tony fleming wrote:

Dr Photon wrote:

tony fleming wrote:

[snips for brevity]

This IS physics brian, it takes
the magnetic field into account which bohr theory didn't do.

nonsense - it was by taking the magnetic field into account that they
found the solutions radiated.

You're not watching what I'm writing here; I'm saying the EM solution
pathway (as distinct from the QM pathway) post relativity and pre-QM,
did NOT take a magnetic effect into account. ie Bohr theory. QM DID
take the radiation into account, but continued to use the old-type
field which is why it has problems with uncertainty becuase it is too
primitive, you need a higher degree of distance to model the photon's
actual motions, and the electron's actual motions; you just can't do it
with a point-point distance a la coulomb because you will ALWAYS end up
with an error, an uncertainty.

I still don't get you. I thought you were using Maxwell's eqns, which
was historically investigated as to orbital stability and found
lacking. This analysis certainly included the magnetic field.

Bohr knew this didn't match experiment, so made up a few ad hoc rules
where Maxwell's eqn equations didn't apply, but which matched
experiment
http://en.wikipedia.org/wiki/Bohr%27s_Atomic_Theory
even though he didn't know why.

So Bohr's theory is incompatible with Maxwell's eqns per se, and
comparing your model to Bohr's seems totally apples and oranges, never
mind magnetic fields.

Also on the wikipedia site it states
"The Bohr model gives an incorrect value L=hbar for the ground state
orbital angular momentum. The angular momentum in the true ground state
is known to be zero."

Your model also has a ground state orbital angular momentum so
disagreeing with experiment. I'll find some reference to experiment
when I have some more time. In the mean time, check out the
Stern-Gerlach measurement on neutral hydrogen atoms
http://www.chemistry.mcmaster.ca/esam/Chapter_4/section_2.html
How do you explain this?

[snip]

As to the dimensionality of equations 10, 13 and 14 I think you're
right; this is a typo, there should be a another factor by v

the LHS and RHS are off by a metre not by a metre/second, as is 1d

Yes you're correct, the velocity should be a unit vector, so this makes
the currect density a current per unit area, many thanks, then 1d IS
dimensionally inconsistent as it stands and needs a unit tilde above
the v,

what do you mean by a unit tilde exactly? Do you mean a unit hat or
unit caret?
http://en.wikipedia.org/wiki/Unit_vector
which in any case won't save you, as v-hat still has units of m/s.

Well what I mean is that the velocity is a vector with unit magnitude;
now if you use one or two symbols to indicate both then whatever, I
personally use a tilde underneath to signify a vector, and a unit hat
to indicate a unit magnitude; some however, use a unit hat to indicate
both.

AFAICT, this only adds an extra problem. The dimensions are still
wrong, and now the magnitude of current doesn't depend on the magnitude
of the velocity of the electron. hmmm.

OTOH, maybe I can't comment until I see what you actually write down
this time.

AND this affects some equations below. Nevertheless the final
results and conclusions are unaffected by this error.

even if you managed to write down 1d in a dimensionally correct form,
it still doesn't guarantee that the physics is right - there's no point
commenting on that until there is something worth looking at.

Ok, let me modify the web site copy of this paper and I'll leave it
there for you to comment.

do

As I said, I
will add an errata sheet to amend the errors.

speaking of errors, what do you think eqn 2 is describing? To me, you
have written down a spherically symmetric trial solution to a ~planar
orbital problem. If this is the case then it is certainly wrong by
construction. What von Hippel was referring to I can't say as I don't
have his book, so you will have to expand a little. Can you find any
on-line reference for this?

I doubt it, but let me try; I'll try a google search for you.
http://www.nd.edu/~condmat/research/pdf/mrs.pdf
The above link reveals that Von Hippel's life spanned THREE
centuries!!!

which is the only thing that reference gives. I was looking for an
example of how the exp(phi) term is used in the eqn(2) E-field, to see
exactly what he was getting at, and whether you have misapplied it. I
still don't have a reference for this.

What he was doing in his book was to redo Hertz's work
using his Hertzian potentials to derive the radiation energy from an
electric dipole antenna. Hertz had performed a famous experiment and
found the theory behind radiofrequency radiation. So he ended up with
the H-field and E-field far-field energy densities. We can see from
the expressions that they are similar except for a factor of the
imaginary number "j", or "I". It was here I realised we could
have a loop-dipole antenna structure (as distinct from a rod-dipole
antenna) which looks a bit like a cross loop-dipole which gives zero
radiation. So by using space and time phase differences, we end up with
an analogy of the hydrogen atom.

Taking the real component of Eqn2 which you say is " the electron's
E-field" to just focus on radial distance, (you say the imaginary
component points in the theta direction(???)) I get

E=(1/(4 pi eps0)) (q/r^2) cos(omega t) r-hat (2)

so the meaning of this is that the E-field due to the electron is
spherically symmetric, and oscillates in time sinusoidally between plus
and minus values. For a plain electron, even a circulating electron,
this is obviously wrong. Do you agree?

No, I don't. Read the comment in the appendix on the way imaginary
numbers are used in the SFT formulation; they are not standard.

I had actually done that a little bit, which was where my comment
"(you say the imaginary component points in the theta direction(???))"
came from.

Basically, we swap in and out of time and space depending on what we
wish to achieve. But we have to do this in a careful, geometrically
consistent manner

Quoting from the Appendix for your convenience
(d) Imaginary numbers in 4-D coordinate systems
Oftentimes in EM formulations, complex numbers are used from the start,
a theoretical procedure is followed, at the end the real and imaginary
parts are collected and the imaginary parts are discarded. In this
report a physical significance is meant for both real and imaginary
parts of the formulation at all times. This said, imaginary numbers are
treated no differently within this report to their common usage except
that the concept is generalized to the 4-D coordinate system involving
the two coupled spinors as illustrated in Fig. 3. They are 'real'
in the sense that they are orthogonal entities to mathematically real
numbers. Wherever the symbol 'j' appears in 3-D coordinate systems
it can be substituted by a real component in an orthogonal direction.
We may thus think of it as an 'orthogonality operator'. Defined in
terms of imaginary numbers, 2-D spinors are rotations moving in planes
that include axes orthogonal to a stated direction, e.g. (A 3-4) where
time is a parameter of rotation. The interpretation is consistent with
the conventional cyclic ordering of coordinate systems, e.g. Cartesian
(x,y,z), spherical (r, theta, phi)

so lets stop here for a second. My comments previously still stand
then?
I'll quote again lest you forget:

" Taking the real component of Eqn2 which you say is " the electron's
E-field" to just focus on radial distance, (you say the imaginary
component points in the theta direction(???)) I get

E=(1/(4 pi eps0)) (q/r^2) cos(omega t) r-hat (2)

so the meaning of this is that the E-field due to the electron is
spherically symmetric, and oscillates in time sinusoidally between
plus
and minus values. For a plain electron, even a circulating electron,
this is obviously wrong. Do you agree?"

and cylindrical (rho, phi,z). Thus
-j*theta_vectorhat = -phi_vectorhat.

so j*r_hat = theta_hat?
And to just consider the r_hat component of eqn(2), we ignore the
imaginary part, being left with cos(omegat.t) like I wrote.
This eqn is spherically symmetric, as it has dependence on r and no
dependence on theta and phi. So what do you disagree with?

Also to write
E=(1/(4 pi eps0)) (q/r^2) sin(omega t) theta-hat (2b)
seems totally nuts. Do you say this is a valid equation? If not, please
write explicitly the eqn corresponding to the imaginary component.

[snip]

To get oscillating fields the proton is needed at the centre,

why does it?

we were discussing a centrally symmetric electron-proton arrangement.
With the proton present, when the electron is on the "near"-side of the
proton, our E-field can point towards the COM, whereas when the
electron is on the "far"-side of the proton, the E-field points towards
us from the COM (neglecting retardation for the moment...)

Without the proton what have you got? Even taking a circulating
electron motion, if you are far from the electron orbit the E-field you
experience may have slight changes in strength due to the varying
observer-electron distance, but it won't change sign. I was wondering
what on earth the cos(omega.t) referred to. It seems to imply that the
electron charge is pulsating between + and -1 (ugh!).

with the
electron orbiting - maybe you mean this instead of "the electron's
E-field",

but each charge causes its own E-field.

ok, so you really do mean eqn2 is just the electron

but then there is no accounting of the proton charge,

not if what your referring to is the simple case where we assume an
'infinite mass' proton, no but yes there is for a 'finite-mass' proton

eh? You mean if the proton is stationary (infinite mass), it has no
charge??? Eqn (2) is about E-fields remember, and even if
phi_proton=omega_proton.t=0, then exp(phi_proton)=1.

or the electron-proton distance, or the fact that it shouldn't be spherically
symmetric, so it is still wrong.

Also, if it is due to an electron orbiting a proton, there should be a
retarded term depending on distance

yes of course, but the fact is that in the simple case (the principal
mode), the retardation is constant at all times and equal to a fraction
of a wavelength so as to make the total nett radiation zero. what is
paramount when we are talking about those modes where the distances are
NOT constant (say the elliptical orbits)

if you write an equation using a non-radiating E-field mode, do you
think you have proven radiation doesn't exist?

br