QFT: Point-Like Particles vs Wave-Particle Duality

[Islam Hassan]

Is there a (theoretical) partial or total inconsistency in QFT's postulate/premise/description of elementary particles as dimensionless, point-like objects with respect to the wave-particle duality nature of QM? This is in the sense that such description is *only* particle-like.

Clearly, even if there were such inconsistency, QFT remains an extraordinarily successful descriptive framework of nature. If the inconsistency is there then, what theoretical issues would it give rise to?

 

[Bill_K]

No, this is not even a QFT issue. Plain old Schrödinger quantum mechanics has always been about point-like particles. When you write H = p²/2m + V(r), you are writing the Hamiltonian of a point particle.

 

[harrylin]

[..] Plain old Schrödinger quantum mechanics has always been about point-like particles. [..]

Not according to plain old Schrödinger himself - quite "the opposite":

"The point of view taken here [..] is rather that material points consist of, or are nothing more but, wave systems.
[..] "the opposite point of view [..] treats only the motion of material points [..]".

[addendum:] And while he admits that both points of view are "extremes", his hypothesis was that the electron charge is not concentrated in a point.

-http://web.archive.org/web/20081217040121/http://home.tiscali.nl/physis/HistoricPaper/Schroedinger/Schroedinger1926c.pdf

 

[Bill_K]

Not according to plain old Schrödinger himself - quite "the opposite":

IMO there's little value in requoting what was thought or said nearly a century ago, even by such giants as Schrödinger or Einstein. Physics has come a long way since then. Basing your understanding of QM on a 1920's paper is like trying to learn mechanics from Newton's Principia.

In Schrödinger's day the idea that material particles possessed a wavelike nature was new, to himself as well as others, and for this reason deserved special emphasis. To see that the particle described in introductory QM is pointlike, one only need look at cases where more general systems are described. Nuclear physics, for example, often deals with the QM of an extended body - a rigid rotator, or a vibrating object. There are extra degrees of freedom, and correspondingly extra terms in the Hamiltonian.

And while he admits that both points of view are "extremes", his hypothesis was that the electron charge is not concentrated in a point.

If so, he was totally wrong about that.

 

[Jazzdude]

Interestingly the notion of a "point particle" in QT and QFT has little to do with the wave particle duality or interpretation issues. When we speak today of point particles we mean something entirely else than little mass points that move around. We mean two things: 1) There is no lower bound for the localizability of a particle if you have enough energy available. That is, the space a particle state occupies in its position expansion can be made arbitrarily small. 2) The interaction term is only of finite order in spatial derivatives. That makes sure the interactions will make the state evolve as if it was made of a dense collection of independent local "points". There are pathological examples of interactions that don't behave like that, like when you take the square root of (some function of) the momentum operator for constructing the hamiltonian.

Cheers,

Jazz

 

[Jazzdude]

If so, he was totally wrong about that.

I'd say he was totally right about that. The charge of an electron is proportional to the square modulus of it's spatial state expansion, because that's what the EM field couples to. (It's a little more complicated in QED, but essentially, that's what it is.)

Cheers,

Jazz

 

[Bill_K]

I'd say he was totally right about that.

Well then you're wrong too. The charge distribution of an object is described by giving its form factor. To the utmost accuracy, the form factor of an electron is that of a point particle, and this is what all of QED is based upon. For example if it were not the case, the experimentally measured magnetic dipole moment would fail to agree with the QED prediction.

 

[jarekd]

We usually operate on QFT in the perturbative approximation - consider Feynman distribution among infinite family of possible scenarios. In each of these scenarios particles are point-like.

So where is the wave nature? In the need of using ensembles.
To understand it, we need to start with the simplest "need for using ensembles": interference.
How to cope the indivisibility of charge with the fact that electron undergoes interference?
There is not a problem in de Broglie's interpretation - each particle has an internal periodic motion, creating waves conjugated with them. Exactly like in Couder's walking droplets, in interference e.g. electron goes a single way, while the "pilot" wave it creates goes both ways, finally causing interference.
From the observer's perspective there is no difference if the corpuscle came one or another way - it is enough to focus on its wave here - what we do in the quantum description.

Huygens principle says that every point is a source of wave, so from ensemble of two paths to consider, we have to go to a continuous family in the path integral formulation of quantum mechanics - focusing on waves conjugated with the particle, "piloting" it through one of these trajectories.
Additionally allowing for varying the number of particles, in QFT we get ensemble of possible scenarios: Feynman diagrams.

 

[Jazzdude]

Well then you're wrong too. The charge distribution of an object is described by giving its form factor. To the utmost accuracy, the form factor of an electron is that of a point particle, and this is what all of QED is based upon. For example if it were not the case, the experimentally measured magnetic dipole moment would fail to agree with the QED prediction.

Not so fast. I think we're talking about different things here. The form factor comes in specifically when you're calculating scattering outcomes and that based on point-like interaction vertices. Of course, if you ask for the behavior of point like interactions you get a result that agrees with point-like interactions (and an associated charge distribution).

What I'm talking about is how the interaction terms in QED relate to the position expansion of the electron, if you forgive me to use 1st quantization terminology here. In terms of fields that becomes much more complicated to calculate, but what comes out must treat every part of the spatial superposition of an electronic excitation equally, which means every spatial aspect of the electron contributes to the interaction and therefore holds "charge".

Cheers,

Jazz

 

[harrylin]

IMO there's little value in requoting what was thought or said nearly a century ago [..]

You are not even sorry?!
IMO it's entirely without merit and even Very Bad to misrepresent other people's opinions or theories, no matter of how long ago.

[..] he was totally wrong about that.

If I correctly understood the explanations on this forum about QFT, then the main modern point of view is that Schrödinger was quite right about that.
See also http://ajp.aapt.org/resource/1/ajpias/v81/i3/p211_s1 :
"each electron extends over both slits in the two-slit experiment and spreads over the entire pattern".
A few critical comments on that article have been published, but it looks to me that all agree that on a fundamental level there are no particles.

 

[Bill_K]

What I'm talking about is how the interaction terms in QED relate to the position expansion of the electron, if you forgive me to use 1st quantization terminology here. In terms of fields that becomes much more complicated to calculate, but what comes out must treat every part of the spatial superposition of an electronic excitation equally, which means every spatial aspect of the electron contributes to the interaction and therefore holds "charge".

For a given electron wavefunction ψ(x) there's an associated charge distribution e |ψ|². That seems to be what you're referring to. For an electron in a Bohr orbit there's a charge distribution smeared out over several Angstroms. But this does not mean the electron fails to be pointlike. Because ψ(x) is only a probability amplitude of finding the pointlike electron at position x. And likewise e |ψ|² is a probability distribution for finding the charge at x.

IMO it's entirely without merit and even Very Bad to misrepresent other people's opinions or theories, no matter of how long ago.

We agree on that! Unfortunately one runs across a lot of it, both here on PF and elsewhere.

If I correctly understood the explanations on this forum about QFT, then the main modern point of view is that Schrödinger was quite right about that.
See also http://ajp.aapt.org/resource/1/ajpias/v81/i3/p211_s1 :
"each electron extends over both slits in the two-slit experiment and spreads over the entire pattern".

Again, this is talking about a probability distribution. There is NO suggestion that the electron
is so large that it actually extends over both slits.

 

[harrylin]

Is there a (theoretical) partial or total inconsistency in QFT's postulate/premise/description of elementary particles as dimensionless, point-like objects with respect to the wave-particle duality nature of QM? This is in the sense that such description is *only* particle-like.

Clearly, even if there were such inconsistency, QFT remains an extraordinarily successful descriptive framework of nature. If the inconsistency is there then, what theoretical issues would it give rise to?

There may be something presented in the AJP paper by Hobson that I linked to in my earlier message: "several phenomena showing particles are incompatible with quantum field theories". I have only quickly glanced over it and I'm a layman concerning QFT, so I'm not sure if his arguments are pertinent.

 

[harrylin]

[..] We agree on that! Unfortunately one runs across a lot of it, both here on PF and elsewhere.
[..] Again, this is talking about a probability distribution. There is NO suggestion that the electron
is so large that it actually extends over both slits.

And it continues: according to my word finder, "probability distribution" is not even mentioned in the whole article, according to which there are no particles. Not only he states as I already cited that:
"each electron extends over both slits in the two-slit experiment and spreads over the entire pattern",
he adds in his paper:
"In QFT the interactions, including creation and destruction, occur at specific locations x, but the fundamental objects of the theory, namely, the fields, do not have positions because they are infinitely extended."

 

[Jano L.]

Resolving the question "is electron particle or field" is a messy task because the answer depends on the theory one chooses to answer it. In the theory based on the Born interpretation of $|\psi(q)|^2$ and Schroedinger's equation, the particles are points as Bill_K nicely explained. The delocalized nature of $\psi$ is a property of $\psi$, not of the electrons. It is similar to the delocalized nature of Hamilton's principal function $S(q)$ used in the Hamilton-Jacobi theory, or the probability distribution function in statistical physics.

In quantum field theory, on the other hand, a different kind of description is often used, where the state of the system may be such that the number of the particles does not even have sense. The field operator $\hat \psi(x)$ may still have sense in such situation soI can understand that many people infer that the real object the theory is about is not a collection of point particles, but this (delocalized) operator field.

However, the radius of the electron was measured in experiments, and interpreted based on quantum electrodynamics. In these papers the radius of the electron is reported to be smaller than $10^{-18~}$m or so which suggests that the electron is regarded as a point-like particle and may be even a point with zero radius.

There are also people who regard quantum field as only an auxiliary device that exists "only on paper", as dextercioby said in some post some time ago.

So I think the original question of Islam Hassan is a very good one, and it would be great if people knowledgeable in QFT could offer some insight on this.

 

[Jazzdude]

Because ψ(x) is only a probability amplitude of finding the pointlike electron at position x. And likewise e |ψ|² is a probability distribution for finding the charge at x.

Now that goes very deep down the interpretational tunnel. If you think that's what quantum mechanics is then I cannot argue with you. For me what you refer to is part of the measurement process, and not the underlying physical theory. I would not really like to take this discussion to the quantum measurement problem and the interpretation of quantum theory (yet again), so please see all my statement in context of a realist understanding of the unitary evolution of states in quantum theory and quantum field theory. What I said applies there and is the view shared by most working theoretical physicists I know.


Cheers,

Jazz