Harry:

"Bilge" wrote in message
ue-al.net...
Gerald L. O'Barr:
SNIP

In LET, the physical situation that allows the math
invariance in SR to work is clearly established.

Then interpret dirac's relativistic wave equation and the electron spin
means in terms of LET. Tell me why LET would identify negative energy
solutions as anti-particles. This should be simple if those things are
"clearly established". On the other hand, this will be impossible if you
have no idea what these things are and you are simply rattling off
soundbites. Don't post a hundred lines of excuses, just give me the
"clearly established" meaning of these things.

I saw a paper from D.L.Hotson about that (Infinite Enegy issues 43 and 44,
2002), after I heard him talk on the subject. It seems that Dirac himself
proposed something compatible to LET. Dirac's work was according to some of
his fellows "learned trash", according to Hotson.


I can't say, unless you're referring to dirac's "hole theory", in which
case one could attempt to interpret it as an ether, but doing so
convincingly would be pretty difficult. That's one reason no one tries to
interpret it that way. The other reason is that you can't play the same
game with the klein-gordon equation, but you can interpret the dirac
equation the same way as the klein-gordon equation.

As a side note, I have pointed out to several of the die hard ether
affecianados on the newsgroup that their best shot at a viable theory
would be to reinterpret the stand- ard model as a condensed matter theory,
which would involve taking dirac's hole theory to literally be holes in a
medium. There is a lot of literature in which the standard model and in
particular the higgs mechanism is described by analogy to supercondutors
in which the broken symmetry provides a higgs boson (the cooper pairs)
which gives the photon a mass. So far, none of them have indicated they
know what I'm talking about. The responses have ranged from the knee-jerk
anti-relativity spiel to silence.

Before going on, I like to do a little test to get an idea if Hotson makes
sense. He claims that when an electron-positron pair is formed, the total
energy of each is more than 0.511 MeV, as they have each spin hbar/2. I
don't know what to think of that. Your comment please!

Don't waste your time. The spin is already part of the formalism
that renormalizes the mass and charge of the electron through the
self-interaction with its electromagnetic field. This D.L.Hotson
sounds like he's probably strung together a lot of sound bites without
ever having studied dirac's theory. It's your time to waste, but
you'll get more out of your time by reading the first 5 or 10 pages
of a book on relativistic quantum mechanics.

I'll anticipate the next question and state that there isn't another way
to deal with the mass. Anyone that objects to renormalization in favor of
attempting to explain the electron mass classically or semi-classically,
is not only faced with having to renormalize it as well, but to do so
using maxwell's equations, which are completely unrenormalizable.

"Bilge" wrote in message
...
Harry:

"Bilge" wrote in message
ue-al.net...
Gerald L. O'Barr:
SNIP

In LET, the physical situation that allows the math
invariance in SR to work is clearly established.

Then interpret dirac's relativistic wave equation and the electron
spin
means in terms of LET. Tell me why LET would identify negative energy
solutions as anti-particles. This should be simple if those things are
"clearly established". On the other hand, this will be impossible if
you
have no idea what these things are and you are simply rattling off
soundbites. Don't post a hundred lines of excuses, just give me the
"clearly established" meaning of these things.

I saw a paper from D.L.Hotson about that (Infinite Enegy issues 43 and
44,
2002), after I heard him talk on the subject. It seems that Dirac
himself
proposed something compatible to LET. Dirac's work was according to some
of
his fellows "learned trash", according to Hotson.


I can't say, unless you're referring to dirac's "hole theory", in which
case one could attempt to interpret it as an ether, but doing so
convincingly would be pretty difficult. That's one reason no one tries to
interpret it that way. The other reason is that you can't play the same
game with the klein-gordon equation, but you can interpret the dirac
equation the same way as the klein-gordon equation.

As a side note, I have pointed out to several of the die hard ether
affecianados on the newsgroup that their best shot at a viable theory
would be to reinterpret the stand- ard model as a condensed matter theory,
which would involve taking dirac's hole theory to literally be holes in a
medium.

Indeed, that seems to be roughly the way Hodson approaches it.

There is a lot of literature in which the standard model and in
particular the higgs mechanism is described by analogy to supercondutors
in which the broken symmetry provides a higgs boson (the cooper pairs)
which gives the photon a mass. So far, none of them have indicated they
know what I'm talking about. The responses have ranged from the knee-jerk
anti-relativity spiel to silence.

Before going on, I like to do a little test to get an idea if Hotson
makes
sense. He claims that when an electron-positron pair is formed, the
total
energy of each is more than 0.511 MeV, as they have each spin hbar/2. I
don't know what to think of that. Your comment please!

Don't waste your time. The spin is already part of the formalism
that renormalizes the mass and charge of the electron through the
self-interaction with its electromagnetic field.

That is close to the accusation that Hodson makes. He points out that spin
represents energy, and formalism can only hide it, not make it go away.

This D.L.Hotson
sounds like he's probably strung together a lot of sound bites without
ever having studied dirac's theory. It's your time to waste, but
you'll get more out of your time by reading the first 5 or 10 pages
of a book on relativistic quantum mechanics.

There can be no doubt that he studied it. He even claims to explain the
harmonics of the solar system's orbits with Dirac's theory (but I have not
analysed it yet).

I'll anticipate the next question and state that there isn't another way
to deal with the mass. Anyone that objects to renormalization in favor of
attempting to explain the electron mass classically or semi-classically,
is not only faced with having to renormalize it as well, but to do so
using maxwell's equations, which are completely unrenormalizable.

I did not see him make a link to Maxwell's equations. What is the problem?

Harald

Harry:

Don't waste your time. The spin is already part of the formalism
that renormalizes the mass and charge of the electron through the
self-interaction with its electromagnetic field.

That is close to the accusation that Hodson makes. He points out that spin
represents energy, and formalism can only hide it, not make it go away.

The fact that the spin appears in the dirac hamiltonian means that the
spin is already included in any sort of energy. The definition of the
hamiltonian is the total energy. However, I took your question to be more
involved, so I don't think you understood what I meant. I probably should
have just mentioned the hamiltonian up front. But,... In the dirac
theory, the relativistic wave equation is _not_ E^2 = p^2 + m^2. It's a
first order equation derived from factoring the above as:

E^2 = (a.p + bm)^2

solving for a and b (which in the very simplest case must be at least
4x4 matrices) and then obtaining the covariant form by defining,

\gamma^0 = b and \gamma^i = ba, i = x,y,z

and multiplying the equation through by b to get,

\gamma^0 E = \gamma^i p^i + m, and rearranging it to obtain,

\gamma^0 E - \gamma^i p^i - m = 0, or in four-vector notation,

\gamma^u p_u - m = 0

Now, the spin is contained in that \gamma matrix and it already
has been taken into account by the very derivation required to
obtain the dirac equation. It makes no sense to say that the
spin represents energy independently of the electron itself.
It's not possible to even describe an electron without the spin
and you can see by the form of the equation,

\gamma^u p_u = m

that the spin is already included in anything having to do with the mass.
It's impossible to say anything about the electron from the dirac equation
without the spin being there by default.

This D.L.Hotson
sounds like he's probably strung together a lot of sound bites without
ever having studied dirac's theory. It's your time to waste, but
you'll get more out of your time by reading the first 5 or 10 pages
of a book on relativistic quantum mechanics.

There can be no doubt that he studied it.

He certainly didn't understand what he supposedly studied. I've
read the two articles you referenced, so I'll give a couple of
examples.

His sidebar in part 1 describes the spin as an angular momentum and
asks the rhetorical question "Isn't angular momentum energy", which
he answers in the affirmative. Well, spin is not what he imagines it
to be. There is nothing "spinning". The spin cannot be considered
a three dimensional rotation no matter how you slice it. It doesn't
even posses the same symmetry as an angular momentum. Spin is a
spinor. It has two components. Angular momentum is a vector. it has
three components. Spin is a relativistic feature. Next from
From the introduction on the same page:

``Dirac's wave equation is a relativistic generalization of the
schroedinger wave equation. In 1934, this brilliantly successful
equation was shorn of half of its solutions by a questionable bit
of mathematical sleight-of-hand. Because it was 'politically correct',
this mathematical juggling became the accepted interpretation''


Well, no. Most, if not the entire paragraph, is completely false. One
might debate the first sentence, claiming that the dirac equation is a
generalization of the schroedinger equation, but the first attempt to find
such an equation for quantum mechanics was the klein-gordon equation
(1920) which is fully relativistic. Inter- pretational problems led to it
being temporarily discarded and the schroedinger equation being adopted.
So, quantum mechanics was developed with the idea of a relativistically
correct theory in mind from the start. The klein-gordon equation was
essentially just the mass-energy relation, E^2 = p^2 + m^2 with the
replacements p = -i\hbar\grad and E = i\hbar d/dt. The problem was that
it was second order in the time and that meant that probabilities
could be negative. Schroedinger remendied that by inserting those
replacements into the newtonian version of that relation, E = p^2/2m.
Dirac chose an alternate path and looked for an equation that was
linear in time by factoring the relativistic mass-energy relation.
It would be more accurate to say that both relativistic equations reduce
to schroedinger's in the appropriate limit.

What is totally inaccurate is that the equation was ever shorn of
half its solutions. Hotson goes on to say that ``Dirac's _complete_
equation describes a quantum spinor field, which has as its solutions,
four different kinds of electrons: electrons and positrons of positive
energy and electrons and positrons of negative energy''.

The emphasis on _complete_ is his, indicating that he doesn't think
modern physics considers the field to be a spinor field or at least
not the spinor field he thinks it describes. Modern physics certainly
considers the solutions to be spinors. However, he is wrong about
what the solutions represent. The solutions for a free particle
are straight forward to write down. Since the equation is a matrix
equation, the solutions will be column vectors. Without any mathematical
tricks, those a

[1] [0] [0] [0]
[0] [1] [0] [0]
[0] \exp(-iwt), [0] \exp(-iwt, [1] \exp(iwt) [0] \exp(iwt)
[0] [0] [0] [1]


with w = mc^2/hbar

The sign in the exponent implies that the mass in the first two
solutions is positive and in the second two, negative. Them's is the
solutions, so I'm not sure to what he refers. The negative energy states
are the anti-particles of the positive energy states. The dirac equation
says nothing at all about which sign you should take for the charge. It
can be taken to describe positive energy electrons and and negative energy
electrons (which are postitive energy positrons), _or_ it can be taken to
describe positive energy positrons and negative energy positrons (which
are electrons). In principle, you could use the dirac equation to describe
both situations, but there is nothing to be gained from doing so. You
simply have a sea of both positrons and electrons in which case one might
ask the question, "why wouldn't they anihilate", which is exactly the
question I asked my advisor when I first started studying the dirac
equation at the start of graduate school. (So, I have thought about
precisely the things being addressed here, except that I apparently
realized right away the posibility of anihilation). As it turns out, my
advisor told me the same thing occurred to him when he started out and
gave me what is now the rather obvious answer, but the paper never asks
the question and I don't think the author would accept the answer.


Next, I'll mention some statements which are so ridiculously false as to
border on being a malicious attempt to push his viewpoint regardless of
experimental evidence. He asserts that the particles in the standard model
such as quarks are unobservable, even in principle. In fact he refers to
some 100 particles in the standard model. The fact is, that the standard
model says nothing of the kind. The standard model only states that quarks
cannot be isolated. Quarks (and gluons) are routinely observed by the same
type of experiments that "observe" the nucleus in an atom. Scattering. If
a scattering experiment can't onserve the quarks in a nucleus, they can't
observe the nucleus in an atom or observe the atoms in a crystal. Other
evidence for quarks comes from hadron and meson spectroscopy. The
\delta is just an excited state of the nucleon. If spectroscopy is
not valid as evidence, then you'll have to rule out spectroscopy as
evidence for atomic structure and molecular structure along with
electrons. It's the same thing.

Second, the standard model doesnn't contain 100 particles. It contains
24. 6 quarks, 3 charged leptons, 3 neutrinos, 8 gluons, the W+/- and Z,
the photon and a higgs. Every single one of those is observed with the
exception of the higgs. The belief in the higgs for the standard model is
supported by the fact that the same basic theory applies to super-
conductors in which the higgs is known because it is the basis for the
supercurrent in the form of cooper pairs. (Nothing dictates that the higgs
is not a composite particle).


He even claims to explain the harmonics of the solar system's
orbits with Dirac's theory (but I have not analysed it yet).

That is completely over the top. The dirac equation describes
objects which have properties that are not found in any macroscopic
object. There is no classical analog to spin. It is _not_ any kind
of mechanical angular momentum and most definitely does _not_
imply anything is spinning. The term "spin" probably stuck due
to the fact that the dirac hamiltonian doesn't commute with either
the angular momentum or the spin separate, but only the sum of
both.

I'll anticipate the next question and state that there isn't another way
to deal with the mass. Anyone that objects to renormalization in favor of
attempting to explain the electron mass classically or semi-classically,
is not only faced with having to renormalize it as well, but to do so
using maxwell's equations, which are completely unrenormalizable.

I did not see him make a link to Maxwell's equations. What is the problem?


Consider some arbitrary classical charge distribution. To assemble the
charge distribution, you start with an infinitessimal charge, dq, then
bring the next dq in from infinity, which requires work to be done that is
equal to the potential energy e^2/r. You continue the process until you've
assembled a total charge q, in whatever configuration you want for the
charge density, \rho(x,y,z). This just comes from coulomb's law. Now, the
charge distribution which minimizes the amount of work needed to assemble
it (and therefore, the energy required to hold it together) is a sphere.
You can calculate the radius of a sphere for which the energy is equal to
the measured electron mass. It's called the classical electron radius and
in the early 20th century, it was regarded seriously as defining the size
of the electron. The value is 2.8179 fm (1 fm = 10^-15 meters). The
problem is that the electron radius is known to be no larger than about
1/1000th of that radius. This is rather puzzling. The way out of this
in qed is to examine the feynman diagrams, and in particular, the vacuum
polarization diagram:

\ ..
\ . . where the .'s represent the fluctuation of a photon
/~~ .. ~~~ into a virtual e+/e- pair.
/


You then note that in the limit of large r, your measurement must contain
many such such loops, so that the actual charge and mass of the electron
are the asymptotic values, not the mass and charge of the electron if you
stripped away the loops. The asymptotic value (the 0.511 MeV/c^2 you find
in the tables) is also called the "renormalized mass". The electron charge
that is in the tables, is also called the "renormalized charge".

Instead, at high energy when your probe gets closer and closer to the
electron, you expect to measure a _different_ charge and mass. (This has
been confirmed by experiment, by the way). In the limit where you are
"right at" the elctron, you expect to find what is called the "bare mass"
and "bare charge". Essentially, what one is saying is that you have
some bare charge, e_b and some bare mass m_b, and the measured values
of these quantities are the bare values + the contributions from the
loops, so that you have a relationship something like:

e_renorm = e_b x some function,

which you want to find. However, you know e_renom, but don't know e_b, so
you have to do a rather complicated song and dance to try and invert that
relationship if you want to compare the theory with experiment. To further
complicate matters, there is no way to solve the lagrangian exactly, so
you have to do it as a perturbation series, where the number of integrals
you need to evaluate increaes rapidly with each order in the series. For
example, the calculation of the electron magnetic moment which is
considered to be the hallmark of qed and the most successful agreement of
theory and experiment in history, is calculated only to third order and
the calculation contains a small uncertainty due to the difficulty of
evaluating the integrals.

You might be tempted to think that this is a rather nebulous procedure,
and could be applied to anything and succeed. For a long time, a lot of
people expressed the opinion that it was a nebulous procedure, but that
was because it wasn't certain whether the procedure was ever valid.
There are two basic questions. Does the series converge and do the
integrals at each order give a finite result? It turns out that it's
possible to prove that the series is finite at each order (see
"ward identities" for further information that specifically addresses
this).

The success of renormalization hinges on how "fast" the terms in
the series diverge with decreasing radius or equivalently, with the
increasing momentum of your probe, since that is the paramater
you have to work with to renormalize the charge.

With classical E&M (maxwell's theory), this divergence is quadratic
and the terms will diverge at every order. There is no way to make
it work for classical E&M. Qed is non-linear however and the divergence
is only logarithmic. The details and justification for the procedure
are rather long and involved, but may be found in most texts on field
theory as well as some texts on elementary particle physics. In any
case, this is becoming rather long and doing justice to only those
things I've mentioned would take much longer.

Basically, hotson appears to have given a sort of popularized
description of the dirac equation in the form that might be found
in "In Search of Schroedinger's Cat", which is ok as far as it
goes. He really goes off into la-la land as soon as he tries to
go into the dirac equation in any depth. The only thing that I
agree with is his comment about the elegance of the dirac theory.
Personally, I found that the more I understood what dirac did,
the more I was awed by dirac's insight - much more so than any
other physicist I can think of. As a side note, the traditional dirac
spinor is not the only spinor that solves the equation. Majorana
spinors also solve it, but only for neutral fermions, like perhaps
neutrinos, in which case the neutrino is it's own anti-particle
with he helicity reversed. This is an open question, the abswer to
which is being sought in experiments searching for neutrinoless
double beta decay.

"Bilge" wrote in message
...
Harry:

Don't waste your time. The spin is already part of the formalism
that renormalizes the mass and charge of the electron through the
self-interaction with its electromagnetic field.

That is close to the accusation that Hodson makes. He points out that
spin
represents energy, and formalism can only hide it, not make it go away.

The fact that the spin appears in the dirac hamiltonian means that the
spin is already included in any sort of energy. The definition of the
hamiltonian is the total energy. However, I took your question to be more
involved, so I don't think you understood what I meant. I probably should
have just mentioned the hamiltonian up front. But,... In the dirac
theory, the relativistic wave equation is _not_ E^2 = p^2 + m^2. It's a
first order equation derived from factoring the above as:

E^2 = (a.p + bm)^2

solving for a and b (which in the very simplest case must be at least
4x4 matrices) and then obtaining the covariant form by defining,

\gamma^0 = b and \gamma^i = ba, i = x,y,z

and multiplying the equation through by b to get,

\gamma^0 E = \gamma^i p^i + m, and rearranging it to obtain,

\gamma^0 E - \gamma^i p^i - m = 0, or in four-vector notation,

\gamma^u p_u - m = 0

Now, the spin is contained in that \gamma matrix and it already
has been taken into account by the very derivation required to
obtain the dirac equation. It makes no sense to say that the
spin represents energy independently of the electron itself.
It's not possible to even describe an electron without the spin

Now that's a clear and convincing statement indeed.

and you can see by the form of the equation,

\gamma^u p_u = m

that the spin is already included in anything having to do with the mass.
It's impossible to say anything about the electron from the dirac equation
without the spin being there by default.

Thanks for the clarification!

This D.L.Hotson
sounds like he's probably strung together a lot of sound bites without
ever having studied dirac's theory. It's your time to waste, but
you'll get more out of your time by reading the first 5 or 10 pages
of a book on relativistic quantum mechanics.

There can be no doubt that he studied it.

He certainly didn't understand what he supposedly studied. I've
read the two articles you referenced, so I'll give a couple of
examples.

Nice surprise! I have no comments on your comments, which are almost a
review.
I'll just swallow it for now... Maybe worth to send on to Hodson, for his
comments.

Thanks again,
Harald

His sidebar in part 1 describes the spin as an angular momentum and
asks the rhetorical question "Isn't angular momentum energy", which
he answers in the affirmative. Well, spin is not what he imagines it
to be. There is nothing "spinning". The spin cannot be considered
a three dimensional rotation no matter how you slice it. It doesn't
even posses the same symmetry as an angular momentum. Spin is a
spinor. It has two components. Angular momentum is a vector. it has
three components. Spin is a relativistic feature. Next from
From the introduction on the same page:

``Dirac's wave equation is a relativistic generalization of the
schroedinger wave equation. In 1934, this brilliantly successful
equation was shorn of half of its solutions by a questionable bit
of mathematical sleight-of-hand. Because it was 'politically correct',
this mathematical juggling became the accepted interpretation''

Well, no. Most, if not the entire paragraph, is completely false. One
might debate the first sentence, claiming that the dirac equation is a
generalization of the schroedinger equation, but the first attempt to find
such an equation for quantum mechanics was the klein-gordon equation
(1920) which is fully relativistic. Inter- pretational problems led to it
being temporarily discarded and the schroedinger equation being adopted.
So, quantum mechanics was developed with the idea of a relativistically
correct theory in mind from the start. The klein-gordon equation was
essentially just the mass-energy relation, E^2 = p^2 + m^2 with the
replacements p = -i\hbar\grad and E = i\hbar d/dt. The problem was that
it was second order in the time and that meant that probabilities
could be negative. Schroedinger remendied that by inserting those
replacements into the newtonian version of that relation, E = p^2/2m.
Dirac chose an alternate path and looked for an equation that was
linear in time by factoring the relativistic mass-energy relation.
It would be more accurate to say that both relativistic equations reduce
to schroedinger's in the appropriate limit.

What is totally inaccurate is that the equation was ever shorn of
half its solutions. Hotson goes on to say that ``Dirac's _complete_
equation describes a quantum spinor field, which has as its solutions,
four different kinds of electrons: electrons and positrons of positive
energy and electrons and positrons of negative energy''.

The emphasis on _complete_ is his, indicating that he doesn't think
modern physics considers the field to be a spinor field or at least
not the spinor field he thinks it describes. Modern physics certainly
considers the solutions to be spinors. However, he is wrong about
what the solutions represent. The solutions for a free particle
are straight forward to write down. Since the equation is a matrix
equation, the solutions will be column vectors. Without any mathematical
tricks, those a

[1] [0] [0] [0]
[0] [1] [0] [0]
[0] \exp(-iwt), [0] \exp(-iwt, [1] \exp(iwt) [0] \exp(iwt)
[0] [0] [0] [1]


with w = mc^2/hbar

The sign in the exponent implies that the mass in the first two
solutions is positive and in the second two, negative. Them's is the
solutions, so I'm not sure to what he refers. The negative energy states
are the anti-particles of the positive energy states. The dirac equation
says nothing at all about which sign you should take for the charge. It
can be taken to describe positive energy electrons and and negative energy
electrons (which are postitive energy positrons), _or_ it can be taken to
describe positive energy positrons and negative energy positrons (which
are electrons). In principle, you could use the dirac equation to describe
both situations, but there is nothing to be gained from doing so. You
simply have a sea of both positrons and electrons in which case one might
ask the question, "why wouldn't they anihilate", which is exactly the
question I asked my advisor when I first started studying the dirac
equation at the start of graduate school. (So, I have thought about
precisely the things being addressed here, except that I apparently
realized right away the posibility of anihilation). As it turns out, my
advisor told me the same thing occurred to him when he started out and
gave me what is now the rather obvious answer, but the paper never asks
the question and I don't think the author would accept the answer.

Next, I'll mention some statements which are so ridiculously false as to
border on being a malicious attempt to push his viewpoint regardless of
experimental evidence. He asserts that the particles in the standard model
such as quarks are unobservable, even in principle. In fact he refers to
some 100 particles in the standard model. The fact is, that the standard
model says nothing of the kind. The standard model only states that quarks
cannot be isolated. Quarks (and gluons) are routinely observed by the same
type of experiments that "observe" the nucleus in an atom. Scattering. If
a scattering experiment can't onserve the quarks in a nucleus, they can't
observe the nucleus in an atom or observe the atoms in a crystal. Other
evidence for quarks comes from hadron and meson spectroscopy. The
\delta is just an excited state of the nucleon. If spectroscopy is
not valid as evidence, then you'll have to rule out spectroscopy as
evidence for atomic structure and molecular structure along with
electrons. It's the same thing.

Second, the standard model doesnn't contain 100 particles. It contains
24. 6 quarks, 3 charged leptons, 3 neutrinos, 8 gluons, the W+/- and Z,
the photon and a higgs. Every single one of those is observed with the
exception of the higgs. The belief in the higgs for the standard model is
supported by the fact that the same basic theory applies to super-
conductors in which the higgs is known because it is the basis for the
supercurrent in the form of cooper pairs. (Nothing dictates that the higgs
is not a composite particle).


He even claims to explain the harmonics of the solar system's
orbits with Dirac's theory (but I have not analysed it yet).

That is completely over the top. The dirac equation describes
objects which have properties that are not found in any macroscopic
object. There is no classical analog to spin. It is _not_ any kind
of mechanical angular momentum and most definitely does _not_
imply anything is spinning. The term "spin" probably stuck due
to the fact that the dirac hamiltonian doesn't commute with either
the angular momentum or the spin separate, but only the sum of
both.

I'll anticipate the next question and state that there isn't another
way
to deal with the mass. Anyone that objects to renormalization in favor
of
attempting to explain the electron mass classically or
semi-classically,
is not only faced with having to renormalize it as well, but to do so
using maxwell's equations, which are completely unrenormalizable.

I did not see him make a link to Maxwell's equations. What is the
problem?


Consider some arbitrary classical charge distribution. To assemble the
charge distribution, you start with an infinitessimal charge, dq, then
bring the next dq in from infinity, which requires work to be done that is
equal to the potential energy e^2/r. You continue the process until you've
assembled a total charge q, in whatever configuration you want for the
charge density, \rho(x,y,z). This just comes from coulomb's law. Now, the
charge distribution which minimizes the amount of work needed to assemble
it (and therefore, the energy required to hold it together) is a sphere.
You can calculate the radius of a sphere for which the energy is equal to
the measured electron mass. It's called the classical electron radius and
in the early 20th century, it was regarded seriously as defining the size
of the electron. The value is 2.8179 fm (1 fm = 10^-15 meters). The
problem is that the electron radius is known to be no larger than about
1/1000th of that radius. This is rather puzzling. The way out of this
in qed is to examine the feynman diagrams, and in particular, the vacuum
polarization diagram:

\ ..
\ . . where the .'s represent the fluctuation of a photon
/~~ .. ~~~ into a virtual e+/e- pair.
/


You then note that in the limit of large r, your measurement must contain
many such such loops, so that the actual charge and mass of the electron
are the asymptotic values, not the mass and charge of the electron if you
stripped away the loops. The asymptotic value (the 0.511 MeV/c^2 you find
in the tables) is also called the "renormalized mass". The electron charge
that is in the tables, is also called the "renormalized charge".

Instead, at high energy when your probe gets closer and closer to the
electron, you expect to measure a _different_ charge and mass. (This has
been confirmed by experiment, by the way). In the limit where you are
"right at" the elctron, you expect to find what is called the "bare mass"
and "bare charge". Essentially, what one is saying is that you have
some bare charge, e_b and some bare mass m_b, and the measured values
of these quantities are the bare values + the contributions from the
loops, so that you have a relationship something like:

e_renorm = e_b x some function,

which you want to find. However, you know e_renom, but don't know e_b, so
you have to do a rather complicated song and dance to try and invert that
relationship if you want to compare the theory with experiment. To further
complicate matters, there is no way to solve the lagrangian exactly, so
you have to do it as a perturbation series, where the number of integrals
you need to evaluate increaes rapidly with each order in the series. For
example, the calculation of the electron magnetic moment which is
considered to be the hallmark of qed and the most successful agreement of
theory and experiment in history, is calculated only to third order and
the calculation contains a small uncertainty due to the difficulty of
evaluating the integrals.

You might be tempted to think that this is a rather nebulous procedure,
and could be applied to anything and succeed. For a long time, a lot of
people expressed the opinion that it was a nebulous procedure, but that
was because it wasn't certain whether the procedure was ever valid.
There are two basic questions. Does the series converge and do the
integrals at each order give a finite result? It turns out that it's
possible to prove that the series is finite at each order (see
"ward identities" for further information that specifically addresses
this).

The success of renormalization hinges on how "fast" the terms in
the series diverge with decreasing radius or equivalently, with the
increasing momentum of your probe, since that is the paramater
you have to work with to renormalize the charge.

With classical E&M (maxwell's theory), this divergence is quadratic
and the terms will diverge at every order. There is no way to make
it work for classical E&M. Qed is non-linear however and the divergence
is only logarithmic. The details and justification for the procedure
are rather long and involved, but may be found in most texts on field
theory as well as some texts on elementary particle physics. In any
case, this is becoming rather long and doing justice to only those
things I've mentioned would take much longer.

Basically, hotson appears to have given a sort of popularized
description of the dirac equation in the form that might be found
in "In Search of Schroedinger's Cat", which is ok as far as it
goes. He really goes off into la-la land as soon as he tries to
go into the dirac equation in any depth. The only thing that I
agree with is his comment about the elegance of the dirac theory.
Personally, I found that the more I understood what dirac did,
the more I was awed by dirac's insight - much more so than any
other physicist I can think of. As a side note, the traditional dirac
spinor is not the only spinor that solves the equation. Majorana
spinors also solve it, but only for neutral fermions, like perhaps
neutrinos, in which case the neutrino is it's own anti-particle
with he helicity reversed. This is an open question, the abswer to
which is being sought in experiments searching for neutrinoless
double beta decay.

"David Canzi" wrote in message ...
In article ,
Androcles wrote:
I am but a simple man, and sorely perplexed by these deliberations, for it
is truly astounding that these assertions be true. Explain this wondrous
concept without mathematics, but gently, for it shall surely confound me and
cause my head to ache.

You would never ask for a mathematics-free explanation of how far a
dropped object falls in "t" seconds. Why ask for a mathematics-free
explanation of a relativity problem?

Check and Mate.
http://users.pandora.be/vdmoortel/di...s/MatFree.html
Better late than never, sorry.

Dirk Vdm



--
David Canzi --