Infinite Charged Electron in QFT

[rogerl]

Not yet but in the right direction. In condensed matter, the bare theory makes sense in principle, since (due to lack of particle creation and annihilation) it is the theory of the asymptotic particles at zero temperature. But to do calculations, one wants to think of the effective degrees of freedom of the solid, which are the ground state excitations. One wants to consider the ground state to be the vacuum, and the collective excitations to be the (quasi-)particles. To get this view, one needs to renormalize the theory - this is like in particle physics, except that, because the bare theory is physically meaningful, all renormalizations are finite.

In relativistic quantum field theory, there is no substance (aether) that would fill the ground state (vacuum), upon which one could build the theory. The bare particles pretend to be such a substance but is found inadequate, as seen by the divergences. But by taking careful limits and adjusting the parameters of the bare theory to diverge while taking the limit - which is possible only since the bare stuff is unphysical - one can still arrive at a renormalized theory in which the vacuum is a Poincare invariant state and the Hilbert space has the required property of carrying covariant and causal field operators.

This has nothing to do with being or not being an effective theory - the latter only need an infinite number of renormalization parameters for their construction.

It has also nothing to do with nonlinearities - the field equations underlying condensed matter are also nonlinear. The difference to condensed matter theory comes from the requirement of causality, which necessitates processes that change particle number.

You mentioned that the vacuum is a poincare invariant state. So the quantum vacuum is another mathematical figment of imagination just like the virtual particles?? Or is quantum vacuum located in space? Or not? If not, then space has only empty contents that has no vacuum and virtual particles?

 

[A. Neumaier]

Well, I was wondering if we can tell whether the bare theory is unphysical, simiply by looking at the field equation.

Yes, one can tell from that: Trying to solve the field equations together with equal-time CCR produces the dreaded infinities. This was the major obstacle in using QED between 1930 and 1948.

all the condensed matter books I've seen so far, simply start from the Fock space and consider how the Coulomb potential acts on the space, but never care to quantize the original field equation from the beginning. Doesn't this cause any problem theoretically?

No, as long as one keeps the particle number fixed. The reason is that particle number N is conserved. Usually, the thermodynamic limit N --> inf is done at a late stage where this is also harmless.

 

[A. Neumaier]

Ok. I can accept what you said that virtual particles are just mathematical artifacts or multivariate integrals. But virtual particles produce an *observable* effect.

No. Interactions produce an observable effect. The interactions are represented pictorially by vertices in Feynman diagrams representing perturbative contributions to a scattering amplitude, and the lines between them are pictorially called virtual particles.
They cause nothing.

You said mathematics only describe reality and they can't affect the physical. But how come the physical can be described perfectly by mathematics?

This is one of the great insights of science throughout the centuries, starting with Pythagoras and a^2+b^2=c^2. But the description is not perfect. All our models are only approximations to reality.

That it works so well is a miracle whose splendedness increases the better we understand nature.
http://en.wikipedia.org/wiki/Unreasonable_Effectiveness
It is easiest explained by assuming that God created the world according to a well-planned overall design. Some explain it instead by assuming that it is the result of chance and necessity - without being able to say where the laws defining necessity come from.
Some explain it instead by saying it is our minds who impose order on the universe, - but where is the evidence that we have such a power when confronted with a mess of any kind?

 

[A. Neumaier]

You mentioned that the vacuum is a poincare invariant state. So the quantum vacuum is another mathematical figment of imagination just like the virtual particles?? Or is quantum vacuum located in space? Or not? If not, then space has only empty contents that has no vacuum and virtual particles?

Physical states describe the possible contents of space-time. One of the many possibilities (and one not realized in a world containing us) is that it is completely empty. Then there is no way to distinguish one point from another or one orientation from another, which is why this state is Poincare invariant. (In general relativity it is even much more invariant.)

 

[rogerl]

Physical states describe the possible contents of space-time. One of the many possibilities (and one not realized in a world containing us) is that it is completely empty. Then there is no way to distinguish one point from another or one orientation from another, which is why this state is Poincare invariant. (In general relativity it is even much more invariant.)

Are you saying that space is synonymous to the quantum vacuum? I was asking about the quantum vacuum and whether it is another mathematical figment of imagination like virtual particles and you answered that space could be empty. Are you saying that space is another mathematical figment of imagination? But we move in space, how could that be? Unless you mean space is real while the quantum vacuum is just a mathematical entity or only in the mathematics like virtual particles. Is this what you mean?

 

[rogerl]

No. Interactions produce an observable effect. The interactions are represented pictorially by vertices in Feynman diagrams representing perturbative contributions to a scattering amplitude, and the lines between them are pictorially called virtual particles.
They cause nothing.


This is one of the great insights of science throughout the centuries, starting with Pythagoras and a^2+b^2=c^2. But the description is not perfect. All our models are only approximations to reality.

That it works so well is a miracle whose splendedness increases the better we understand nature.
http://en.wikipedia.org/wiki/Unreasonable_Effectiveness
It is easiest explained by assuming that God created the world according to a well-planned overall design. Some explain it instead by assuming that it is the result of chance and necessity - without being able to say where the laws defining necessity come from.
Some explain it instead by saying it is our minds who impose order on the universe, - but where is the evidence that we have such a power when confronted with a mess of any kind?

In Special Relativity. If faster than light is possible, there are frames of references in which things can go back in time. This is why scientists believe faster than light is never possible. But since you mentioned about God. Let's speak of the God Frame in which He can simultaneously contact every part of the whole universe with billions of galaxies at once. Do you believe it is possible for a superluminal signal to exist that doesn't imply backward in time, like some kind of a special priveleged frame (like perhaps the God Frame) which can violate Lorentz Invariance? Pls. elaborate how this is possible using other privileged frame or try to criticize Special Relativity if you think it can be bypassed using your superior mathematics. Or do you believe that Lorentz Invariance is a law that can't be broken meaning faster than light is totally impossible?

 

[A. Neumaier]

Are you saying that space is synonymous to the quantum vacuum?

As I use the word ''real'', space and time are real. If space contains nothing then one calls the resulting reality the vacuum, whereas if space contains something (which is the more interesting case) then one calls it a beam of light, a hydrogen atom, or a galaxy, depending on what one happens to consider.

 

[A. Neumaier]

In Special Relativity. If faster than light is possible,

In special relativity, faster than light is impossible. Thus you are talking about virtual things.

But since you mentioned about God. Let's speak of the God Frame in which He can simultaneously contact every part of the whole universe

God cannot be discussed in terms of physical laws, especially if you ascribe to him these particular qualities.

 

[rogerl]

As I use the word ''real'', space and time are real. If space contains nothing then one calls the resulting reality the vacuum, whereas if space contains something (which is the more interesting case) then one calls it a beam of light, a hydrogen atom, or a galaxy, depending on what one happens to consider.

How do you think is quantum matter coupled to spacetime? How does the interface work? What is your theory of quantum gravity or quantum spacetime that doesn't use Superstring Theory? One of the problems in modern physics is that General Relativity is incompatible with Quantum Mechanics or Quantum Field Theory. One is continuous, the other one is discrete. They both belong to the same world. This doesn't have only to do with the Planck scale which you may say is not relevant in daily life because we can use both in our world in terms of effective field theory in the lower energy limit. I'm referring to the detailed coupling between the two as when quantum matter is coupled to spacetime. How are they coupled or how to unite them? With your superior mathematics why not solve for quantum gravity and win a Nobel or two?

 

[weejee]

Yes, one can tell from that: Trying to solve the field equations together with equal-time CCR produces the dreaded infinities. This was the major obstacle in using QED between 1930 and 1948.


No, as long as one keeps the particle number fixed. The reason is that particle number N is conserved. Usually, the thermodynamic limit N --> inf is done at a late stage where this is also harmless.

I'm now reading your paper on renormalization. It is quite illuminating and what you have said makes more sense now. It also seems far more efficient than asking you every single question at this forum.

Anyway, thanks a lot!

 

[A. Neumaier]

How do you think is quantum matter coupled to spacetime?

Spacetime is just the manifold whose coordinates are used to parameterize the quantum fields. It doesn't interact at all - its the arena where things happen.

why not solve for quantum gravity and win a Nobel or two?

I am only explaining the standard material about quantum field theory in flat space, in a language a bit improved compared to the common, opaque and/or confusing textbook language. This is far less than what's needed for a Nobel prize.

 

[A. Neumaier]

I'm now reading your paper on renormalization. It is quite illuminating and what you have said makes more sense now. It also seems far more efficient than asking you every single question at this forum.

Yes, definitely! After each answer, one should read as much as the answer suggests, and then come back with questions that remain. This is the most efficient way to use interaction on PF.

 

[rogerl]

Spacetime is just the manifold whose coordinates are used to parameterize the quantum fields. It doesn't interact at all - its the arena where things happen.

Spacetime appears to be pure mathematics just like virtual particles. The Manifold is completely math. You said it's the arena where things happen. But quantum fields are real while the manifold is pure math. How do they bind together?

Anyway. Do you think it's possible gravity is not really caused by General Relativity but by some kind of force that has more physical cause?

I am only explaining the standard material about quantum field theory in flat space, in a language a bit improved compared to the common, opaque and/or confusing textbook language. This is far less than what's needed for a Nobel prize.

Any idea how to put quantum field theory in curved spacetime? Since your theory is different from others. Maybe you have insight others don't? Or is your views of quantum gravity the same as the mainstream where General Relativity is continuous, QFT is discrete and there is no way to bind the two especially in the Planck region.

 

[A. Neumaier]

Spacetime appears to be pure mathematics just like virtual particles. The Manifold is completely math.

What exists exists _in_ spacetime; the latter exists only in a weaker, observer-dpendent sense, since shifting or rotating spacetime doesn't affect physics at all. This is called a gauge transformation. What exists must be gauge-invariant. For example, distances between marked points exist in the strong sense, which means that there are associated observables, and their expectations can be predicted from the state.

You said it's the arena where things happen. But quantum fields are real while the manifold is pure math. How do they bind together?

Lets talk about a classical matter density field since the quantum aspect is irrelevant here. This field contains some conspicuous density peaks called stars and another one called Greenwich, which can be used to define a coordinate system. Every other object then gets coordinates by the usual process discussed in an introduction to relativity and implemented in the GPS. That we see the matter field is enough to have the arena around, but what acts and interacts is the matter, not space-time.

Do you think it's possible gravity is not really caused by General Relativity but by some kind of force that has more physical cause?

Any idea how to put quantum field theory in curved spacetime?

The gravitational field is a field like any other field - except that it has spin 2, which means that we may interpret it as a metric of spacetime. I have nothing interesting to say about it beyond that.

Since your theory is different from others.

My theory is not different from others. It is the standard textbook material explained in a hopefully more rational way.

 

[rogerl]

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.

 

[A. Neumaier]

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.

The electromagnetic field is real and measurable, and the mediating photons are virtual and not measurable. They exist in certain approximative treatments. But for example in the Coulomb gauge (one of the respectable formulations of QED), there are no virtual photon mediating the Coulomb field - instead there is an explicit Coulomb potential in the interaction. (This is the version of QED universally used by chemists.)

 

[rogerl]

The electromagnetic field is real and measurable, and the mediating photons are virtual and not measurable. They exist in certain approximative treatments. But for example in the Coulomb gauge (one of the respectable formulations of QED), there are no virtual photon mediating the Coulomb field - instead there is an explicit Coulomb potential in the interaction. (This is the version of QED universally used by chemists.)

What can you say about a real photon? I mean. The way you display real photon in the Feynman Diagram is also by way of internal lines. Since you said internal lines as virtual particles are only multivariate integrals and just mathematical and not real. Then are you implying the photon (from real light) are also not real since they are modeled also as internal lines in the Feynman Diagram too for example in the Feynman diagram of compton scattering?

 

[A. Neumaier]

What can you say about a real photon? I mean. The way you display real photon in the Feynman Diagram is also by way of internal lines. Since you said internal lines as virtual particles are only multivariate integrals and just mathematical and not real. Then are you implying the photon (from real light) are also not real since they are modeled also as internal lines in the Feynman Diagram too for example in the Feynman diagram of compton scattering?

No. Real photons are represented by external lines only. They correspond to wave functions between which the scattering matrix element is computed. These wave functions represent physical states that must be prepared and can be measured.

 

[rogerl]

No. Real photons are represented by external lines only. They correspond to wave functions between which the scattering matrix element is computed. These wave functions represent physical states that must be prepared and can be measured.

But I read that "The propagator for a photon on an internal line is *identical* and satisfies the very same wave equation as an external photon does."

And

"In order to measure a real photon, it has to interact with a detector electron, rendering it now a virtual photon by the parlance you are espousing. Whether it is represented in a *drawing* as an external line makes no difference to that reality.

As another example, you can easily draw a Feynman diagram with a pion on an external line, or a b-quark, for that matter. Nevertheless, it is known experimentally that those will decay with a known average lifetime, meaning that at some point there is an interaction vertex where that external line terminates, which by your parlance means that it is a virtual particle." (by P.D.)

The above is comment from a particle physicist in sci.physics. Comment?

 

[A. Neumaier]

But I read that "The propagator for a photon on an internal line is *identical* and satisfies the very same wave equation as an external photon does."

And

"In order to measure a real photon, it has to interact with a detector electron, rendering it now a virtual photon by the parlance you are espousing. Whether it is represented in a *drawing* as an external line makes no difference to that reality.

As another example, you can easily draw a Feynman diagram with a pion on an external line, or a b-quark, for that matter. Nevertheless, it is known experimentally that those will decay with a known average lifetime, meaning that at some point there is an interaction vertex where that external line terminates, which by your parlance means that it is a virtual particle." (by P.D.)

The above is comment from a particle physicist in sci.physics. Comment?

Physicists use the language of virtual photons to express properties of multivariate integrals, and the language of state vectors to express properties of real systems propagating in time. Virtual particles have no associated state vector, while real particles (even decaying ones) have. When talking loosely, they allow themselves liberities that disappear upon closer inspection.

For an example of the way such loose talk is to be interpreted, see the entry ''Can virtual particles become real? A case study'' in Chapter A7 of my theoretical physics FAQ at http://arnold-neumaier.at/physfaq/physics-faq.html#becomeReal

 

[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.