there, they exhibit exactly the DeB' modulation wavelength proportional to the particle's momentum.  The only mysterious feature then is that the proportionality is to the CNONICAL momentum, i.e., including the vector potential of whatever exterior E&M interactions are in-coming.  Nevertheless, everything works our without contradiction.  A particle oscillates in place at its Zitter freq. while the Zitter signals are modulated by the DeB' wavelength as they move through slits, say.
>>>>>>  
>>>>>> ciao,  L
>>>>>>  
>>>>>> Gesendet: Freitag, 05. Februar 2016 um 12:28 Uhr
>>>>>> Von: "Albrecht Giese"  <mailto:genmail at a-giese.de><genmail at a-giese.de> <mailto:genmail at a-giese.de>
>>>>>> An: "Richard Gauthier"  <mailto:richgauthier at gmail.com><richgauthier at gmail.com> <mailto:richgauthier at gmail.com>, <mailto:general at lists.natureoflightandparticles.org>general at lists.natureoflightandparticles.org <mailto:general at lists.natureoflightandparticles.org>
>>>>>> Betreff: Re: [General] De Broglie Wave
>>>>>> Hi Richard and Al, hi All,
>>>>>> 
>>>>>> recently we had a discussion here about two topics:
>>>>>> 
>>>>>> 1. The functionality of the de Broglie wave, particularly its wavelength
>>>>>> if seen from a different inertial system. Such cases lead to illogical
>>>>>> situations.
>>>>>> 2. The problem of the apparent asymmetry at relativistic dilation.
>>>>>> 
>>>>>> I have investigated these cases and found that they are in some way
>>>>>> connected. Relativistic dilation is not as simple as it is normally
>>>>>> taken. It looks asymmetric if it is incorrectly treated. An asymmetry
>>>>>> would falsify Special Relativity. But it is in fact symmetrical if
>>>>>> properly handled and understood.
>>>>>> 
>>>>>> It is funny that both problems are connected to each other through the
>>>>>> fact that de Broglie himself has misinterpreted dilation. From this
>>>>>> incorrect understanding he did not find another way out than to invent
>>>>>> his "theorem of phase harmony"; with all logical conflicts resulting
>>>>>> from this approach.
>>>>>> 
>>>>>> If relativity is properly understood, the problem seen by de Broglie
>>>>>> does not exist. Equations regarding matter waves can be derived which
>>>>>> work properly, i.e. conform to the experiments but avoid the logical
>>>>>> conflicts.
>>>>>> 
>>>>>> As announced, I have composed a paper about this. It can be found at:
>>>>>> 
>>>>>>  <https://www.academia.edu/21564534/The_Conflict_with_the_De_Broglie_Wavelength>https://www.academia.edu/21564534/The_Conflict_with_the_De_Broglie_Wavelength <https://www.academia.edu/21564534/The_Conflict_with_the_De_Broglie_Wavelength>
>>>>>> .
>>>>>> 
>>>>>> I thank Richard Gauthier for the discussion which we had about this
>>>>>> topic. It caused me to investigate the problem and to find a solution.
>>>>>> 
>>>>>> Albrecht
>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> 
>>>>>> ---
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