Dear Oliver,

"...do physicists commit a fallacy in the Whitehead sense or are are we not in the arena of "logical reasoning"? "

That depends. Of course, we can argue logically with Feynman diagrams as long as we and our conversation partners know the mathematical terms symbolized by the lines and stick to the logic of the Feynman rules. Most physicists use Feynman diagrams in this way.

However, if the internal lines are "explained" as particles that are able to leave their mass shell, then this is a fallacy, because such explanations leave the logical arena of the Feynman rules.

Although well-intentioned, such pseudo-explanations are superfluous for the experts and give the laymen a false understanding of particle physics.

Walter

Oliver

It is fair to say that almost all advanced modern physics is close to speculation. Field theory; Maxwell's electro-magnetic theory; Newton's gravity theories; Einstein's Space-time theories; Higg's Boson  and many others are all cases in point. We constantly delve in areas that our current instruments and observational capabilities are struggling to understand.

That said, we use the best explanation available to us at any time to interpret what we measure or experience.

Feynman's work, like Newton's or anyone else's who explores advanced physics is expected to be surpassed and built upon.

That we use historical terminology and ideas as part of our scientific culture in no way detracts from their work or their subsequent redundancy.

We could, or example, pick apart the use of the word 'gravity', which in Newton's day expressed a medical condition or emotional state, rather than an attractive force or a warping of a continuum.

However to express some support for Feynman, his exchange particles or energy packets as I prefer to think of them are simply the best explanation around for a number off common phenomena such as atomic forces, heat conduction or light refraction. In my view at least.

Ian

Oliver,

Let me see if I got your point: we know that, for example, the eletromagnetic interaction occurs by mean of a coupling between Dirac field and photon field. So, why treat the interaction as a exchange of bosons, instead of, for example, treating the photon field as a mediator itself (not the particle states) for the fermions, like two oscilating balls in a water tank interact via wave propagations in the water?

It's a good question (if that is the point), and I stick with Ian's answer. But, the Feynman's interpretation seens reasonable to me (altough reasonability don't means reality), because of the fact that the fermions irradiate. I learned in classical eletrodynaics that radiation is a consequence of acceleration of the particle under a potential. After learning the few things I know about QFT, I started wondering if it's not the acceleration that's a consequence of radiation (or, more precisely, from the exchanging of photons between the particle and the potential's source).

But it's just a divagation and I may be missing fundamental concepts here.

Thanks for your contributions!

@ Ian: I am not sure if Feynman's work can count as an explanation in the strict sense. In the end it is a extremely useful tool to predict observed phenomena, to be sure. But the single Feynman diagram can hardly be interpeted physically.

@Marcos: I think you got my point! We do have a coupling term in the Lagrangian and the talk about "exchange particles" is kind of metaphorical...

"the single Feynman diagram can hardly be interpreted physically."

Oliver,

I have read Feynman's collected lectures three times now and from my understanding of them, the diagrams were developed from real life observations and were intended to represent a specific kind of reality, that of the motion and interaction of photons and similar energy packets as they travel through space and near other energy packets and 'physical matter'.

Very specifically they have helped me to understand the basics behind refraction and heat containment within electromagnetic environments.

In the wider world it was Feynman's little arrows and exchange particles that gave us a structure (physical basis) in which we could demonstrate quantum entanglement.

So I certainly disagree with your comment above. Given an adequate background in the toolset and a set of assumptions used in preparing the diagram, a single Feynman diagram can represent real-world,  dynamic phenomena.

Thus the diagram above gives a simple but compelling message.

Ian

Ian and Oliver,

I'll abuse your goodwill to learn a few more things and clarify my visions. Thinking, for instance, in Bhabha scattering, we can "easily" interpret the 2-vertex diagrams as annihilation and scattering process, both mediated by photons. But, when we go for 4-vertex diagrams , like in the figure (sorry for the bad drawing), we have more complicated structures. How can we interpret the fermionic loop between the two "scattering" parts of the diagram?

Deepening the question, at higher orders, we see more and more complicated diagrams. In this case, will we interpret those ones as several subprocess like annihilations, creations and other, all them occuring by photon exchange? I have to agree with Oliver that things become more surreal at this point.

I still think that messenger bosons interpretation are reasonable, but i don't know if the Feynmann diagrams alone are suffice to convince everyone of this. Perhaps an empirical approach is necessary.

Dear Ian,

thanks for your contribution. it is getting exciting! Let me try to explain my remark in more detail:

My claim is that Feynman diagrams do not represent physical processes but only formulae. That was, by the way, the position of Freeman Dyson as well (see hisCornell lecture from 1951). The two main arguments come from (i) superposition and (ii) topological equivalence.

Ad (i): A single diagram represents a term in the expansion of the S matrix. All physical observations are related to |S|2 . That means that there are additional interference terms which do not relate to any Feynman diagram individually. Recall a similar situation in QM. When dealing with the double slit you do have probability amplitudes for the electron passing through slit 1 or 2. The observable pattern is the square of sums. Now, can you ask whether the electron actually went through one slit or the other? A single FD is like the amplitude for the slit 1 and slit 2 contribution.

Ad (ii): Two diagrams are said to be "topological equivalent" if you can continuously transform them into each other. Top. equiv. diagrams stand for the same amplitude and you have to choose one in order to avoid double counting. A textbook example is Compton scattering in lowest order. There, two diagrams contribute already in leading order (see picture below) . b) and c) are equivalent although they picture apparently completely different processes. In c) even a positron plays a role which is absent in b)! That is, FD do not tell a stroy...

By the way: Given that already in QM there is no way to tell what is going on between preparation and measurement, it would be rather odd if QFT allows for such stories to be told...

Given all that I wonder how the talk about "exchange particles" could be understood...

best regards,

Oliver

@Marcos: your point seems to me related!

Oliver,.

" ... the notion of (virtual) exchange particles appears to me questionable (i.e. based on an artefact, like the specific solution technique of perturbation theory) "

In Feynman's 1949/50 papers, where he introduced his popular diagrams,

he used the wording "virtually exchanged quanta". This was not meant in a speculative sense, but referred explicitly to certain well-defined terms of the perturbation algorithm connecting two particle states. Later on, this notion was replaced ("reified") by "virtual particles", which is a figure of speech and should be understood as such.

Alfred North Whitehead noted: ``reification is part of normal usage of natural language, as well as of literature, where a reified abstraction is intended as a figure of speech, and actually understood as such. But the use of reification in logical reasoning or rhetoric is misleading and usually regarded as a fallacy.'' (Whitehead, A.N.: Science and the Modern World. Lowell Lectures, 1925. Pelican Mentor Books, New York (1948))

The sheer endless discussions about the reality of "virtual particles" result from the confusion of figures of speech with reality.

See also: David Mermin, "It is a bad habit of physicists to take their most successful abstractions to be real properties of our world." (Physics Today, May 2009).

Walter

Dear Walter,

beautiful and illuminating in may ways. Not just particle physics...

But: do physicists commit a fallacy in the Whitehead sense or are are we not in the arena of "logical reasoning"?

Oliver

Dear Oliver,

"...do physicists commit a fallacy in the Whitehead sense or are are we not in the arena of "logical reasoning"? "

That depends. Of course, we can argue logically with Feynman diagrams as long as we and our conversation partners know the mathematical terms symbolized by the lines and stick to the logic of the Feynman rules. Most physicists use Feynman diagrams in this way.

However, if the internal lines are "explained" as particles that are able to leave their mass shell, then this is a fallacy, because such explanations leave the logical arena of the Feynman rules.

Although well-intentioned, such pseudo-explanations are superfluous for the experts and give the laymen a false understanding of particle physics.

Walter

Of course-the Feynman diagrams are just one way of representing the transition amplitudes.

That photons, W and Z bosons and gluons describe certain kinds of forces can be expressed using Feynman diagrams-but the diagrams represent only part of the story, namely the perturbative expansion about free fields.

But even that doesn't matter that much-what matters are the transition probabilities from any given state of particles to any other given state of particles-these are the only ``physical'' quantities. How they're obtained is a question of personal taste.

Feynman diagrams aren't to be interpreted-they're a computational tool. The result of the computation only matters, not how it's obtained. For many computations these diagrams are useful, because they make doing those computations very easy.

Dear Stam,

I agree completely. We do have coupling terms between certain fields in the lagrangian and as a result the transition probabilities for certain reactions are like they are. So, would you agree that we have actually little reason to talk about "exchange" particles and that this way of talking is only mataphorical (at best)?

Indeed-any particle can be exchanged, depending on the process. What is special is that certain particles, namely the photon, the W and Z bosons and the gluons, are one-particle states of gauge fields and other particles aren't.

Dear Oliver,

Although you are right that the concept of "exchanged particles" is an invention of Feynman diagrams to picture elementary particles interacting or decaying, using the quantum field theoretical formalism, that doesn't mean that they are only mathematical artifacts. Notice that the lines between the vertices are position holders for the energy and momentum and quantum number exchanges between incoming and outgoing, and are under the integral (propagator) which the diagram represents. What is non-real is the role played by the virtual particles in an inner closed loop where they are off mass shell and therefore its mass must not be real (or the energy-momentum doesn't follow the usual relation). Without the virtual particles nowadays would be difficult to understand and even calculate many different interactions and the physical tables of particles are full of them.

Perhaps a deeper question remains, in what sense are real the particles that we call real? For instance, what is one electron? An electron as an excitation of the electron field that exists previously to electrons themselves and permeates all of our space-time. In fact we assume that the electron field has nothing to do with the electric field the electron creates!! What imports to the physicists is that we have a coupling gauge term in the density of Lagrangian relating the electric charge, the Dirac field and the gauge electromagnetic potential. This is in fact what we can understand of one electron as particle, whose only difference with a virtual particle is that we always can follow its energy and momentum. Thus artifacts in Physics are all the fundamental particles!

Dear Igael,

I suppose that you refer to the sentence:

physical tables of particles are full of them.

where I wanted to say that there are many different particles in the tables of

particles, mainly the gauge bosons of the interactions which are defined as internal lines of the Feynman diagrams. See

https://en.wikipedia.org/wiki/Virtual_particle

But let me to explain a little deepler.Feynman diagrams describe how the terms in a series expansion of the S-matrix elements arise in a perturbative treatment of the interactions as linear combinations of multiple integrals. Each such multiple integral is a product of vertex contributions and propagators, and each propagator depends on a 4-momentum vector that is integrated over. In additon, there is a dependence on the momenta of the ingoing (prepared) and outgoing (in principle detectable) particles. In such a form that each such integral can be represented by a Feynman diagram. This is obtained associating with each vertex a node of the diagram and with each momentum a line. For ingoing momenta there is an external line ending in a node, while for outgoing momenta there is an external line starting in a node, and for the propagator momenta an internal line between two nodes. These are the usual graphical rules.

A virtual particle has defined values of 4-momentum, spin, and charges, characterizing the propagator. But their 4-momentum is integrated over all of spacetime and therefore, there is no mass shell constraint, hence virtual particles are off-shell, i.e. they are only limited by the uncertainty principle. States involving virtual particles cannot be created for lack of corresponding creation operators in the theory. Thus it is impossible to represent a virtual particle by means of states. Which means that they cannot have a detection probability, a decay time or a dynamics in general.

Going to the physical world the main virtual particles are associated to the gauge bosons of interactions. Actually the word particle doesn't fit particularly well to microscopic nature of matter,i.e. the quantum fields describing matter has not well defined position, momentum and energy at particular time too. We can think in an accelerator of particles during the interaction of two electrons by means of a photon, which will never be measured. This is what we could call virtual photon and represent it within an inner line of the Feynman diagram.

This is from the point of view of the scattering, but we could think in more simple situation in one electron in an hydrogen atom where the measured particle is in fact the photon exchanged with the proton instead of the electron or the proton. Thus in such a case the electron could be the virtual particle instead of the photon such as it is done sometimes in solid state physics for certain atoms.

The calculations for particle theories and perturbative. They represent an expansion in a small coupling constant. Among the terms of the expansion there are "propagators" between particles which are virtual, that is they are not free particles. We call these particles "exchanged particles". No matter what you call them propagators will appear in a perturbative solution. They are the analoque of Green's functions in differential equations.

For exact solutions of field theories one must investigate what replaces them.