Re: an electron question

FrediFizzx a écrit : 
"srp" <srp2@xxxxxxxxxxxxxxxx> wrote in message
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|FrediFizzx a écrit :
|>"srp" <srp2@xxxxxxxxxxxxxxxx> wrote in message
|>news:43C7EA49.8000602@xxxxxxxxxxxxxxxxxxx
|>| FrediFizzx a écrit :
|>| > "srp" <srp2@xxxxxxxxxxxxxxxx> wrote in message
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[snip]

| > |
| > | Indeed! Wish I had that option on my hand calculator.
| > |
| > | Hey, maybe you'd be curious about my latest baby:
| > |
| > |
http://pages.globetrotter.net/srp/discrete_electromagnetic_fields.pdf
| > |
| > | Totally mks however :-]
| > |
| > | André Michaud
| >
| > Hi André,
| >
| > Read your paper above. Your equation (34) seems to be 6 orders | > of magnitude too big for the absolute value of the B_0 magnetic field
| > of a photon. This is easy to see in your conversion to the |E_0| | > field in equation (38). Plugging in a 10 centimeter wavelength gives | > a value of
| > about 14.6 volts/meter. This certainly has to be way too big for a
| > photon with a 10 cm wavelength. I am getting deja vous here. ;-) I
| > think we were discussing this before a few months ago. My
| > calculations give me about 1.06E-5 volts/meter for a 10 cm photon. | > Which seems much more reasonable. In SI units my equations for a | > free space photon are,
| >
| > |E_0| = e/(2*eps0*sqrt(alpha)*lambda^2)
| >
| > |B_0| = mu0*e*c/(2*sqrt(alpha)*lambda^2)
| >
| > So I think you made a mistake somewhere leading up to equation (34)
| > but I have not pin-pointed it yet. I am sure it has something to | > do with the 1/alpha^3 factor. I don't know exactly what you mean | > by "absolute" wavelength either.
|
| OK, I'll definitely look again (thanks for caring to have a look
| yourself). I remember the conversation we had but I couldn't pinpoint
| either any error in my sequence of derivation from Marmet's equations
| at the time, and I trippled checked that Marmet's derivation were
| clean to start with.
|
| What comforts me that there may be no mistake, despite appearences,
| is that the actual relativistic velocities of the electron can be
| calculated with precision for any carrying energy from these
| derivations.
|
| But I will recheck your point.

Well, we can do some simple dimensional analysis also.  The energy of a
photon is E = hbar*w; it should also be of the order of E =
eps0*E_0^2*volume.  Equating we get,

|E_0| = sqrt(hbar*w/(eps0*vol))

We can sub 2pi*c/lambda for w,

|E_0| = sqrt(2pi*hbar*c/(eps0*vol*lambda))

Assuming the volume is of order of the photon wavelength we sub lambda^3
(IOW, a *whole* photon of a certain wavelength can't really fit in a
volume much smaller than this--it maybe comes out to lambda^3/2pi in
actuality),

|E_0| = sqrt(2pi*hbar*c/eps0)(1/lambda^2),

and we note that sqrt(2pi*hbar*c) = e/sqrt(2*eps0*alpha),

|E_0| = e/(eps0*sqrt(2*alpha)*lambda^2)

So we can see that this is only different from my original |E_0| by a
factor of 1/sqrt(2).  For your equation (40), I think you would have to
have a volume that a whole photon wouldn't fit into.  It would be much
too small wrt its wavelength.  Some time ago, I ran across a Cavity QED
experiment that was using an expression close to mine in value for E_0
of a photon and getting sensible answers, but I can't find the
experiment now.  I think they were simply using,

|E_0| = sqrt(hbar*c)/lambda^2 in cgs units.  Mine is,

|E_0| = 2pi*sqrt(hbar*c)/lambda^2 in cgs units.

So I am pretty sure it is close to being correct.  At least of the same
magnitude.


Ok, I'll analyze what you are saying here. But from the calculations
I just made, I can tell you that I agree with your equations (I'll
explain further next), so what you just wrote will most probably
also make sense to me upon analysis.

When I say I agree with your equations for E_0 and B_0. Upon
resolving vor U, we obviously obtain the total amont of energy
in joules for one .1 meter wavelength photon if it were alone
in one cubic meter of space, but on the other hand, this doesn't
localize the energy of the photon anywhere into that volume as
a local lump of energy, an energy that if it were concentrated
in a local lump, would locally have a density way higher (per
cubic meter) than if it were evenly spread out over the whole
unit volume of 1 m^3.

IF you analyze Marmet's paper, you will see that he integrates
the magnetic energy of the electron from infinity to r_c
precisely to localize it (concentrate it in a local lump of
energy that more closely corresponds to the electron being
a localized particle.

Upon close analysis, that r_c (the electron classical radius)
simply is the absolute amplitude of the wavelength of the
electron divided by alpha.

alpha has this value simply because integrating any nearer
to r=0 would accumulate too much energy and any further from
r=0 would not accumulate enough energy to account for the
verified complement of energy making up the mass of the
electron.

I found that this inferior limit of integration
(lamda/2pi)/alpha turns out to corresponds a universal lower limit
of integration for any such spherical integration from infinity.

The 3 alpha you find in my equation (alpha^3) corresponds to
the spherical integration of the three aspects of EM energy in
the 3 spaces model electric, magnetic, and "energy sustaining the
velocity of the particle"

The result is to give the mean "local" energy density within
the mean volumes that the cycling energy of the particle will
occupy, which, being way smaller than the reference 1 cubic
meter volume, you will certainly relate to the fact that that
local density will be higher, and most probably by many orders
of magnitude than if the photons energy was spread out over
the total reference volume.

These local densities are what my E and B give.

As for the associated volumes, I simply don't know how to assess
them precisely since the energy probably is constantly pulsating
(cycling between E and B states) as it moves. They may even have
little to do with the actual wavelength, which, if you think about
it, is simply the physical distance covered by a photon during
one cycle of its frequency. The varying volume aspect remains
to be addressed.

There probably is a yet to be found way to brige the gap between
your E and B equations for "uniformly spread energy into the
reference volume" and my E and B equations for "localized lump
of energy within the reference volume"

| By "absolute wavelength", I mean the wavelength that the energy
| making up the rest mass of a particle would have it if were free
| energy,
|
| Lambda_A = h / m c
|
| For the carrying energy, it is the wavelength that this energy
| would have if it was free (not carrying a massive particle)
|
| Lambda_A = hc / E
|
| For example, the absolute wavelength of the energy making up
| the rest mass of the electron would be Compton wavelength,
| of course
|
| André Michaud

OK, I guess you mean an invariant type of wavelength. 

Yes. The wavelength that any amount of energy would have it
was moving at the speed of light.

If you dig into the second part, regarding relativistic velocities
of moving electron, you will see how my E and B equations
combine to allow calculating relativistic velocities strictly
from EM considerations. To me, this is the confirmation that
my approach by localizing the photon's energy is a promising
avenue.

André Michaud
http://pages.globetrotter.net/srp/
.

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