[General] Electron Torus

Richard Gauthier richgauthier at gmail.com
Fri May 29 12:11:18 PDT 2015


Hello Chip and all,

The following recent graphical results (particularly in green but perhaps in red as well) may be relevant to anyone with an electron model composed of a single-loop or double-loop photon, that can move in a helical trajectory in the z-direction when the circulating photon in the resting electron (or in an electron with a very small velocity in the z-direction) circulates in the x-y plane. The generic (structureless) photon’s green trajectory would correspond to the trajectory of the photon in your circulating EM photon model of the electron in the case of a relativistic electron and also to Vivian’s model (although his photon model may be purely the generic one), and perhaps to John W and Martin’s 1997 toroidal model of the electron and also to John M’s spacetime model of the electron. The generic model of the electron cannot alone account for the spin 1/2 hbar of the electron at relativistic velocities because the spin of the generic model decreases to zero at relativistic velocities, so a photon with a finite-size internal energy structure is needed for this. 

I’ve continued (earlier results were presented on May 24 and are repeated here) calculating and graphing the end view (along the z-axis) and side view of both the generic (green) and TEQ models (red) of the relativistic electron as a helically moving charged photon, from gamma = 0 (resting electron) out to values of gamma^2 = 2^10=1024   (or gamma = 2^5 = 32.) In this series, the largest value of v of the electron is v=0.9995 c corresponding to gamma = 32 . The gamma in current high-energy electron experiments obvious goes much higher than this, into the order of magnitude range of gamma=10^4 or higher. In each successive graphic figure below (starting with the resting electron whose TEQ moves on the surface of a horn torus)  the value of gamma^2 doubles, so the radius Ro/gamma^2 of the helical trajectory (where Ro=hbar/2mc) of the generic photon having no internal structure and moving at light-speed (green trajectory) decreases by a factor of 2, while the radius Ro/gamma of the transluminal energy quantum or TEQ’s helical trajectory (red trajectory) around its green helical axis decreases by a factor of sqrt(2)=1.414 . The first image on the second row is the same as the last image on the first row, but the linear scale of the second row is magnified to show greater detail. In the second and third figures (showing the two sideways sets of views of the generic model and TEQ model of the charged photon ) the pattern of increase of gamma^2 from one image to the next is the same, with the last view of the first set of sideways images being the same as the first view of the second set of sideways images having greater magnification.

You can see the the radius Ro/gamma^2 of the generic electron’s helical trajectory appears to go to nearly zero (to the limit of the graphic resolution) in the first set of figures (end views along z-axis) and becomes nearly a straight line (again to the limit of the graphic resolution) in the second (sideways) set of figures, while the radius Ro/gamma of the TEQ’s helical trajectory is still easily visible in both the end views and and in the sideways views. The end view of the TEQ trajectory becomes circular with decreasing radius Ro/gamma while the side view of the TEQ’s trajectory shows an interesting apparently constant structure of decreasing size (also decreasing as Ro/gamma) with increasing gamma. The apparent “wavelength” of the sideways diagrams is the helical pitch of the generic photon (green trajectory) which at high values of gamma is nearly 1/2 the wavelength of the helically circulating charged photon (due to the double-looping structure of the resting electron and the double-looping structure of the 1/2 hbar TEQ charged photon model) and also the green helical pitch is nearly 1/2 of the electron’s de Broglie wavelength at highly relativistic speeds. See “The electron is a charged photon with the de Broglie wavelength" for details about the pitch of the generic photon model of the electron.

Richard




> On May 24, 2015, at 12:57 AM, Richard Gauthier <richgauthier at gmail.com> wrote:
> 
> Chip and others,
>   I was able to send a set of 3D graphic files of my relativistic electron model from my older computer to my present computer. It is an electron model generated by a circulating spin 1/2 charged photon composed of a transluminal energy quantum (TEQ).
> In the 2 figures, the red figure in the torus represents the transluminal energy quantum (TEQ) circulating along a horn torus surface in a resting electron (top and side view). The five other figures in each graphic represent a relativistic electron going past the resting electron at various relativistic speeds, seen end on in the first figure and from the side in the second figure. The electron velocities are choses so that gamma^2 = 2,4,8,16 and 32. This makes the radius of the trajectory of the photon (green circle) get divided by 2 in each successive figure, since this radius is proportional to 1/ gamma^2 in my relativistic electron model. The correspond electron speeds are v= 0.707c , 0.866c, 0.935c, 0.963 c and 0.984c . The green and red dots indicate the position of the photon on its helical trajectory, and the position of the TEQ relative to this helical trajectory. You can see that the smaller the radius of the helical trajectory, the faster the electron is moving: the red and green dots are further to the right for the smaller trajectory radii in the second figure (the figures are actually animated in my graphic program, so the dots move along the figures.)
>        Richard
> <moving electron animation spin half photon bitmap 1.bmp>
> <moving electron animation spin half photon bitmap 2.bmp>
> 
>> On May 22, 2015, at 11:41 PM, Richard Gauthier <richgauthier at gmail.com <mailto:richgauthier at gmail.com>> wrote:
>> 
>> Chip,
>>   Thanks for doing the graphic for the proposed spin 1/2 circulating photon composing a relativistic electron. I will send my graphics for this in 1-2 days. I have to transfer them from an old pc that has my 3D graphics program.
>>         Richard
>> 
>>> On May 22, 2015, at 6:18 AM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>> 
>>> Hi John W
>>>  
>>> Thank you.  We can Skype. Just let me know a good time.
>>>  
>>> Chip
>>>  
>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of John Williamson
>>> Sent: Friday, May 22, 2015 8:02 AM
>>> To: Nature of Light and Particles - General Discussion
>>> Subject: Re: [General] Electron Torus
>>>  
>>> Hello Chip,
>>> 
>>> Have been meaning to say for some time: you are producing some beautiful models.
>>> 
>>> Would be good to talk at some stage.
>>> 
>>> Regards. John (W)
>>> 
>>> 
>>> 
>>> 
>>> 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 Chip Akins [chipakins at gmail.com <mailto:chipakins at gmail.com>]
>>> Sent: Friday, May 22, 2015 1:59 PM
>>> To: 'Nature of Light and Particles - General Discussion'
>>> Subject: Re: [General] Electron Torus
>>> 
>>> Hi Richard
>>>  
>>> Sorry I was modeling what I though was the spin 1 photon model of the electron.
>>> This is what I perceive to be your spin ½ photon model of the electron to be with velocity.  Same velocity steps as before.
>>>  
>>> Nested set of models,
>>>  
>>> <image001.png>
>>>  
>>> Slow trajectory lines, purple, faster trajectory lines tending toward green.
>>>  
>>> Here is the code for the electron’s reference frame for the above graphic:
>>> X(ii)=Roc*(1/y^2+(1/y)*cosd(y*c*(t)/Roc))*cosd(y*c*(t)/Roc);
>>> Y(ii)=Roc*(1/y^2+(1/y)*cosd(y*c*(t)/Roc))*sind(y*c*(t)/Roc);
>>> Z(ii)=(Roc/y)*sind(y*c*(t)/Roc);
>>>  
>>> Note: there is still a very small electron model (with velocity 0.9988c) at the center of this graphic. In this model the contraction is in all directions, not just longitudinally.  I think this is correct, but it does not agree with some interpretations of relativity.  It is also difficult to see how this model, without spiral fields, would look the same to a moving observer when the electron is “at rest”.  
>>>  
>>> And the model is of course not really spherical.
>>> Does this match your results?
>>> Can you share the graphics model you have done?
>>>  
>>> Chip
>>>  
>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>> Sent: Friday, May 22, 2015 7:31 AM
>>> To: Nature of Light and Particles - General Discussion
>>> Subject: Re: [General] Electron Torus
>>>  
>>> John D., Chip and Andrew,
>>>  
>>>    Isn’t it the case that in standard physics (experimentally confirmed) the measured spin of an electron is relative to the motion of the observer of the electron, just as the observed momentum of an electron is relative to the motion of the observer of the electron? If an observer moving west to east with a relativistic velocity v1  passes a “stationary” electron (in some reference frame) , the electron has an observed momentum (when it measured) going west, and a spin either up or down (when it is measured) in the east-west direction  and a de Broglie wavelength corresponding to the relative velocity v1, while when an observer moving relativistically south to north with velocity v2 passes a “stationary" electron , the electron has an observed momentum (when it is measured) going south, a spin that is up or down (when it is measured) in the north-south direction, and a de Broglie wavelength corresponding to its relative velocity v2. (In QM,  velocity, spin and de Broglie wavelength probably can’t all be measured at the same time). 
>>>  
>>> The relativistic energy-momentum equation for the electron E^2 = p^2 c^2 + m^2 c^4 applies to the electron described above when observed by two observers with two different relativistic velocities compared to the electron. I showed in my article “the electron is a charged photon with the de Broglie wavelength” that the same relativistic energy-momentum equation applies to a helically moving double-looping photon that may compose an electron, where E is the energy of the photon (the same as the total energy of the electron composed by the photon), p is the longitudinal momentum of the helically moving photon (the same as the momentum p of the electron being modeled), E/c is the total momentum of the photon along its helical path, and mc is the transverse momentum of the helically moving photon, which contributes to the electron’s spin up or spin down value hbar/2 in the case of a slow moving electron (modeled by the double-looping photon). So every electron observed to have a momentum p will in this view also have a spin hbar/2 up or down in the direction of its momentum. 
>>>  
>>> Also, when a photon is Doppler shifted-due to relative motion of the light source away from or towards the observer, the observed wavelength of the photon is lengthened or shortened accordingly. Doesn’t this imply that the length of the whole photon (if it consists of a certain number of wavelengths) is also lengthened or shortened accordingly?
>>>  
>>> Richard
>>>  
>>>> On May 22, 2015, at 12:06 AM, John Duffield <johnduffield at btconnect.com <mailto:johnduffield at btconnect.com>> wrote:
>>>>  
>>>> David:
>>>>  
>>>> Why don’t photons get length contracted? Because they’re just waves in space moving at the speed of waves in space. A ripple in a rubber mat doesn’t get length contracted, nor do waves in space. Then when you make those waves go round and round, they still don’t get length-contracted. Then when you move past them fast, they still don’t get length contracted. You might say the path of those waves is different, but it isn’t, they didn’t change, you did. And if you boil yourself down to a single electron, and boil that down to a ring, then draw circles and helixes, I think it gets to the bottom of things. 
>>>>  
>>>> Chip:
>>>>  
>>>> Yes, I’m certain relative velocity is a determining factor.  But note that “we” are made of electrons and things, so IMHO it’s best to start with two particles, such as the electron and the positron. If you set them down with no initial relative motion they move linearly together, and we talk of electric force.  
>>>>  
>>>> <image005.jpg>
>>>> However if you threw the postiron over the top of the electron they’d move together and go around one another, whereupon we talk of magnetic force. Note that this is relative velocity, not relativistic velocity. I’ve seen people explain the magnetic field around the current-in-the-wire using length contraction <http://physics.stackexchange.com/questions/65335/how-do-moving-charges-produce-magnetic-fields>, but IMHO that’s a fairy tale, and I prefer a “screw” answer <http://physics.stackexchange.com/questions/184055/atomic-explanation-of-magnetic-field/184079?noredirect=1#comment388570_184079>.   
>>>>  
>>>> Regards
>>>> John D
>>>>  
>>>> From: General [mailto:general-bounces+johnduffield=btconnect.com at lists.natureoflightandparticles.org <mailto:general-bounces+johnduffield=btconnect.com at lists.natureoflightandparticles.org>] On Behalf Of Chip Akins
>>>> Sent: 21 May 2015 21:39
>>>> To: 'Nature of Light and Particles - General Discussion'
>>>> Subject: Re: [General] Electron Torus
>>>>  
>>>> Hi John D
>>>>  
>>>> Regarding…
>>>> Sorry, I don’t think that can be right because you could go past an electron at .9988c.
>>>>  
>>>> Yes, I am coming to think that maybe the spiral fields caused by limited field propagation velocity, might play a larger role than I had first considered.
>>>> I think Martin was onto this aspect already.
>>>> Wondering if relative velocity is a factor in determining what portion of the spiral field we detect or interact with? And if so, how that might work.
>>>>  
>>>> <image006.png>
>>>>  
>>>> The earlier electron model graphics are created from the math that Richard developed for his spin ½ electron.
>>>>  
>>>> Chip
>>>>  
>>>>  
>>>>  
>>>>  
>>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of John Duffield
>>>> Sent: Thursday, May 21, 2015 3:15 PM
>>>> To: 'Nature of Light and Particles - General Discussion'
>>>> Subject: Re: [General] Electron Torus
>>>>  
>>>> Chip:
>>>>  
>>>> Sorry, I don’t think that can be right because you could go past an electron at .9988c.
>>>>  
>>>> Andrew:
>>>>  
>>>> Photons don’t get length contracted, and electrons are made out of photons in pair production. If you simplify the electron to a photon going round in a circle, then take one point on the circumference, you would say it describes a circular path. But when you move past the electron fast, you would say that point was describing a helical path. Then when you consider all points of the circumference, you might say the electron was a cylinder rather than a circle. And if you were that electron, everything to you would look length-contracted, because you’re smeared out. If I was a motionless  electron you’d say I was length contracted. But I might say I was the one moving, and that you’re length-contracted.  
>>>>  
>>>> Regards
>>>> John
>>>>  
>>>> From: General [mailto:general-bounces+johnduffield=btconnect.com at lists.natureoflightandparticles.org <mailto:general-bounces+johnduffield=btconnect.com at lists.natureoflightandparticles.org>] On Behalf Of Chip Akins
>>>> Sent: 21 May 2015 17:52
>>>> To: 'Nature of Light and Particles - General Discussion'
>>>> Subject: Re: [General] Electron Torus
>>>>  
>>>> Hi Andrew
>>>>  
>>>> Images from the electron’s reference frame.
>>>>  
>>>> For Richard’s model using the spin 1 photon, and drawing in the electron’s reference frame, his math produces the following image for a set of nested electron models with velocities up to 0.9988c.
>>>> <image007.png>
>>>>  
>>>> The small grey sphere in the center is the electron model for 0.9988c. 
>>>>  
>>>> So in this model the electron shrinks in all directions, but remains principally spherical when viewed from the electron’s reference frame.
>>>>  
>>>> Chip
>>>>  
>>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Andrew Meulenberg
>>>> Sent: Thursday, May 21, 2015 11:15 AM
>>>> To: Nature of Light and Particles - General Discussion; Andrew Meulenberg
>>>> Subject: Re: [General] Electron Torus
>>>>  
>>>> Dear Chip,
>>>> 
>>>> I learn something new every time. However, it may not be true.
>>>> 
>>>> If I interpret your images properly, the fastest electrons are the longest. However, relativistic shortening should shrink the length. I had expected the electron to 'pancake' in the direction of motion. You show the opposite. Is the pancake only in the electron's frame and the appearance from our frame is one of an extended structure? If both, do they cancel and, in reality, it is still spherical?
>>>> 
>>>> Andrew
>>>>  
>>>> On Thu, May 21, 2015 at 7:36 PM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>>>> Hi Richard
>>>>>  
>>>>> So it is a bit more difficult to visualize exactly what is going on from the graphics with velocity.
>>>>>  
>>>>> We increase the velocity is in steps from zero through 0.9988c.
>>>>>  
>>>>> From the Z axis the illustration looks like:
>>>>> <image008.jpg>
>>>>>  
>>>>> Showing the reduced radius with velocity.
>>>>>  
>>>>> But when we look at the model slightly off axis (Z axis) we see this:
>>>>>  
>>>>> <image009.jpg>
>>>>>  
>>>>> So this is a set of nested electron models with different velocities, each starting from the same point (upper right of the illustration). These are drawn from an external observers frame and are not shown in the electron’s reference frame. 
>>>>>  
>>>>> In the electron’s reference frame we would see closure to the trajectory, but in this reference frame, the trajectory (since it is moving) is not closed.
>>>>>  
>>>>> Chip
>>>>>  
>>>>> From: General [mailto:general-bounces+chipakins <mailto:general-bounces%2Bchipakins>=gmail.com at lists.natureoflightandparticles.org <mailto:gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>>>> Sent: Thursday, May 21, 2015 6:29 AM
>>>>> 
>>>>> To: Nature of Light and Particles - General Discussion
>>>>> Subject: Re: [General] Electron Torus
>>>>>  
>>>>> Chip,
>>>>>    Please correct a couple of typos in my last email. The TEQ (transluminal energy quantum) moves on the surface of a torus, not a helix. Also the first helical radius mentioned should have been Ro sqrt(2) = 1.414 Ro , not Ro sqrt(2)/2 = 1.414 Ro since sort(2)/2 = 0.707 not 1.414 .  Thanks.
>>>>>     Richard
>>>>>  
>>>>>> On May 20, 2015, at 6:42 PM, Richard Gauthier <richgauthier at gmail.com <mailto:richgauthier at gmail.com>> wrote:
>>>>>>  
>>>>>> Chip,
>>>>>>      Nice graphics!
>>>>>>  
>>>>>>     Shouldn’t the electric field lines of an electron at some distance from the electron model be pointing inward linearly towards the electron from infinity on all sides, since the electron's electric field (due to its electric charge) falls off as 1/r^2 . I don’t understand why the electric field lines appear closed in your diagrams.
>>>>>>  
>>>>>>     In my original resting electron model the TEQ was a circulating negative electric charge which circulated on the surface of a helix. I called the circulating TEQ a photon-like object since it was similar to my TEQ model of a photon.  I was assuming at that time that the photon in my resting electron model had spin 1, even though I had adjusted the helical radius so that the circulating TEQ generated the magnetic moment of the electron of 1 Bohr magneton, requiring a helical radius for the TEQ of Ro sqrt(2)/2 = 1.414 Ro which created the spindle torus in my model . So this was actually neither a spin 1 photon (whose radius for a resting electron would have been 2Ro, or a spin 1/2 photon, whose radius for a resting electron would be Ro, as in the 3D models that you and I generated from the moving electron equations I proposed. Since I currently prefer the model of an electron composed of a spin 1/2 circulating photon, this doesn’t generate the electron’s magnetic moment of 1 Bohr magneton. But it generates a magnetic moment more than 1/2 Bohr magneton which would be produced by a charge circulating at light speed in a simple double loop of radius Ro. I haven’t done the calculation for the magnetic moment generated by my spin 1/2 photon model of the electron, but I suspect that it would be 0.707 Bohr magneton (just a guess at this point). The calculation of this magnetic moment from the TEQ trajectory equations for a charged TEQ in the spin 1/2 photon model is relatively straightforward though.
>>>>>>  
>>>>>>     By the way, have you looked at the side view of the actual TEQ trajectory at various values of v/c of the electron in the spin 1/2 photon moving-electron model that I proposed (and that you programmed and graphed in 3D to show how the model size changes as 1/gamma at various values of v/c)? The side view of the TEQ trajectory for a moving electron contains some surprises, at least for me. I thought that at high values of v/c (say 0.99 or 0.999) the TEQ would just appear from the side view to rotate helically around its reducing and increasingly more linear helical trajectory  (whose trajectory reduces as 1/(gamma^2), with the TEQ’s helical radius reducing as 1/gamma. But that’s apparently not what happens. Could you check this with your 3D program? 
>>>>>>  
>>>>>>      Richard
>>>>>>  
>>>>>>  
>>>>>>> On May 19, 2015, at 8:45 AM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>>>>>>  
>>>>>>> Hi Richard
>>>>>>>  
>>>>>>> If your spin 1 photon model of the electron is similar to John W and Martin’s model in that the field lines always orient with the negative end outwards (providing for charge) the estimated field distribution is similar to this illustration. (Equatorial View)
>>>>>>>  
>>>>>>> <image001.jpg>
>>>>>>>  
>>>>>>> (Top View from Z axis)
>>>>>>> <image002.jpg>
>>>>>>>  
>>>>>>> (45 degree elevation view)
>>>>>>> <image004.jpg>
>>>>>>>  
>>>>>>> Red lines represent negative ends of field lines, Blue lines represent positive, black is the transport radius, faint green line is one circulation at the transport radius.
>>>>>>> Photon field amplitude is shown as a cosine function of wavelength/2.
>>>>>>>  
>>>>>>> Chip
>>>>>>>  
>>>>>>>  
>>>>>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>>>>>> Sent: Tuesday, May 05, 2015 10:06 AM
>>>>>>> To: Nature of Light and Particles - General Discussion
>>>>>>> Subject: Re: [General] Electron Torus
>>>>>>>  
>>>>>>> Chip,
>>>>>>>    Perfect! It would also be good to have the pair of tori seen an an angle from above their ‘equator’ to get a more 3-D quality.
>>>>>>>       Richard
>>>>>>>  
>>>>>>>> On May 5, 2015, at 6:07 AM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>>>>>>>  
>>>>>>>> Hi Richard
>>>>>>>>  
>>>>>>>> How do these look?
>>>>>>>>  
>>>>>>>> <image003.png>
>>>>>>>> <image001.jpg>
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>> Chip
>>>>>>>>  
>>>>>>>>  
>>>>>>>>  
>>>>>>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>>>>>>> Sent: Monday, May 04, 2015 1:18 PM
>>>>>>>> To: Nature of Light and Particles - General Discussion
>>>>>>>> Subject: Re: [General] Electron Torus
>>>>>>>>  
>>>>>>>> Hi Chip,
>>>>>>>>   The radius of the circle in the horn torus (spin 1/2 photon model) should visually be (since it is actually) 1/2 of the radius of the circle in the spindle torus (spin 1 photon model) -- the spin 1/2 photon model is smaller than the spin 1 photon model. Thanks! And could you perhaps show the energy quantum trajectory in a different color that the torus background so the trajectory stands out better?
>>>>>>>>     Richard
>>>>>>>>  
>>>>>>>> On Mon, May 4, 2015 at 10:42 AM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>>>>>>>> Hi Richard
>>>>>>>>>  
>>>>>>>>> <image004.png>
>>>>>>>>>  
>>>>>>>>>  
>>>>>>>>> <image005.png>
>>>>>>>>>  
>>>>>>>>> Chip
>>>>>>>>>  
>>>>>>>>> From: General [mailto:general-bounces+chipakins <mailto:general-bounces%2Bchipakins>=gmail.com at lists.natureoflightandparticles.org <mailto:gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>>>>>>>> Sent: Monday, May 04, 2015 12:19 PM
>>>>>>>>> To: Nature of Light and Particles - General Discussion
>>>>>>>>> Subject: Re: [General] Electron Torus
>>>>>>>>>  
>>>>>>>>> Hi Chip,
>>>>>>>>>    Thanks. And finally, the vertical ovals of the tori should be circles because the circulating quantum has the same radius in the vertical and horizontal directions.
>>>>>>>>>         Richard
>>>>>>>>>  
>>>>>>>>>> On May 4, 2015, at 9:32 AM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>>>>>>>>>  
>>>>>>>>>> Hi Richard
>>>>>>>>>>  
>>>>>>>>>> Thank you.
>>>>>>>>>>  
>>>>>>>>>> Here you go:
>>>>>>>>>> <image001.png>
>>>>>>>>>>  
>>>>>>>>>> <image002.png>
>>>>>>>>>>  
>>>>>>>>>> Chip
>>>>>>>>>>  
>>>>>>>>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>>>>>>>>> Sent: Monday, May 04, 2015 10:43 AM
>>>>>>>>>> To: Nature of Light and Particles - General Discussion
>>>>>>>>>> Subject: Re: [General] Electron Torus
>>>>>>>>>>  
>>>>>>>>>> Hi Chip,
>>>>>>>>>>   Both tori should be symmetrical above and below the z-axis and center on z=0.
>>>>>>>>>>       Richard
>>>>>>>>>>  
>>>>>>>>>>> On May 4, 2015, at 8:16 AM, Chip Akins <chipakins at gmail.com <mailto:chipakins at gmail.com>> wrote:
>>>>>>>>>>>  
>>>>>>>>>>> Hi Richard
>>>>>>>>>>>  
>>>>>>>>>>> <image001.jpg>
>>>>>>>>>>>  
>>>>>>>>>>> Viewed from the Z axis:
>>>>>>>>>>> <image002.jpg>
>>>>>>>>>>>  
>>>>>>>>>>> And from the equatorial plane:
>>>>>>>>>>> <image003.jpg>
>>>>>>>>>>>  
>>>>>>>>>>> Chip
>>>>>>>>>>>  
>>>>>>>>>>> From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org <mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org>] On Behalf Of Richard Gauthier
>>>>>>>>>>> Sent: Sunday, May 03, 2015 11:07 PM
>>>>>>>>>>> To: Nature of Light and Particles - General Discussion
>>>>>>>>>>> Subject: Re: [General] position
>>>>>>>>>>>  
>>>>>>>>>>> Chip and all,
>>>>>>>>>>>    Here are some equations that relate to the modeling of a circulating photon as an electron. The second and third set include my own model of the photon. The first set doesn’t require a particular model for the photon, except as mentioned below. The first model is the one that generates the de Broglie wavelength as explained in my article mentioned below.
>>>>>>>>>>>  
>>>>>>>>>>> 1. Here is the set of parametric equations for the helical trajectory of double-looping photon that models a free electron, and  whose circular radius for a resting electron is Ro=hbar/2mc. The speed of the photon along this trajectory is always c. The longitudinal or z-component of the photon’s speed is the electron’s velocity v along the z-axis. The frequency of the photon around the helical axis is proportional to the circulating photon/electron's energy E=gamma mc^2. The distance of the photon’s helical trajectory from the z-axis for an electron whose speed is v, is proportional to 1/gamma^2. This equation is in my article “The electron is a charged photon with the de Broglie wavelength”. This equation does not include a particular model of the photon, but assumes that the photon follows the relations c=f lambda, E=hf and p=h/lambda. Both helicities of the helical trajectory are given.
>>>>>>>>>>> _______________________________________________
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>>>>>>>>>> 
>>>>>>>>>>  
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