[General] Weyl Fermions
Richard Gauthier
richgauthier at gmail.com
Wed Jul 29 13:14:10 PDT 2015
Hello John,
Thank you for your detailed replies to my questions about your electron model. I think that despite our significant differences in modeling the electron, we could agree on the following statement: "The electron is a spin 1/2 light-speed configuration having the electron’s charge, rest mass and 720-degree symmetry, and generating the de Broglie wavelength.” Agree or not? (And Chip and Vivian would you agree with this or not?)
Your approach to modeling the electron with a light-speed configuration gives more detailed models of the photon and the electron, including approximate calculations of the electron’s magnetic moment and electric charge. My generic approach to a circulating photon modeling a relativistic electron does not include a specific model of the photon that models a relativistic electron, but emphasizes 1) the charged photon's total circulating energy, momentum and wavelength, 2) the charged photon’s helical trajectory and how it depends on the electron’s speed, and 3) gives a short derivation of the de Broglie wavelength and the quantum wave function for a free electron from the helically circulating charged photon’s wavelength.
One point where we differ on terminology is whether the electron model's light-speed configuration should be called a spin 1/2 charged photon or a spin 1/2 light-speed configuration (or re-circulating configuration) with an associated electric charge. I emphasize what is in common with the light-speed configurations for an electron and a photon: both configurations move at light-speed with a frequency f and a wavelength lambda related by c=f lambda, where E=hf and p=h/lambda. You emphasize the differences in the two configurations (spin 1/2 configuration versus spin 1 configuration, curving motion versus straight motion, rest mass versus no rest mass, and charge versus no charge.) I hope I am not oversimplifying here. This is why I favor two photon “varieties" having some similar and some different features.
I’ve gone through your two SPIE papers on the photon and the electron, passing lightly over the proposed new algebra. I noticed a significant typo (the same in both papers) where you state (on page 14 in the photon paper and page 8 in the electron paper) that the photon’s rotation horizon = c w (where w is omega) where it should actually be rotation horizon = c/w .
I have a related question about how you derive hbar for the photon’s z-component of spin in your photon paper on p 14, which you repeat in your electron paper on p 8. You use the photon's experimental momentum (hbar w)/c to derive a maximum angular momentum of the photon hbar for your model, by multiplying the electron’s experimental momentum (hbar w)/c by the photon’s rotation horizon = c/w (when the typo is corrected ) to get spin hbar. But if the electron’s momentum is in the z (longitudinal) direction, you cannot derive the z-component Sz of the photon’s spin from the photon’s z-component of momentum (hbar w)/c . You would need to have a circulating component of the photon’s momentum in the transverse or x-y plane to derive by S = r x p a spin component Sz of the photon in the z direction. Or am I missing something? (In my model of the photon, described elsewhere, I do have such a momentum component in the transverse direction).
with best regards,
Richard
> On Jul 21, 2015, at 6:45 AM, John Williamson <John.Williamson at glasgow.ac.uk> wrote:
>
> Hi Richard,
>
> Answers in blue
> From: Richard Gauthier [richgauthier at gmail.com <mailto:richgauthier at gmail.com>]
> Sent: Tuesday, July 21, 2015 8:06 AM
> To: Nature of Light and Particles - General Discussion; John Williamson
> Subject: Re: [General] Weyl Fermions
> Hello John,
> Thank you for resending your updated position paper as a text file. Somehow I missed the pdf version.
>
> I find your new approach to modeling the electron by a light-speed configuration of waves quite exciting. It definitely seems like an important step in the right direction of describing the electron as a circulating light-speed configuration having the electron’s rest mass and spin 1/2 hbar and a 720-degree symmetry.
>
> The following are several questions that I would ask of your electron model or any other specific model of a light-speed configuration modeling an electron.
>
> 1) Is the rest mass of your light-speed configuration invariant for all speeds of the electron you are modeling?
>
> Yes
>
> 2) Does your light-speed configuration follow a helical trajectory for a moving electron? If so, what is the radius of this helical trajectory in terms of Ro = hbar/2mc and how does it depend on gamma of the electron?
>
> Mu. The question makes no sense. As I keep saying, for me it makes no sense to ask about the electrons "trajectory". One calculates momenta. It has a specific angular momentum. This is related by a size and a (perpendicular) momentum (this is ok). Even by the (much simpler) uncertainty principle, one cannot say where the (precisely defined) momentum is at all. It is completely undefined. The electron is a function of seven components in the new theory, none of which are space or time alone. You need to project the trajectory onto space, but even if you do this it will absolutely not represent what is really going on. If you want to put space in as well you will have ten. This cannot be simply modelled by a 3D path! Gamma is, for me, too simple. It pertains to the effect on a little lump of mass. You have to get gamma out. You should not be putting it in! The electron is not, and cannot be, modelled by a little lump of mass whizzing about. The internal wave-function (Eq. 21 on p9 in the first paper) varies by the factor R explained in my first paper – which only gives gamma as an average – as described there.
>
> 3) Does your light-speed configuration for an electron reduce to a size of around 10^-18 meters or less in high energy electron scattering experiments, as is experimentally found for the electron?
>
> Yes
>
> 4) Does your electron model follow the relativistic energy-momentum equation E^2 = p^2 c^2 + m^2 c^4 where m is the electron’s rest mass? If yes, what is the meaning of p in this equation, in relation to the light-speed configuration modeling the electron?
>
> Yes. Usual meaning. P is the momentum of the object as a whole. Just as in the solutions for the Dirac model.
>
> 5) Is the spin of your light-speed configuration for an electron 1/2 hbar or -1/2 hbar for all electron speeds less than c, including highly relativistic electron speeds, and not just for a resting electron?
>
> Yes ... spin is invariant under an L.T. Energy goes up by R, size goes down by 1/R.
>
> 6) Is the internal frequency f of your light-speed configuration of an electron proportional to the total energy of the light-speed configuration for a moving electron, i.e. does hf=gamma mc^2 for your light-speed configuration?
>
> There are two frequencies. They obey the "harmony of phases". One of these follows hf=gamma mc^2.
>
> 7) Is there an internal wavelength lambda of your light-speed configuration for a moving electron and is it found from c= lambda f, so that lambda = h/(gamma mc)?
> Kind of - but it is a bit more complicated than that – as above.
>
> 8) Does your light-speed configuration for an electron generate the de Broglie wavelength along the direction that the light-speed configuration is moving? Does it generate the electron’s group velocity c^2/v in this direction?
>
> Yes
>
> 9) Does your light-speed electron wave equation generate the quantum wave function Ae^i(kx-wt) for a free electron along the direction that the electron is moving, where k is p/hbar of the electron and w = E/hbar of the electron?
>
> No. Definitely not. Firstly there is no such thing as i. Secondly, the above equation is anyway too simple. It is not relativistic. It is just a solution to the non-rel Scroedinger equation. That is as good as we have had for a century or so, but we need to do better!
>
> A proper (in the relativistic sense) wave-function should look just like "light in a box". Like eq. 21 then. If solutions such as that are confined, the co-moving and anti-moving components generate an equation with both a de-Broglie wave (from interference) and a Compton wave. This is like wave (like light in a box) -with two different "velocities" those these are only apparent w.r.t. the observer frame. Within the system itself everything remains at light-speed. The changes are only apparent because of the relative velocity of observer and observed – according to the normal laws of relativity.
>
> with best regards,
> Richard
> Regards, John.
>
> On Jul 19, 2015, at 7:12 PM, John Williamson <John.Williamson at glasgow.ac.uk <mailto:John.Williamson at glasgow.ac.uk>> wrote:
>>
>> Hello Richard,
>>
>> Do not have a "Word" document I'm afraid. Gave up on it a couple of decades ago. Here it is in marked up plain text (below). You have an abstract as well ... not available in the pdf as it is commented out. You could get this by changing "tex" to "txt" and just opening the attachment with word or any other text editor. Could you not read the pdf version?
>>
>> Regards, John.
>>
>>
>> \title{Electron nature: light, vacuum or something else?}
>>
>> %>>>> The author is responsible for formatting the
>> % author list and their institutions. Use \skiplinehalf
>> % to separate author list from addresses and between each address.
>> % The correspondence between each author and his/her address
>> % can be indicated with a superscript in italics,
>> % which is easily obtained with \supit{}.
>>
>> \author{J.G.Williamson\supit{a}
>> \skiplinehalf
>> \supit{a} University of Glasgow, College of Science \& Engineering, Glasgow G12 8LT, Scotland;
>> }
>>
>> %>>>> Further information about the authors, other than their
>> % institution and addresses, should be included as a footnote,
>> % which is facilitated by the \authorinfo{} command.
>>
>> \authorinfo{Further author information: (Send correspondence to J.G. Williamson)\\J.G <x-msg://67/UrlBlockedError.aspx>. Williamson: E-mail: john.williamson at glasgow.ac.uk <mailto:john.williamson at glasgow.ac.uk>, Telephone: +44 141 330 4923}
>> %%>>>> when using amstex, you need to use @@ instead of @
>>
>>
>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>> %>>>> uncomment following for page numbers
>> %\pagestyle{plain}
>> %>>>> uncomment following to start page numbering at 301
>> %\setcounter{page}{301}
>>
>> \begin{document}
>> \maketitle
>>
>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>> %\begin{abstract}
>> %A minimal theory is developed of the flow of root-energy with forms based on the experimental properties of four-dimensional space-time. In light, this encompasses the Maxwell equations, but allows only quantised solutions. For (rest-massive-) particles, it reflects the same solution set as the Dirac equation, spin up and spin down electrons and positrons, but over such things as fields and currents rather than more abstract concepts such as spinors. In interactions it underpins quantum electrodynamics in that it derives charge, sees the electromagnetic interaction as an exchange of energy between charged particles through light, but gives a more physical perspective on the origins of results such as the anomalous magnetic moment. \end{abstract}
>>
>> %>>>> Include a list of keywords after the abstract
>>
>> %\keywords{Electromagnetic electron positron photon}
>>
>> %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
>> \section{Position}
>> \label{sec:intro} % \label{} allows reference to this section
>>
>>
>> Firstly: nature (as measured in experiment) is primary. Theories are merely speculations one makes up to try to describe her underlying processes. Mathematics is a powerful, but formal and strictly limited, language which may be used to try to describe certain aspects of whatever nature does in reality. Mere mathematics, however, must not be allowed to cloud any of the fundamental features of nature observed in experiment. Any (practically useful) mathematics should follow nature, not the other way round. If one cannot measure it, it is, (for all practical purposes) not there. Any theories predicting things which are (observed to be) just not there should be modified or discarded. This is the proper process of the scientific method. It may be that the logical conclusion of this process, the solution of Hilbert's sixth problem such that a complete mathematical system describing all of nature just and no more, is not possible at all. Though that remains to be seen, it is worth striving for.%It may, however, be possible to prove at some point that such a system is not possible.
>>
>> Having said this, the body of theory as it stands in the early twenty-first century, is a marvellous intellectual achievement garnered through generations of the thinking of many excellent folk. Human theory encapsulates a great deal of truth about the nature of reality. Any new theories should either encompass, improve on, or underpin that thinking - or they are likely to fail. The creation of new theories may be a deeply creative process - but it is also strongly constrained.
>>
>> Taking a particular position, then, is not an easy choice. Thinking is fluid. Theory is something one makes up. It is perfectly possible to consider many points of view - each with their merits and problems, all at the same time. It is still possible to the see the merits and beauty of Martin van der Mark's and my quarter-century-old model of the electron as a localised photon, while no longer believing in the existence as independent entities of, not only the photon but also the electron. This is not to say, of course, that I was wrong then and am right now - who knows?
>>
>> My current favoured position is that there is only space, time and a sort of root-energy. These five degrees of freedom, for me, are sufficient to describe most, if not all, of that which has been so far observed in human experiment. In particular they are sufficient to derive models of the photon, electron and other particles. It proves possible to derive why and how light is quantised, what the underlying nature of the elementary charge and the quantum spin is and what the underlying nature of some of the fundamental forces of nature are. They are also, in my view, sufficient to either encompass, underpin or improve the existing practical theories of current physics. The development of a new, continuous linear theory to describe this has been the subject of the papers presented last year at FFP14 and submitted this year to this conference. If this approach should prove of any merit, it will remain the work of many man-years to develop the solutions to the level of those of Schroedinger, Maxwell or Dirac theories. Even if the new theory is worth anything, there remains much work to be done.
>>
>> The new theoretical view holds that space and time are primary. They exist everywhere (and for all time!), whether or not any energy is present within them or not. The root four dimensions of space and time may also manifest in products and quotients of the base four ``directions". This allows root-energy to manifest not only in vectors, but also such things as physical areas - as the product of space with perpendicular space. Multiplying any space (or time) with a parallel space gives a conceptually different kind of object to an area. The sequence area-line-point would identify this with a ``point". This object, however, is not a point in the way the word is usually understood. Just as a line may be extended to one of any length (magnitude), this kind of point may also have any magnitude. If one attributes the experimentally measured (relativistic) properties of space and time to lines in space and time, then the lines must vary as a four-vector, the plane product as a field, and the point product as a Lorentz invariant. Introducing root-energy into these forms then gives stuff with the physical properties of a 4-current density, an electromagnetic field and a a rest-mass, respectively. Further, the volume forms act as a root angular momentum - a spin. It is simple to show that the equations describing this for the field are identical to the four, coupled differential equations known as the Maxwell equations. A new, general, equation over the sixteen terms (1 scalar, 4-vector, 6-field, 4-spin, 1 pseudo-scalar) is then:
>>
>>
>> \begin{eqnarray}
>> \label{Max+}
>> %\begin{flalign}
>> \mathcal{D}_4 G_{16} = \alpha_0(\vec{\nabla}\inprod\vec{E} + \partial_{0} P)+ \alpha_{123}(\vec{\nabla}\inprod\vec{B} + \partial_{0} Q) +
>> \alpha_{i}\left(\vec{\nabla}\times\vec{B} - \partial_0\vec{E} - \vec{\nabla} P\right) +
>> \alpha_{0ij} (\vec{\nabla}\times\vec{E}
>> + \partial_0\vec{B} + \vec{\nabla} Q) + \nonumber\\
>> \alpha_{P} (\vec{\nabla}\inprod\vec{A} + \partial_0 A_{0}) +
>> \alpha_{0123}(\vec{\nabla}\inprod\vec{T}+\partial_0 T_{0})
>> + \alpha_{i0} \left( \partial_0\vec{A} + \vec{\nabla} A_{0} + \vec{\nabla}\times\vec{T} \right)+
>> \alpha_{jk} \left( \partial_0\vec{T} + \vec{\nabla} T_{0} - \vec{\nabla}\times\vec{A}\right) = 0
>> %\end{flalign}
>> \end{eqnarray}
>>
>> Here the basis vectors, denoted by the $\alpha$'s have one numerical index for the vectors, two for the planes, three for the volumes and four for the 4-volume. $\mathcal{D}_4$ is a 4-vector differential. $E$ and $B$ denote the electric and magnetic fields, and $A$ and $T$ the vector and tri-vector potential respectively. $P$ and $Q$ are rest-mass like components invariant under a Lorentz transformation. The special root-energy density scalar is denoted $\alpha_P$. For the field only part, the first four equations without the $P$ and $Q$ terms, this reduces to Maxwell's equations. The new approach, however, allows new kinds of holomorphic, covariant solutions to the pure field (light-speed) Maxwell equations describing a covariant wave. Viz, for a single photon travelling in the ``$z$" direction:
>>
>> \begin{eqnarray}
>> \label{CircL+}
>> F_{L} = H_0 U_F R {{\mathcal{E }} (\alpha_{10} + \alpha_{31}) e^{ {\mathcal{E } \over \hbar} R( \alpha_{3} {z \over c }- \alpha_{0} t) \alpha_{012}}} = {F_{0} R (\alpha_{10} + \alpha_{31}) e^{ R(k\alpha_{3} {z }- \omega \alpha_{0} t) \alpha_{012}}} = \mathcal{F} \mathcal{W}
>> \end{eqnarray}
>>
>> Except for $U_F$, which is a new universal constant converting to field units and related to $\hbar$, the pre-factor terms are normalisation terms in phase ($H_0$) and energy ( R and $\mathcal{E}$). The crucial features of this new wave function are that the photon energy ($\mathcal{E}$), appears in both pre-factor and exponent, that the argument of the exponential is not a simple number but contains explicitly the proper nature of space and time in the form of $\alpha_{3}$ a proper unit vector in the direction of $z$ and $\alpha_{0}$, a proper unit vector in the direction of time and that a proper unit angular momentum ($\alpha_{012}$) is required for this to be a travelling wave solution. Lorentz transformations are described in the wave-function by the single parameter $R$ - scaling both field and frequency linearly. This allows the same photon to be described in different frames - particularly those of the emitter and absorber. The function describes photons of any energy from gamma to radio and beyond - right to the limit of as close as you like to zero energy. %It is, to the knowledge of the author, the first proper, covariant photon wave-function.
>>
>> Extending the theory to include some of the new terms, especially the root invariant rest-mass term $P$, allows qualitatively new kinds of solutions. These contain, as well as the rest-mass component, re-circulating field components. Such solutions are necessarily charged, have half-integral spin and have the proper 720 degree symmetry of fermions. These solutions are identified with the electron and positron. The new theory then describes both light-speed field only solutions corresponding to the photon and re-circulating solutions corresponding to the electron on the same footing. It allows, for the first time, the description of the process of particle-antiparticle pair creation within a single linear theory.
>>
>> Within the theory, the elementary charge $q$ may be estimated in terms of the elementary spin $\hbar$ (or vice-versa) and is found to be close to the value observed in experiment. The new solutions describe both both light and material particles and arise from the constraints imposed by the deeper principles of the nature of space and time and the linearity of field and energy. Quantisation arises from the rigorous development of relativity.
>>
>> In the new theory space and time - the defining components of the physical vacuum, are primary and are always present. Space and time condition any root-energy into different forms, manifesting as mass (scalar), charge and current (vector), fields (areas), spin (volumes) and a spin root (a 4-dimensional volume).The theory allows, however, for the possibility that the root-energy at certain places may go to zero - an empty vacuum. For all practical purposes, of course, ``free" space is always full of the photons that paint our world - even if they are only those of the 3K background radiation. The answer then, for me, to the question posed in the title is ``all three". With ``something else", here being the proper nature of space and time - the underlying form of the ``vacuum" present at all localities.
>>
>> - John Williamson, Troon, Scotland, July 17th, 2015
>>
>>
>> \end{document}
>>
>> From: General [general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticles.org <mailto:general-bounces+john.williamson=glasgow.ac.uk at lists.natureoflightandparticles.org>] on behalf of Richard Gauthier [richgauthier at gmail.com <mailto:richgauthier at gmail.com>]
>> Sent: Monday, July 20, 2015 12:51 AM
>> To: Nature of Light and Particles - General Discussion
>> Subject: Re: [General] Weyl Fermions
>>
>> Hi John,
>> Could you please send your position document in Word or as a text file. I am unable to open a tex (Latex) file. Thanks.
>> Richard
>>
>>
>>> On Jul 18, 2015, at 10:17 AM, John Williamson <John.Williamson at glasgow.ac.uk <mailto:John.Williamson at glasgow.ac.uk>> wrote:
>>>
>>> Dear all,
>>>
>>> Please find attached the "position" document I sent to SPIE this morning.
>>>
>>> Regards, John W.
>>> <SPIE-position-JGW.pdf>_______________________________________________
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