# Art Hobson's "No Particles"

1. Aug 22, 2014

### atyy

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2. Aug 22, 2014

### atyy

OK, so if he's using second quantization, then it is ok to view the Schroedinger ψ as a space filling field. But then that makes his point even stranger - the Hilbert space, which is a Fock space is a space of particles! One can even invent a number operator and show that the number of particles is conserved in the second quantized Schroedinger equation.

If he wants to argue that the Hilbert space is not a Fock space, he has to believe that our universe is described by a rigourous interacting relativistic field theory, which by Haag's theorem does not have a Hilbert space that is a Fock space.

Last edited: Aug 22, 2014
3. Aug 23, 2014

### Staff: Mentor

Mate exactly how you recover usual QM from QFT as some kind of limit is beyond my current knowledge.

I am sure it can be done eg:
http://www.mat.univie.ac.at/~neum/physfaq/topics/position.html

But that is beyond my level.

Also this crops up every now and then. One issue is that when someone says there are no particles, only fields thay are not saying QFT doesn't have particles - obviously it does - but they are the excitations of the field, rather than the fundamental thing itself.

Second quantisation is IMHO a really bad way of looking at QFT.

Its simply this. Model the field as an interacting dust where the interaction is between neighbouring bits of dust. One then assumes the dust value (whatever it is) is described by some kind of Langrangian so you have a conjugate momentum, and you apply the standard QM commutation relations to quantise it. Then you take the limit as the dust size goes to zero to get a QFT.

One then imposes certain symmetry conditions on this field to get various field like the EM field. Zee, in his book on QFT, calls this approach Landau-Ginsberg and IMHO is a much better way to view it than so called second quantization.

Thanks
Bill

Last edited: Aug 23, 2014
4. Aug 23, 2014

### atyy

5. Aug 23, 2014

### stevendaryl

Staff Emeritus
But on the other hand, the semantics of the field operators is described in terms of how they act on Fock states, and the Fock states themselves represent states of particles, right? I mean that the Fock space is a disjoint union of states with 0 particles, 1 particle, etc.

But maybe it's not necessary to introduce Fock space, and simple define the states axiomatically, without mentioning particle states.

6. Aug 23, 2014

### Staff: Mentor

Well the books I have read such as Zee start out with an operator at each point and, via the commutation relations, show that the space they act on is the Fock space.

Many books and notes explain it eg:
http://hitoshi.berkeley.edu/221b/QFT.pdf

It would seem that its whole point. A quantum field implies it acts on the space of creation and annihilation operators which is how you get the picture of the particles being 'excitations' of the field.

It a completely different picture than standard QM.

It must however reduce to it - but my knowledge is not advanced enough to understand how its done.

That however doest seem to be be the issue Atty had with Art Hopson's paper.

He claims that viewing it as a fields helps understanding things like the double slit experiment, and I must say I agree.

It doesn't perturb me at all its inherently unobservable - a state isn't either.

Thanks
Bill

7. Aug 23, 2014

### atyy

In Hobson's description of the double slit http://arxiv.org/abs/1204.4616 (Eq 4), the quantity in his equation is the state vector, which does correspond to the wave function in the first quantized description. It is not the field operator. The field operator used to define the second quantized Hamiltonian can be thought of as a space filling field, but the wave function of more than one particle cannot. If he wants to talk about the matter field evolving, he has to use the Heisenberg picture and talk about the field operator evolving.

One can also see Hobson's error by looking at his Eq 8, following which he says "$\psi(x)$ is the Schroedinger field", which is wrong if by Schroedinger field he means the field operator. For comparison, we can look at bhobba's link to Hitoshi Murayama's http://hitoshi.berkeley.edu/221b/QFT.pdf (Eq 31 and 32): "Note that $\Psi(\vec{x})$ is a $c$-number function which determines a particular superposition of the position eigenstates $|\vec{x}\rangle$. But it turns out that this $\Psi(\vec{x})$ corresponds to the Schroedinger wave function in the particle quantum mechanics."

Last edited: Aug 23, 2014
8. Aug 23, 2014

### RUTA

Two responses to Hobson and his rebuttal: http://physics.uark.edu/hobson/pubs/13.09.b.AJP.pdf [Broken]

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9. Aug 23, 2014

### Staff: Mentor

Again we get back to exactly how does QFT reduce to standard QM eg maybe in some kind of limit it can be.

Also, as I have mentioned before, I think second quantisation is a bad name best avoided, even though the link I gave used that terminology.

Thanks
Bill

10. Aug 23, 2014

### atyy

There's no limit that needs to be taken to get from the second quantized to the first quantized Schroedinger equation. First quantization is the quantization of particles, second quantization is the quantization of fields. Hobson is using the second quantized Schroedinger equation. The second quantized theory is exactly the same theory as the first quantized theory of identical particles. If you have normal non-relativistic QM with Schroedinger's equation for one or more identical particles, that can be rewritten exactly as a quantum field theory. It is the same theory in two different languages. In the second quantized theory, there is the field operator and the wave function. The field operator can be considered a field in space, because it is just the operator counterpart of a classical field. The wave function is the same wave function as the usual first quantized wave function, and it is not a field in space, but rather it exists in Hilbert space. In Hobson's Eq 8, what he calls the Schroedinger field, presumably meaning the field operator, is not the field operator, but the wave function. So his paper is wrong.

Last edited: Aug 23, 2014
11. Aug 23, 2014

### akhmeteli

Could anyone explain the following statement by Hobson in his rebuttal: "My argument about the two-slit experiment is: each individual quantum responds to the fact that both slits are open; this cannot be due to any long-distance force (or call it an “interaction” or a “potential” if you don’t like the word “force”) that extends over the distance from one slit to the other. Thus each quantum must come through both slits."?

Why cannot this be due, say, to the Coulomb potential?

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12. Aug 23, 2014

### Staff: Mentor

What Couloumb potential would that be?

Atoms, molecules etc are electrically neutral.

Thanks
Bill

13. Aug 24, 2014

### Staff: Mentor

Come again.

Forget the second quantisation rubbish - its just that - rubbish - well IMHO anyway.

But if it was true, then the claim that the wave-function is some kind of limit of the second quantised matter-field is trivial in the the same way the EM field is a limit of the quantized EM field. However I am not going to argue along those lines because I don't agree that's the correct way to view it.

What's going on IMHO, is you are applying the idea of a quantum field (which is operators at each point) and symmetries to get various QFT's.

For definiteness lets assume we are using electrons in the double slit

Now what needs to be shown is from that description, in some find of limit, the normal Schroedinger equation results so that wave-function is a reasonable approximation to the field. If that's true then there is no issue - it can be viewed as Hopson suggests.

The reference I mentioned previously - Giuliano Preparata - Introduction to Realistic Physics - purports to show just that - see section 4.4 'The "quantum-mechanical" limit of QFT: The Schroedinger wave-function'

However I am not conversant with QFT enough to say for sure its analysis is valid - although it looks OK to me.

Thanks
Bill

Last edited: Aug 24, 2014
14. Aug 24, 2014

### bohm2

But they can possess dipole moments. I'm not sure if this is what akhmeteli was thinking about?

15. Aug 24, 2014

### atyy

Second quantization as a name is rubbish, but that does not mean that the rubbish name names a wrong concept. Second quantization has two modern meanings, both correct.

(1) In non-relativistic quantum mechanics of a fixed number of identical particles, second quantization is translating the Schroedinger equation governing the wave function (first quantized) into a quantum field theory (second quantized). The two forms describe exactly equivalent physics, without any need to take limits or approximations.

(2) Second quantization is the quantization of a classical field. For relativistic particles like photons or electrons, we usually use only second quantized descriptions, and often the first quantized counterparts do not exist as complete quantum theories.

Hobson uses the term "Schroedinger field". So he has already assumed a non-relativistic limit. He would be correct if the "Schroedinger field" he is referring to is the field operator. But when you look at his equations the "Schroedinger field" he is referring to is the wave function. In the link you gave http://hitoshi.berkeley.edu/221b/QFT.pdf Eq 32 contains both the Schroedinger field operator $\psi^{\dagger}(\vec{x})$ and the Schreodinger wave function $\Psi(\vec{x})$. Hobson mistakenly refers to the quantity that is the Schroedinger wave function as the Schroedinger field operator.

Last edited: Aug 24, 2014
16. Aug 24, 2014

### Staff: Mentor

Oh dear oh dear.

I thought these guys would have better sense than to get caught up in metaphysical semantics like the following (from Art Hopson's response):

'He states (paragraph 5) that, “A microscopic entity obeying HUP cannot actually possess the property of being always present somewhere in space,” and “Whatever its true nature,a microscopic entity is a non-spatial entity.” It is clear from de Bianchi’s letter, from his Ref. 5, and also from the work of D. Aerts referenced therein, that he defines a “non-spatial entity” as an entity that always exists but that does not exist in space-time except when it is momentarily “pulled” into space-time by interacting with a macroscopic detection apparatus. This notion that electrons and photons, not to mention other quanta such as molecules, spend most of their existence residing somewhere outside of space-time is unusual, to say the least. Do molecules reside in space and time only when they are observed? In claiming that electrons and photons do not always reside in space-time, de Bianchi makes one of those extraordinary claims that, as Carl Sagan put it, requires extraordinary evidence. de Bianchi’s only evidence is EPR’s reality criterion. However, this criterion for “reality” is not the only one possible. In fact, the EPR paper (de Bianchi’s Ref. 2) states quite sensibly that “this criterion, while far from exhausting all possible ways of recognizing a physical reality, at least provides us with one such way.” Furthermore, de Bianchi claims the EPR criterion to be both a necessary and sufficient (“if and only if,” paragraph 4) condition for a property to be real, while EPR and common sense recognize it as only a sufficient condition. It is not, as de Bianchi claims, a necessary condition. In other words, a property’s reality does not necessarily imply that the property is predictable. For example, the decay of a nucleus is surely a real event, but it is not predictable. Thus, we cannot conclude, on the basis of the uncertainty principle and EPR’s reality criterion, that quanta reside outside of space-time.'

When not observed QM is silent on properties a system has. It doesnt say it resides outside space-time, in space-time etc etc. It says nothing - its silent.

I still believe the real issue is, in analysing things like the double slit experiment with electrons (photons are a much more difficult animal because they don't have a position) can the wave-function be thought of as some kind of limit of the matter field. If so then the arguments Art uses looks valid.

That's the view of Giuliano Preparata. In fact that's why he wrote the book:
'Most contemporary physicists have no doubt that QFT must be involved in the still mysterious workings of these fascinating phenomena, but, beyond a few phenomenological attempts, such as the Landau-Ginsburg approach, no real headway has ever been made into this kind of physics. And, I contend, the fallacious philosophy of QM is largely responsible for this unfortunate state of affairs. Conversely, couldn't the situation improve, indeed change drastically if we were to realize the centrality of QFT and find that QM is but some kind of approximation of QFT in a well defined, limiting physical situation? This is precisely what this Essay proposes to show'

Now I do not entirely agree with that - but most certainly I do believe many of the difficulties with QM are more naturally approached and understood via QFT than QM.

Thanks
Bill

Last edited: Aug 24, 2014
17. Aug 24, 2014

### Staff: Mentor

In the double slit experiment, the assumption is made whatever objects you are using only interacts with the screens, and that only interaction is to be absorbed by it.

If anyone thinks that isn't true then produce your analysis where its accounted for in some other way.

Thanks
Bill

18. Aug 24, 2014

### Staff: Mentor

Protons and electrons obey exactly the same Schroedinger equation - but their matter field is entirely different - I am not even sure a protons matter field exists since its a composite particle.

A QFT is NOT taking the Schroedinger equation, treating its expansion of the state in terms of position, as a field, like the EM field, and quantising it. That doesn't even make any sense.

What it is, is considering QFT's in general, is showing that certain types of quantum fields are good models for certain particles, then showing they, in the weak dilute limit, as Giuliano Preparata calls it, Schroedinger's equation is a valid approximation.

Thanks
Bill

Last edited: Aug 24, 2014
19. Aug 24, 2014

### atyy

Great, so we can just use the Schroedinger wave equation for many identical particles in the non-relativistic limit.

The non-relativistic Schroedinger equation governing the wave function for many identical particles can be exactly rewritten as a quantum field theory. This makes sense and is called second quantization. It is certainly not taking the Schroedinger wave function of a quantum theory and quantizing it again, which doesn't make any sense.

Last edited: Aug 24, 2014
20. Aug 25, 2014

### akhmeteli

It seems obvious that interaction of diffracting particles with the screen can be explained by (or, if you wish, reduced to) their interaction with the particles comprising the screen (by the way, in reality, a diffracting particle can pass the screen, reflect from it or get absorbed in it). Depending on the specific diffracting particles and screen particles, we can have Coulomb interaction, dipole interaction, or something totally different, say, something like Yukawa potential. However, even Yukawa potential, while decreasing fast with distance, does not vanish totally at relatively large distances. That means that particles, such as electrons, neutrons, ions, atoms, molecules carry some fields such as Coulomb field, so they can exchange quanta of that field with the screen. That is compatible with the ideas of Duane and Lande (please see references and comments at https://www.physicsforums.com/showpost.php?p=3724011&postcount=8 ). Even in the case of Yukawa potential I cannot exclude a possibility of exchange of relatively long-wavelength interaction-mediating particles (as a result of a resonance).

Actually, the picture I am describing is close to that of the Couder experiment, which emulates quantum diffraction in classical-physics conditions, and it's clear there that the silicone oil drop passes through one of the slits, but interacts with its own wave on the surface of silicon oil, which passes through both slits.

Another circumstance that makes me wonder if this picture can be indeed reasonable. In my article http://download.springer.com/static/pdf/480/art%253A10.1140%252Fepjc%252Fs10052-013-2371-4.pdf?auth66=1409124342_b333214309d72bc6325575e90f655700&ext=.pdf [Broken] (published in the European Physical Journal C ) I show how matter field can be algebraically eliminated from the equations of electrodynamics (such as scalar electrodynamics or, with some important caveats, spinor electrodynamics), and the resulting equations describe independent evolution of electromagnetic field. This is also possible if you add some external conserved currents (that can describe the screen). So, say, electron diffraction can be equivalent to some interaction of electromagnetic field with external currents (of the screen).

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