Infinite Charged Electron in QFT

[kexue]

Hi Arnold. I've been reviewing about your virtual particles and how they are just mathematical artifacts and your articles in the website are convincing. But I have one question you haven't made clear. In 2 electrons feeling the electromagnetic force, there are said to be virtual photons being exchanged. I understand you emphasized that only higher order interaction vortexes with their virtual particles are just being multivariate integrals. But how about this simple electromagnetic interaction between 2 electrons. Is the virtual photons here also considered as virtual particles? They are only mathematical artificat? If so, then you are implying that only the electromagnetic force is real and there is really no virtual photons between exchanged which are just multivariate integrals? Thanks.

Rogerl, this is the exactly the same question I asked three months ago in another thread. What does QFT say about the transmission of forces?

I read here in a http://arxiv.org/PS_cache/hep-th/pdf/9803/9803075v2.pdf" on page 3 the following.

The second [general feature] is the association of forces and interactions with particle exchange. When Maxwell completed the equations of electrodynamics, he found that they supported source-free electromagnetic waves. The classical electric and magnetic fields thus took on a life of their own. Electric and magnetic forces between charged particles are explained as due to one particle acting as a source for electric and magnetic fields, which then influence others. With the correspondence of fields and particles, as it arises in quantum field theory, Maxwell’s discovery corresponds to the existence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory.

To me that made perfect sense. But here I got told by a few poster, especially, A.Neumaier, that virtual particles have no physical content, they are just in the mathematics, they are silly, illustrations for the lay audience, and so on.

What does relativistic quantum physics say about transmission of the electric force? Nothing, according to A.Neumaier! They are only described by classical fields!

Well, then I got curious and wrote many, many emails to all kinds of physicists in high energy physics and asked them, what they think about virtual particles. I got many answers, and if one thing I can assure is that A.Neumaier's view is nowhere near any "mainstream view".

One who also answerd, was again Wilczek, which very kindly gave the following reply, which I think comes closest to what the most physicist think of virtual particles:

It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. By that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. Of course, they do appear when you allow yourself a very little boldness in interpreting observations. It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics.

 

[rogerl]

Rogerl, this is the exactly the same question I asked three months ago in another thread. What does QFT say about the transmission of forces?

I read here in a http://arxiv.org/PS_cache/hep-th/pdf/9803/9803075v2.pdf" on page 3 the following.

The second [general feature] is the association of forces and interactions with particle exchange. When Maxwell completed the equations of electrodynamics, he found that they supported source-free electromagnetic waves. The classical electric and magnetic fields thus took on a life of their own. Electric and magnetic forces between charged particles are explained as due to one particle acting as a source for electric and magnetic fields, which then influence others. With the correspondence of fields and particles, as it arises in quantum field theory, Maxwell’s discovery corresponds to the existence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory.

To me that made perfect sense. But here I got told by a few poster, especially, A.Neumaier, that virtual particles have no physical content, they are just in the mathematics, they are silly, illustrations for the lay audience, and so on.

What does relativistic quantum physics say about transmission of the electric force? Nothing, according to A.Neumaier! They are only described by classical fields!

Well, then I got curious and wrote many, many emails to all kinds of physicists in high energy physics and asked them, what they think about virtual particles. I got many answers, and if one thing I can assure is that A.Neumaier's view is nowhere near any "mainstream view".

One who also answerd, was again Wilczek, which very kindly gave the following reply, which I think comes closest to what the most physicist think of virtual particles:

It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. By that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. Of course, they do appear when you allow yourself a very little boldness in interpreting observations. It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics.

Different physicists seem to differ in interpretations. I wonder if these are like those between Copenhagen vs Many Worlds in quantum theory. But let's sort out the confusions by standardizatin of terms. First, Definition of External Lines and Internal Lines in Feynman Diagram. I think Neumaier emphasized on their distinctions while other physicists just use the standard wiggling lines to denote the forces.

Now from http://blogs.uslhc.us/lets-draw-feynman-diagams

External lines= one free end
Internal lines = both ends attached to a vertex

Now from the following passage in http://en.wikipedia.org/wiki/Virtual_particle

Everything seems clearer:


"It is sometimes said that all photons are virtual photons.[3] This is because the world-lines of photons always resemble the dotted line in the above Feynman diagram: the photon was emitted somewhere (say, a distant star), and then is absorbed somewhere else (say a photoreceptor cell in the eyeball). Furthermore, in a vacuum, a photon experiences no passage of (proper) time between emission and absorption. This statement illustrates the difficulty of trying to distinguish between "real" and "virtual" particles as mathematically they are the same objects and it is only our definition of "reality" which is weak here. In practice, a clear distinction can be made: real photons are detected as individual particles in particle detectors, whereas virtual photons are not directly detected; only their average or side-effects may be noticed, in the form of forces or (in modern language) interactions between particles.".


So real photons are detected as individual particles, whereas virtual photons are not directly detected. In the latter, you believe they are still real and it is the limitation of our device that can't detect them? In Neumaier point of view. They can't be detected by theory even if we have the technology because they don't exist. So I guess it's like between Copenhagen where the wave function is pure math versus the Bohmian where they exist in some way? So you tend to be like Copenhagen while Neumaier is like Bohmian right?

Now for you who believe virtual particles have physical existence even though not yet possible to be measured now. Are you saying that the infinity of virtual particles are real? They are infinite because in any interaction vortex lines (both ends connected), there many infinite ways the virtual particles can be exchanged. This is why we have Renormalization that solves for it. Are you saying the infinity is really physical?? It is due to this that others like Neumaier thinks it's only in the math because something can't be infinite. But you believe the infinity is physical?

 

[A. Neumaier]

So real photons are detected as individual particles, whereas virtual photons are not directly detected. In the latter, you believe they are still real and it is the limitation of our device that can't detect them? In Neumaier point of view. They can't be detected by theory even if we have the technology because they don't exist. So I guess it's like between Copenhagen where the wave function is pure math versus the Bohmian where they exist in some way?

No, it isn't. For the purpose of this discussion, you can take ''exist'' to mean ''have a time-dependent wave function''. This objectively distinguishes real particles from virtual ones.

 

[rogerl]

No, it isn't. For the purpose of this discussion, you can take ''exist'' to mean ''have a time-dependent wave function''. This objectively distinguishes real particles from virtual ones.

The past few days I asked other physicists especially particle physicists like you. Some of them believed virtual particles are really. Their reasoning is that the distinction between external and internal lines are fuzzy. So what if the photon comes from the sun then the internal lines of this where the interaction vortex got connected is between the sun and earth. So what seems to be external lines becomes internal lines. Now. You said real particles have wave function and virtual particles if they have to be real has to pull stunt like ""imaginary mass, violation of the conservation of energy, violation of causality, traveling faster than light or backwards in time, popping in and out of the vacuum via ''vacuum fluctuations''. But other physicists believe "so what if nature has to pull them".

Particle physicist P.D. stated when someone in sci.physics google newsgroup asked for his opinion about your utmost belief virtual particles are totally imaginary. Inquirer said "In Neumaier point of view. They can't be detected by theory even if we have the technology because they don't exist."

P.D. answered:

"And this is where things get dodgy. The model uses their existence to make predictions, which are successful to an unparalleled degree. In science, if a model supposes elements that are not directly observed, but the predictions of those unobserved elements are accurately reproduced in measurement, then this stands as affirmation of those unobserved elements. Neumaier is taking an uncharacteristically harder stand, that success of predictions should not stand as evidence for the unobserved elements. The problem is that Neumaier is arguing that another model *could* conceivably step into the gap, providing the same predictive success with a different set of supposed elements, ones that perhaps would be more amenable to direct observation. That may well be, but if so, it hasn't been put forward yet. The reigning model is always the one among the *available pool* that has the greatest success. Quantum field theory is that reigning model."

Inquirer asked P.D.: "Are you saying the infinity is really physical??"

P.D. Answers:

"Feynman, who is probably the most articulate at explaining this, does in fact say this, but in a guarded way. What he says is that nature acts JUST AS IF intermediate particles took all available trajectories between initial and final states simultaneously. He then goes on to say that, if it is impossible to resolve whether nature is behaving JUST AS IF this is true or nature is behaving BECAUSE IT IS true, then the distinction is specious.

He furthermore dismisses presuppositions (and so do I) like "But no self-respecting theory ought to have infinities conceived in it." That is VERY treacherous ground. You get into assumptions very quickly that simply have no experimental support, but which can confine your thinking needless for decades, if not centuries. Things like "Now is 'now' for all observers," and "nature behaves with strict causal determinism in all things," and "objects like rest as a natural state and things cannot move forever without the imposition of an external force to sustain that motion."

Inquirer asked P.D.: "It is due to this that others like Neumaier thinks it's only in the math because something can't be infinite. But you believe the infinity is physical?"

P.D. answers:

"*Measurable* quantities are taken to be finite, but there is no necessity to rule out infinity of anything physical at all. Heck, what's the physical slope of a vertical surface? That seems to
be both ordinary and physically sensible."


Comment Mr or is it Dr. Neumaier? Many thanks.

 

[A. Neumaier]

The past few days I asked other physicists especially particle physicists like you. Some of them believed virtual particles are really.

As I discussed in the FAQ, the problem is that different people mean something different when they say something is ''real''.

Those with a vague concept of reality may consider virtual particle real. But pressed with telling more about their properties they end up claiming fantastic things that cannot be verified by experiment, are claimed nowhere else in physics, and are unable to back them up with mathematical models. The reason is that - unlike everything else in physics - virtual particles are not defined by properties of a state but by properties of a diagram appearing in an illustration of some intermediate calculation.

If you prefer such a weird and unreal view of reality then let it be so; I force nobody to a particular philosophy of reality.

Comment Mr or is it Dr. Neumaier?

You can check on my home page at http://arnold-neumaier.at/

 

[Epaminondas]

I'm reading this book "Deep Down Things" by Bruce A. Schumm about Quantum Field Theory. It says that the charge of the bare electron is infinite. Since the virtual particles calculations produced infinities too. Renormalization means substracting the infinite bare electron by infinite virtual particle calculations to come up with the small values of the charge. Do you actually believe this is true, that is, can the bare electron be really infinite in charge? How can this be?? QFT actually says this. But how can a bare particle be infinite in charge? Is this figurative or literal?

Dirac said that this is because the Dirac equation is wrong.

Erroneous equations often lead to divergences. To illustrate this, let us consider the following example:

x=x+17 (1)

The solution can easily be obtained using normal rules of mathematics. Obviously, the solution is:

x=±∞

However, if physicists cannot be satisfied by infinite value of x, they can introduce additional parameters in the equation (1):

x=x+17+ λ/δ (2)

and then by assuming that

λ/δ → -17 ∀ λ,δ

they will obtain the new equation, that allows for finite values of x and “does not depend” on the values of parameters λ,δ:

x=x (3)

However, the value of x still cannot be identified from equation (3) and is eventually obtained from experiment.

After in-depth analysis of the equation (2) physicists see that expression λ/δ has the form of “propagator”, but its value (which is equal to -17) is “unphysical”, because “propagator” can only have positive values.

All this looks like a magic. We started with equation (1) that leads to divergent value of x, and gradually transformed it to equation (3) that allows for finite values of x.

The process explained above looks too much similar to renormalization, isn’t it?

What causes the divergences? In relativistic particle physics the mass of elementary particle is primarily introduced via mass term in “free” Dirac equation.

It is usually assumed that “free” Dirac equation describes an evolution of a “free” spin ½ particle (such as electron, muon, tau etc.). In this context “free particle” means a fermion which is not interacting with other particles and fields. This is despite the fact that, for instance, electron had never been observed apart from its electromagnetic field.

I believe that mass has an electromagnetic origin, and the correct form of "free" equation for the electron shall include coupling with it's own electromagnetic field.

Let's, for instance, consider the following system of simultaneous equations:

i∂ψ=mψ (4)
i∂ψ=Aψ (5)

where the first equation looks like the "free" Dirac equation, and the second equation looks like Dirac equation for a "massless" particle in electromagnetic field. Consistency of the above equations mean that mass is nothing but the effect of particle's own electromagnetic field action.

In QED the following generalization of "free" Dirac equation is used:

i∂ψ - Aψ = mψ (6)

If we assume that equations (4-5) are satisfied, then equation (6) will immediately lead to divergences.

2mψ = mψ => m=0 or m= ±∞

This looks very similar to the situation with equation (1).

 

[rogerl]

As I discussed in the FAQ, the problem is that different people mean something different when they say something is ''real''.

Those with a vague concept of reality may consider virtual particle real. But pressed with telling more about their properties they end up claiming fantastic things that cannot be verified by experiment, are claimed nowhere else in physics, and are unable to back them up with mathematical models. The reason is that - unlike everything else in physics - virtual particles are not defined by properties of a state but by properties of a diagram appearing in an illustration of some intermediate calculation.

If you prefer such a weird and unreal view of reality then let it be so; I force nobody to a particular philosophy of reality.

You can check on my home page at http://arnold-neumaier.at/

Neumaier. So your model is subject to your own interpretation and preference which is not the mainstream view at all, or better yet half half, just like half now believe in the Copenhagen and half believe in other interpretations like Many Worlds, Etc. Now with regards to virtual particles in Quantum Field Theory. Particle physicist P.D. further commented in google sci.physics newsgroup about your belief that virtual particles are just figment of the imagination (pls. comment, thanks.).

"Earlier I said that Neumaier and I had a couple of basic disagreements about quantum field
theory.

The first one is that he attributes firmly the notion of "virtual particles" to be internal lines on Feynman diagrams. Notice how different that is from the more physical meaning I gave very early on in this thread. You'll also recall that I showed why, in the case of photons, meaning that Neumaier connotes cannot possibly have usable value, because *all* detected photons would then be considered virtual by his definition, even though he *declares* detected photons to be real -- his position is self-contradictory.

Secondly, he complains that "they end up claiming fantastic things that cannot be verified by experiment, are claimed nowhere else in physics, and are unable to back them up with mathematical models." These are either specious comments or flat wrong. As an example, the
invariance of the speed of light *regardless* of the motion of the source or the observer is also a "fantastic thing" that is "claimed nowhere else in physics". And yet this claim has very definite predictions which can be checked directly in experiment -- such as how long a high-speed muon can be expected to survive in a vacuum pipe before it decays. The fact that this prediction matches exactly what is observed IS IN FACT evidence that backs up the claim that the speed of light is invariant. Likewise, the fact that the existence of virtual particles makes a very definite prediction about the anomalous magnetic moment of the muon, and that prediction is correct to *twelve decimal places* is rather stunning evidence that backs up the claim of virtual particles. As for "unable to back them up with mathematical models", I'd like to ask how it is he thinks the calculations that provide these predictions are done if there isn't a mathematical model that backs them up.

While I respect a lot of things that Neumaier wrote in his FAQ, in this chapter I'm afraid I think he's off the mark."

 

[A. Neumaier]

Neumaier. So your model is subject to your own interpretation and preference which is not the mainstream view at all,

Of course, the definition of what is ''real'' is always an interpretation, about which one can have different philosophies. I specified precisely how I use the word.

Now with regards to virtual particles in Quantum Field Theory. Particle physicist P.D. further commented in google sci.physics newsgroup about your belief that virtual particles are just figment of the imagination (pls. comment, thanks.).

"Earlier I said that Neumaier and I had a couple of basic disagreements about quantum field
theory.

The first one is that he attributes firmly the notion of "virtual particles" to be internal lines on Feynman diagrams. Notice how different that is from the more physical meaning I gave very early on in this thread.

Maybe you should tell us which more physical meaning he subscribes to.

You'll also recall that I showed why, in the case of photons, meaning that Neumaier connotes cannot possibly have usable value, because *all* detected photons would then be considered virtual by his definition, even though he *declares* detected photons to be real -- his position is self-contradictory.

This is not correct.

By definition, the outgoing legs of a Feynman diagram are those that are detected in a scattering experiment - otherwise S-matrix elements would not be observable at all. Thus detected particles correspond to real, external lines.

Secondly, he complains that "they end up claiming fantastic things that cannot be verified by experiment, are claimed nowhere else in physics, and are unable to back them up with mathematical models." These are either specious comments or flat wrong. As an example, the
invariance of the speed of light *regardless* of the motion of the source or the observer is also a "fantastic thing" that is "claimed nowhere else in physics".

It is claimed in all of classical and quantum relativity; and is well understood, nothing fantastic at all.

As for "unable to back them up with mathematical models",

One cannot write down a dynamics for the state of a virtual particle that shows how it
moves with superluminal speed.

I'd like to ask how it is he thinks the calculations that provide these predictions are done if there isn't a mathematical model that backs them up.

The calculations are done solely with recipes for integrals represented by internal lines of Feynman diagrams, that were derived from the dynamics of real particles by an asymptotic abstraction.

 

[rogerl]

Of course, the definition of what is ''real'' is always an interpretation, about which one can have different philosophies. I specified precisely how I use the word.

Maybe you should tell us which more physical meaning he subscribes to.

This is not correct.

By definition, the outgoing legs of a Feynman diagram are those that are detected in a scattering experiment - otherwise S-matrix elements would not be observable at all. Thus detected particles correspond to real, external lines.

It is claimed in all of classical and quantum relativity; and is well understood, nothing fantastic at all.

One cannot write down a dynamics for the state of a virtual particle that shows how it
moves with superluminal speed.

The calculations are done solely with recipes for integrals represented by internal lines of Feynman diagrams, that were derived from the dynamics of real particles by an asymptotic abstraction.

I'm familiar with his arguments already. It's like this. You subscribe internal lines for example between virtual photons in 2 electrons feeling the electromagnetic field. But a real photon between the sun and detector on Earth can be considered internal line too (internal line between 2 connected interaction vertexes.. one vertex is the sun emitting the photon, the second vortex the detector on earth. This is what he meant by more physical... because he can define the internal line as containing the more physical photon and the distance between the vertexes 93 million miles between sun and earth.

About superluminal speed. Since virtual particles can't convey information much like entangled pair, then superluminal speed is not disallowed. He considers the integrals being real even though undetected.. real in the sense that under the time allowed by uncertainty.. it exists physically although no wave function. There is no a priori reason to believe physical corresponds to Newtonian reality or even einsteinian reality and he believes infinite electron can really be infinite as I stated before.. there is no a priori reason that disallowed it much like an object once moves can move forever unless acted on by a force.. something like that.

Since we don't know what is the true reality and nature. We can't have a priori reasons why certain things are that way. For example. You prefer Copenhagen while others prefer Many Worlds and it is not possible to distinguish the two. So you can be likened to Copenhagen and he Bohmian or Many worlds as he believes virtual particles to be real and undetected particles. But if you define real as something that can be measured. Then it is your definition and model of real(ity) while others can define real in any preference since we don't have any a priori reason for what is real.

My analysis of the differences of your belief in comparison to him is right, agree?

 

[A. Neumaier]

I'm familiar with his arguments already. It's like this. You subscribe internal lines for example between virtual photons in 2 electrons feeling the electromagnetic field. But a real photon between the sun and detector on Earth can be considered internal line too (internal line between 2 connected interaction vertexes.. one vertex is the sun emitting the photon, the second vortex the detector on earth. This is what he meant by more physical... because he can define the internal line as containing the more physical photon and the distance between the vertexes 93 million miles between sun and earth.

Of course one can do games like this. But all this happens on the draw level. One can draw many things and use it with blabla explanations.

But for a physical interpretation one needs to be able to do the reverse: give a state to the lines that enables one to say what it means for a particle to be with some probability at some place at some time. This can be done for the real photon, but not for the virtual one.

About superluminal speed. Since virtual particles can't convey information much like entangled pair, then superluminal speed is not disallowed.

But the question is how this is represented on the formal level. A spees means a derivative of something with respect to time. A real photon has a speed, since it has a time-dependent state. But there is no object corresponding to the state that would do the same for a virtual photon. So there is no time derivative and hence no speed.

 

[dm4b]

I didn't read this entire thread so hopefully what I am about to say wasn't already covered.

It seems that it is being suggested that virtual particles "effect nothing".

But, as I understand it, in QFT, the "message" of the Electromagnetic force is conveyed via the quanta of the field - virtual photons! (Likewise for the other forces and their respective force-carrying particles/bosons)

Isn't this depicted in Feynman diagrams for electron scattering. You have two incoming electrons with an internal wiggly line, which represents a virtual photon, drawn between them and then two outgoing electrons on the opposite side of the vertices. It's the exchange of that virtual photon that conveyed the message "repel".

If virtual photons effect nothing, do nothing, and are just mathematical figments for convenience, just how does the electromagnetic force physically get conveyed?

 

[lightarrow]

...
If virtual photons effect nothing, do nothing, and are just mathematical figments for convenience, just how does the electromagnetic force physically get conveyed?

A field is not something physical for you?

 

[A. Neumaier]

If virtual photons effect nothing, do nothing, and are just mathematical figments for convenience, just how does the electromagnetic force physically get conveyed?

Classically, the field interacts locally with the charges according to the Maxwell equations. Since force carrier and force recipient are at the same spot, nothing needs to be ''conveyed''.

A quantum field behaves essentially in the same way as a classical field, but with quantum fluctuations.

 

[dm4b]

A field is not something physical for you?

It is something physical - with an emphasis on something.

But, if the force carriers, or the discrete quanta that make up a field, are virtual particles, than saying a field is physical but the virtual particles are not, is like saying a brick wall is physical, but the individual bricks are not. Or, perhaps an analogy somewhat closer to home, that a laser is physical but the (real) photons it is composed of are not physical.

 

[dm4b]

Classically, the field interacts locally with the charges according to the Maxwell equations. Since force carrier and force recipient are at the same spot, nothing needs to be ''conveyed''.

A quantum field behaves essentially in the same way as a classical field, but with quantum fluctuations.

But particles participating in a force are NOT always in the same spot. How does that force get conveyed, physically?

In the most extreme case - take the gravitational force between two distant planets? Granted quantum gravity is far from worked out, but in a quantum view, what conveys the force? Is it not the graviton - a particle which would be depicted as an internal line, or virtual particle, in a Feynman diagram?

In many textbooks the analogy given is that the virtual particles "mediate" the force? is this false? If not, what does it mean to you?

By the way, wouldn't you agree that there are distinct differences between a quantum field and a classical field?

I definitely don't fully understand virtual particles myself. But, I'm under the viewpoint that nobody does. Feynman said when he was near the top of his game, "I think I can safely say nobody understands quantum mechanics". Or, when it comes to virtual particles perhaps the old Hindu aphorism is best, "He who thinks he knows, does not know. He who knows he does not know, knows" ;-)

 

[lightarrow]

But, if the force carriers, or the discrete quanta that make up a field

The quanta "make up a field"? Not at all. There is the field and there are quanta of the field. It's incorrect to say that "the quanta make up the field", this is your mistake, you still want to think that the only essentially physical concept is that of the corpuscle.

 

[A. Neumaier]

But particles participating in a force are NOT always in the same spot. How does that force get conveyed, physically?

Particles are localized bundles of energy in a quantum field, local maxima of the mean energy density. Forces are transported essentially in the same way as for water wavelets, which are sort of classical particles of the water field. But the analogy is imperfect, as these are not conserved under collisions.

In the most extreme case - take the gravitational force between two distant planets? Granted quantum gravity is far from worked out, but in a quantum view, what conveys the force? Is it not the graviton - a particle which would be depicted as an internal line, or virtual particle, in a Feynman diagram?

No. In quantum field theory, it is the gravitational field. This can be measured easily.
The graviton is a quantized gravitational wave, which hasn't been observed so far, but would be expected to exist in a quantum gravity theory.

In many textbooks the analogy given is that the virtual particles "mediate" the force? is this false? If not, what does it mean to you?

It is linguistic imagery for the fact that to compute the force in covariant perturbation theory, one evaluates Feynman diagrams with internal graviton propagators. In a Hamiltonian version corresponding to the Coulomb gauge in QED, the force would appear instead as the gradient of a gravitational interaction term. Thus the imagery is very representation-dependent.

By the way, wouldn't you agree that there are distinct differences between a quantum field and a classical field?

Of course. The classical field is the limiting case when hbar approaches zero. In the quantum case, there are therefore (1-loop) corrections of order hbar. And for sufficiently intense fields there are interesting nonclassical (e.g., squeezed) states of the field.

I definitely don't fully understand virtual particles myself. But, I'm under the viewpoint that nobody does. Feynman said when he was near the top of his game, "I think I can safely say nobody understands quantum mechanics". Or, when it comes to virtual particles perhaps the old Hindu aphorism is best, "He who thinks he knows, does not know. He who knows he does not know, knows" ;-)

This was many years ago.

I think I can safely say that I understand quantum mechanics, with exceptions of some of the deeper things in rigorous quantum field theory that I hope to understand in the near future.

 

[dm4b]

Alright guys, let's look at a simple example. Since it sounds like you both have studied QFT, I'm going to assume you have a copy of Peskin and Schroeder around.

I'm re-reading QFT here again lately, and finding it just as difficult the 2nd time around, so any extra insight into this example can't hurt me either ;-)

Go to chapter 6, where he talks about the next order correction to the electron-vertex function. A virtual photon connects an ingoing eletron leg to an external electron leg in the Feynman diagram.

In the next couple of sections he proceeds to show these higher order corrections give rise to the anomalous magnetic moment - the difference between what the Dirac equation predicts and what higher order theory gives you.

Looking at this on the surface, it would appear that including the "effects" of the virtual photon explains the origin of the anomalous magnetic moment.

But, if virtual photons do nothing, what really does physically cause the anomalous magnetic moment? What causes it to be different than what the Dirac Equation predicts? And, don't just say it's wrong. Explain why. Explain what physical effects are being included in these higher order corrections that hone in the answer to match reality? Or, rather explain what physical effects are being left out when they are not included.

Thanks, because any added insight into this chapter would also be much appreciated ;-)

 

[dm4b]

The quanta "make up a field"? Not at all. There is the field and there are quanta of the field. It's incorrect to say that "the quanta make up the field", this is your mistake, you still want to think that the only essentially physical concept is that of the corpuscle.

Alright, so a field is essentially made up of energy and energy comes in discrete bundles. Please explain this: if you take away the discrete bundles of energy, what is left of the field?

I'm not trying to say that either the corpuscle OR the field is the only physical concept. I'm trying to say, how can you have one without the other?

 

[dm4b]

Particles are localized bundles of energy in a quantum field, local maxima of the mean energy density. Forces are transported essentially in the same way as for water wavelets, which are sort of classical particles of the water field. But the analogy is imperfect, as these are not conserved under collisions.

It sounds like you just said forces are sort of transported by particles. Aren't these particles depicted in Feynman diagrams as internal lines? If not, please explain better if you got the time.

No. In quantum field theory, it is the gravitational field. This can be measured easily.
The graviton is a quantized gravitational wave, which hasn't been observed so far, but would be expected to exist in a quantum gravity theory.

Okay, here is the simplest example I can think of. Go to chapter 4 of Sean Carrol's book on General Relativity. Here he depicts Feynman diagrams which contain gravitons (real and virtual) in oder to show how they couple to each other, etc, in opposition to how photons do not in the electromagnetic field. Is he wrong to draw gravitons into Feynman diagrams to show how the gravitational field couples to itself? If so, why?

If he is wrong, please explain the physical mechanism of how the gravitational field couples to itself, without referencing gravitons.

 

[dm4b]

This was many years ago.

I think I can safely say that I understand quantum mechanics, with exceptions of some of the deeper things in rigorous quantum field theory that I hope to understand in the near future.

Are you saying you know QFT better than Feynman did. Has that much really changed since his day? That's a bold statement, even if it has ;-)

 

[A. Neumaier]

In the next couple of sections he proceeds to show these higher order corrections give rise to the anomalous magnetic moment - the difference between what the Dirac equation predicts and what higher order theory gives you.

Looking at this on the surface, it would appear that including the "effects" of the virtual photon explains the origin of the anomalous magnetic moment.

Vague language breeds fuzzy understanding.

Calculating a relativistic effect by a Taylor expansion in 1/c and getting better agreement with the second-order term added, one may conclude that it is the second-order term that ''causes'' or ''explains'' the effect. But this is not a physical cause in the sense that a fire is caused by striking a match. Nothing is caused by a mathematical calculation.

Or, rather explain what physical effects are being left out when they are not included.

Using a more approximate formula produces less accurate results.

The interactions of QED cause the anomalous magnetic moment, and the Feynman expansion is just a way of calculating it.

 

[A. Neumaier]

Alright, so a field is essentially made up of energy and energy comes in discrete bundles. Please explain this: if you take away the discrete bundles of energy, what is left of the field?

There is always the field, which has some expectation value, and there may be particles, which describe localized excitations of this field, modifying it a little. It is like having a drum and beating it. An unbeaten drum is still a drum.

 

[A. Neumaier]

It sounds like you just said forces are sort of transported by particles. Aren't these particles depicted in Feynman diagrams as internal lines? If not, please explain better if you got the time.

Forces are transported by field and currents. Particles are a semiclassical approximation, of the same kind as geometric optics approximates Maxwell equations.

Feynman diagrams without any loops describe precisely the _classical_ field theory, solved by perturbation theory. But nobody ever has taken virtual particles for real in a classical field. Quantum field theory only adds more diagrams - namely those with loops; the k-loop diagrams providing k-th order corrections in hbar.

he depicts Feynman diagrams which contain gravitons (real and virtual) in oder to show how they couple to each other, etc, in opposition to how photons do not in the electromagnetic field. Is he wrong to draw gravitons into Feynman diagrams to show how the gravitational field couples to itself?.

No. Diagrams just represent tensors with as many indices as there are external lines. These occur in all sorts of mathematics. Among others, one can also use them to describe interaction terms in a Lagrangian, and low order expansions of scattering matrix elements. Drawing diagrams abbreviates some complex integral operator in a shorthand way. It is fully legitimate to use it in this way in physics.

But this usage should not be taken as an indication of any causal relationship between the concepts attached to the drawing.

 

[A. Neumaier]

Are you saying you know QFT better than Feynman did. Has that much really changed since his day? That's a bold statement, even if it has ;-)

I said: I understand quantum mechanics.

This is completely independent of Feynman's statement. (I never got to know him.)

 

[dm4b]

There is always the field, which has some expectation value, and there may be particles, which describe localized excitations of this field, modifying it a little. It is like having a drum and beating it. An unbeaten drum is still a drum.

I have always like that analogy. And, it may just be a good jumping off point to illustrate the problem I am having too.

First, I think I basically agree with you, but I'm not sure at this point. I've been sorting of paying devil's advocate to help get me past my own misgivings in the material I am reading.

Here's how I view virtual particles. Basically it boils down to the fact that there are no exactly solvable interacting field theories (in the number of dimensions required to represent reality). So to get around that, we treat the interaction term, Hint, as a perturbation, and treat the problem using perturbative techniques. Feynam diagrams are just really fancy mnemonics used to represent each term in that perturbation series, and saves us from pages of laborius math involving Wick Contractions and the sort. But they represent nothing physical in and of themselves. Hence, neither do the virtual particles.

Do you agree with that? Is it correct?

If so, here is where some of my additional confusion on the subject lies.

(1) I have no problem with saying the field is fundamental, but I just don't see how you can consider the field without considering particles. I mean, that's the whole reason we NEED QFT in the first place - to explain the creation and annihilation of particles. Shrodinger's non-relativistic description is incapable of that. So, as far as reality goes, a field and particles go hand in hand, do they not?

(2) Back to the drum. What does an unbeaten drum do? Nothing! BUT, does an "unbeaten" field do nothing? Formally, the field is composed of an infinite number of harmonic oscillators in momentum space, with each having a quantum "zero-point" energy. This, of course, would eventually lead us to the whole cosmological constant problem and the famous 120 orders of magnitude, but I think it indicates that something is going on - and not nothing like the unbeaten drum. Do you agree?

In relation to that, the vacuum is said to be seething with quantum fluctuations. Aren't these represented as virtual particles? If so, what's really going on? Perhaps wait until you read my #3 next before answering this point.

(3) On page 255 in Peskin and Shroeder, they interpret vacuum polarization as a screening cloud of virtual electron-positron pairs, which gives the electron an "apparent charge" and hiding the "true" charge from us. The virtual electron-positron pairs are "effective" dipoles of ~ 1/m. It's not until you penetrate the screening cloud of virtual electron-positron pairs, that you could "see" the true charge. Once again, after writing off virtual particles as unphysical/unreal, as I did above, here they are again in another interpretation of a certain phenomenon. If virtual particles are truly unphysical, what is really going on here? What is P&S leaving lacking in there interpretive description?

 

[bapowell]

(2) Back to the drum. What does an unbeaten drum do? Nothing! BUT, does an "unbeaten" field do nothing? Formally, the field is composed of an infinite number of harmonic oscillators in momentum space, with each having a quantum "zero-point" energy. This, of course, would eventually lead us to the whole cosmological constant problem and the famous 120 orders of magnitude, but I think it indicates that something is going on - and not nothing like the unbeaten drum. Do you agree?

See: Inflation

 

[dm4b]

I said: I understand quantum mechanics.

This is completely independent of Feynman's statement. (I never got to know him.)

You do realize I was just playing around here? ;-)

 

[dm4b]

See: Inflation

I'm sorry, but your overly verbose post is not helping me ;-)

Seriously though, I have read a little on inflation but not enough to understand or make a connection here. What is your point?

Thanks.

 

[bapowell]

Seriously though, I have read a little on inflation but not enough to understand or make a connection here. What is your point?

Sorry. I suppose my response was a tad terse and now I see premature. I missed your reference to the cosmological constant. I was going to point out that vacuum energy is indeed important in any theory with gravity!

However, in contrast to the CC, inflation is typically implemented via a rolling scalar field with a non-zero vacuum energy. This is one example where the field value, which determines this energy, is particularly relevant without any discussion of particles.

 

[dm4b]

Sorry. I suppose my response was a tad terse and now I see premature. I missed your reference to the cosmological constant. I was going to point out that vacuum energy is indeed important in any theory with gravity!

However, in contrast to the CC, inflation is typically implemented via a rolling scalar field with a non-zero vacuum energy. This is one example where the field value, which determines this energy, is particularly relevant without any discussion of particles.

ahhh, okay. Is this a quantum scalar field? Are there no creation or annihilation operators for the field? Could there be within the framework of the theory?

I guess it sounds different than the QFT discussed above, which was developed for the need to explain particle creation, etc - but maybe it's not?

As you can tell, I'm not familar with the details of inflation theory at all

This also raised about 10 more questions in my head, that I am going to hold off on, since this thread is busy enough already ;-)

 

[bapowell]

Inflation is typically implemented with a quantum scalar field, although the phenomenon of accelerated expansion from the equation of state p \leq -\rho/3 is a classical result. The scalar field that drives the expansion is imaginatively called the inflaton. As a quantum field, you do with it what you would any other -- it has a Fourier decomposition, creation/annihilation operators, and perturbative interactions.

QFT is much bigger than the explanation of particle creation -- it's the way we understand particle interactions. This motivated the need for gauge theories and spontaneous symmetry breaking, and along came the first hypothetical scalar in the Standard Model -- the Higgs boson. The inflaton was originally believed to have been one of the Grand Unified Higgs bosons, but these models soon ran into problems. So, scalar fields, whether we use them to break symmetries or drive inflation, are ubiquitous in the Standard Model and theories beyond.

But since we are getting a bit afield of the OP, feel free to start a new thread if you have more questions!

 

[A. Neumaier]

Here's how I view virtual particles. Basically it boils down to the fact that there are no exactly solvable interacting field theories (in the number of dimensions required to represent reality). So to get around that, we treat the interaction term, Hint, as a perturbation, and treat the problem using perturbative techniques. Feynam diagrams are just really fancy mnemonics used to represent each term in that perturbation series, and saves us from pages of laborius math involving Wick Contractions and the sort. But they represent nothing physical in and of themselves. Hence, neither do the virtual particles.

Do you agree with that? Is it correct?

Yes. Classical field theories are usually also not exactly solvable. Solving them by perturbation theory also produces Feynman tree diagrams, with ''virtual particle'' lines, though there are no particles at all.

(1) I have no problem with saying the field is fundamental, but I just don't see how you can consider the field without considering particles. I mean, that's the whole reason we NEED QFT in the first place - to explain the creation and annihilation of particles.

No. QED was invented before particle creation and annihilation was known. Particles can be fully explained as approximations in terms of fields, whereas the other direction meets with unsurmountable difficulties.

Shrodinger's non-relativistic description is incapable of that. So, as far as reality goes, a field and particles go hand in hand, do they not?

The nonrelativistic description is an approximation to QFT in case c^{-1} can be neglected. One can have nonrelativistic particle theories or nonrelativistic field theories, and one can set up equivalences in certain cases.

(2) Back to the drum. What does an unbeaten drum do? Nothing!

It exists. By its existence it exerts gravitational forces upon its environment. It also limits the space where the surrounding air can flow.

BUT, does an "unbeaten" field do nothing? Formally, the field is composed of an infinite number of harmonic oscillators in momentum space, with each having a quantum "zero-point" energy.

No. This is already a computational device that only covers the free case. Formally, a quantum field is just a space-time-dependent operator valued distribution.

In relation to that, the vacuum is said to be seething with quantum fluctuations. Aren't these represented as virtual particles?

The vacuum is completely inert. Nothing happens. The quantum fluctuations are fictions of the imagination. See the entry ''Does the vacuum fluctuate?'' in Chapter A7 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#vacfluc

(3) On page 255 in Peskin and Shroeder, they interpret vacuum polarization as a screening cloud of virtual electron-positron pairs, which gives the electron an "apparent charge" and hiding the "true" charge from us.

The above FAQ entry tells what happens instead on the level of quantum fields:
The vacuum polarization tensor is defined nonperturbatively in terms of it, as
(q^2 eta - q tensor q)Pi(q^2) := Delta_free(q) - Delta_ren(q),
which is equivalent to Dyson's equation (cf. Weinberg,Vol. I, p.451). Its scalar part Pi(p^2) is related to the running fine structure constant as described in
http://en.wikipedia.org/wiki/Vacuum_polarization
This contains all the physics of vacuum polarization, and is completely independent of virtual particles.

What is P&S leaving lacking in there interpretive description?

They are lacking the nonperturbative perspective that would show that the picture they draw is an artifact of perturbation theory.

 

[dm4b]

Y
No. QED was invented before particle creation and annihilation was known.

That's completely besides the point. Lorentz Equations were invented before Special Relativity, but Lorentz Transformations are the tools needed to complete the theory. QFT is the tool we needed to explain particle creation, annihilation and interactions. Fields that are quantized in the theory give rise to particle creation/annihilation operators. As I said, quantum fields and particles go hand-in-hand. I'm not sure why you would disagree with that (and every short history blurb I have seen in physics texts that describe the historical need for QFT)

Y
Particles can be fully explained as approximations in terms of fields, whereas the other direction meets with unsurmountable difficulties.

I never said otherwise.

The vacuum is completely inert. Nothing happens. The quantum fluctuations are fictions of the imagination.

The above FAQ entry tells what happens instead on the level of quantum fields:
The vacuum polarization tensor is defined nonperturbatively in terms of it, as
(q^2 eta - q tensor q)Pi(q^2) := Delta_free(q) - Delta_ren(q),
which is equivalent to Dyson's equation (cf. Weinberg,Vol. I, p.451). Its scalar part Pi(p^2) is related to the running fine structure constant as described in
http://en.wikipedia.org/wiki/Vacuum_polarization
This contains all the physics of vacuum polarization, and is completely independent of virtual particles.

Maybe I'll just quote the Wikipedia article you linked to answer this one:

"According to quantum field theory, the ground state of a system with interacting particles is not simply empty space. Rather, it contains short-lived "virtual" particle-antiparticle pairs which are created out of the vacuum and then annihilate each other.

Some of these particle-antiparticle pairs are charged; e.g., virtual electron-positron pairs. Such charged pairs act as an electric dipole. In the presence of an electric field, e.g., the electromagnetic field around an electron, these particle-antiparticle pairs reposition themselves, thus partially counteracting the field (a partial screening effect, a dielectric effect). The field therefore will be weaker than would be expected if the vacuum were completely empty. This reorientation of the short-lived particle-antiparticle pairs is referred to as vacuum polarization."

Well, I guess I have the same misgivings I had at the start.

Seems like you keep saying some abstract mathematical quantity (like the polarization tensor above) contains all the physics, without being able to give a clear, succinct and intuitive description of what really physically causes vacuum polarization, etc, while at the same time saying mathematical calculations cause nothing.

I'll check out your links though, thanks.

 

[A. Neumaier]

You do realize I was just playing around here? ;-)

In discussions here on PF, I always try to take statements seriously, if possible.
Unless they are explicitly marked by a smiley.

To discuss this seriously beyond just asserting something would require to first agree on a common interpretation of what it means to understand a subject. We can only speculate about the interpretation Feynman gave to the word, but we could try to get agreement between the two of us.

 

[A. Neumaier]

As I said, quantum fields and particles go hand-in-hand. I'm not sure why you would disagree with that

For example, I don't think quarks exist as (localized) particles, only as (delocalized) fields. Particles make sense only in a semiclassical approximation, which never applies for quarks.

Maybe I'll just quote the Wikipedia article you linked to answer this one:
"According to quantum field theory, the ground state of a system with interacting particles is not simply empty space. Rather, it contains short-lived "virtual" particle-antiparticle pairs which are created out of the vacuum and then annihilate each other.

This is a misrepresenting account of what quantum field theory claims. With my link, I didn't endorse the content of the Wikipedia article, but only the relation of vacuum polarization to the fine structure constant.

There hasn't been a single publication about the life-time of virtual particles - there is no such concept.

Seems like you keep saying some abstract mathematical quantity (like the polarization tensor above) contains all the physics, without being able to give a clear, succinct and intuitive description of what really physically causes vacuum polarization, etc, while at the same time saying mathematical calculations cause nothing.

What is intuitive about a formula depends on the training one has.

There is no valid intuition about the quantum regime devoid of mathematics.

 

[dm4b]

For example, I don't think quarks exist as (localized) particles, only as (delocalized) fields. Particles make sense only in a semiclassical approximation, which never applies for quarks.

Of course, that has been a given since the advent of quantum mechanics, and it in no way invalidates what I was saying. In it, when I said "particles" I mean it in the quantum sense of the term. Seems like this is boiling down into a useless argument on semantics?

What is intuitive about a formula depends on the training one has.

There is no valid intuition about the quantum regime devoid of mathematics.

There's an old saying (might have been Feynman): "If you can't explain your theory in layman's terms, there is either something wrong with your theory, or there is something wrong with you".

I don't think it is too much to ask to explain mechanism of some simple things in physical (and not mathematical) terms, such as force, vacuum polarization, etc, in a clear and concise way, that a layman can understand. I have yet to see that done here. Unless the claim is that abstract mathematics actually "drive" the Universe?

Granted the Internet isn't the best tool for this kind of thing somethimes. With that said, I will eventually check out your personal links, which I appreciate you providing.

 

[dm4b]

In discussions here on PF, I always try to take statements seriously, if possible.
Unless they are explicitly marked by a smiley.

To discuss this seriously beyond just asserting something would require to first agree on a common interpretation of what it means to understand a subject. We can only speculate about the interpretation Feynman gave to the word, but we could try to get agreement between the two of us.

This would take us into the realm of philosophy.

A photon cannot "sense the passage of time". What does that truly mean?

Spacetime is warped. What does that truly mean?

An electron passes through both slits in the double-slit experiment. What does that truly mean?

Nobody can give fully satisfactory answers to the above questions, and there are plenty more like them.

You see, just understanding the math, and being able to work the problems isn't enough for me.

I want to understand - in the fullest sense of the term - the reality behind these bizarre behaviors seen in nature.

I believe this is what Feynman meant when he said "he didn't [truly?] understand QM". I know that it's what I mean ;-)

I also think we should always have misgivings about our current theories. It helps us to see beyond them.

 

[lightarrow]

Alright, so a field is essentially made up of energy

I wouldn't say this, because they are two distinct things. Energy is just a "property" of a field (and just one among some).

and energy comes in discrete bundles. Please explain this: if you take away the discrete bundles of energy, what is left of the field?
I'm not trying to say that either the corpuscle OR the field is the only physical concept. I'm trying to say, how can you have one without the other?

You can't, however I see that Neumaier has already explained this (and certainly better than what I could do because I'm just a student).

 

[A. Neumaier]

This would take us into the realm of philosophy.

Indeed. But all talk about the precise nature of the virtuality of virtual particles is philosophy, since there is nothing observable about them.

A photon cannot "sense the passage of time". What does that truly mean?

It means something similar as the phrase ''a blind man cannot sense colors''.

It needs receptors to sense something. Being able to sense the passage of time is very closely related to being able to form the concept of a history.

Spacetime is warped. What does that truly mean?

Whether it is warped is a matter of interpretation. The existence of a symmetric tensor field need not be interpreted as warpedness.

An electron passes through both slits in the double-slit experiment. What does that truly mean?

It means that the electron is a wave, not a particle. There is nothing more behind it.

Nobody can give fully satisfactory answers to the above questions, and there are plenty more like them.

What are your criteria for being fully satisfactory? Can you at least give fully satisfactory criteria? If not, it might be the fault of the latter, not of understanding.

You see, just understanding the math, and being able to work the problems isn't enough for me.

What is missing?

I want to understand - in the fullest sense of the term - the reality behind these bizarre behaviors seen in nature.

Understanding a ghost may mean convincing oneself of its nonexistence, and reinterpreting the signs of ghostiness in a more profitable way.

I also think we should always have misgivings about our current theories. It helps us to see beyond them.

But this is useful only if there is a need to see beyond. Which means - only in those aspects of a theory where its predictions do not match reality.