What are space-like and time-like virtual photons?

[Hans de Vries]

Hi Hans!
I'm still not quite clear whether your saying that "virtual particles" are real.

Hi, Tiny Tim

The math describes EM fields. These fields follow Maxwell's laws and originate
from the charge current density in the scattering zone just as they would classically.
If I use the term "virtual photon" then it's just a nickname for the EM field.

Yes, I'm happy to accept that \psi^\ast\gamma^\mu\psi is a current density and therefore real.

And that the associated field is therefore real.

ok

Which part of \psi^\ast\gamma^\mu\psi is the transition current you're talking about?

(I wiki'ed and googled "transition current", but didn't find anything helpful, and it's not in the index of Weinberg's QTF, Vol I, which is the source of most of my knowledge. I vaguely recall seeing \psi_f^\ast (\partial_\mu \psi_i)\ -\ (\partial_\mu \psi_f^\ast)\psi_i somewhere else, but I think it left out an A² term, and I don't see where it comes in the the simple derivation of the Dyson series, nor why an approximation made of an artificial combination of idealised initial and final fields should be regarded as in any way modelling the real field in the "scattering zone" of an interaction. )

An electron in a scattering zone can change its momentum suddenly from an initial
momentum to a final momentum. Not via a gradually changing path but under a sharp
angle. The reason that it can do so is because an electron can interfere with itself.

For some time the electron will be in a transition state going from initial to final
momentum. Its wavefunction will be a linear combination of the two states and these
states interfere with each other. Now what is this transition interference current?

\psi = \psi_f+\psi_i

Thus the charge current density is given by:

\bar{\psi}\gamma^\mu\psi ~=~ \Big(\bar{\psi_f}\gamma^\mu\psi_f~+~\bar{\psi_i}\gamma^\mu\psi_i \Big) ~~+~~ \Big(\bar{\psi_f}\gamma^\mu\psi_i~+~\bar{\psi_i}\gamma^\mu\psi_f\Big)

The last two terms (the crossterms) represent the interference current. The two
interference terms are each others complex conjugate. Each term contains all
information needed. The Feynman diagram expressions use the first of the two terms.
The basic interference pattern is the same as in the case of a Klein Gordon particle:

\psi_{int} ~~=~~ \exp\left\{ -i(p_f^\mu-p_i^\mu)x_\mu \right\}~+~ \exp\left\{ -i(p_f^\mu-p_i^\mu)x_\mu \right\} ~~=~~ 2\cos\left\{ (p_f^\mu-p_i^\mu)x_\mu \right\}

The cosine functions represents an alternating charge density pattern in case of
a Klein Gordon particle which shifts with a speed of anywhere between 0 and c.
However, we are dealing with a Dirac particle field which also has a spin density.

The alternating spin density is the same as an alternating transverse current density
pattern according to Stokes law. You can see this in figure 1.7 in my book here.
http://physics-quest.org/Book_Chapter_EM_basic.pdf"

The left side of figure 1.7 is effectively the same as the right side according to
Stokes. If you google for "Gordon decomposition" then this is the extra term from
spin in the vector current.

The electromagnetic field from the alternating charge current pattern is derived
in the classical way and this is what is "nicknamed" the "virtual photon"


Regards, Hans

 

[Frame Dragger]

Hi, Tiny Tim

The math describes EM fields. These fields follow Maxwell's laws and originate
from the charge current density in the scattering zone just as they would classically.
If I use the term "virtual photon" then it's just a nickname for the EM field.



ok





An electron in a scattering zone can change its momentum suddenly from an initial
momentum to a final momentum. Not via a gradually changing path but under a sharp
angle. The reason that it can do so is because an electron can interfere with itself.

For some time the electron will be in a transition state going from initial to final
momentum. Its wavefunction will be a linear combination of the two states and these
states interfere with each other. Now what is this transition interference current?

\psi = \psi_f+\psi_i

Thus the charge current density is given by:

\bar{\psi}\gamma^\mu\psi ~=~ \Big(\bar{\psi_f}\gamma^\mu\psi_f~+~\bar{\psi_i}\gamma^\mu\psi_i \Big) ~~+~~ \Big(\bar{\psi_f}\gamma^\mu\psi_i~+~\bar{\psi_i}\gamma^\mu\psi_f\Big)

The last two terms (the crossterms) represent the interference current. The two
interference terms are each others complex conjugate. Each term contains all
information needed. The Feynman diagram expressions use the first of the two terms.
The basic interference pattern is the same as in the case of a Klein Gordon particle:

\psi_{int} ~~=~~ \exp\left\{ -i(p_f^\mu-p_i^\mu)x_\mu \right\}~+~ \exp\left\{ -i(p_f^\mu-p_i^\mu)x_\mu \right\} ~~=~~ 2\cos\left\{ (p_f^\mu-p_i^\mu)x_\mu \right\}

The cosine functions represents an alternating charge density pattern in case of
a Klein Gordon particle which shifts with a speed of anywhere between 0 and c.
However, we are dealing with a Dirac particle field which also has a spin density.

The alternating spin density is the same as an alternating transverse current density
pattern according to Stokes law. You can see this in figure 1.7 in my book here.
http://physics-quest.org/Book_Chapter_EM_basic.pdf"

The left side of figure 1.7 is effectively the same as the right side according to
Stokes. If you google for "Gordon decomposition" then this is the extra term from
spin in the vector current.

The electromagnetic field from the alternating charge current pattern is derived
in the classical way and this is what is "nicknamed" the "virtual photon"


Regards, Hans

This would seem to predict the absence of the observed Casimir Effect.

 

[Hans de Vries]

This would seem to predict the absence of the observed Casimir Effect.

Why?

Regards, Hans

 

[Frame Dragger]

Why?

Regards, Hans

You say that 'virtual photon' is just a nickname essentially, for the classical EM field. If that's the case, explain the Casmimir Effect within that framework. I don't see how you could. Expand that to vacuum polarization and virtual photon to 'virtual any-particle' and I don't see how your argument is consistant.

 

[Hans de Vries]

You say that 'virtual photon' is just a nickname essentially, for the classical EM field. If that's the case, explain the Casmimir Effect within that framework. I don't see how you could. Expand that to vacuum polarization and virtual photon to 'virtual any-particle' and I don't see how your argument is consistant.

You would first have to give a definition of a "virtual photon". Many different things get
all called "virtual photon" causing a lot of confusion.

I'm describing the literal physical meaning of the Dirac algebra in the case of a "virtual
photon" exchange in a Feynman diagram.

In case of the Casimir force the EM field is quantized as a result of the boundary conditions
represented by the flat plates. These are very different processes.Regards, Hans

 

[tiny-tim]

what is the issue?

Hi Hans!

The math describes EM fields. These fields follow Maxwell's laws and originate
from the charge current density in the scattering zone just as they would classically.
If I use the term "virtual photon" then it's just a nickname for the EM field.

Now I'm completely confused as to what we're talking about.

I was hoping we were discussing what other people mean by "virtual particles".

Are you now saying that your use of the phrase "virtual particle" or "virtual photon" is only your use? If so, of course you're perfectly entitled to have a personal use of language, but it doesn't answer the OP's question …

"What are space-like and time-like virtual photons?"​

… since (I assume) he meant, what do people generally mean by "virtual photons"?

I'll restate (or state? in case there's any doubt) my position, which is:

People generally fall into two categories:
i] either they regard virtual particles as simply a mathematical trick (in which case i agree with them),
ii]or they regard virtual particles as real things which are capable of having various properties such as position, time of creation/annihilation, momentum, etc (in which case, I think they're wrong because I see neither experimental evidence nor theoretical prediction of things with such properties).​

Or are you saying that using "virtual photon" simply as another name for the EM field is a common usage (at least among a substantial proportion of authors and/or "laity")?

If so, I doubt that the OP was referring to that usage (and btw I've certainly not come across it) when he asked specifically about time-like and space-like virtual photons, and about how long they exist and can they be directly observed …

Hi,
I'm trying to get my story straight about virtual photons. So far, my understanding of them is that they are the particles that mediate the electromagnetic interaction, and they only exist a short time due to the Heisenberg uncertainty principle meaning that they can't be directly observed.
I've heard of time-like and space-like virtual photons though, and google as I might, I just can't find out what these terms mean. Can anyone explain them to me?
Thanks.

hmm … I'm tempted to suggest wrapping it up like this …

are you saying: "The 'virtual photons' the OP was talking about aren't real, and the term should be used only as a nickname for the EM field" ?

but unfortunately I have a completely different difficulty …

when you say "it's just a nickname for the EM field", I'm not entirely following what you mean by "field" …

i] the electromagnetic (EM) field itself has nothing to do with quantum field theory, or indeed quantum theory of any sort … the EM field was well known to Maxwell, and most of its aspects can be understood perfectly well by high school students …

ii] the field in Quantum Field Theory (QFT) refers to a specific technique, of representing a specific particle (with a specific momentum etc) by a field composed of operators representing every possible momentum etc …

so if you mean i], I don't see how "virtual photons", which are a QFT concept, can be regarded by people generally as referring to a nineteenth-century pre-quantum-theory field

and if you mean ii], calling that field the "EM field" seems to me misleading: in QFT, isn't it the particles (electrons, photons, etc) that have fields, while the force (or interaction) just has a Hamiltonian (composed, admittedly, of fields of particles)?

 

[Frame Dragger]

I'm with Tim on this one. I appreciate what you're saying, and maybe you've had terrible experiences with people inserting virtual particles into basic EM theory, but this doesn't fit the definition of virtual that I know. Virtual photons are mathematical artifacts used in Perturbation Theory... you're talking about something interesting, but different.

 

[Hans de Vries]

Hi, Tiny Tim

I see that you are using Weinberg's The Quantum Theory of Fields vol.I for studying QFT.

Well, It's a very valuable reference work but you'll only understand what he writes
it if you already know about, and understand, the subjects he is talking about...

For understanding Feynman diagrams the most effective road is using David Griffith's
introduction to elementary particles, especially chapters 6 and 7.

Then, for the most important stuff missing in Griffith's, for example the Poincaré group,
the theory of gauge invariance, the Lagrangian formulation, use Lewis H. Ryder's book
Quantum Field Theory.

To see how the path integral formalism can be used to generate series of Feynman
diagrams, take Anthony Zee's book: Quantum Field Theory in a nutshell which starts
of directly with the path integral formalism.

Hi Hans!


Now I'm completely confused as to what we're talking about.

I was hoping we were discussing what other people mean by "virtual particles".

Are you now saying that your use of the phrase "virtual particle" or "virtual photon" is only your use? If so, of course you're perfectly entitled to have a personal use of language, but it doesn't answer the OP's question …

"What are space-like and time-like virtual photons?"​

… since (I assume) he meant, what do people generally mean by "virtual photons"?

I'll restate (or state? in case there's any doubt) my position, which is:

People generally fall into two categories:
i] either they regard virtual particles as simply a mathematical trick (in which case i agree with them),
ii]or they regard virtual particles as real things which are capable of having various properties such as position, time of creation/annihilation, momentum, etc (in which case, I think they're wrong because I see neither experimental evidence nor theoretical prediction of things with such properties).​

Or are you saying that using "virtual photon" simply as another name for the EM field is a common usage (at least among a substantial proportion of authors and/or "laity")?

If so, I doubt that the OP was referring to that usage (and btw I've certainly not come across it) when he asked specifically about time-like and space-like virtual photons, and about how long they exist and can they be directly observed …

I think the best way to answer the OP's question …
What are space-like and time-like virtual photons?"

is to discuss the meaning of the actual mathematics which is going into
the Feynman diagrams. This is what I'm trying to do in my posts..

I do work this out in great detail in my book which contains expressions
which describe the transition interference charge/current density:


<br /> \begin{array}{rcrr}<br /> &amp; &amp; \textbf{\mbox{\textsf{vector transition current}}} ~~~~~~~ &amp; \\<br /> \frac{1}{2m} J^0_{Vfi}~~=<br /> &amp; + &amp; &amp; ~~~\gamma\cos(\omega) \\<br /> &amp; + &amp; \hat{\phi} \cdot\hat{s}~ &amp; ~~i\gamma\sin(\omega) \\<br /> &amp;&amp;&amp;\\<br /> \frac{1}{2m} \vec{J}_{Vfi}~~=<br /> &amp; + &amp; (~\hat{\beta}~+~i\hat{\beta}\times\hat{s}) &amp; ~\beta\gamma\cos(\omega) \\<br /> &amp; + &amp; (~(\hat{\phi}\cdot\hat{\beta})\hat{s}+i\hat{\phi}\times\hat{\beta}-(\hat{\phi}\times\hat{\beta})\times\hat{s}) &amp; i\beta\gamma\sin(\omega) \\&amp;&amp;&amp;\\&amp;&amp;&amp;\\<br /> &amp; &amp; \textbf{\mbox{\textsf{axial transition current}}} ~~~~~~~~ &amp; \\<br /> \frac{1}{2m} J^0_{Afi}~~=<br /> &amp; + &amp; \hat{\beta}\cdot\hat{s}~ &amp; ~\beta\gamma\cos(\omega) \\<br /> &amp; + &amp; (\hat{\phi}\cdot\hat{\beta}+i(\hat{\phi}\times\hat{\beta})\cdot\hat{s}) &amp; i\beta\gamma\sin(\omega) \\<br /> &amp;&amp;&amp;\\<br /> \frac{1}{2m} \vec{J}_{Afi}~~=<br /> &amp; + &amp; \hat{s}~ &amp; ~~~\gamma\cos(\omega) \\<br /> &amp; + &amp; (~\hat{\phi }~+~i\hat{\phi }\times\hat{s}) &amp; ~~i\gamma\sin(\omega) \\<br /> &amp;&amp;&amp;\\<br /> \end{array}<br />

The above expressions are for an electron initially at rest with spin s
and a final state corresponding with a boost to a velocity beta and
a rotation of the spin pointer over an angle w around the axis phi.

The above expression has to be multiplied with the interference
cosine function of my previous post. I intent to post the chapter
online when it is ready.

hmm … I'm tempted to suggest wrapping it up like this …

are you saying: "The 'virtual photons' the OP was talking about aren't real, and the term should be used only as a nickname for the EM field" ?

but unfortunately I have a completely different difficulty …

when you say "it's just a nickname for the EM field", I'm not entirely following what you mean by "field" …

i] the electromagnetic (EM) field itself has nothing to do with quantum field theory, or indeed quantum theory of any sort … the EM field was well known to Maxwell, and most of its aspects can be understood perfectly well by high school students …

Fortunately, that's not true at all . The electromagnetic potential field A
becomes the "wave-function" of the photon in Quantum Electro Dynamics and
the classical Lagrangian density is the same one as the one used in QED

The EM potential field A is related to the charge/current density j via the
classical EM relation. This is the same relation as the one which is used in
the Feynman diagrams

<br /> \Box A^\mu =\ \mu_o j^\mu<br />

\begin{center}<br /> \mbox{d&#039;Alembertian operator: }~~~~<br /> \Box\ =\ \frac{1}{c^2}\frac{\partial^2}{\partial t^2} - \nabla^2<br />


In momentum space this operator is q^2 and its inverse operator is 1/q^2
Multiplying the transition current in the momentum domain with 1/q^2 means
that we are deriving the EM field A in momentum space which is emitted
from the transition charge/current density.

The final step in the Feynman diagram expression for (for instance) electron-
electron scattering is the absorption of this field by transition current of the
other electron. This requires the transition currents to be equal but opposite.

Everything in the Feynman diagrams can be physically understood. It is
just a question of working it out mathematically.


Regards, Hans

 

[tiny-tim]

Hi Hans!

Before I answer the rest of your post, may I just ask for an example that may clear up my misunderstanding: you say …

Everything in the Feynman diagrams can be physically understood. It is just a question of working it out mathematically.

… ok then … what is the physical understanding of an internal electron line in an EM Feynman diagram?

oh, and just a quick question about terminology that I may be misunderstanding (since Weinberg's book makes me used to deriving the 1/(q² + m²) factor without any differentiating in sight ): you say (of the d'Alembertian differential operator) …

In momentum space this operator is q^2 and its inverse operator is 1/q^2

… am I right in thinking that the same operator is more generally 1/(q² + m²), operating equally on both "virtual photons" and "virtual electrons" in the same momentum space?

 

[Hans de Vries]

Hi Hans!

Before I answer the rest of your post, may I just ask for an example that may clear up my misunderstanding: you say …… ok then … what is the physical understanding of an internal electron line in an EM Feynman diagram?

Hi Tiny Tim,

The internal electron line is most easily thought of as the propagation from
the interaction between the incoming electron and photon. Starting from the
interactive Dirac equation.

<br /> \gamma^\mu \left\{~ i\,\mbox{\Large $\partial$}_\mu ~-~ e\mbox{\Large A}_\mu ~\right\}\psi ~=~ m\,\psi<br />

We can isolate the interaction term at the left hand side.

<br /> \Big(\gamma^\mu e\mbox{\Large A}_\mu \Big)\psi ~~=~~<br /> \Big(~ i\gamma^\mu\,\mbox{\Large $\partial$}_\mu ~-~ m ~\Big) \psi <br />

The propagator for the internal electron is the inverse of the operator on the
right hand site. The operator's Fourier transform in the momentum domain is.

<br /> \gamma^\mu\,p_\mu - m<br />

and so the inverse operator is

<br /> \frac{1}{\gamma^\mu\,p_\mu - m} ~~=~~ \frac{\gamma^\mu\,p_\mu ~+~ m}{p^2-m^2}<br />

oh, and just a quick question about terminology that I may be misunderstanding (since Weinberg's book makes me used to deriving the 1/(q² + m²) factor without any differentiating in sight ): you say (of the d'Alembertian differential operator) …… am I right in thinking that the same operator is more generally 1/(q² + m²), operating equally on both "virtual photons" and "virtual electrons" in the same momentum space?

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.Regards, Hans

 

[Frame Dragger]

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.

Is this not equivalent to saying that virtual particles are a mathematical trick to describe/calculate those interactions within Perturbation Theory!?

 

[tiny-tim]

Hi Hans!

… ok then … what is the physical understanding of an internal electron line in an EM Feynman diagram?

The internal electron line is most easily thought of as the propagation from the interaction between the incoming electron and photon. Starting from the interactive Dirac equation …
…
We can isolate the interaction term at the left hand side.
…
The propagator for the internal electron is the inverse of the operator on the
right hand site. The operator's Fourier transform in the momentum domain is.
…
and so the inverse operator is …

That's the mathematical process that the line represents.

A Feynman diagram is just a diagram. It, and any line in it, does no more than represent a mathematical process. And that mathematical process may or may not represent a physical process.

I'm asking, what is the physical understanding of an internal electron line?

d'Alembertian operator: …

In momentum space this operator is q^2 and its inverse operator is 1/q^2

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.

I'm really asking whether it's the same d'Alembertian operator (in coordinate space).

Differential operators as a way of getting to Feynman diagrams are completely foreign to me.

I'm just asking whether there are two d'Alembertian operators, d'A_e for an electron, and d'A_φ for a photon, or is there just one operator, d'A ?

 

[Hans de Vries]

The operators (propagators) always use the invariant mass of the particle.
The off-the-shell "masses" are not really masses. The virtual particles are
always interactions between the fermion field and the electromagnetic field.
The two different types of field always propagate with their own invariant
mass.

Is this not equivalent to saying that virtual particles are a mathematical trick to describe/calculate those interactions within Perturbation Theory!?

I would says that it shows that using the term "virtual particle" is a bad
and confusing habbit. I do it, and everybody does it but it doesn't
behave as such.

A "space-like virtual particle" would propagate with an imaginary mass
and FTL. In reality there is (in QED) only the massless photon propagator
and the lepton propagator its invariant mass.


Regards, Hans

 

[Frame Dragger]

I would says that it shows that using the term "virtual particle" is a bad
and confusing habbit. I do it, and everybody does it but it doesn't
behave as such.

A "space-like virtual particle" would propagate with an imaginary mass
and FTL. In reality there is (in QED) only the massless photon propagator
and the lepton propagator its invariant mass.


Regards, Hans

I agree that a better term should be used, and in general I think the lexicon of SR/GR/QM needs to be revised and codified. That said, it seems that you're agreeing with me, which would disagree with your previous position and therefore agreeing with Tiny-Tim. I'm confused.

 

[Hans de Vries]

Hi Hans!

That's the mathematical process that the line represents.

A Feynman diagram is just a diagram. It, and any line in it, does no more than represent a mathematical process. And that mathematical process may or may not represent a physical process.

I'm asking, what is the physical understanding of an internal electron line?


I'm really asking whether it's the same d'Alembertian operator (in coordinate space).

Differential operators as a way of getting to Feynman diagrams are completely foreign to me.

I'm just asking whether there are two d'Alembertian operators, d'A_e for an electron, and d'A_φ for a photon, or is there just one operator, d'A ?

Hi, Tiny Tim

The Dirac algebra describes real physics, Just like the equations of the electromagnetic
field, and the mathematical symbol handling in Feynman diagrams can be understood
in terms of real physics, or at least in geometrical terms with vectors, axial vectors
and so on. But indeed, the textbooks usually don't get beyond the purely abstract
mathematical symbol handling, which is really sad.
To gain understanding one can to do the following.

-Start with the observables.
These are things which can be visualized: The charge/ current density, the axial
current density, the magnetization/polarization tensor.- Gain an understanding what propagators are in position space,
how the mass less 1/q propagator spreads a signal on the light cone, and how other
propagators can always be derived from (interacting) mass less propagators.-Study how the Weyl bispinor consist out of two interacting Chiral components
(the mass less left and right handed chiral components. How the direction of each
component is both a momentum direction and a spin direction, one with a left handed
chiralty and one with a right handed chiralty.-Understand what the pauli matrices do geometrically,
and what the i does geometrically:

Multiplying by -i\sigma^i rotates the spinor by 180^o around the x^i-axis
Multiplying by i rotates the spinor by -180^o around its own axis

This means that a multiplication of an x-up-spinor by the pauli-x-matrix is rotated
by 0 degrees while the same multiplication rotates an x-down-spinor by 360 degrees,
(which amounts to a multiplication by -1). This provides us with a way to obtain
the x-component of the spin vector of the spinor. The spin-vector is consequently
given by:

<br /> \vec{(\xi)} ~=~<br /> \left(\begin{array}{c}<br /> \xi^*\sigma^x\xi \\ \xi^*\sigma^y\xi \\ \xi^*\sigma^z\xi<br /> \end{array}\right)<br />

This vector represents both a current as well as a spin direction. It means that we
can express the total vector-current, as well as the total axial current, with the
mass-less spin vectors as:

<br /> \begin{array}{ll}<br /> \mbox{vector current:} ~~ &amp; =~~ +\vec{(\xi)}_R - \vec{(\xi)}_L \\<br /> \mbox{axial current:} ~~ &amp; =~~ -\vec{(\xi)}_R - \vec{(\xi)}_L \\<br /> \end{array}<br />

So, now we have already derived these two basic observables in a geometrical
way which we can visualize with pictures representing the underlying physics.Regards, Hans

 

[tiny-tim]

Hi Hans!

Yes, I understand all of that.

(though I don't see what propagators in position space have to do with virtual particles which can only exist in momentum space )

But i don't understand, and you're still not answering, …

what is the physical understanding of an internal electron line? ​

 

[Hans de Vries]

Hi Hans!

Yes, I understand all of that.

(though I don't see what propagators in position space have to do with virtual particles which can only exist in momentum space )

But i don't understand, and you're still not answering, …

what is the physical understanding of an internal electron line? ​

It's an electron propagating under the influence of an electromagnetic field.

An internal electron line originates from the original electron but has a changed
momentum so that the interference charge/current density between the two
generates an electromagnetic field which negates (absorbs) the em field of the
incoming photon.

Regards, Hans

 

[Frame Dragger]

It's an electron propagating under the influence of an electromagnetic field.

An internal electron line originates from the original electron but has a changed
momentum so that the interference charge/current density between the two
generates an electromagnetic field which negates (absorbs) the em field of the
incoming photon.

Regards, Hans

That happens, but that's not a virtual photon.

 

[tiny-tim]

virtual electrons?

Everything in the Feynman diagrams can be physically understood. It is just a question of working it out mathematically.

… ok then … what is the physical understanding of an internal electron line in an EM Feynman diagram?

It's an electron propagating under the influence of an electromagnetic field.

An internal electron line originates from the original electron but has a changed momentum so that the interference charge/current density between the two generates an electromagnetic field which negates (absorbs) the em field of the incoming photon.

(Do you mean "an internal electron originates from the original electron but has a changed momentum {etc}"?)

I don't understand the physical meaning of "originates from the original electron".

"originates" how? where? and how/where does it de-originate?

And are you saying then that there is a physical internal electron for each internal electron line in each Feynman diagram (of which of course there are infinitely many) for the particular process?

And are you saying that there is a separate physical interference charge/current density between the original electron and each separate internal electron? And is there similarly a physical interference charge/current density between each pair of internal electrons?

Finally, what "incoming photon" (whose em field is to be negated)?

I didn't specify either an incoming or an outgoing photon in the interaction, and there doesn't have to be one!​

 

[Hans de Vries]

That happens, but that's not a virtual photon.

They call it a "virtual electron" instead...

 

[Hans de Vries]

(Do you mean "an internal electron originates from the original electron but has a changed momentum {etc}"?)

Yes

I don't understand the physical meaning of "originates from the original electron".

"originates" how? where? and how/where does it de-originate?

It is the original electron field pertubated by the (alternating) photon field.
You have to think about the interaction of planewaves. The scattering zone
is considered wide enough to make this assumption valid.

And are you saying then that there is a physical internal electron for each internal electron line in each Feynman diagram (of which of course there are infinitely many) for the particular process?

In higher order diagrams there are electron and positron fields. Again, calling something
an electron and basing this on one of the quantization methods (electrons as
quantized excitations of the electron field) is something what you can do, or not do,
but it is not relevant for the end result. The pertubative series development is valid
with or without this interpretation of the individual terms.

And are you saying that there is a separate physical interference charge/current density between the original electron and each separate internal electron? And is there similarly a physical interference charge/current density between each pair of internal electrons?

No. The interaction is only with the photon which is connected to the interaction vertex.

Finally, what "incoming photon" (whose em field is to be negated)?

I didn't specify either an incoming or an outgoing photon in the interaction, and there doesn't have to be one!​

There has to be a photon, either incoming, outgoing or internal (if you are restricting
this to QED).


Regards, Hans

 

[Frame Dragger]

They call it a "virtual electron" instead...

I don't see how that helps in any way.

 

[Hans de Vries]

I don't see how that helps in any way.

Are you agreeing or objecting? Because I gave some reasons against
calling them "virtual particles" or worse, "space-like virtual particles"

Vacuum polarization could be associated with "virtual particles" if you
like, as long as the off-the-shell behavior is interpreted as the result
from interaction rather than from a propagator with an off-the-shell
mass.

Regards, Hans

 

[Frame Dragger]

Are you agreeing or objecting? Because I gave some reasons against
calling them "virtual particles" or worse, "space-like virtual particles"

Vacuum polarization could be associated with "virtual particles" if you
like, as long as the off-the-shell behavior is interpreted as the result
from interaction rather than from a propagator with an off-the-shell
mass.

Regards, Hans

I disagree with your definition of a virtual photon, but I agree that the term can be misleading... just not for the reasons you seem to think.

 

[Hans de Vries]

I disagree with your definition of a virtual photon, but I agree that the term can be misleading... just not for the reasons you seem to think.

I don't have a definition of what a "virtual photon" is...

-I have a definition of what goes on in a feynman diagram with an internal photon.
-I have a definition of what does not exist: virtual photons with a space-like imaginary mass.

Can you be more specific?

Regards, Hans

 

[Frame Dragger]

I don't have a definition of what a "virtual photon" is...

-I have a definition of what goes on in a feynman diagram with an internal photon.
-I have a definition of what does not exist: virtual photons with a space-like imaginary mass.

Can you be more specific?

Regards, Hans

I don't mean this as any kind of insult, but page 5 is too late to restart this discussion from basic principles. I think we're ultimately talking about the same physical (and transitional non-physical) processess, but we're not communicating that well. I think at this point You, myself, and Tiny-Tim are unlikely to change our views when they seem to be so entrenched. That, or against all odds, you're completely wrong, and I don't feel qualified or confident enough to show that. Tiny-Tim and you seem to be a better match; I'm no physicist, just a duffer.

 

[tupos]

An internal electron line originates from the original electron but has a changed
momentum

Regards, Hans

Nonsense. The definition of real electron

p^2 = -m_{R}^2 where m_{R} is a real experimental mass.

There is no evidence to conclude that p^2 is equal to m^2 for internal electron line.

The same with photon, no evidence to say that k^2 = 0 for internal photon line.


Regards.

 

[Hans de Vries]

Nonsense. The definition of real electron

p^2 = -m_{R}^2 where m_{R} is a real experimental mass.

There is no evidence to conclude that p^2 is equal to m^2 for internal electron line.

The same with photon, no evidence to say that k^2 = 0 for internal photon line.Regards.

Read my posts before shouting. Where did I ever make these statements which you
call nonsense? On the contrary, I'm protesting against descriptions which implicitly
make such assumptions, such as: "space-like virtual photons"

 

[tupos]

Hello Hans,

I didn't shout. Sorry if you get me wrong, I agree with you that there is no sense in space like and so on.

But you wrote and I commented it that "An internal electron line originates from the original electron but has a changed
momentum" you wrote it. I agree that nonsense is too strong word for this, maybe slightly incorrect is better

 

[Hans de Vries]

Hello Hans,

I didn't shout. Sorry if you get me wrong, I agree with you that there is no sense in space like and so on.

Hi, Tupos It's fine thank you.

But you wrote and I commented it that "An internal electron line originates from the original electron but has a changed
momentum" you wrote it. I agree that nonsense is too strong word for this, maybe slightly incorrect is better

Maybe that's a too popular description for you? A more technical description was given
here in this post: https://www.physicsforums.com/showpost.php?p=2574073&postcount=60

Regards, Hans

 

[tupos]

I know very well what is internal electron line. I just wanted to point out your attention that internal electron line is not a real electron because for this virtual particle it is not necessary that p=-m^2, that's all.