## [SOLVED] The time it takes to emit one photon

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.

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.

 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.
 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.
 On 2005-08-28, Eugene Stefanovich wrote: > "Igor Khavkine" 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, -^2. When this quantity is large, the field description is more appropriate. For coherent states -^2 ~ . On the other hand, field intensity is proportional to . So if you change the intensity from high to low, you are changing from high to low, and hence changing -^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  On 2005-08-28, Eugene Stefanovich wrote: > "Igor Khavkine" 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, -^2. When this quantity is large, the field description is more appropriate. For coherent states -^2 ~ . On the other hand, field intensity is proportional to . So if you change the intensity from high to low, you are changing from high to low, and hence changing -^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
 On 2005-08-28, Eugene Stefanovich wrote: > "Igor Khavkine" 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, -^2. When this quantity is large, the field description is more appropriate. For coherent states -^2 ~ . On the other hand, field intensity is proportional to . So if you change the intensity from high to low, you are changing from high to low, and hence changing -^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  On 2005-08-28, Eugene Stefanovich wrote: > "Igor Khavkine" 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, -^2. When this quantity is large, the field description is more appropriate. For coherent states -^2 ~ . On the other hand, field intensity is proportional to . So if you change the intensity from high to low, you are changing from high to low, and hence changing -^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
 On 2005-08-28, Eugene Stefanovich wrote: > "Igor Khavkine" 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, -^2. When this quantity is large, the field description is more appropriate. For coherent states -^2 ~ . On the other hand, field intensity is proportional to . So if you change the intensity from high to low, you are changing from high to low, and hence changing -^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  On 2005-08-28, Eugene Stefanovich wrote: > "Igor Khavkine" 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, -^2. When this quantity is large, the field description is more appropriate. For coherent states -^2 ~ . On the other hand, field intensity is proportional to . So if you change the intensity from high to low, you are changing from high to low, and hence changing -^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