[General] research papers

Wed Oct 21 15:06:18 PDT 2015

"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>
> 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
>
>
>
>
> ------------------------------
> [image: Avast logo] <https://www.avast.com/antivirus>
> Diese E-Mail wurde von Avast Antivirus-Software auf Viren geprüft.
> www.avast.com <https://www.avast.com/antivirus>
>
>
>
> _______________________________________________
> If you no longer wish to receive communication from the Nature of Light
> and Particles General Discussion List at martin.van.der.mark at philips.com
> <a href="
> http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/martin.van.der.mark%40philips.com?unsub=1&unsubconfirm=1
> ">
> Click here to unsubscribe
> </a>
>
>
> ------------------------------
> The information contained in this message may be confidential and legally
> protected under applicable law. The message is intended solely for the
> addressee(s). If you are not the intended recipient, you are hereby
> notified that any use, forwarding, dissemination, or reproduction of this
> message is strictly prohibited and may be unlawful. If you are not the
> intended recipient, please contact the sender by return e-mail and destroy
> all copies of the original message.
> _______________________________________________
> If you no longer wish to receive communication from the Nature of Light
> and Particles General Discussion List at richgauthier at gmail.com
> <a href="
> http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/richgauthier%40gmail.com?unsub=1&unsubconfirm=1
> ">
> Click here to unsubscribe
> </a>
>
>
>
> _______________________________________________
> If you no longer wish to receive communication from the Nature of Light
> and Particles General Discussion List at afokay at gmail.com
> <a href="
> http://lists.natureoflightandparticles.org/options.cgi/general-natureoflightandparticles.org/afokay%40gmail.com?unsub=1&unsubconfirm=1
> ">
> Click here to unsubscribe
> </a>
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.natureoflightandparticles.org/pipermail/general-natureoflightandparticles.org/attachments/20151021/ba77ab10/attachment.htm>