[General] research papers
Dr. Albrecht Giese
genmail at a-giese.de
Sun Oct 25 06:21:53 PDT 2015
Hello Richard,
thanks for your detailed explanation. I think that it becomes more and
more visible, how difficult it is to visualize such a 3-dimensional
process.
I have added some further comments below in your text.
Am 23.10.2015 um 22:41 schrieb Richard Gauthier:
> Hello Albrecht (and others)
>
> Thank for your further comments. You arguments are correct,
> according to how I previously explained the plane waves emitted by the
> charged photon along its helical axis. I realized that I
> misinterpreted and therefore poorly explained my own proposed quantum
> plane wave function describing quantum waves coming from the
> circulating charged photon. The left side of Figure 2 is NOT merely
> the mathematically unwrapped helical trajectory of the charged photon.
> It is instead (or in addition) one of many “rays” of quantum plane
> waves emitted continuously from the circulating charged photon.
>
> The circulating charged photon’s proposed quantum plane wave
> function Ae^i(k dot r - wt) , where k = (gamma mv)/hbar and w =
> (gamma mc^2)/hbar are the wave vector and the angular frequency of
> the circulating charged photon, describes quantum plane waves emitted
> from the circulating charged photon in the direction that the charged
> photon is moving at any point in time.
The relation k = (gamma mv)/hbar cannot be applicable here, if I
understand correctly that v is the speed of the electron. If the
electron is at rest, then v=0 and so
k=0. But for a photon k=0 is not possible. It is in permanent motion
and has energy, which you describe with w = (gamma mc^2)/hbar .
Here you try to apply the de Broglie wave length to the circling photon
which you cannot do by two reasons:
1.) Your intention is to derive the de Broglie wave length. But you
cannot do this by using the validity of the de Broglie wave length as a
precondition. That would be circular reasoning.
2.) And anyway, for a photon the de Broglie wave length is identical the
wave length of the phase wave as v=c .
> While emitting these quantum plane waves, the charged photon curves
> away on its helical trajectory, continuing to emit newer quantum plane
> waves at its own frequency and wavelength. But the quantum plane waves
> previously emitted by the charged photon continue in a straight line
> direction tangent to the helical trajectory at the point along the
> trajectory where they were emitted. Those quantum plane waves emitted
> from the circulating charged photon at one location move out into
> space at light-speed away from the charged photon, as indicated by the
> left side of the big triangle in my Figure 2, and in the recently
> posted figure showing 4 wave fronts. Their quantum plane wave fronts
> DO intersect the charged photon’s helical axis further along the axis
> to the right, as shown in the two figures, creating de Broglie
> wavelengths along the helical axis. And these de Broglie wavelengths
> DO travel away to the right along the helical axis at the phase
> velocity c^2/v because their speed is (from the geometry shown in
> Figure 2) Vphase = speed of charged photon / cos(theta) =
> c/cos(theta) = c/(v/c) = c^2/v .
Your Figures 2 and 4 assume that the circling photon emits a plane wave.
Is that possible? It means that the wave which just leaves the photon
with a certain phase is immediately spread out to all sides until
infinity. Otherwise it is not a /plane /wave. But if it does so, it
means an infinite propagation speed to all directions perpendicular to
the speed vector of the photon. This is in my understanding in strong
conflict with relativity. (And it means also that for an observer in a
system moving relative to this system there can be a violation of
causality. He can observe that a part of the plane may exist at a
certain phase even before this phase is emitted from the photon.)
If you assume such kind of plane wave then your considerations about the
wave on the axis caused by the sequence of intercept points are
applicable. But again: a plane wave of this kind violates causality.
You mention further down as a visualization the case of a laser moving
along the helix. A laser emits indeed a sort of a plane wave, however in
a limited region given by the diameter of the laser's body. This plane
wave is the result of a superposition of a huge number of photons
oscillating forth and back in the laser. In contrast to this the photon
in your model is a point source. If it emits waves then those are
restricted to the speed of light. So they will leave the photon as a
cone with a half angle of 45 degrees. (In acoustics this is called
Mach's cone.) If we start now to follow this process using this way of
propagation, we have to look how the cone touches the axis. The motion
of these intercept points on the axis seems to be non-linear, and as
further phases follow, there will be an overlay of such phases. - Do you
think it is worth to follow this? I would like to first check whether we
find an agreement at this point.
>
> All these emitted quantum plane waves from the charged photon,
> described above by Ae^i(k dot r - wt) , intersect the helical axis, as
> described by the derived relativistic de Broglie matter-wave function
> A^i(Kdb z -wt) where Kdb is the wave number corresponding to the de
> Broglie wavelength Ldb = h/(gamma mv). So Kdb =2pi /Ldb = (gamma
> mv)/hbar , and w =(gamma mc^2)/hbar the angular frequency of the
> charged photon, corresponding to f=(gamma mc^2)/h as before.
I understand that these considerations follow again the assumption of a
"plane" wave which I do not believe to be possible as explained above.
So I shall wait for your response to that.
>
> This process can roughly be compared to a broad plane-wave beam
> emitted from a laser while the laser moves along a helical trajectory,
> directing its beam in new directions as the laser moves along its
> helical path. The parallel waves fronts from the laser intersect the
> axis and generate one de Broglie-like wavelength along the axis for
> each photon wavelength coming from the laser.
For the laser example please see above.
Best regards
Albrecht
>
> Does this new explanation answer your fundamental objection?
>
> with best regards,
> Richard
> .
>> On Oct 22, 2015, at 10:18 AM, Dr. Albrecht Giese <genmail at a-giese.de
>> <mailto:genmail at a-giese.de>> wrote:
>>
>> Hello Richard,
>>
>> thank you and see my comments below.
>>
>> Am 22.10.2015 um 00:32 schrieb Richard Gauthier:
>>> Hello Albert (and all),
>>>
>>> I think your fundamental objection that you mentioned earlier can
>>> be answered below.
>>>
>>> The left side of the big triangle in Figure 2 in my article is a
>>> purely mathematical unfolding of the path of the helical trajectory,
>>> to hopefully show more clearly the generation of de Broglie
>>> wavelengths from plane waves emitted by the actual charged photon
>>> moving along the helical trajectory. Nothing is actually moving off
>>> into space along this line.
>>>
>>> Consider an electron moving with velocity v horizontally along the
>>> helical axis. Since in Figure 2 in my article, cos (theta) = v/c ,
>>> the corresponding velocity of the charged photon along the helical
>>> path is v/ cos(theta) = c , the speed of the charged photon, which
>>> we knew already because the helical trajectory was defined so that
>>> this is the case. In a short time T, the electron has moved a
>>> distance Delectron = vT horizontally and the photon has moved a
>>> distance Dphoton = Delectron/cos(theta) =vT/cos(theta) = cT along
>>> its helical trajectory.
>> I agree.
>>> A plane wave front emitted from the photon at the distance Dphoton =
>>> cT along the photon’s helical path will intersect the base of the
>>> big triangle (the helical axis) at the distance along the base given
>>> by Dwavefront = Dphoton / cos(theta) = cT/ (v/c) = T * (c^2)/v
>>> which means the intersection point of the plane wave with the
>>> helical axis is moving with a speed c^2/v which is the de Broglie
>>> wave’s phase velocity.
>> Here I disagree. If we assume the wave front as an extended layer
>> through the photon and with an orientation perpendicular to the
>> actual direction of the photon, then the intersect point of this
>> layer with the axis has the same z coordinate as the z-component of
>> the photon's position. This is essential. (I have built myself a
>> little 3-d model to see this.)
>>
>> When now, say at time T_0 , a phase maximum of the wave front leaves
>> the photon, then the same phase maximum passes the intersect point on
>> the axis with the same z coordinate. After a while (i.e. after the
>> time T_p =1/frequency) the next phase maximum will exit from the
>> photon and simultaneously the next phase maximum will cross the axis.
>> The new z-value (of the photon and of the intersect point) is now
>> displaced from the old one by the amount delta_z = v * T_p . During
>> this time the photon will have moved by c * T_p on its helical path.
>>
>> Now the spacial distance between these two phase maxima, which is the
>> wavelength, is: lambda_photon = c * T_p , and lambda_electron = v *
>> T_p .
>>
>> This is my result. Or what (which detail) is wrong?
>>
>> best wishes
>> Albrecht
>>
>>
>>> The length of the de Broglie wave itself as shown previously from
>>> Figure 2 is Ldb = Lambda-photon / cos(theta) = h/(gamma mc) / (v/c)
>>> = h/(gamma mv). So as the electron moves with velocity v along the
>>> z-axis, de Broglie waves of length h/(gamma mv) produced along the
>>> z-axis are moving with velocity c^2/v along the z-axis. The de
>>> Broglie waves created by the circulating charged photon will speed
>>> away from the electron (but more will be produced) to take their
>>> place, one de Broglie wave during each period of the circulating
>>> charged photon (corresponding to the moving electron). As mentioned
>>> previously, the period of the circulating charged photon is 1/f =
>>> 1/(gamma mc^2/h) = h/(gamma mc^2/). As the electron speeds up (v and
>>> gamma increase) the de Broglie wavelengths h/(gamma mv) are shorter
>>> and move more slowly, following the speed formula c^2/v .
>>>
>>>
>>>
>>> Unpublished graphic showing the generation of de Broglie waves from
>>> a moving charged photon along its helical trajectory. The
>>> corresponding moving electron is the red dot moving to the right on
>>> the red line. The charged photon is the blue dot moving at light
>>> speed along the helix.The blue dot has moves a distance of one
>>> charged photon wavelength h/(gamma mc) along the helix from the left
>>> corner of the diagram On the left diagonal line (representing the
>>> mathematically unrolled helix), the blue dots correspond to
>>> separations of 1 charged photon h/(gamma mc) wavelength along the
>>> helical axis. In this graphic, v/c = 0.5 so cos(theta)= 0.5 and
>>> theta= 60 degrees. The group velocity is c^2/v = c^2/0.5c = 2 c, the
>>> speed of the de Broglie waves along the horizontal axis . The
>>> distances between the intersection points on the horizontal line
>>> each correspond to 1 de Broglie wavelength, which in this example
>>> where v=0.5 c is h(gamma mv) = 2 x charged photon wavelength
>>> h/(gamma mc).
>>>
>>> It is true that when the electron is at rest, the wave fronts
>>> emitted by the circulating charged photon all pass through the
>>> center of the circular path of the charged photon and do not
>>> intersect any helical axis, because no helical axis is defined for a
>>> resting electron, i.e. the pitch of the helix of the circulating
>>> charged photon is zero. For a very slowly moving electron, the pitch
>>> of the helix of the circulating charged photon is very small but
>>> non-zero, but the de Broglie wavelength is very large, much larger
>>> than the helical pitch. Perhaps you are confusing these two lengths
>>> — the helical pitch of the circulating charged photon and the de
>>> Broglie wavelength generated by the wave fronts emitted by the
>>> circulating charged photon. The pitch of the helix starts at zero
>>> (for v=0 of the electron) and reaches a maximum when the speed of
>>> the electron is c/sqrt(2) and theta = 45 degrees (see my charged
>>> photon paper) and then the helical pitch decreases towards zero as
>>> the speed of the electron further increases towards the speed of
>>> light. But the de Broglie wavelength Ldb starts very large (when the
>>> electron is moving very slowly) and decreases uniformly towards zero
>>> as the speed of the electron increases, as given by Ldb = h/gamma
>>> mv. It is the de Broglie wavelength generated by the charged photon
>>> that has predictive physical significance in diffraction and
>>> double-slit experiments while the helical pitch of the charged
>>> photon’s helical trajectory has no current predictive physical
>>> significance (though if experimental predictions based on the
>>> helical pitch could be made, this could be a test of the charged
>>> photon model).
>>>
>>> I don’t have any comments yet on your concerns about the de
>>> Broglie wavelength that you just expressed to John W (below).
>>>
>>> all the best,
>>> Richard
>>>
>>>> On Oct 21, 2015, at 12:42 PM, Dr. Albrecht Giese
>>>> <genmail at a-giese.de <mailto:genmail at a-giese.de>> wrote:
>>>>
>>>> Dear John W and all,
>>>>
>>>> about the_de Broglie wave_:
>>>>
>>>> There are a lot of elegant derivations for the de Broglie wave
>>>> length, that is true. Mathematical deductions. What is about the
>>>> physics behind it?
>>>>
>>>> De Broglie derived this wave in his first paper in the intention to
>>>> explain, why the internal frequency in a moving electron is
>>>> dilated, but this frequency on the other hand has to be increased
>>>> for an external observer to reflect the increase of energy. To get
>>>> a result, he invented a "fictitious wave" which has the phase speed
>>>> c/v, where v is the speed of the electron. And he takes care to
>>>> synchronize this wave with the internal frequency of the electron.
>>>> That works and can be used to describe the scattering of the
>>>> electron at the double slit. - But is this physical
>>>> understanding? De Broglie himself stated that this solution does
>>>> not fulfil the expectation in a "complete theory". Are we any
>>>> better today?
>>>>
>>>> Let us envision the following situation. An electron moves at
>>>> moderate speed, say 0.1*c (=> gamma=1.02) . An observer moves
>>>> parallel to the electron. What will the observer see or measure?
>>>> The internal frequency of the electron will be observed by him as
>>>> frequency = m_0 *c^2 /h , because in the observer's system the
>>>> electron is at rest. The wave length of the wave leaving the
>>>> electron (e.g. in the model of a circling photon) is now not
>>>> exactly lambda_1 = c/frequency , but a little bit larger as the
>>>> rulers of the observer are a little bit contracted (by gamma =
>>>> 1.02), so this is a small effect. What is now about the phase speed
>>>> of the de Broglie wave? For an observer at rest it must be quite
>>>> large as it is extended by the factor c/v which is 10. For the
>>>> co-moving observer it is mathematically infinite (in fact he will
>>>> see a constant phase). This is not explained by the time dilation
>>>> (=2%), so not compatible. And what about the de Broglie wave
>>>> length? For the co-moving observer, who is at rest in relation to
>>>> the electron, it is lambda_dB = h/(1*m*0), which is again infinite
>>>> or at least extremely large. For the observer at rest there is
>>>> lambda_dB = h/(1.02*m*0.1c) . Also not comparable to the co-moving
>>>> observer.
>>>>
>>>> To summarize: these differences are not explained by the normal SR
>>>> effects. So, how to explain these incompatible results?
>>>>
>>>> Now let's assume, that the electron closes in to the double slit.
>>>> Seen from the co-moving observer, the double slit arrangement moves
>>>> towards him and the electron. What are now the parameters which
>>>> will determine the scattering? The (infinite) de Broglie wave
>>>> length? The phase speed which is 10*c ? Remember: For the co-moving
>>>> observer the electron does not move. Only the double slit moves and
>>>> the screen behind the double slit will be ca. 2% closer than in the
>>>> standard case. But will that be a real change?
>>>>
>>>> I do not feel that this is a situation which in physically understood.
>>>>
>>>> Regards
>>>> Albrecht
>>>>
>>>>
>>>> Am 21.10.2015 um 16:34 schrieb John Williamson:
>>>>> 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 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> 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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