[SOLVED] The time it takes to emit one photon

Eugene Stefanovich

Igor Khavkine wrote:

>>You are saying that the interference patterns in the high-intensity
>>and low-intensity regimes must be interpreted as manifestations of
>>two different physical laws. I am saying that there is no difference.
>>In both cases the interference appears due to the quantum law
>>of addition of particle quantum amplitudes.
>>In the high-intensity case the
>>particle nature of light is hidden by the huge number of particles
>>involved.
>
>
> There is no difference between the diffraction patterns because they are
> predicted by the same set of linear equations. What is different is what
> these equations are applied to. In one case they are applied to
> classical fields (continuous intensity, no quantum effects), while in
> the other case they are applied to the wave function (the interference
> pattern is built up individual dots exactly the same way as for single
> electron diffraction, obvious quantum effects). The "thing" that
> satisfies the equations in each case cannot be the same.

Let us then use the analogy between photon diffraction/interference
and electron diffraction/interference. I.e., instead of Young's
experiment with light use Feynman's double-slit experiment with
electrons. There are lot of similarities. By adjusting electrons
energies one can get the diffraction pattern almost the same as in
the case with photons. I would expect that theoretical descriptions
should be very similar for photons and electrons.

If we follow your logic, then electron diffraction in the case
of a weak electron source (electrons emitted one-by-one) should be
described in terms of particle quantum mechanics. I agree
with you here. However, by your logic, if we use high intensity
electron gun (individual particles cannot be distinguished), then
instead of QM description we need to use some kind of "classical
field" description (similar to Maxwell's equations). I don't think
such a classical wave theory of electrons even exists.

In my view, for both photons and electrons and in both low-intensity
and high-intensity cases one should use good old quantum mechanics
in order to describe the diffraction and interference effects.
When intensity of the source goes up, nothing changes in the quantum
properties of individual particles (photons or electrons).
So, Maxwell's equations used for photons in the high intensity regime
are, actually, a simplified way of doing quantum mechanics.
Maxwell just found a clever way to substitute the wave function of
billions of photons by two vector functions E(x,t) and B(x,t).

Eugene.

Eugene Stefanovich

Igor Khavkine wrote:

>>You are saying that the interference patterns in the high-intensity
>>and low-intensity regimes must be interpreted as manifestations of
>>two different physical laws. I am saying that there is no difference.
>>In both cases the interference appears due to the quantum law
>>of addition of particle quantum amplitudes.
>>In the high-intensity case the
>>particle nature of light is hidden by the huge number of particles
>>involved.
>
>
> There is no difference between the diffraction patterns because they are
> predicted by the same set of linear equations. What is different is what
> these equations are applied to. In one case they are applied to
> classical fields (continuous intensity, no quantum effects), while in
> the other case they are applied to the wave function (the interference
> pattern is built up individual dots exactly the same way as for single
> electron diffraction, obvious quantum effects). The "thing" that
> satisfies the equations in each case cannot be the same.

Let us then use the analogy between photon diffraction/interference
and electron diffraction/interference. I.e., instead of Young's
experiment with light use Feynman's double-slit experiment with
electrons. There are lot of similarities. By adjusting electrons
energies one can get the diffraction pattern almost the same as in
the case with photons. I would expect that theoretical descriptions
should be very similar for photons and electrons.

If we follow your logic, then electron diffraction in the case
of a weak electron source (electrons emitted one-by-one) should be
described in terms of particle quantum mechanics. I agree
with you here. However, by your logic, if we use high intensity
electron gun (individual particles cannot be distinguished), then
instead of QM description we need to use some kind of "classical
field" description (similar to Maxwell's equations). I don't think
such a classical wave theory of electrons even exists.

In my view, for both photons and electrons and in both low-intensity
and high-intensity cases one should use good old quantum mechanics
in order to describe the diffraction and interference effects.
When intensity of the source goes up, nothing changes in the quantum
properties of individual particles (photons or electrons).
So, Maxwell's equations used for photons in the high intensity regime
are, actually, a simplified way of doing quantum mechanics.
Maxwell just found a clever way to substitute the wave function of
billions of photons by two vector functions E(x,t) and B(x,t).

Eugene.

Eugene Stefanovich

Igor Khavkine wrote:

>>You are saying that the interference patterns in the high-intensity
>>and low-intensity regimes must be interpreted as manifestations of
>>two different physical laws. I am saying that there is no difference.
>>In both cases the interference appears due to the quantum law
>>of addition of particle quantum amplitudes.
>>In the high-intensity case the
>>particle nature of light is hidden by the huge number of particles
>>involved.
>
>
> There is no difference between the diffraction patterns because they are
> predicted by the same set of linear equations. What is different is what
> these equations are applied to. In one case they are applied to
> classical fields (continuous intensity, no quantum effects), while in
> the other case they are applied to the wave function (the interference
> pattern is built up individual dots exactly the same way as for single
> electron diffraction, obvious quantum effects). The "thing" that
> satisfies the equations in each case cannot be the same.

Let us then use the analogy between photon diffraction/interference
and electron diffraction/interference. I.e., instead of Young's
experiment with light use Feynman's double-slit experiment with
electrons. There are lot of similarities. By adjusting electrons
energies one can get the diffraction pattern almost the same as in
the case with photons. I would expect that theoretical descriptions
should be very similar for photons and electrons.

If we follow your logic, then electron diffraction in the case
of a weak electron source (electrons emitted one-by-one) should be
described in terms of particle quantum mechanics. I agree
with you here. However, by your logic, if we use high intensity
electron gun (individual particles cannot be distinguished), then
instead of QM description we need to use some kind of "classical
field" description (similar to Maxwell's equations). I don't think
such a classical wave theory of electrons even exists.

In my view, for both photons and electrons and in both low-intensity
and high-intensity cases one should use good old quantum mechanics
in order to describe the diffraction and interference effects.
When intensity of the source goes up, nothing changes in the quantum
properties of individual particles (photons or electrons).
So, Maxwell's equations used for photons in the high intensity regime
are, actually, a simplified way of doing quantum mechanics.
Maxwell just found a clever way to substitute the wave function of
billions of photons by two vector functions E(x,t) and B(x,t).

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Eugene Stefanovich

"Igor Khavkine" <igor.kh@gmail.com> wrote in message
news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...

> > So far so good. The only thing is that quantum fields are not necessary
> > for describing the systems with a variable number of particles in the
> > Fock space. Such a description can be formulated entirely in the
> > language of "composite" wavefunctions, where each fixed-particle-number
> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
> > coefficient, and the sum of squares of all such coefficients is 1.
>
> Necessity is a subjective notion. Necessary to whom? To yourself, who
> does not use the field formulation? Or to the hunderds (thousands?) of
> physicists who do? Equivalence is what it is. You either either
> contradict it or you don't. If you do, I suggest you avail yourself of
> the references I cited numerous times and follow the proof yourself. If
> you don't, you've said nothing to change other people's opinions of QFT.

Thank you for acknowledging that my particle-based approach is equivalent
to the traditional field-based aproach. I may agree with you that both
approaches
lead to the same numerical results. However, I hope you'd agree that they
offer
two different perspectives. One approach says: "Fields are basic
ingredients.
Particles are excitations of fields". Another approach says: "Particles are
basic
ingredients. Fields are just formal mathematical constructs"

I hope you'd also agree that having more than one perspectives or equivalent
formulations of the theory is a very useful thing. Take for example quantum
mechanics.
Heisenberg's matrix mechanics, Schroedinger's wave mechanics, and Feynman's
path integrals are three different perspectives that enhance and enrich each
other.
Some property that may look obscure in one formulation may be completely
transparent in
another formulation.

Another example is the old debate about the center of the universe.
Now we know that the choice of the frame of reference - either connected
to the Sun or to the Earth - is completely arbitrary. We can write all
equations
in both these frames. However, it appears that equations governing the
movement
of planets take especially simple form in the heliocentric system. This was
crucial
for formulation of the law of gravitation by Newton.

> > This is not a purely philosophical debate. Particle picture is
> > essential to make the "dressing transformation" in QFT and to
> > eliminate "bare particles" and "ultraviolet infinities" for good.
>
> Yes it is. The ultraviolet infinities have been eliminated long before
> your philosophy or "dressing transformation" existed. Old news. We've
> been there.

Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
True, one can have a completely finite formulation in terms of
Glazek-Wilson "similarity renormalization". However, this approach
requires unphysical "bare particles". The only approach to QFT that
can be formulated from the beginning to the end without encountering
a single divergent integral or bare particles is RQD.

> > The number of particles (including photons) in the Universe is finite.
> > Field theories seem to disregard this important fact. They use infinite
> > number of degrees of freedom to describe even one electron
> > with its field.
>
> Your objection is void. Any normalizable state in Fock space has a
> finite expectation value for the number of particles. Just like,
> classically, any physical field configuration has finite energy.

I was talking about the number of degrees of freedom, which is infinite
for fields in any finite volume. Please understand me, I am not saying that
field
theories are wrong. I am saying that there exists an alternative
particle-based
approach that seems to be simpler and more intuitive.

> > Take the Young's double-slit experiment. Maxwell's wave theory describes
> > the light intensity on the screen by continuous functions E(x) and
> > B(x). This is all fine while the intensity of light is high: there are
> > many photons, and the light intensity appears continuous on the screen.
> > At low intensities, when we can distinguish individual
> > photons on the screen, the field description doesn't work anymore.
> > The light intensity produced by one photon is more like a
> > delta-function. One can reconsile these two contradicting
> > descriptions in the tradition
> > of quantum mechanics.
>
> This situation is handled no differently than single electron
> diffraction. The distribution pattern of detections is predicted by the
> amplitude of the single photon wave function. As I illustrated above,
> this wave function satisfies the wave equation for a relativistic vector
> particle. There aren't that many wave equations that have this property.
> In fact, there is only one, we call it "Maxwell's equations".

Let me rephrase what you said to see if I understood it correctly.
You are saying:
1. In the case of high intensities, the light diffraction is a classical
phenomenon described by Maxwell's wave equation.
2. In the case of low intensity, the diffraction pattern has quantum
origin, but individual photons are still described by the same Maxwell's
equation, so the diffraction pattern does not change.

What I cannot understand is how the switch is ossured (physically, not
formally) between quantum and classical mechanisms when we simply change
the light intensity (the number of photons) without changing anything else.

> > One can say that E(x) and B(x) are "sort of"
> > photon wave functions, and when the photon reaches the screen these
> > wavefunctions collapse to produce a single observable dot.
> > This is my interpretation of Maxwell's theory: the fields E(x) and B(x)
> > there are some surrogates of multi-photon wavefunctions that remained
> > after we took the (incomplete) classical limit from QED to the theory in
> > which electrons are treated classically, while photons (due to their
> > zero mass) are treated in a "sort of" quantum way.
>
> What would be really nice is if you could give an even "sort of" precise
> and quantitative statement of this correspondence. Something like a
> formula relating these many-photon states to the electric and magnetic
> fields, perhaps?

First, I don't think that the task is to reproduce Maxwell's fields E(x)
and B(x) and related equations. I think, these fields and equations are
phenomenological constructs. They were designed to fit Faraday's
empirical observations, and I am not sure that Maxwell's theory will
folow in its entirety as a "classical" limit of the more general QED.

My goal is to have a simplified formulation of QED in which electrons
are treated in the classical (hbar -> 0) limit, while (some simplified)
quantum desription is used for photons. I started to do that in my book,
but this task is not completed. In the case of low accelerations, when
radiation can be neglected, I have a theory of charged particles
interacting at a distance. Taking into account the emission and
absorption of photons is more tricky. One needs to find a way to
approximate multi-photon wavefunctions by functions with a few
arguments. It has not been done yet.

Eugene.

Igor Khavkine

On 2005-08-28, Eugene Stefanovich <eugene_stefanovich@usa.net> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...
>
>> > So far so good. The only thing is that quantum fields are not necessary
>> > for describing the systems with a variable number of particles in the
>> > Fock space. Such a description can be formulated entirely in the
>> > language of "composite" wavefunctions, where each fixed-particle-number
>> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
>> > coefficient, and the sum of squares of all such coefficients is 1.
>>
>> Necessity is a subjective notion. Necessary to whom? To yourself, who
>> does not use the field formulation? Or to the hunderds (thousands?) of
>> physicists who do? Equivalence is what it is. You either either
>> contradict it or you don't. If you do, I suggest you avail yourself of
>> the references I cited numerous times and follow the proof yourself. If
>> you don't, you've said nothing to change other people's opinions of QFT.
>
> Thank you for acknowledging that my particle-based approach is
> equivalent to the traditional field-based aproach.

Before you go giddy with joy, let me point out that both approaches are
taditional, that even the equivalence between them is traditional, and
that you have no priority claim to either of them. The Hilbert space
consisting of (anti)symmetrized wave functions with a variable number of
arguments lies at the very core of second quantization. It is explicitly
used, for example, in F.A. Berezin, _Method of Second Quantization_
(1966), and many other places.

>> > This is not a purely philosophical debate. Particle picture is
>> > essential to make the "dressing transformation" in QFT and to
>> > eliminate "bare particles" and "ultraviolet infinities" for good.
>>
>> Yes it is. The ultraviolet infinities have been eliminated long
>> before your philosophy or "dressing transformation" existed. Old
>> news. We've been there.
>
> Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
> True, one can have a completely finite formulation in terms of
> Glazek-Wilson "similarity renormalization". However, this approach
> requires unphysical "bare particles". The only approach to QFT that
> can be formulated from the beginning to the end without encountering a
> single divergent integral or bare particles is RQD.

Are you not forgetting something? Previous discussion has made it clear
that you use the same renormalization procedures, that you so deplore,
to construct the coefficients in the Hamiltonian of your theory. This
voids any claims of superiority that your theory can make. I also seem
to recall that this point has been made on half a dozen separate
occasions. Do you intend to repeat the above claim again?

> Please understand me, I am
> not saying that field theories are wrong. I am saying that there
> exists an alternative particle-based approach that seems to be simpler
> and more intuitive.

Does a particle based approach exist? Yes. Does it always exist? No.
The cases where it fails have already been discussed in the thread
news:TmTje.9720$Db6.6575@okepread05 . Simpler and more intuitive? That
entirely depends on your personal preference. Anyone is free to make up
their own mind, especially since both approaches are described in
standard texts. What is unfortunate is that their equivalence is not
made as explicit as it could be.

> Let me rephrase what you said to see if I understood it correctly.
> You are saying: 1. In the case of high intensities, the light
> diffraction is a classical phenomenon described by Maxwell's wave
> equation. 2. In the case of low intensity, the diffraction pattern
> has quantum origin, but individual photons are still described by the
> same Maxwell's equation, so the diffraction pattern does not change.
>
> What I cannot understand is how the switch is ossured (physically, not
> formally) between quantum and classical mechanisms when we simply
> change the light intensity (the number of photons) without changing
> anything else.

In either case, the underlying description is quantum. One way to obtain
the classical limit is to look at a particular set of states that
reproduce the classical results, through expectation values, to high
videlity. These are so called coherent states.

Let N be the particle number operator. The particle description is
appropriate when its expectation value has a small variance,
<N^2>-<N>^2. When this quantity is large, the field description is more
appropriate. For coherent states <N^2>-<N>^2 ~ <N>. On the other hand,
field intensity is proportional to <N>. So if you change the intensity
from high to low, you are changing <N> from high to low, and hence
changing <N^2>-<N>^2 from high to low. In other words, you are smoothly
going from the (classical) field description to the (classical) particle
description. The underlying quantum formalism does not change.

> First, I don't think that the task is to reproduce Maxwell's fields
> E(x) and B(x) and related equations. I think, these fields and
> equations are phenomenological constructs. They were designed to fit
> Faraday's empirical observations,

There is no higher goal of theoretical physics than fitting empirical
observations. Maxwell's equations do so admirably and any theory that
claims to supercede them must reproduce them in the limits where they
are known to be valid.

> and I am not sure that Maxwell's
> theory will folow in its entirety as a "classical" limit of the more
> general QED.

Maxwell's equations do follow from QED. This has been known (read
demonstrated) since the time of Pauli, Dirac and Fermi.

> My goal is to have a simplified formulation of QED in which electrons
> are treated in the classical (hbar -> 0) limit, while (some
> simplified) quantum desription is used for photons. I started to do
> that in my book, but this task is not completed. In the case of low
> accelerations, when radiation can be neglected, I have a theory of
> charged particles interacting at a distance. Taking into account the
> emission and absorption of photons is more tricky. One needs to find a
> way to approximate multi-photon wavefunctions by functions with a few
> arguments. It has not been done yet.

It's an admirable goal, and I wish you luck with it. However, it would
greatly help your theory to be taken seriously if you avoid
premature/ill-informed claims of success, superiority, priority, or
deficiencies of existing theories.

Igor

Igor Khavkine

On 2005-08-28, Eugene Stefanovich <eugene_stefanovich@usa.net> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...
>
>> > So far so good. The only thing is that quantum fields are not necessary
>> > for describing the systems with a variable number of particles in the
>> > Fock space. Such a description can be formulated entirely in the
>> > language of "composite" wavefunctions, where each fixed-particle-number
>> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
>> > coefficient, and the sum of squares of all such coefficients is 1.
>>
>> Necessity is a subjective notion. Necessary to whom? To yourself, who
>> does not use the field formulation? Or to the hunderds (thousands?) of
>> physicists who do? Equivalence is what it is. You either either
>> contradict it or you don't. If you do, I suggest you avail yourself of
>> the references I cited numerous times and follow the proof yourself. If
>> you don't, you've said nothing to change other people's opinions of QFT.
>
> Thank you for acknowledging that my particle-based approach is
> equivalent to the traditional field-based aproach.

Before you go giddy with joy, let me point out that both approaches are
taditional, that even the equivalence between them is traditional, and
that you have no priority claim to either of them. The Hilbert space
consisting of (anti)symmetrized wave functions with a variable number of
arguments lies at the very core of second quantization. It is explicitly
used, for example, in F.A. Berezin, _Method of Second Quantization_
(1966), and many other places.

>> > This is not a purely philosophical debate. Particle picture is
>> > essential to make the "dressing transformation" in QFT and to
>> > eliminate "bare particles" and "ultraviolet infinities" for good.
>>
>> Yes it is. The ultraviolet infinities have been eliminated long
>> before your philosophy or "dressing transformation" existed. Old
>> news. We've been there.
>
> Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
> True, one can have a completely finite formulation in terms of
> Glazek-Wilson "similarity renormalization". However, this approach
> requires unphysical "bare particles". The only approach to QFT that
> can be formulated from the beginning to the end without encountering a
> single divergent integral or bare particles is RQD.

Are you not forgetting something? Previous discussion has made it clear
that you use the same renormalization procedures, that you so deplore,
to construct the coefficients in the Hamiltonian of your theory. This
voids any claims of superiority that your theory can make. I also seem
to recall that this point has been made on half a dozen separate
occasions. Do you intend to repeat the above claim again?

> Please understand me, I am
> not saying that field theories are wrong. I am saying that there
> exists an alternative particle-based approach that seems to be simpler
> and more intuitive.

Does a particle based approach exist? Yes. Does it always exist? No.
The cases where it fails have already been discussed in the thread
news:TmTje.9720$Db6.6575@okepread05 . Simpler and more intuitive? That
entirely depends on your personal preference. Anyone is free to make up
their own mind, especially since both approaches are described in
standard texts. What is unfortunate is that their equivalence is not
made as explicit as it could be.

> Let me rephrase what you said to see if I understood it correctly.
> You are saying: 1. In the case of high intensities, the light
> diffraction is a classical phenomenon described by Maxwell's wave
> equation. 2. In the case of low intensity, the diffraction pattern
> has quantum origin, but individual photons are still described by the
> same Maxwell's equation, so the diffraction pattern does not change.
>
> What I cannot understand is how the switch is ossured (physically, not
> formally) between quantum and classical mechanisms when we simply
> change the light intensity (the number of photons) without changing
> anything else.

In either case, the underlying description is quantum. One way to obtain
the classical limit is to look at a particular set of states that
reproduce the classical results, through expectation values, to high
videlity. These are so called coherent states.

Let N be the particle number operator. The particle description is
appropriate when its expectation value has a small variance,
<N^2>-<N>^2. When this quantity is large, the field description is more
appropriate. For coherent states <N^2>-<N>^2 ~ <N>. On the other hand,
field intensity is proportional to <N>. So if you change the intensity
from high to low, you are changing <N> from high to low, and hence
changing <N^2>-<N>^2 from high to low. In other words, you are smoothly
going from the (classical) field description to the (classical) particle
description. The underlying quantum formalism does not change.

> First, I don't think that the task is to reproduce Maxwell's fields
> E(x) and B(x) and related equations. I think, these fields and
> equations are phenomenological constructs. They were designed to fit
> Faraday's empirical observations,

There is no higher goal of theoretical physics than fitting empirical
observations. Maxwell's equations do so admirably and any theory that
claims to supercede them must reproduce them in the limits where they
are known to be valid.

> and I am not sure that Maxwell's
> theory will folow in its entirety as a "classical" limit of the more
> general QED.

Maxwell's equations do follow from QED. This has been known (read
demonstrated) since the time of Pauli, Dirac and Fermi.

> My goal is to have a simplified formulation of QED in which electrons
> are treated in the classical (hbar -> 0) limit, while (some
> simplified) quantum desription is used for photons. I started to do
> that in my book, but this task is not completed. In the case of low
> accelerations, when radiation can be neglected, I have a theory of
> charged particles interacting at a distance. Taking into account the
> emission and absorption of photons is more tricky. One needs to find a
> way to approximate multi-photon wavefunctions by functions with a few
> arguments. It has not been done yet.

It's an admirable goal, and I wish you luck with it. However, it would
greatly help your theory to be taken seriously if you avoid
premature/ill-informed claims of success, superiority, priority, or
deficiencies of existing theories.

Igor

Igor Khavkine

On 2005-08-28, Eugene Stefanovich <eugene_stefanovich@usa.net> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...
>
>> > So far so good. The only thing is that quantum fields are not necessary
>> > for describing the systems with a variable number of particles in the
>> > Fock space. Such a description can be formulated entirely in the
>> > language of "composite" wavefunctions, where each fixed-particle-number
>> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
>> > coefficient, and the sum of squares of all such coefficients is 1.
>>
>> Necessity is a subjective notion. Necessary to whom? To yourself, who
>> does not use the field formulation? Or to the hunderds (thousands?) of
>> physicists who do? Equivalence is what it is. You either either
>> contradict it or you don't. If you do, I suggest you avail yourself of
>> the references I cited numerous times and follow the proof yourself. If
>> you don't, you've said nothing to change other people's opinions of QFT.
>
> Thank you for acknowledging that my particle-based approach is
> equivalent to the traditional field-based aproach.

Before you go giddy with joy, let me point out that both approaches are
taditional, that even the equivalence between them is traditional, and
that you have no priority claim to either of them. The Hilbert space
consisting of (anti)symmetrized wave functions with a variable number of
arguments lies at the very core of second quantization. It is explicitly
used, for example, in F.A. Berezin, _Method of Second Quantization_
(1966), and many other places.

>> > This is not a purely philosophical debate. Particle picture is
>> > essential to make the "dressing transformation" in QFT and to
>> > eliminate "bare particles" and "ultraviolet infinities" for good.
>>
>> Yes it is. The ultraviolet infinities have been eliminated long
>> before your philosophy or "dressing transformation" existed. Old
>> news. We've been there.
>
> Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
> True, one can have a completely finite formulation in terms of
> Glazek-Wilson "similarity renormalization". However, this approach
> requires unphysical "bare particles". The only approach to QFT that
> can be formulated from the beginning to the end without encountering a
> single divergent integral or bare particles is RQD.

Are you not forgetting something? Previous discussion has made it clear
that you use the same renormalization procedures, that you so deplore,
to construct the coefficients in the Hamiltonian of your theory. This
voids any claims of superiority that your theory can make. I also seem
to recall that this point has been made on half a dozen separate
occasions. Do you intend to repeat the above claim again?

> Please understand me, I am
> not saying that field theories are wrong. I am saying that there
> exists an alternative particle-based approach that seems to be simpler
> and more intuitive.

Does a particle based approach exist? Yes. Does it always exist? No.
The cases where it fails have already been discussed in the thread
news:TmTje.9720$Db6.6575@okepread05 . Simpler and more intuitive? That
entirely depends on your personal preference. Anyone is free to make up
their own mind, especially since both approaches are described in
standard texts. What is unfortunate is that their equivalence is not
made as explicit as it could be.

> Let me rephrase what you said to see if I understood it correctly.
> You are saying: 1. In the case of high intensities, the light
> diffraction is a classical phenomenon described by Maxwell's wave
> equation. 2. In the case of low intensity, the diffraction pattern
> has quantum origin, but individual photons are still described by the
> same Maxwell's equation, so the diffraction pattern does not change.
>
> What I cannot understand is how the switch is ossured (physically, not
> formally) between quantum and classical mechanisms when we simply
> change the light intensity (the number of photons) without changing
> anything else.

In either case, the underlying description is quantum. One way to obtain
the classical limit is to look at a particular set of states that
reproduce the classical results, through expectation values, to high
videlity. These are so called coherent states.

Let N be the particle number operator. The particle description is
appropriate when its expectation value has a small variance,
<N^2>-<N>^2. When this quantity is large, the field description is more
appropriate. For coherent states <N^2>-<N>^2 ~ <N>. On the other hand,
field intensity is proportional to <N>. So if you change the intensity
from high to low, you are changing <N> from high to low, and hence
changing <N^2>-<N>^2 from high to low. In other words, you are smoothly
going from the (classical) field description to the (classical) particle
description. The underlying quantum formalism does not change.

> First, I don't think that the task is to reproduce Maxwell's fields
> E(x) and B(x) and related equations. I think, these fields and
> equations are phenomenological constructs. They were designed to fit
> Faraday's empirical observations,

There is no higher goal of theoretical physics than fitting empirical
observations. Maxwell's equations do so admirably and any theory that
claims to supercede them must reproduce them in the limits where they
are known to be valid.

> and I am not sure that Maxwell's
> theory will folow in its entirety as a "classical" limit of the more
> general QED.

Maxwell's equations do follow from QED. This has been known (read
demonstrated) since the time of Pauli, Dirac and Fermi.

> My goal is to have a simplified formulation of QED in which electrons
> are treated in the classical (hbar -> 0) limit, while (some
> simplified) quantum desription is used for photons. I started to do
> that in my book, but this task is not completed. In the case of low
> accelerations, when radiation can be neglected, I have a theory of
> charged particles interacting at a distance. Taking into account the
> emission and absorption of photons is more tricky. One needs to find a
> way to approximate multi-photon wavefunctions by functions with a few
> arguments. It has not been done yet.

It's an admirable goal, and I wish you luck with it. However, it would
greatly help your theory to be taken seriously if you avoid
premature/ill-informed claims of success, superiority, priority, or
deficiencies of existing theories.

Igor

Igor Khavkine

On 2005-08-28, Eugene Stefanovich <eugene_stefanovich@usa.net> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...
>
>> > So far so good. The only thing is that quantum fields are not necessary
>> > for describing the systems with a variable number of particles in the
>> > Fock space. Such a description can be formulated entirely in the
>> > language of "composite" wavefunctions, where each fixed-particle-number
>> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
>> > coefficient, and the sum of squares of all such coefficients is 1.
>>
>> Necessity is a subjective notion. Necessary to whom? To yourself, who
>> does not use the field formulation? Or to the hunderds (thousands?) of
>> physicists who do? Equivalence is what it is. You either either
>> contradict it or you don't. If you do, I suggest you avail yourself of
>> the references I cited numerous times and follow the proof yourself. If
>> you don't, you've said nothing to change other people's opinions of QFT.
>
> Thank you for acknowledging that my particle-based approach is
> equivalent to the traditional field-based aproach.

Before you go giddy with joy, let me point out that both approaches are
taditional, that even the equivalence between them is traditional, and
that you have no priority claim to either of them. The Hilbert space
consisting of (anti)symmetrized wave functions with a variable number of
arguments lies at the very core of second quantization. It is explicitly
used, for example, in F.A. Berezin, _Method of Second Quantization_
(1966), and many other places.

>> > This is not a purely philosophical debate. Particle picture is
>> > essential to make the "dressing transformation" in QFT and to
>> > eliminate "bare particles" and "ultraviolet infinities" for good.
>>
>> Yes it is. The ultraviolet infinities have been eliminated long
>> before your philosophy or "dressing transformation" existed. Old
>> news. We've been there.
>
> Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
> True, one can have a completely finite formulation in terms of
> Glazek-Wilson "similarity renormalization". However, this approach
> requires unphysical "bare particles". The only approach to QFT that
> can be formulated from the beginning to the end without encountering a
> single divergent integral or bare particles is RQD.

Are you not forgetting something? Previous discussion has made it clear
that you use the same renormalization procedures, that you so deplore,
to construct the coefficients in the Hamiltonian of your theory. This
voids any claims of superiority that your theory can make. I also seem
to recall that this point has been made on half a dozen separate
occasions. Do you intend to repeat the above claim again?

> Please understand me, I am
> not saying that field theories are wrong. I am saying that there
> exists an alternative particle-based approach that seems to be simpler
> and more intuitive.

Does a particle based approach exist? Yes. Does it always exist? No.
The cases where it fails have already been discussed in the thread
news:TmTje.9720$Db6.6575@okepread05 . Simpler and more intuitive? That
entirely depends on your personal preference. Anyone is free to make up
their own mind, especially since both approaches are described in
standard texts. What is unfortunate is that their equivalence is not
made as explicit as it could be.

> Let me rephrase what you said to see if I understood it correctly.
> You are saying: 1. In the case of high intensities, the light
> diffraction is a classical phenomenon described by Maxwell's wave
> equation. 2. In the case of low intensity, the diffraction pattern
> has quantum origin, but individual photons are still described by the
> same Maxwell's equation, so the diffraction pattern does not change.
>
> What I cannot understand is how the switch is ossured (physically, not
> formally) between quantum and classical mechanisms when we simply
> change the light intensity (the number of photons) without changing
> anything else.

In either case, the underlying description is quantum. One way to obtain
the classical limit is to look at a particular set of states that
reproduce the classical results, through expectation values, to high
videlity. These are so called coherent states.

Let N be the particle number operator. The particle description is
appropriate when its expectation value has a small variance,
<N^2>-<N>^2. When this quantity is large, the field description is more
appropriate. For coherent states <N^2>-<N>^2 ~ <N>. On the other hand,
field intensity is proportional to <N>. So if you change the intensity
from high to low, you are changing <N> from high to low, and hence
changing <N^2>-<N>^2 from high to low. In other words, you are smoothly
going from the (classical) field description to the (classical) particle
description. The underlying quantum formalism does not change.

> First, I don't think that the task is to reproduce Maxwell's fields
> E(x) and B(x) and related equations. I think, these fields and
> equations are phenomenological constructs. They were designed to fit
> Faraday's empirical observations,

There is no higher goal of theoretical physics than fitting empirical
observations. Maxwell's equations do so admirably and any theory that
claims to supercede them must reproduce them in the limits where they
are known to be valid.

> and I am not sure that Maxwell's
> theory will folow in its entirety as a "classical" limit of the more
> general QED.

Maxwell's equations do follow from QED. This has been known (read
demonstrated) since the time of Pauli, Dirac and Fermi.

> My goal is to have a simplified formulation of QED in which electrons
> are treated in the classical (hbar -> 0) limit, while (some
> simplified) quantum desription is used for photons. I started to do
> that in my book, but this task is not completed. In the case of low
> accelerations, when radiation can be neglected, I have a theory of
> charged particles interacting at a distance. Taking into account the
> emission and absorption of photons is more tricky. One needs to find a
> way to approximate multi-photon wavefunctions by functions with a few
> arguments. It has not been done yet.

It's an admirable goal, and I wish you luck with it. However, it would
greatly help your theory to be taken seriously if you avoid
premature/ill-informed claims of success, superiority, priority, or
deficiencies of existing theories.

Igor

Igor Khavkine

On 2005-08-28, Eugene Stefanovich <eugene_stefanovich@usa.net> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...
>
>> > So far so good. The only thing is that quantum fields are not necessary
>> > for describing the systems with a variable number of particles in the
>> > Fock space. Such a description can be formulated entirely in the
>> > language of "composite" wavefunctions, where each fixed-particle-number
>> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
>> > coefficient, and the sum of squares of all such coefficients is 1.
>>
>> Necessity is a subjective notion. Necessary to whom? To yourself, who
>> does not use the field formulation? Or to the hunderds (thousands?) of
>> physicists who do? Equivalence is what it is. You either either
>> contradict it or you don't. If you do, I suggest you avail yourself of
>> the references I cited numerous times and follow the proof yourself. If
>> you don't, you've said nothing to change other people's opinions of QFT.
>
> Thank you for acknowledging that my particle-based approach is
> equivalent to the traditional field-based aproach.

Before you go giddy with joy, let me point out that both approaches are
taditional, that even the equivalence between them is traditional, and
that you have no priority claim to either of them. The Hilbert space
consisting of (anti)symmetrized wave functions with a variable number of
arguments lies at the very core of second quantization. It is explicitly
used, for example, in F.A. Berezin, _Method of Second Quantization_
(1966), and many other places.

>> > This is not a purely philosophical debate. Particle picture is
>> > essential to make the "dressing transformation" in QFT and to
>> > eliminate "bare particles" and "ultraviolet infinities" for good.
>>
>> Yes it is. The ultraviolet infinities have been eliminated long
>> before your philosophy or "dressing transformation" existed. Old
>> news. We've been there.
>
> Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
> True, one can have a completely finite formulation in terms of
> Glazek-Wilson "similarity renormalization". However, this approach
> requires unphysical "bare particles". The only approach to QFT that
> can be formulated from the beginning to the end without encountering a
> single divergent integral or bare particles is RQD.

Are you not forgetting something? Previous discussion has made it clear
that you use the same renormalization procedures, that you so deplore,
to construct the coefficients in the Hamiltonian of your theory. This
voids any claims of superiority that your theory can make. I also seem
to recall that this point has been made on half a dozen separate
occasions. Do you intend to repeat the above claim again?

> Please understand me, I am
> not saying that field theories are wrong. I am saying that there
> exists an alternative particle-based approach that seems to be simpler
> and more intuitive.

Does a particle based approach exist? Yes. Does it always exist? No.
The cases where it fails have already been discussed in the thread
news:TmTje.9720$Db6.6575@okepread05 . Simpler and more intuitive? That
entirely depends on your personal preference. Anyone is free to make up
their own mind, especially since both approaches are described in
standard texts. What is unfortunate is that their equivalence is not
made as explicit as it could be.

> Let me rephrase what you said to see if I understood it correctly.
> You are saying: 1. In the case of high intensities, the light
> diffraction is a classical phenomenon described by Maxwell's wave
> equation. 2. In the case of low intensity, the diffraction pattern
> has quantum origin, but individual photons are still described by the
> same Maxwell's equation, so the diffraction pattern does not change.
>
> What I cannot understand is how the switch is ossured (physically, not
> formally) between quantum and classical mechanisms when we simply
> change the light intensity (the number of photons) without changing
> anything else.

In either case, the underlying description is quantum. One way to obtain
the classical limit is to look at a particular set of states that
reproduce the classical results, through expectation values, to high
videlity. These are so called coherent states.

Let N be the particle number operator. The particle description is
appropriate when its expectation value has a small variance,
<N^2>-<N>^2. When this quantity is large, the field description is more
appropriate. For coherent states <N^2>-<N>^2 ~ <N>. On the other hand,
field intensity is proportional to <N>. So if you change the intensity
from high to low, you are changing <N> from high to low, and hence
changing <N^2>-<N>^2 from high to low. In other words, you are smoothly
going from the (classical) field description to the (classical) particle
description. The underlying quantum formalism does not change.

> First, I don't think that the task is to reproduce Maxwell's fields
> E(x) and B(x) and related equations. I think, these fields and
> equations are phenomenological constructs. They were designed to fit
> Faraday's empirical observations,

There is no higher goal of theoretical physics than fitting empirical
observations. Maxwell's equations do so admirably and any theory that
claims to supercede them must reproduce them in the limits where they
are known to be valid.

> and I am not sure that Maxwell's
> theory will folow in its entirety as a "classical" limit of the more
> general QED.

Maxwell's equations do follow from QED. This has been known (read
demonstrated) since the time of Pauli, Dirac and Fermi.

> My goal is to have a simplified formulation of QED in which electrons
> are treated in the classical (hbar -> 0) limit, while (some
> simplified) quantum desription is used for photons. I started to do
> that in my book, but this task is not completed. In the case of low
> accelerations, when radiation can be neglected, I have a theory of
> charged particles interacting at a distance. Taking into account the
> emission and absorption of photons is more tricky. One needs to find a
> way to approximate multi-photon wavefunctions by functions with a few
> arguments. It has not been done yet.

It's an admirable goal, and I wish you luck with it. However, it would
greatly help your theory to be taken seriously if you avoid
premature/ill-informed claims of success, superiority, priority, or
deficiencies of existing theories.

Igor

Igor Khavkine

On 2005-08-28, Eugene Stefanovich <eugene_stefanovich@usa.net> wrote:
> "Igor Khavkine" <igor.kh@gmail.com> wrote in message
> news:slrndgti7m.pc8.igor.kh@corum.multiverse.ca...
>
>> > So far so good. The only thing is that quantum fields are not necessary
>> > for describing the systems with a variable number of particles in the
>> > Fock space. Such a description can be formulated entirely in the
>> > language of "composite" wavefunctions, where each fixed-particle-number
>> > function 1, psi(x), phi(x,y), chi(x,y,z) enters with its own
>> > coefficient, and the sum of squares of all such coefficients is 1.
>>
>> Necessity is a subjective notion. Necessary to whom? To yourself, who
>> does not use the field formulation? Or to the hunderds (thousands?) of
>> physicists who do? Equivalence is what it is. You either either
>> contradict it or you don't. If you do, I suggest you avail yourself of
>> the references I cited numerous times and follow the proof yourself. If
>> you don't, you've said nothing to change other people's opinions of QFT.
>
> Thank you for acknowledging that my particle-based approach is
> equivalent to the traditional field-based aproach.

Before you go giddy with joy, let me point out that both approaches are
taditional, that even the equivalence between them is traditional, and
that you have no priority claim to either of them. The Hilbert space
consisting of (anti)symmetrized wave functions with a variable number of
arguments lies at the very core of second quantization. It is explicitly
used, for example, in F.A. Berezin, _Method of Second Quantization_
(1966), and many other places.

>> > This is not a purely philosophical debate. Particle picture is
>> > essential to make the "dressing transformation" in QFT and to
>> > eliminate "bare particles" and "ultraviolet infinities" for good.
>>
>> Yes it is. The ultraviolet infinities have been eliminated long
>> before your philosophy or "dressing transformation" existed. Old
>> news. We've been there.
>
> Feynman-Schwinger-Tomonaga theory "swept infinities under the rug".
> True, one can have a completely finite formulation in terms of
> Glazek-Wilson "similarity renormalization". However, this approach
> requires unphysical "bare particles". The only approach to QFT that
> can be formulated from the beginning to the end without encountering a
> single divergent integral or bare particles is RQD.

Are you not forgetting something? Previous discussion has made it clear
that you use the same renormalization procedures, that you so deplore,
to construct the coefficients in the Hamiltonian of your theory. This
voids any claims of superiority that your theory can make. I also seem
to recall that this point has been made on half a dozen separate
occasions. Do you intend to repeat the above claim again?

> Please understand me, I am
> not saying that field theories are wrong. I am saying that there
> exists an alternative particle-based approach that seems to be simpler
> and more intuitive.

Does a particle based approach exist? Yes. Does it always exist? No.
The cases where it fails have already been discussed in the thread
news:TmTje.9720$Db6.6575@okepread05 . Simpler and more intuitive? That
entirely depends on your personal preference. Anyone is free to make up
their own mind, especially since both approaches are described in
standard texts. What is unfortunate is that their equivalence is not
made as explicit as it could be.

> Let me rephrase what you said to see if I understood it correctly.
> You are saying: 1. In the case of high intensities, the light
> diffraction is a classical phenomenon described by Maxwell's wave
> equation. 2. In the case of low intensity, the diffraction pattern
> has quantum origin, but individual photons are still described by the
> same Maxwell's equation, so the diffraction pattern does not change.
>
> What I cannot understand is how the switch is ossured (physically, not
> formally) between quantum and classical mechanisms when we simply
> change the light intensity (the number of photons) without changing
> anything else.

In either case, the underlying description is quantum. One way to obtain
the classical limit is to look at a particular set of states that
reproduce the classical results, through expectation values, to high
videlity. These are so called coherent states.

Let N be the particle number operator. The particle description is
appropriate when its expectation value has a small variance,
<N^2>-<N>^2. When this quantity is large, the field description is more
appropriate. For coherent states <N^2>-<N>^2 ~ <N>. On the other hand,
field intensity is proportional to <N>. So if you change the intensity
from high to low, you are changing <N> from high to low, and hence
changing <N^2>-<N>^2 from high to low. In other words, you are smoothly
going from the (classical) field description to the (classical) particle
description. The underlying quantum formalism does not change.

> First, I don't think that the task is to reproduce Maxwell's fields
> E(x) and B(x) and related equations. I think, these fields and
> equations are phenomenological constructs. They were designed to fit
> Faraday's empirical observations,

There is no higher goal of theoretical physics than fitting empirical
observations. Maxwell's equations do so admirably and any theory that
claims to supercede them must reproduce them in the limits where they
are known to be valid.

> and I am not sure that Maxwell's
> theory will folow in its entirety as a "classical" limit of the more
> general QED.

Maxwell's equations do follow from QED. This has been known (read
demonstrated) since the time of Pauli, Dirac and Fermi.

> My goal is to have a simplified formulation of QED in which electrons
> are treated in the classical (hbar -> 0) limit, while (some
> simplified) quantum desription is used for photons. I started to do
> that in my book, but this task is not completed. In the case of low
> accelerations, when radiation can be neglected, I have a theory of
> charged particles interacting at a distance. Taking into account the
> emission and absorption of photons is more tricky. One needs to find a
> way to approximate multi-photon wavefunctions by functions with a few
> arguments. It has not been done yet.

It's an admirable goal, and I wish you luck with it. However, it would
greatly help your theory to be taken seriously if you avoid
premature/ill-informed claims of success, superiority, priority, or
deficiencies of existing theories.

Igor