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A version of QED without ultraviolet divergences

A version of QED without ultraviolet divergences - Physics Forum

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  #31  
Old 08-07-2004, 07:00 AM
Bill Hobba
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Default A version of QED without ultraviolet divergences


"Eugene" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
an
you
for
great

Eugene you admit you do not understand Weinberg's discussion of how Wilson's
view resolves the issue of infinites yet claim you know for sure that 'QFT
swept infinities under the rug'. This I do not follow at all. Surely you
should reserve you opinion until you understand Wilson's approach. The
prediction of QFT is if we have a certain very high cutoff (but not
infinite) for energies much less than that cutoff then our theories look
like they are renomalisable. This view even predicts the scale it starts to
be a problem; it is way beyond our current technology and is before we
believe other theories such as the electroweak theory dominate. This means
the infinites of renormalization are simply a byproduct of the energies we
work at and not necessarily and indication of anything fundamental.

Bill


Without finite Hamiltonian


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  #32  
Old 08-07-2004, 09:54 AM
Eugene
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Posts: n/a
Default A version of QED without ultraviolet divergences



Bill Hobba wrote:


There are many things which I do not understand, I am ready to admit
that. If you do not want to speak my language, I have no
other choice but to learn yours. I spent some time
reading "The floating cutoff" chapter again, and I think I got it.
It does not change my view of renormalization. As Weinberg said there:
"At bottom, the difference between the conventional and the Wilson
approach is one of mathematical convenience rather than of physical
interpretation" Let me explain why, using QED as an example.

Conventional arroach: If we use normal QED Hamiltonian with finite
masses m and charges e, and take all integrals to infinity (cutoff
L=inf), we obtain, as is well known, infinite S-matrix. I will write it
as S(m,e,inf) = inf. For finite cutoff L, the S-matrix S(m,e,L) is,
of course finite, but it has nothing to do with reality. For example,
the Lorentz invariance is violated. The solution of this problem
(renormalization) is to use INFINITE masses M and charges E in the
Hamiltonian. Then, the S-matrix S(M,E, inf) = S(inf, inf, inf) is
finite, Lorentz-invariant and perfectly agrees with experiment. How
do we calculate S(inf, inf, inf)? We identify physical finite mass m
with the pole of the electron propagator, and physical finite charge e
with the coefficient in front of the electron-electron scattering
amplitude at low energies. These two numbers are, of course expressed
by divergent integral as L -> inf, but the same infinite integrals
are present in the expressions for all other elements of the the
S-matrix. So, each time we see
such an infinite integral in the expression for the S-matrix, we
do not calculate it, but simply substitute with the finite number m
or e. This is equivalent to using infinite Hamiltonian, i.e., with
infinite parameters M and E.

Wilson's approach: We assume that the bare masses and charges in the
Hamiltonian are cutoff-dependent m(L) and e(L). In agreement with
the conventional approach, in the limit L -> inf these functions
must tend to infinity m(L) -> M = inf e(L) -> E = inf. The trick of the
approach is to select functions m(L) and e(L), so that at finite
L the S-matrix S(m(L), e(L), L) is close to the accurate value
S(M,E, inf). It can be shown, that indeed, for low energy processes
(momenta much lower that the cutoff L) such a fitting can be done.
Such a theory with finite cutoff is rather ugly: as Weinberg says
"the resulting effective field theory will contain all Lorentz-
and gauge-invariant interactions". Moreover, "the cutoff generally
destroys manifest gauge invariance, and either manifest Lorentz
invariance or unitarity". This theory with finite cutoff has only
two good properties: everything is finite, and low-energy scattering
is described in a good approximation. You can obtain perfectly
accurate S-matrix, just as in the conventional approach, if you
take the limit L->inf, but then again, the parameters in the Hamiltonian
become infinite m(inf) = M = inf and e(inf) = E = inf.

You may say that Wilson's approach solves the problem with the infinite
Hamiltonian and the lack of description of time evolution, which I keep
stressing in each of my postings. Indeed,
in this approach, at finite cutoff L, we do have a Hamiltonian with
finite parameters m(L) and e(L), which we may try to use to calculate
the time evolution. However, this Hamiltonian has serious drawbacks:

1. it is approximate (works only for energies below the cutoff)
2. It has an infinite number of interactions in each perturbation order
3. It is not relativistically invariant (in the sense that there is
no interacting boost operator such that Poincare group commutators are
satisfied, otherwise the S-matrix would be Lorentz invariant, which
is not true).
4. It contains interactions (trilinear and others) which create
particles out of vacuum, and additional particles out of one-particle
states. This leads to the funny and unphysical picture of vacuum as
a "boiling soup" and "dressing" of particles by virtual "coats".

My approach is better: I construct the Hamiltonian which
1. Yields exactly the accurate S-matrix of the renormalized QED
for all energies (of course, at very high energies we need to take
into account the possibility of creation of pairs of heavy particles
not included in the theory. But the same problem is characteristic
for the Wilson's approach)
2. Is finite. The parameters m and e entering my Hamiltonian are
exactly measured mass and charge of the electron.
3. Satisfies exactly the condition of relativistic invariance
(there is an interacting boost operator such that all Poincare
commutators are correct).
4. Vacuum and one-particle states are exactly eigenstates of this
operator, so there is no spontaneous creation of virtual particles
from the vacuum and around single particles. Interaction acts when
there are two or more particles.
5. The interaction terms in this Hamiltonian have direct physical
interpretation: In the 2nd perturbation order I already obtained
usual Coulomb potential plus relativistic corrections: spin-orbit,
contact, spi-spin, etc. The method is proven to work at all perturbation
orders. I am sure that in the 4th order I'll obtain the Uehling
potential and the correct value for the Lamb's shift. What is different
from the S-matrix approach, which can give only the energy of the
Lamb's shift, is that I can also obtain the radiative corrections to the
wave function.



At very high cutoff, the Wilson's Hamiltonian will have very large mass and
charge parameters, and all other ugliness described above. Though,
the S-matrix will look pretty good, I agree.

Eugene.



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  #33  
Old 08-08-2004, 12:21 AM
Bill Hobba
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Posts: n/a
Default A version of QED without ultraviolet divergences


"Eugene" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
Wilson's
'QFT
you

Welcome to the club. I am still trying to get around the idea of the landau
pole and quite a few other things.


I learnt QFT about 4 or 5 years ago now and the effective field theory
approach is what I learnt. In fact what prodded me to investigate the
technicalities was John Baez's review article:
[Only registered users see links. ]. What got me was the
conclusion:

'Wilson's analysis takes just the opposite point of view, that any quantum
field theory is defined fundamentally with a distance cutoff D that has some
physical significance. In statistical mechanical applications, this distance
scale is the atomic spacing. In quantum electrodynamics and other quantum
field theories appropriate to elementary particle physics, the cutoff would
have to be associated with some fundamental graininess of space-time,
perhaps the result of quantum fluctuations in gravity. We discuss some
speculations on the nature of this cutoff in the Epilogue. But whatever this
scale is, it lies far beyond the reach of present-day experiments. Wilson's
arguments show that this this circumstance *explains* the renormalizability
of quantum electrodynamics and other quantum field theories of particle
interactions. Whatever the Lagrangian of quantum electrodynamics was at the
fundamental scale, as long as its couplings are sufficiently weak, it must
be described at the energies of our experiments by a renormalizable
effective Lagrangian.'

The renormalization and it infinites is really nothing to worry about at
all - it fact it would be surprising if you theories were not
renormaliseable and had the problems of the infinities.


Yes.


Yes - but note m(L) and e(L) are written as mr + delta m and the same for
e(l) (except I think the adjustment is multiplicative rather than additive
but that does not really change anything) where mr is the renormalized mass
which is the observed quantity - not m(L). The idea is as L goes to
infinity the renormalized mass can be made arbitrarily close to some fixed
value for L << L0 whew L0 is some very high cutoff. And in fact the theory
that describes the physics in the region of L0 does not even have to be the
same theory - for QED to be renormalisable L simply must be much less than
L0. In fact we know in that region the elctroweak theory operates anyway.


Yes


You bet - but we are looking at questions of principle here.


You bet - as I readily admitted.


The point being the infinity is avoided.


Well it really only works for energies a long way below the cutoff.

and

The point though is this - for energies much less than the cutoff the theory
looks renomlaisable, and has all these infinites even though the real one
may not. That is the key point. We recognize that QED is not findamamental
and so the infinites we 'sweep' under the rug are not fundamental either -
they are simply a result of it being a low energy approximation to another
better theory. That is the basis of the effective field theory approach.

Bill

means
we


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  #34  
Old 08-08-2004, 12:39 AM
Eugene Stefanovich
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Posts: n/a
Default A version of QED without ultraviolet divergences



Bill Hobba wrote:


I am afraid you are mixing here the notions of renormalization and
renormalizability. Renormalizability means that renormalization
(subtraction of infinite integrals, or adding infinite counterterms
to the Hamiltonian in my language) can be performed by modifying
(setting to infinity) a finite number of parameters in the Hamiltonian.
In the case of QED these are mass and charge of the electron.
In non-renormalizable theory you need to modify infinite number of
parameters. QED and standard model are renormalizable, but you
still need to perform the subtraction of divergences there.



OK, we may disgree whether infinites create a problem or not. My
bottomline is this: I have a consistent Hamiltonian which allows
to calculate the time evolution of interacting charged particles.
I claim that existing theory cannot do that. If you think otherwise,
I would appreciate references with the explicit form of the
Hamiltonian, at least in low orders of the perturbation theory.

Eugene.



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  #35  
Old 08-08-2004, 05:18 AM
FrediFizzx
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Posts: n/a
Default A version of QED without ultraviolet divergences

"Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
news:[Only registered users see links. ]...
|
|
| Bill Hobba wrote:
|
| >
| > The renormalization and it infinites is really nothing to worry about at
| > all - it fact it would be surprising if you theories were not
| > renormaliseable and had the problems of the infinities.
|
| I am afraid you are mixing here the notions of renormalization and
| renormalizability. Renormalizability means that renormalization
| (subtraction of infinite integrals, or adding infinite counterterms
| to the Hamiltonian in my language) can be performed by modifying
| (setting to infinity) a finite number of parameters in the Hamiltonian.
| In the case of QED these are mass and charge of the electron.

I think if it were possible to isolate a "bare" electron, you would find
that the mass and charge are zero. As strange as that may seem. Mass and
charge are emergent from the electron's interaction with the quantum vacuum.

| In non-renormalizable theory you need to modify infinite number of
| parameters. QED and standard model are renormalizable, but you
| still need to perform the subtraction of divergences there.

It seems so simple. You just need to get rid of divergences that shouldn't
be there in the first place. I don't see any problem as Bill mentions
below.

| > The point though is this - for energies much less than the cutoff the
theory
| > looks renomlaisable, and has all these infinites even though the real
one
| > may not. That is the key point. We recognize that QED is not
findamamental
| > and so the infinites we 'sweep' under the rug are not fundamental
either -
| > they are simply a result of it being a low energy approximation to
another
| > better theory. That is the basis of the effective field theory
approach.
| >
|
| OK, we may disgree whether infinites create a problem or not. My
| bottomline is this: I have a consistent Hamiltonian which allows
| to calculate the time evolution of interacting charged particles.
| I claim that existing theory cannot do that. If you think otherwise,
| I would appreciate references with the explicit form of the
| Hamiltonian, at least in low orders of the perturbation theory.

What does this mean "to calculate the time evolution of"? Why do we need to
know that? Particles go in and particles come out and we have effective
theory that can describe the initial and final states. Do we really need to
know exactly what is happening "during" the interaction? IMHO, space-time
is funny and wierd at the quantum level anywise.

FrediFizzx

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  #36  
Old 08-08-2004, 06:57 AM
Eugene Stefanovich
Guest
 
Posts: n/a
Default A version of QED without ultraviolet divergences



FrediFizzx wrote:

I would like to see a consistent theory based on this assumption.
In my approach, electron has experimentally measured charge and mass
from the beginning. These parameters are present in the Hamiltonian
and do not change due to renormalization or "interaction with the
quantum vacuum". Actually, there is no interaction unless there are two
or more particles, which is kind of obvious: in order to interact
there should be at least two partners.



The problem is that the charge and mass calculated from the theory are
not the same as the charge and mass put there in the beginning. If this
is your ideal of consistency, then fine. I think, we can do better.


You would probably agree that we can observe time evolution of charged
particles in the macroscopic world: particles move along some
trajectories, or if you like more quantum mechanics, the wave functions
evolve in time. QFT does not provide this kind of description.
So, QFT is completely useless in the macroscopic low-energy limit.
It can predict only asymptotic limits of time evolution.
My suggestion is very simple: we just need to
modify the Hamiltonian of the theory, so that old predictions (S-matrix)
are still valid, and new predictions (time evolution) are now possible.
What's wrong with this idea?

Eugene.



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  #37  
Old 08-08-2004, 05:20 PM
FrediFizzx
Guest
 
Posts: n/a
Default A version of QED without ultraviolet divergences

"Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| FrediFizzx wrote:
| > "Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| > | Bill Hobba wrote:
| > |
| > | >
| > | > The renormalization and it infinites is really nothing to worry
about at
| > | > all - it fact it would be surprising if you theories were not
| > | > renormaliseable and had the problems of the infinities.
| > |
| > | I am afraid you are mixing here the notions of renormalization and
| > | renormalizability. Renormalizability means that renormalization
| > | (subtraction of infinite integrals, or adding infinite counterterms
| > | to the Hamiltonian in my language) can be performed by modifying
| > | (setting to infinity) a finite number of parameters in the
Hamiltonian.
| > | In the case of QED these are mass and charge of the electron.
| >
| > I think if it were possible to isolate a "bare" electron, you would find
| > that the mass and charge are zero. As strange as that may seem. Mass
and
| > charge are emergent from the electron's interaction with the quantum
vacuum.
|
| I would like to see a consistent theory based on this assumption.
| In my approach, electron has experimentally measured charge and mass
| from the beginning. These parameters are present in the Hamiltonian
| and do not change due to renormalization or "interaction with the
| quantum vacuum". Actually, there is no interaction unless there are two
| or more particles, which is kind of obvious: in order to interact
| there should be at least two partners.

I don't think you will find many particle physicists that don't think the
charge of an electron is screened by a cloud of virtual particles. They do
think that and are pretty sure about it (see Topaz experiment). This is a
simple example of an electron *interacting* with the quantum vacuum. And
produces a running coupling "constant". Funny that it is called a constant
because it isn't really constant at all. Actually this is a very big clue
to what is really going on. An electron (or all charged fermions) observed
from a distance is really a product of a "bare" point-like entity and the
quantum vacuum. Virtual e+e- pairs are dominate but there will be some
other pairs also including hadronic pairs to a small extent. All charged
fermions are a mix of all other fermions when you include the quantum vacuum
and you *have* to include quantum vacuum becuase it is impossible to remove
it. So you can see right away that the situation is complex even for a
lonely electron. Do you really think you can get a proper time evolution of
the wavefunction of the electron *during* an interaction with another
charged fermion through this complexity? Feynman was right; it has to be
simplified. The interaction "space" is really a blob and all we care about
are initial states and final states. But it is not wrong for us to
eventually want to know exactly what happens in the "blob". I think we just
don't know what all the quantum vacuum objects are yet is what is preventing
us from figuring out the exact complexity.

For some good analogs of how mass and charge can be emergent from the
quantum vacuum, see Volovik's "The Universe in a Helium Droplet". It is
possible to model the quantum vacuum as if it has bound charge with cells
equal to Q_vac = +,- sqrt(hbar*c). I have been working on this for over a
year now and it gets more consistent as time passes. This means the quantum
vacuum consists of coupled oscillators. Figuring out the exact geometry of
coupling is mind boggling but hopefullly not intractable. It takes quite a
different way of thinking about interactions as gauge bosons require a
different interpretation from the Standard Model.

| > | In non-renormalizable theory you need to modify infinite number of
| > | parameters. QED and standard model are renormalizable, but you
| > | still need to perform the subtraction of divergences there.
| >
| > It seems so simple. You just need to get rid of divergences that
shouldn't
| > be there in the first place. I don't see any problem as Bill mentions
| > below.
|
| The problem is that the charge and mass calculated from the theory are
| not the same as the charge and mass put there in the beginning. If this
| is your ideal of consistency, then fine. I think, we can do better.

True. And you are right; we can do better if we have the correct picture.

| > | > The point though is this - for energies much less than the cutoff
the
| > theory
| > | > looks renomlaisable, and has all these infinites even though the
real
| > one
| > | > may not. That is the key point. We recognize that QED is not
| > findamamental
| > | > and so the infinites we 'sweep' under the rug are not fundamental
| > either -
| > | > they are simply a result of it being a low energy approximation to
| > another
| > | > better theory. That is the basis of the effective field theory
| > approach.
| > | >
| > |
| > | OK, we may disgree whether infinites create a problem or not. My
| > | bottomline is this: I have a consistent Hamiltonian which allows
| > | to calculate the time evolution of interacting charged particles.
| > | I claim that existing theory cannot do that. If you think otherwise,
| > | I would appreciate references with the explicit form of the
| > | Hamiltonian, at least in low orders of the perturbation theory.
| >
| > What does this mean "to calculate the time evolution of"? Why do we
need to
| > know that? Particles go in and particles come out and we have effective
| > theory that can describe the initial and final states. Do we really
need to
| > know exactly what is happening "during" the interaction? IMHO,
space-time
| > is funny and wierd at the quantum level anywise.
|
| You would probably agree that we can observe time evolution of charged
| particles in the macroscopic world: particles move along some
| trajectories, or if you like more quantum mechanics, the wave functions
| evolve in time. QFT does not provide this kind of description.
| So, QFT is completely useless in the macroscopic low-energy limit.
| It can predict only asymptotic limits of time evolution.
| My suggestion is very simple: we just need to
| modify the Hamiltonian of the theory, so that old predictions (S-matrix)
| are still valid, and new predictions (time evolution) are now possible.
| What's wrong with this idea?

There is nothing basically wrong with that idea. I am not sure it is really
needed unless it can give us more fundamental insight as to what is really
going on. Can it?

FrediFizzx

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  #38  
Old 08-09-2004, 02:22 AM
Eugene
Guest
 
Posts: n/a
Default A version of QED without ultraviolet divergences



FrediFizzx wrote:

I am pretty sure that 99.99% of particle physicists believe that
electron is screened by a cloud of virtual particles, and that vacuum
is a "boiling soup" of virtual pairs, and that interaction occurs when
"real" particles "throw virtual particles" to each other. My point is
nobody have seen these virtual particles in experiment. All these
virtual particles, "soups" and "clouds" are just artefacts of
incorrectly written Hamiltonian. I suggested a way how all this nonsense
can be eliminated from the theory, and, still, all observable
predictions can be preserved (S-matrix) and new predictions
(time evolution) can be added. Could you please give me a reference to
the "Topaz experiment", I'll try to explain it without invoking the
concept of virtual particles.



Of course, it is impossible to predict the time evolution of the wave
function in the complex picture with virtual particles. That's my
whle point. Of course, Feynman was right, and it has to be simplified.
That's what I did: I simplified the theory without losing a bit of
its predictive power, and even added to its predictive power.



You cannot figure out what's inside the "blob" because you are using
wrong QED Hamiltonian. I can predict exactly what's inside the "blob".
Note also that in the macroscopic low-energy limit the "blob" becomes
very big: centimeters, meters, etc. in size. So, the interacting
time evolution becomes directly observable. QED cannot predict this time
evolution, as you already pointed out. In order to make such
prediction you need to abandon QED and switch to the classical
Maxwell's theory with point particles and electromagnetic
potentials. My theory works in the full range of energies.


It would be nice to see how somebody can derive electron mass and charge
from something more fundamental. So far, I haven't seen that.
In my approach, vacuum is just a state without particles. Electron
is a single particle with mass and charge taken directly from
experiment. There is no interaction between single electron and the
vacuum. Interaction is present when there are two or more particles.




It gives a lot of new insight.
First, now you can directly calculate the
time evolution of the wave function during interaction.
Second, you can now forget about the mind boggling picture with
virtual particles and work with real particles and potentials
between them, just as in ordinary quantum mechanics.
Third, I predict that the potentials acting between particles
(Coulomb, magnetic, spin-orbit etc.) are instantaneous. This can be
verified by experiment.
Fourth, the theory predicts small (but fundamentally important)
deviations from Einstein's predictions, for example, in the case of
the decay of fast moving particles.
Finally, this approach demonstrates that Lorentz transformations
are not exact and universal, and that Minkowski space-time is an
approximation.

Eugene.


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  #39  
Old 08-09-2004, 03:17 AM
FrediFizzx
Guest
 
Posts: n/a
Default A version of QED without ultraviolet divergences

"Eugene" <[Only registered users see links. ]> wrote:
| FrediFizzx wrote:
| > "Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| > | FrediFizzx wrote:
| > | > "Eugene Stefanovich" <[Only registered users see links. ]> wrote in message
| > | > | Bill Hobba wrote:
| > | > |
| > | > | >
| > | > | > The renormalization and it infinites is really nothing to worry
| > about at
| > | > | > all - it fact it would be surprising if you theories were not
| > | > | > renormaliseable and had the problems of the infinities.
| > | > |
| > | > | I am afraid you are mixing here the notions of renormalization and
| > | > | renormalizability. Renormalizability means that renormalization
| > | > | (subtraction of infinite integrals, or adding infinite
counterterms
| > | > | to the Hamiltonian in my language) can be performed by modifying
| > | > | (setting to infinity) a finite number of parameters in the
| > Hamiltonian.
| > | > | In the case of QED these are mass and charge of the electron.
| > | >
| > | > I think if it were possible to isolate a "bare" electron, you would
find
| > | > that the mass and charge are zero. As strange as that may seem.
Mass
| > and
| > | > charge are emergent from the electron's interaction with the quantum
| > vacuum.
| > |
| > | I would like to see a consistent theory based on this assumption.
| > | In my approach, electron has experimentally measured charge and mass
| > | from the beginning. These parameters are present in the Hamiltonian
| > | and do not change due to renormalization or "interaction with the
| > | quantum vacuum". Actually, there is no interaction unless there are
two
| > | or more particles, which is kind of obvious: in order to interact
| > | there should be at least two partners.
| >
| > I don't think you will find many particle physicists that don't think
the
| > charge of an electron is screened by a cloud of virtual particles. They
do
| > think that and are pretty sure about it (see Topaz experiment).
|
| I am pretty sure that 99.99% of particle physicists believe that
| electron is screened by a cloud of virtual particles, and that vacuum
| is a "boiling soup" of virtual pairs, and that interaction occurs when
| "real" particles "throw virtual particles" to each other. My point is
| nobody have seen these virtual particles in experiment. All these
| virtual particles, "soups" and "clouds" are just artefacts of
| incorrectly written Hamiltonian. I suggested a way how all this nonsense
| can be eliminated from the theory, and, still, all observable
| predictions can be preserved (S-matrix) and new predictions
| (time evolution) can be added. Could you please give me a reference to
| the "Topaz experiment", I'll try to explain it without invoking the
| concept of virtual particles.

[Only registered users see links. ]

There is a postscript article that you can download at the bottom of the
page. I hardly think they are artifacts since real particles are seen to
get a momentum "kick" from invisible vacuum virtual particles in actual
experiments. So you are wrong about that.

| > This is a
| > simple example of an electron *interacting* with the quantum vacuum.
And
| > produces a running coupling "constant". Funny that it is called a
constant
| > because it isn't really constant at all. Actually this is a very big
clue
| > to what is really going on. An electron (or all charged fermions)
observed
| > from a distance is really a product of a "bare" point-like entity and
the
| > quantum vacuum. Virtual e+e- pairs are dominate but there will be some
| > other pairs also including hadronic pairs to a small extent. All
charged
| > fermions are a mix of all other fermions when you include the quantum
vacuum
| > and you *have* to include quantum vacuum becuase it is impossible to
remove
| > it. So you can see right away that the situation is complex even for a
| > lonely electron. Do you really think you can get a proper time
evolution of
| > the wavefunction of the electron *during* an interaction with another
| > charged fermion through this complexity? Feynman was right; it has to
be
| > simplified.
|
| Of course, it is impossible to predict the time evolution of the wave
| function in the complex picture with virtual particles. That's my
| whle point. Of course, Feynman was right, and it has to be simplified.
| That's what I did: I simplified the theory without losing a bit of
| its predictive power, and even added to its predictive power.

What does it predict that is "additional"?

| > The interaction "space" is really a blob and all we care about
| > are initial states and final states. But it is not wrong for us to
| > eventually want to know exactly what happens in the "blob". I think we
just
| > don't know what all the quantum vacuum objects are yet is what is
preventing
| > us from figuring out the exact complexity.
|
| You cannot figure out what's inside the "blob" because you are using
| wrong QED Hamiltonian. I can predict exactly what's inside the "blob".
| Note also that in the macroscopic low-energy limit the "blob" becomes
| very big: centimeters, meters, etc. in size. So, the interacting
| time evolution becomes directly observable. QED cannot predict this time
| evolution, as you already pointed out. In order to make such
| prediction you need to abandon QED and switch to the classical
| Maxwell's theory with point particles and electromagnetic
| potentials. My theory works in the full range of energies.

I am interested in this. Show me a simple example.

| > For some good analogs of how mass and charge can be emergent from the
| > quantum vacuum, see Volovik's "The Universe in a Helium Droplet". It is
| > possible to model the quantum vacuum as if it has bound charge with
cells
| > equal to Q_vac = +,- sqrt(hbar*c). I have been working on this for over
a
| > year now and it gets more consistent as time passes. This means the
quantum
| > vacuum consists of coupled oscillators. Figuring out the exact geometry
of
| > coupling is mind boggling but hopefullly not intractable. It takes
quite a
| > different way of thinking about interactions as gauge bosons require a
| > different interpretation from the Standard Model.
|
| It would be nice to see how somebody can derive electron mass and charge
| from something more fundamental. So far, I haven't seen that.
| In my approach, vacuum is just a state without particles. Electron
| is a single particle with mass and charge taken directly from
| experiment. There is no interaction between single electron and the
| vacuum. Interaction is present when there are two or more particles.

Here is a semi-classical heuristic for electron mass in CGS units.

m_e = (sqrt(hbar*c)e/w_C^2*sqrt(alpha))(2pi/lambda_C)^3

With w = angular frequency, lambda_C = electron compton wavelength and alpha
= fine structure constant. So this tells use that electron mass is an
interaction between vacuum charge and electronic charge divided by frequency
squared per a volume of space. We figure that sqrt(alpha) is a geometric
factor and goes with the volume of space. The above expression reduces to
the familiar electron compton wavelength expression which is known to be
true experimentally.

m_e = 2pi*hbar/lambda_C*c

Now electronic charge is a much tougher one because you have to know the
exact geometrical configuration of the quantum vacuum. But the simple
heuristic is e = sqrt(alpha*hbar*c). The square root of alpha is simply the
ratio between electronic charge and vacuum charge. I believe that alpha is
a geometric factor involving volumes of space.

| > | > | In non-renormalizable theory you need to modify infinite number of
| > | > | parameters. QED and standard model are renormalizable, but you
| > | > | still need to perform the subtraction of divergences there.
| > | >
| > | > It seems so simple. You just need to get rid of divergences that
| > shouldn't
| > | > be there in the first place. I don't see any problem as Bill
mentions
| > | > below.
| > |
| > | The problem is that the charge and mass calculated from the theory are
| > | not the same as the charge and mass put there in the beginning
..Ifthis
| > | is your ideal of consistency, then fine. I think, we can do better.
| >
| > True. And you are right; we can do better if we have the correct
picture.
| >
| > | > | > The point though is this - for energies much less than the
cutoff
| > the
| > | > theory
| > | > | > looks renomlaisable, and has all these infinites even though the
| > real
| > | > one
| > | > | > may not. That is the key point. We recognize that QED is not
| > | > findamamental
| > | > | > and so the infinites we 'sweep' under the rug are not
fundamental
| > | > either -
| > | > | > they are simply a result of it being a low energy approximation
to
| > | > another
| > | > | > better theory. That is the basis of the effective field theory
| > | > approach.
| > | > | >
| > | > |
| > | > | OK, we may disgree whether infinites create a problem or not. My
| > | > | bottomline is this: I have a consistent Hamiltonian which allows
| > | > | to calculate the time evolution of interacting charged particles.
| > | > | I claim that existing theory cannot do that. If you think
otherwise,
| > | > | I would appreciate references with the explicit form of the
| > | > | Hamiltonian, at least in low orders of the perturbation theory.
| > | >
| > | > What does this mean "to calculate the time evolution of"? Why do we
| > need to
| > | > know that? Particles go in and particles come out and we have
effective
| > | > theory that can describe the initial and final states. Do we really
| > need to
| > | > know exactly what is happening "during" the interaction? IMHO,
| > space-time
| > | > is funny and wierd at the quantum level anywise.
| > |
| > | You would probably agree that we can observe time evolution of charged
| > | particles in the macroscopic world: particles move along some
| > | trajectories, or if you like more quantum mechanics, the wave
functions
| > | evolve in time. QFT does not provide this kind of description.
| > | So, QFT is completely useless in the macroscopic low-energy limit.
| > | It can predict only asymptotic limits of time evolution.
| > | My suggestion is very simple: we just need to
| > | modify the Hamiltonian of the theory, so that old predictions
(S-matrix)
| > | are still valid, and new predictions (time evolution) are now
possible.
| > | What's wrong with this idea?
| >
| > There is nothing basically wrong with that idea. I am not sure it is
really
| > needed unless it can give us more fundamental insight as to what is
really
| > going on. Can it?
| >
| > FrediFizzx
| >
|
| It gives a lot of new insight.
| First, now you can directly calculate the
| time evolution of the wave function during interaction.
| Second, you can now forget about the mind boggling picture with
| virtual particles and work with real particles and potentials
| between them, just as in ordinary quantum mechanics.
| Third, I predict that the potentials acting between particles
| (Coulomb, magnetic, spin-orbit etc.) are instantaneous. This can be
| verified by experiment.
| Fourth, the theory predicts small (but fundamentally important)
| deviations from Einstein's predictions, for example, in the case of
| the decay of fast moving particles.
| Finally, this approach demonstrates that Lorentz transformations
| are not exact and universal, and that Minkowski space-time is an
| approximation.

Hmmm... So what is the interpretation of gauge bosons in your idea?

FrediFizzx

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  #40  
Old 08-09-2004, 06:28 AM
Bilge
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Posts: n/a
Default A version of QED without ultraviolet divergences

Eugene:


Consider the decay of the \pi-: \pi- --> \mu-\nubar. Now consider
one of the three diagrams for the weak vector current in a nuclear
beta decay:
e- \nubar
| /
|/
. . The neutron emits a virtual \pi-, the \pi-
\pi- . . \pi_0 decays into a virtual \pi_0, a real e- and
. . a real anti-neutrino.
N ->-+--P-->-+-->

In this instance we have two propagating particles produced by the
weak decay of a vitual pion. If one is to take seriously the idea that
those are virtual pions in the beta decay diagram, then there is an
implied experimental consequence for the decay of the \pi-, namely
the following decay has to exist,

\pi- -> \pi_0 + \e- + \nubar

and in fact, that decay mode was predicted on that basis. The
branching ration is on the order of 10^-8, so this particular
decay was not one of the decays which had been previously
observed (this occured in the 1950's). You also might look up
``fierz interference'', for another example.


I don't really see the objection to virtual particles. Have you ever
observed a dipole moment? How about an angular momentum? Is it physical
non-sense to write out a multipole expansion for a charge or mass
distribution and associate particular phenomena with particular terms in
the distribution? Is a quadrupole operator an artifact or does that mean
something? For some reason, lots of people (not just you) seem to have no
problem at all collecting terms in an equation in a specific way and give
them the physical significance of being responsible for particular
phenomena, yet those same people find it odd to do the same thing where
virtual particles are concerned.

[...]

The relation between the quark charges and lepton charges can be
derived and while the precise value for the lepton and quark masses
are not derivable, the fact that the masses are non-zero _is_ derivable.
The uncertainty regarding the neutrino masses being zero was due to
the fact that the neutrinos have no charge and therefore could have
been massless.


What holds the electron charge together?


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