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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?

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- Thread starter Islam Hassan
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In summary, according to Schrodinger, the point-like nature of particles in QFT is based on the fact that the Hamiltonian is only of finite order in spatial derivatives. Schrodinger also argued that the charge of an electron is proportional to the square modulus of its spatial state expansion, and that the wave-particle duality does not pose any theoretical issues.

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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?

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Not according to plain old Schrodinger himself - quite "the opposite":Bill_K said:[..] Plain old Schrodinger quantum mechanics has always been about point-like particles. [..]

"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

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

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IMO there's little value in requoting what was thought or said nearly a century ago, even by such giants as Schrodinger 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.harrylin said:Not according to plain old Schrodinger himself - quite "the opposite":

In Schrodinger'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.

If so, he was totally wrong about that.harrylin said:And while he admits that both points of view are "extremes", his hypothesis was that the electron charge isnotconcentrated in a point.

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Cheers,

Jazz

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Bill_K said: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

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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.Jazzdude said:I'd say he was totally right about that.

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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.

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Bill_K said: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

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You are not even sorry?!Bill_K said:IMO there's little value in requoting what was thought or said nearly a century ago [..]

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

If I correctly understood the explanations on this forum about QFT, then the main modern point of view is that Schrodinger was quite right about that.[..] he was totally wrong about that.

See also http://ajp.aapt.org/resource/1/ajpias/v81/i3/p211_s1 [Broken] :

"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.

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For a given electron wavefunction ψ(x) there's an associated charge distribution e |ψ|Jazzdude said: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".

We agree on that! Unfortunately one runs across a lot of it, both here on PF and elsewhere.harrylin said:IMO it's entirely without merit and even Very Bad to misrepresent other people's opinions or theories, no matter of how long ago.

Again, this is talking about a probability distribution. There is NO suggestion that the electronharrylin said:If I correctly understood the explanations on this forum about QFT, then the main modern point of view is that Schrodinger was quite right about that.

See also http://ajp.aapt.org/resource/1/ajpias/v81/i3/p211_s1 [Broken] :

"each electron extends over both slits in the two-slit experiment and spreads over the entire pattern".

is so large that it actually extends over both slits. :uhh:

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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.Islam Hassan said:

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?

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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:Bill_K said:[..] 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. :uhh:

"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."

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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.

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Bill_K said: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

In QFT, point-like particles are described as mathematical points with no size or spatial extent. They are represented by fields that exist throughout space and time. On the other hand, wave-particle duality refers to the concept that particles can exhibit both wave-like and particle-like behavior. This duality is a fundamental aspect of quantum mechanics and is described by wave functions that determine the probability of a particle's location.

In QFT, point-like particles are described as excitations of quantum fields. These fields permeate all of space and time and interact with each other to create particles. The behavior of these particles is determined by the interactions between the fields and their corresponding particles, as described by mathematical equations.

Yes, particles in QFT can exhibit both point-like and wave-like behavior. This is due to the wave-particle duality concept, where particles have both particle-like properties (such as mass and charge) and wave-like properties (such as wavelength and frequency).

In QFT, the wave function of a particle describes its probability of being measured at a certain location. This means that the exact position and momentum of a particle cannot be known simultaneously. This is known as the Heisenberg uncertainty principle and is a consequence of wave-particle duality.

Yes, QFT is used in many real-world applications, such as the development of new technologies like transistors and lasers. The understanding of point-like particles and wave-particle duality has also led to advances in fields like quantum computing and cryptography.

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