[General] research papers
Dr. Albrecht Giese
genmail at a-giese.de
Wed Oct 21 07:14:05 PDT 2015
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
>> <mailto: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
>>> <http://www.pa.uky.edu/%7Ekwng/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 lambda_deBroglie
>> = lambda_photon / cos theta , but: lambda_deBroglie = lambda_photon *
>> 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*mc^2 ) / h. So, the
>> geometric distance of the wave maxima passing the slits is lambda_1
>> = c*h / (gamma*mc^2 ). 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
>>>> <mailto: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
>>>>> <https://www.academia.edu/10235164/The_Charged-Photon_Model_of_the_Electron_Fits_the_Schr%C3%B6dinger_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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