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### How did Einstein arrive at E=mc^2?

Posted: Thu Jun 30, 2011 8:30 pm
And how come the measure of joule turns out to be fitted so neatly to the measure of m/s?

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 01, 2011 5:34 am
Jakob wrote:And how come the measure of joule turns out to be fitted so neatly to the measure of m/s?

All I can tell you currently is that the E=mc^2 is only the first term of an infinite series. The rest of the real equation was proven to be insignificant. He used the Lorentz transformations to calculate the energy involved in acceleration and discovered that even a mass at rest must still have that amount of energy.

Why is one meter so perfectly and exactly 100.000... centimeters?
The joule fits so neatly because it was defined to fit so neatly, as were all of the metric standards.

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 01, 2011 1:03 pm
Jakob: have a read of Does the Inertia of a Body Depend upon its Energy-Content? Einstein wrote an L instead of an E, and ended up saying: If a body gives off the energy L in the form of radiation, its mass diminishes by L/c².

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 01, 2011 5:05 pm
Einstein guessed that E = mc^2. He was not smart enough to prove it.

I was told that it was Bohr proved it, but I am not sure.

Additionally, Einstein lied about his knowledge of previous estimates. I think one was E = m(c^2)/4. Maybe Poincare? Not sure.

Ed

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 01, 2011 6:48 pm
Jakob wrote:how come the measure of joule turns out to be fitted so neatly to the measure of m/s?

This is just SI units matching up:

Energy (J) = force (N) x distance (m)
Force (N) = mass (kg) x acceleration (m/s^2)

Substitute the force equation into the energy one:
Energy (J) = mass (kg) x acceleration (m/s^2) x distance (m)

The units "m/s^2" x "m" -> (m/s)^2, which is the units of speed, squared.
So joules are expressable in the units of mass x speed^2

Why the "speed" bit is the speed of light is another story.

Mess around with equations enough and you get all sorts matching up:
Power = energy/time (P=E/t) and, also, power = current x voltage (P=IxV)

So E = IVt = mdd/tt (mass x speed^2), so mass = current x voltage / area (distance^2) x time^3
Mass as expressable through a relationship between amps, volts, area and time?!

What is an area of "time cubed" anyway? A 6th dimensional portal between space-time probabilities? Along with measures of electricity? Hello, sci-fi.

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 01, 2011 10:34 pm
Energy is formed by inertia in motion.. m and c

### Re: How did Einstein arrive at E=mc^2?

Posted: Sat Jul 02, 2011 10:42 pm
James S Saint wrote:Energy is formed by inertia in motion.. m and c

Is it wrong to say that c^2 represents the way a paired photon revolves around itself?
At least this was my intuition, that c^2 represents spin.

### Re: How did Einstein arrive at E=mc^2?

Posted: Sat Jul 02, 2011 11:54 pm
Jakob wrote:
James S Saint wrote:Energy is formed by inertia in motion.. m and c

Is it wrong to say that c^2 represents the way a paired photon revolves around itself?
At least this was my intuition, that c^2 represents spin.

Actually, I deal more with pre-energy "subspace" but your question has got me thinking a little on this matter (mass).
The term "mass" in physics is a little ambiguous but essentially relates to either inertia or gravitational effect. Something is called "massless" when it has neither of those properties even though it is still given a "mass equivalence". Technically, metaphysically, nothing can exist without the property of inertia because that term merely means "reluctance to change".

But if we consider that a photon is a spinning entity that travels forward at the speed of light (by definition), then any actual spin posses an interesting conclusion. If something is moving forward and also spinning, that which is spinning within is actually traveling faster than the over all object. Assuming the spin was at the speed of light and the object was also traveling at the speed of light, the inner wave would represent an affect that was changing at a rate of sqrt(2) = 1.414 times the speed of light. I haven't gotten far enough along with my project to determine whether subspace maximum travel speed is greater than that of photon travel, but I'm getting more suspicious every day.

But the idea of energy came from the notion of how much effort it takes to accomplish "work" or to cause any degree of change. It began, from the equation F = ma because the change being considered was the total effort required to move something against gravity, or any constant acceleration. Once anything reaches any particular speed, given no resistance, by definition it will continue without effort. So only issues of changing something's speed were of interest.

Forces are always applied between two things rather than merely "from" something as many tend to think. So the issue is how much force for how long of a time is required to overcome the inherent inertia (reluctance to be changed) within 2 objects in order to accomplish a degree of changing in state within a degree of time, a velocity per time.

The reluctance is an issue of the inner wave already traveling at a maximum value, so of course the speed of light, or more properly, the speed of affect, would have to come into play in determining the actual amount of inertia or mass each object had in the first place. Then it all becomes a question of how much effort is going to be required to force against said inertia enough to cause a separation at any particular rate. "F = ma" was measured to be pretty exact, but of course it depends on how exactly the terms are defined and in regards to what.

If you multiply the reluctance to change times the speed of changing, you get a value related to m*c. But that assumes no acceleration and basically describes the momentum of an object, inertia in relative motion. But anything already in motion isn't requiring any effort. To get a measure of how much effort it takes to get anything up to a speed, we have to multiply that momentum concept times the speed involved, and thus "Effort = m*c^2".

But all of that is merely referring to energy between objects due to their inertia, not how much potential is within an object to yield that effort if released to do so.

Inside any particle, we have the reluctance to change that is already traveling at a maximum change rate, c' . But it is also curving into a sphere or bundle and thus accelerating by virtue of constant change in direction rather than linear acceleration. And that changing in direction would be occurring at the max speed of change as well. Thus within any particle, we have the reluctance to change, the inertia or mass times its internal speed of changing times its speed of turning =>

Inner Effort = m*c'*c' = mc^2. Again, assuming that the speed of affect is the speed of light or close to it.

I'm sure Einstein didn't take that route at all in his derivation, but it seems that he would have been right in his conclusion merely from a superficial analysis of what is going on. Eventually, if I can complete my project, I can tell you far more precisely exactly what is going on and exactly how much "energy" is related to any inertia (although to relate it to mass would require physics to get their definitions more coherent and precise).

### Re: How did Einstein arrive at E=mc^2?

Posted: Mon Jul 04, 2011 8:35 pm
Thanks for all your explanations, I am grateful for such solid context, this does not happen a lot in philosophy. Still I am forced to think as if this were philosophy since I do not master algebra anywhere near to the extent that I can creatively handle concepts in it.
James -
Inner Effort = m*c'*c' = mc^2. Again, assuming that the speed of affect is the speed of light or close to it.

If mass increases with its acceleration relative to another mass, does perhaps the inner speed of affect within that mass decrease? Perhaps c pertains to the integrity of an object as such.

I was thinking somewhat in similar lines as you do here, when I came up with that spin connection. But it's more like a moving picture than a step by step explanation. I can't fit it in terms of logic, my mind needs more stretch to wrap it around the whole concept of multiplying an absolute to its own power.

If you multiply the reluctance to change times the speed of changing, you get a value related to m*c.

What exactly do you mean by the speed of changing, as opposed to the speed of turning?
Please elaborate on the speed of changing as it partakes in an electron, I have to get a bit more context of the physical interactivity to picture this.

### Re: How did Einstein arrive at E=mc^2?

Posted: Mon Jul 04, 2011 11:34 pm
Jakob wrote:
Inner Effort = m*c'*c' = mc^2. Again, assuming that the speed of affect is the speed of light or close to it.

If mass increases with its acceleration relative to another mass, does perhaps the inner speed of affect within that mass decrease? Perhaps c pertains to the integrity of an object as such.

Actually, it is the inertia (mass) that pertains to the integrity of anything (it's "materialness") but the speed of changing relates to that integrity/inertia. And that inertia increases with acceleration.
Jakob wrote:
If you multiply the reluctance to change times the speed of changing, you get a value related to m*c.

What exactly do you mean by the speed of changing, as opposed to the speed of turning?
Please elaborate on the speed of changing as it partakes in an electron, I have to get a bit more context of the physical interactivity to picture this.

This is getting into the fundamentals of Rational Metaphysics and I haven't prepped a thesis on that yet, but..

Metaphysics of Particles
In Rational Metaphysics, we have;
1) Affect, "a"
2) Potential to affect, "p"
3) Potential of potential to affect, "m"

Affect is exactly what the word means, to alter or change [anything]
Potential to affect means the ability to affect [the universe] once the surrounding situation provides for a means.
Potential for the potential is a little more complicated, but it is just what it says.

If you have an apple, you have an affector/entity (the physical universe is nothing but affect upon affect, affectors affecting affectees).
If you place that apple upon a table, you have the potential for the apple to fall, an effect.
If you haven't placed the apple upon the table yet, but can, you have the potential for the potential for the apple to fall.

These 3 quantities are critical in all existence. They are analogous to (and the meta-form of) the physics;

1) electric current (affecting in process)
2) electric field (electric potential)
3) magnetic field (potential for the electric field)

These 3 fields cause the mass that you are talking about.

Affecting means changing. That is simply what the word means. So you could merely say;

1) Changing
2) Potential to change
3) Potential to potentially change

All of these fields create what we call "time" and "distance/dimensions"; "spacetime", "space", "fabric of space, "space-time continuum".

Within a particle, these fields are relocating/repositioning constantly in a pattern. That is what I have been referring to as a "bundled"/"quantumized" electromagnetic field (EM field) "chasing its tail".

As the affecting of affect (changing of potential to affect) takes place, the potential to affect relocates, moves its higher density center, much like a wave moving on the ocean surface except in 3D. In an ocean wave, the water itself is not moving as the wave although it does have a little forward motion involved. The water is rising, giving the wave potential to fall. As that potential actualizes (effects a falling), the center of the wave propagates. Laterally, the water stays where it was. The wave center propagates, not the water. Similarly, but more purely, subspace (the field of affectance) doesn't move but instead the center of potential to affect relocates to cause what we call an "EM wave". In a very real sense, nothing in the universe actually ever moves (depending on what we call a "thing"), but rather merely gives up its potential to exist over to the next position in subspace. You might have to reread that a few times. I need pictorials for a more formal explanation.

Such waves in subspace necessarily always travel at the speed of affect (the maximum speed any affect can take place). And also the potential to affect, p, cannot increase/decrease any faster than the maximum speed of affect. But because it is "moving" at the maximum rate and can move no faster, any effort to cause it to move faster is met with reluctance. So when things get "pushed", p increases, but the actual affecting, a, cannot happen any faster. So the entity doesn't immediately move as the force being applied would request. It displays "inertia" and must build up to the force's requested speed. As p actualizes into a forward relocating, a, a "motion", the entity appears to have moved forward. But because it was pushed into a situation of creating a higher p, before affecting, it continues to move forward even after the pushing stops, p causes a which causes p ad infinitum. This is the effect we call momentum. (I intentionally left out the issue of "m" just to simplify. It plays into why the wave turns).

In the case of a particle (your electron or any particle), that relocating is happening in a bundled fashion, a 3D circling wave. The relocating is happening a c' (the speed of affect). What is relocating is the reluctance to affect (the potential being pushed to its limit). So what we have is the inertia traveling at c' as the momentum effect. But the motion isn't merely in a straight line. It is being "pulled" (or "pushed" depending on perspective) transverse to its direction of affect. The potential to affect is being coerced into relocating to one side of where it was headed. That requires an additional "force" (forces, pushing and pulling, don't really exist in subspace, but we are accustom to thinking in such terms).

So we have a case in a particle of a momentum that is being forced to constantly change its velocity. That is a constant effort, also known as a constant "energy". The force is the result of the maximum speed for the potential to relocate, c'. But there is also the force that is the result of the circular relocating at the maximum speed, c'. So the end total effort involved, the "energy", will be related to the inertia (expressed as mass, "m") multiplied by the speed, c' and again by that same speed: E = mc'^2.

Sorry for that not being more clearly worded. Like I said, I don't have anything written down on all of this except within my program (in programese). My PC is the only thing that listens to me so it is only in its language (machines learn faster than homosapians)..

### Re: How did Einstein arrive at E=mc^2?

Posted: Wed Jul 06, 2011 11:06 pm
Jakob wrote:Is it wrong to say that c^2 represents the way a paired photon revolves around itself? At least this was my intuition, that c^2 represents spin.
Yes. In the electron the photon revolves around itself with a c^2.5 factor. It isn't a paired photon.

### Re: How did Einstein arrive at E=mc^2?

Posted: Thu Jul 07, 2011 12:05 am
Saint, I think you make a lot of sense. It takes time to process though.

Farsight wrote:
Jakob wrote:Is it wrong to say that c^2 represents the way a paired photon revolves around itself? At least this was my intuition, that c^2 represents spin.
Yes. In the electron the photon revolves around itself with a c^2.5 factor. It isn't a paired photon.

Ah, I thought this was what pair-production was about.

my question then becomes: how does what precisely (in physical terms?) arrive at the c^2.5 factor?

### Re: How did Einstein arrive at E=mc^2?

Posted: Thu Jul 07, 2011 1:47 am
An electron is extremely small compared to a photon, so don't go thinking in terms of merely a couple of photons spinning around each other and forming an electron. Just because you get photons formed after you breakup an electron, doesn't mean there were tiny little photons inside just waiting to puff up and be free.

### Re: How did Einstein arrive at E=mc^2?

Posted: Thu Jul 07, 2011 11:33 am
Jakob wrote:Ah, I thought this was what pair-production was about.
In pair production you start with a photon and "split it" into two to make an electron and a positron. If you annihilate an electron with a positron you typically get two photons. Think of the electron as one photon going round and round, and the positron as another.

Jakob wrote:my question then becomes: how does what precisely (in physical terms?) arrive at the c^2.5 factor?
I can't tell you I'm afraid. I saw it in a draft paper, and I promised I wouldn't reveal any details until after the paper is published. I probably shouldn't have mentioned the 2.5.

James S Saint wrote:An electron is extremely small compared to a photon, so don't go thinking in terms of merely a couple of photons spinning around each other and forming an electron. Just because you get photons formed after you breakup an electron, doesn't mean there were tiny little photons inside just waiting to puff up and be free.
The photon is a wave, it doesn't really have a size, like that picture you put up where you mentioned standard deviations. The electron has a wavelike nature, it doesn't really have a size either. The smallness that people talk about it something like the smallness of the eye of a storm. Think of the electron's electromagnetic field as being "part of what it is".

### Re: How did Einstein arrive at E=mc^2?

Posted: Thu Jul 07, 2011 2:28 pm
James S Saint wrote:An electron is extremely small compared to a photon, so don't go thinking in terms of merely a couple of photons spinning around each other and forming an electron. Just because you get photons formed after you breakup an electron, doesn't mean there were tiny little photons inside just waiting to puff up and be free.

Farsight wrote:In pair production you start with a photon and "split it" into two to make an electron and a positron. If you annihilate an electron with a positron you typically get two photons. Think of the electron as one photon going round and round, and the positron as another.

James & Farsight, I can't make sense of your texts together. They seem to contradict.

Farsight - if one foton becomes an electron and a positron, why do the latter two when they collide or merge become two fotons? Could these fotons then also be merged again into one "heavier" foton?

Jakob wrote:my question then becomes: how does what precisely (in physical terms?) arrive at the c^2.5 factor?
I can't tell you I'm afraid. I saw it in a draft paper, and I promised I wouldn't reveal any details until after the paper is published. I probably shouldn't have mentioned the 2.5.

Well, thanks anyway, I'd hate to be straining myself to understand things that aren't even so.

### Re: How did Einstein arrive at E=mc^2?

Posted: Thu Jul 07, 2011 7:13 pm
What's New;
Einstein’s derivation of E=mc^2 wrote:Assuming that bodies at rest with zero mass necessarily have zero energy, this implies the famous formula E = mc^2 – but only for bodies which are at rest. For moving bodies, there is a similar formula, but one has to first decide what the correct definition of mass is for moving bodies; I will not discuss this issue here, but see for instance the Wikipedia entry on this topic.

Broadly speaking, the derivation of the above proposition proceeds via the following five steps:

Using the postulates of special relativity, determine how space and time coordinates transform under changes of reference frame (i.e. derive the Lorentz transformations).

Using 1., determine how the temporal frequency \nu (and wave number k) of photons transform under changes of reference frame (i.e. derive the formulae for relativistic Doppler shift).

Using Planck’s law E = h\nu (and de Broglie’s law p = \hbar k) and 2., determine how the energy E (and momentum p) of photons transform under changes of reference frame.

Using the law of conservation of energy (and momentum) and 3., determine how the energy (and momentum) of bodies transform under changes of reference frame.

Comparing the results of 4. with the classical Newtonian approximations KE \approx \frac{1}{2} m|v|^2 (and p \approx mv), deduce the relativistic relationship between mass and energy for bodies at rest (and more generally between mass, velocity, energy, and momentum for moving bodies).

### Re: How did Einstein arrive at E=mc^2?

Posted: Thu Jul 07, 2011 8:15 pm
Jakob wrote:James & Farsight, I can't make sense of your texts together. They seem to contradict.
They shouldn't. There will be some differences in the language and the detail, but it's the same general picture.

Jakob wrote:Farsight - if one foton becomes an electron and a positron, why do the latter two when they collide or merge become two fotons? Could these fotons then also be merged again into one "heavier" foton?
It's a bit like two opposite knots cancelling each others' knottedness to free up the photon that's configured as an electron and the photon that's configured as the positron. Yes, you can merge two photons to create one photon with half the wavelength. At least I think you can. You can definitely split a photon into two photons with double the wavelength, and most things in physics are reversible because they're just wavefunction configuration changes.

Jakob wrote:Well, thanks anyway, I'd hate to be straining myself to understand things that aren't even so.
No probs. When I can tell you, you'll appreciate that It's horribly simple.

### Re: How did Einstein arrive at E=mc^2?

Posted: Sun Jul 10, 2011 1:31 pm
Assuming that bodies at rest with zero mass necessarily have zero energy, this implies the famous formula E = mc^2 – but only for bodies which are at rest.

I don't understand. Can such a rationale not produce justification for any formula? If values on both sides of the equation are zero, how much can this imply?

Jakob wrote:
James S Saint wrote:An electron is extremely small compared to a photon, so don't go thinking in terms of merely a couple of photons spinning around each other and forming an electron. Just because you get photons formed after you breakup an electron, doesn't mean there were tiny little photons inside just waiting to puff up and be free.

In what way do you mean "small"? I don't so much think in terms of spatial size with these things, rather in quantum of energy. I thought you meant the electrons quantum of energy is small compared to the photons - where I thought the energy of one form becomes the energy of another.

### Re: How did Einstein arrive at E=mc^2?

Posted: Sun Jul 10, 2011 11:24 pm
What are the minimum and maximum electrical charges of a photon and of an electron?

### Re: How did Einstein arrive at E=mc^2?

Posted: Mon Jul 11, 2011 12:36 am
Jakob wrote:What are the minimum and maximum electrical charges of a photon and of an electron?

In physics, photons don't have charge and an electron has (amazingly) exactly 1 electron volt.
{{ seems suspiciously like Intelligent Design to me..hmm..}}

### Re: How did Einstein arrive at E=mc^2?

Posted: Mon Jul 11, 2011 11:24 am
Sorry for continuing to ask silly questions James (I got that Joule-joke the first time though)
I am just curious as to the type of changes that happen between an electron and a photon.

How does the energy of a photon amount to electrical charge in an electron? What exactly is electrical charge?

### Re: How did Einstein arrive at E=mc^2?

Posted: Mon Jul 11, 2011 3:03 pm
Jakob wrote:Sorry for continuing to ask silly questions James (I got that Joule-joke the first time though)
I am just curious as to the type of changes that happen between an electron and a photon.

How does the energy of a photon amount to electrical charge in an electron? What exactly is electrical charge?

Well, before I get into another lengthy and boring lecture on Rational Metaphysics, I need to know whether, when speaking to me, you are asking of the physics or of the Truth. Physics can only determine measurements between the measured. Science is an effort to reverse engineer nature using nature. Rational Metaphysics is the mental engineering of nature taken from the Genesis approach, starting from "nothing" and building up to what can be measured.

But then realize also that Rational Metaphysics is a mountain growing from under the sea ("subspace") and hasn't yet reached the surface where it meets the theories of Science and can be clearly seen.

In physics, electric charge is simply the attraction between positive and negative particles. That attraction constitutes a "field" involving distance and volume. Physics can't tell you why anything is so, but only that it is so (after they give "names to the creatures/creations of the field"). They give you the names and their distinction from the other named creations. Rational Metaphysics gets into exactly why they are positive or negative and why they attract but such is a much more complicated explanation and not entirely ready for display (reached the surface of the sea).

### Re: How did Einstein arrive at E=mc^2?

Posted: Mon Jul 11, 2011 6:10 pm
Jakob wrote:How does the energy of a photon amount to electrical charge in an electron?
It doesn't. A photon might have an energy of 0.511MeV, which is the "rest energy" of an electron, but the photon has zero charge, whilst the electron charge is −1.602×10^−19 Coulombs. See http://en.wikipedia.org/wiki/Electronvolt and http://en.wikipedia.org/wiki/Electron#F ... properties. Energy and charge are different.

Jakob wrote:What exactly is electrical charge?
It's a "standing electromagnetic field variation" with a particular disposition. The photon or electromagnetic wave is an electromagnetic field variation that goes past you at c. The field variation is sinusoidal, with a positive followed by a negative. If you fix this so that it's going round and round in a stable configuration where the negative field variation is on the outside, what you've got is a negatively charged particle.

If you want to get more fundamental, the electromagnetic wave is a wave of displacement current. A charged particle is where you've got an isotropic all-round spatial displacement which diminishes with distance.

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 15, 2011 2:55 pm
James S Saint wrote:Well, before I get into another lengthy and boring lecture on Rational Metaphysics, I need to know whether, when speaking to me, you are asking of the physics or of the Truth. Physics can only determine measurements between the measured. Science is an effort to reverse engineer nature using nature. Rational Metaphysics is the mental engineering of nature taken from the Genesis approach, starting from "nothing" and building up to what can be measured.

In the end thats what Im interested in.

But then realize also that Rational Metaphysics is a mountain growing from under the sea ("subspace") and hasn't yet reached the surface where it meets the theories of Science and can be clearly seen.

Great to hear that it's progressing toward the surface.

Farsight wrote:
Jakob wrote:What exactly is electrical charge?
It's a "standing electromagnetic field variation" with a particular disposition. The photon or electromagnetic wave is an electromagnetic field variation that goes past you at c. The field variation is sinusoidal, with a positive followed by a negative. If you fix this so that it's going round and round in a stable configuration where the negative field variation is on the outside, what you've got is a negatively charged particle.

Wow, that's a great explanation. From my perspective very useful, at least. If this means that we could (if we were to distinguish categories "force" and "form") classify electrical charge in the category of form.
That sheds a new light on the compatibility of positive and negative charges.

Is there an analogous explanation for a positive charge?

### Re: How did Einstein arrive at E=mc^2?

Posted: Fri Jul 15, 2011 7:15 pm
Jakob wrote:Wow, that's a great explanation. From my perspective very useful, at least.
Thanks Jakob. One of the reasons I talk on forums is to try to hone the descriptions to get them as brief and clear and robust as possible. It's nice to get some feedback that says I'm hitting the mark.

Jakob wrote:If this means that we could (if we were to distinguish categories "force" and "form") classify electrical charge in the category of form.
I guess so. I probably would have said geometry, but that's "form" I suppose. But note the distinction is probably not so much between force and form as between fundamental and form. In electromagnetism there's the electrostatic force and the magnetic force, both of which are the result of the electromagnetic field. Some would say they're the result of charge, but charge isn't fundamental. You can create and destroy charge via pair production and annihilation. You can liken this to angular momentum - if you're an astronaut in space poised in front of a satellite and neither of you are spinning, it's like there's no charge. If you grab the satellite and spin it clockwise, you'll find that the reaction causes you to spin anticlockwise. Angular momentum is conserved - there wasn't any, now there is, but it nets to zero.

Jakob wrote:That sheds a new light on the compatibility of positive and negative charges. Is there an analogous explanation for a positive charge?
You could say that the positive field variation is on the outside, but it's probably better to get a handle on the "form" of a charged particle like an electron. It's a spin ½ particle. I think it's something like this, with a steering-wheel spin along with a smoke-ring spin:

Reverse the direction of the arrowhead to go from an electron to a positron. That's like going from clockwise to anticlockwise, only in three dimensions. See http://www.cybsoc.org/cybcon2008prog.htm#jw for background reading. The authors of Is the electron a photon with a toroidal topology? were at CERN for 6 years and know their stuff, but this paper has been largely overlooked. Or perhaps "studiously ignored" is closer to the mark. Funny old business is physics.