Are quantum fields real objects in space?

[DarMM]

Yea right. We are so good looking we have an area we have to look at to discuss posts that need looking at. I am sure its meant to age us so whatever looks we have are soon gone - assuming they are there to begin with.

No sympathy from me, you know it takes six of us Advisors to carry you lot in one of your golden palanquins?

(Alright I'll stop dragging the thread off topic now! )

 

[martinbn]

No, I'm not using it in two sense. In Haag's description there is nothing physically real obeying field equations, hence there are no physically real fields. There is only the algebra of local observables. Fields only appear as one method of constructing the algebra.

I think the problem in communication comes in the use of the phrase "physically real". Here is the question, is there something out there or do we have empty space? If there is something, we need to give it a name, say a particle or a field. That is what is physically real, that is what exists. That thing can be described mathematically by say a mathematical field, that obeys the equations. Of course the mathematical object doesn't exist, but the there is something that does, which is also called a field.

I don't understand why this whole busyness is so hard to understand. Even with my poor writing skills, it should be clear.

 

[Demystifier]

No, not at all. The particle is not the state. Take for example classical mechanics. The particle is described by six numbers. The particle is not a six-tple of numbers.

But whatever mathematical property follows from those six numbers, we say it is a property of the particle itself. For instance, if the particle equations of classical mechanics have a property of nonlocality, as e.g. in Newton theory in gravity, we say that particles themselves obey nonlocal laws.

So in that sense, do you agree that your view of particle in QM implies non-locality? If not, why not?

And you didn't answer my question. If the particle doesn't exist, do we have empty space?

In a sense, yes. We have the wave function, but not a physical object associated it. This is like "classical mechanics" in which we have the Hamiltonian $H(x,p)$, but not a particle with the trajectory $X(t)$.

 

[martinbn]

But whatever mathematical property follows from those six numbers, we say it is a property of the particle itself. For instance, if the particle equations of classical mechanics have a property of nonlocality, as e.g. in Newton theory in gravity, we say that particles themselves obey nonlocal laws.

So in that sense, do you agree that your view of particle in QM implies non-locality? If not, why not?

Wait, what has that to do with the discussion? Locality or non-locality is a separate question. The question is are the fields/particles real in space?

In a sense, yes. We have the wave function, but not a physical object associated it. This is like "classical mechanics" in which we have the Hamiltonian H(x,p)H(x,p), but not a particle with the trajectory X(t)X(t).

This seems very inconsistent. If we have empty space, then what is the difference between one particle and two? It's just empty space in both cases. In the example of classical mechanics what is the Hamiltonian of? How can you not have a particle?

 

[DarMM]

I think the problem in communication comes in the use of the phrase "physically real". Here is the question, is there something out there or do we have empty space? If there is something, we need to give it a name, say a particle or a field.

In Haag and other versions of Copenhagen what is taken to exist are events in macroscopic objects like detection devices. Fields are simply tools used to assists in computing correlations between these events.

What actually does exist they are silent on. Though Bohr, Omnés and Haag take a similar view that the fundamentally stochastic nature of QM and results like Bell's theorem (obviously not in the case of Bohr) indicate a limit in the applicability of human mathematics to nature and thus the fundamental stuff is incomprehensible.

So the reason one has no hidden variables is because the "stuff" doesn't admit a mathematical description.

That thing can be described mathematically by say a mathematical field, that obeys the equations

In this view the physically real things do not obey field equations.

 

[martinbn]

In Haag and other versions of Copenhagen what is taken to exist are events in macroscopic objects like detection devices. Fields are simply tools used to assists in computing correlations between these events.

What actually does exist they are silent on. Though Bohr, Omnés and Haag take a similar view that the fundamentally stochastic nature of QM and results like Bell's theorem (obviously not in the case of Bohr) indicate a limit in the applicability of human mathematics to nature and thus the fundamental stuff is incomprehensible.

So the reason one has no hidden variables is because the "stuff" doesn't admit a mathematical description.

Ok, now I understand, and it is perfectly fine. My problem is not with what actually exists, but with atyy's claim that it doesn't exist. I did say earlier that in my impression Copenhagen is silent on the issue. Demistifier said that some versions are not silent and say that the particle/field doesn't exist.

In this view the physically real things do not obey field equations.

Of course not. The baseball ball doesn't obey any equations. The functions that describe it obey the equations.

 

[Demystifier]

Wait, what has that to do with the discussion? Locality or non-locality is a separate question. The question is are the fields/particles real in space?

It's related, as seen e.g. in the EPR argument and the Bell theorem.

 

[bhobba]

I think the problem in communication comes in the use of the phrase "physically real". Here is the question, is there something out there or do we have empty space?

We do give it a name EM fields etc. I explained why classically most physicists consider them real - they carry, via Noether, momentum and energy which generally physicists think of as real. It's of course a deep philosophical question if they are, but if you are commonsenseical you tend to go down that path. As Weinberg said in his article about Kuhn (I must be frank I am no fan of Kuhn, Popper is better, but even he doesn't quite capture it as Feynman does) when he talks about reality, and wants to be careful, he says - whatever that is. Its just that physically most think of things like energy and momentum as real - again using whatever conception of real they hold to. After all mass is a form of energy, so fields can in principle be converted to mass, and if you do not think of mass as real, again under whatever you think real is, you are in very strange territory indeed (Penrose may be in that very territory) - I think physicists will generally not go that far. Now if classical EM are real and they are a limit of EM QFT fields, it's hard to think exactly at what point in taking that limit it becomes real, so generally speaking most would think them real. Remember though a QFT field is a field of quantum operators and we know they have a very real aspect - the eigenvalues are the possible outcomes of observations - and observations are very real. Some say QM is incomplete because we do not know exactly what is an observation - but that is getting off topic.

Thanks
Bill

 

[DarMM]

Ok, now I understand, and it is perfectly fine. My problem is not with what actually exists, but with atyy's claim that it doesn't exist. I did say earlier that in my impression Copenhagen is silent on the issue. Demistifier said that some versions are not silent and say that the particle/field doesn't exist.

Of course not. The baseball ball doesn't obey any equations. The functions that describe it obey the equations.

Well more so, if there are no objects describing them that obey field or particle equations you cannot really call them particles or fields. I mean those terms really only mean "a thing described by particle/field theories". So there is "stuff" but it's not particles or fields.

I'm not saying I agree with this, but I do think @atyy's description is right.

 

[martinbn]

Well more so, if there are no objects describing them that obey field or particle equations you cannot really call them particles or fields. I mean those terms really only mean "a thing described by particle/field theories". So there is "stuff" but it's not particles or fields.

That's just terminology, whether it is particles, fields or something else is secondary for this question. The point is that there is something.

I'm not saying I agree with this, but I do think @atyy's description is right.

Well, he claims that there isn't anything according to Copenhagen. He doesn't say that there is something, which isn't fields, and the fields aren't real, they are mathematical descriptions of something real. He says that if no one measures there is nothing.

 

[Demystifier]

If we have empty space, then what is the difference between one particle and two?

When we perform the measurement (which for no-reality interpretations is a misnomer, one should rather call it the experiment), we hear one or two clicks in the detector. That's the difference.

In the example of classical mechanics what is the Hamiltonian of? How can you not have a particle?

Mathematically it makes perfect sense to have a Hamiltonian as an object by its own. Physically, for a version of classical mechanics without particle trajectories see my https://link.springer.com/article/10.1007/s10702-006-1009-2

 

[Demystifier]

The point is that there is something.

The Bell theorem says that if there is something, then this something obeys nonlocal laws. And yet, if I remember correctly, in other threads you deny nonlocality. My point is that it is inconsistent to accept that both (i) there is something and (ii) this something obeys local laws.

 

[Demystifier]

But, there is no such interpretation. At least so far you havn't shown one. In all your citations there wasn't even a hint that particles/fields don't exist.

How about the following quotes of Mermin, taken from https://en.wikipedia.org/wiki/Relational_quantum_mechanics#History_and_development :
David Mermin has contributed to the relational approach in his "Ithaca interpretation."[8] He uses the slogan "correlations without correlata", meaning that "correlations have physical reality; that which they correlate does not", so "correlations are the only fundamental and objective properties of the world".

In the same paragraph on wikipedia:
The moniker "zero worlds"[9] has been popularized by Ron Garret[10] to contrast with the many worlds interpretation.

 

[DarMM]

The way I see Bell's theorem and the interpretive camps.

The assumptions of the theorem are:

1. Ontological Framework Axioms (Single World, No RetroCausality, No Superdeterminism)
2. Relativistic Causation, i.e. no physical effects that reach outside their relativistic light cone
3. Common cause. That is some event can be considered the cause of other events, i.e. C is a common cause of A,B if there correlations would be absent without C
4. Decorrelating Explanation. There is an event, conditioned on which the correlations between A,B vanish, hence it explains their correlation.

Non-Realist interpretations tend to drop number 4, that is they don't view the correlations in Bell's inequality as being explained by any event in spacetime. There can be causes (i.e. the device that prepares the Bell state), however that only allows the correlations to exist, it doesn't explain them.

Or more clearly, the preparation of the Bell state is necessary to find the correlations, but what actual achieves them is not a mechanistic (in the sense of admitting a mathematical description) process occurring in spacetime.

 

[atyy]

Well, he claims that there isn't anything according to Copenhagen. He doesn't say that there is something, which isn't fields, and the fields aren't real, they are mathematical descriptions of something real. He says that if no one measures there is nothing.

There is certainly nothing you are reading correctly.

 

[Lord Jestocost]

According to some versions of Copenhagen interpretation, the Moon does not exist when nobody looks at it. For instance, Wheeler said that “no phenomenon is a real phenomenon until it is an observed phenomenon.”

Regarding Wheeler’s statement, P. C. W. Davies and Julian R. Brown say in “The Ghost in the Atom: A Discussion of the Mysteries of Quantum Physics”:

“It means that, on its own an atom or electron or whatever cannot be said to 'exist' in the full, common-sense, notion of the word.” (italics in the original)

Or, as N. David Mermin (in “Making Better Sense of Quantum Mechanics”) has recently read some of Bohr’s quotations:

“Both quotations state that physics is not so much about phenomena, as it is about our experience of those phenomena.”

What you term “moon” is first and foremost a mental image, which is in your mind and not in the external world, at the end an encodement of a set of potentialities or possible outcomes of measurements. The Copenhagens merely warn people not to mistake this map for the territory.

 

[Demystifier]

The Copenhagen’s merely warn people not to mistake this map for the territory.

Actually, we have three things that should be distinguished:
1) The map (mathematical formalism of QM).
2) The territory (the physical objects existing irrespective of our observations).
3) Our vision of the territory (the measurement outcomes).
I view Copenhagen as a statement that we should talk seriously about 1) and 3), but not about 2). Realists, on the other hand, view 2) as the central object of research, while 1) and 3) are just the research tools.

 

[bhobba]

Well, he claims that there isn't anything according to Copenhagen.

I will not get into a discussion on what nothing means, form your own view of that, but clearly there is something under what most would think as 'something'. Consider a particle in a box and you measure its position. If there is no particle you will never - doesn't matter how many times you measure a position - you will never get an an answer. If there is a particle you will always get an answer. It modifies the usual idea of something somewhat - but most would say there is something there - we just do not know its properties until measured and can only predict probabilities. What's going on when not measured Copenhagen as far as I know from the various versions I have read says - we do not know - not there is nothing. Certainly the formalism doesn't say anything.

Thanks
Bill

 

[Lord Jestocost]

1) The map (mathematical formalism of QM).
2) The territory (the physical objects existing irrespective of our observations).
3) Our vision of the territory (the measurement outcomes).

I, personally, would beware of restricting the "Territory" to "physical objects".

 

[slufoot]

they are as real as anything.if it has an effect on any thing it is real

 

[martinbn]

I will not get into a discussion on what nothing means, form your own view of that, but clearly there is something under what most would think as 'something'. Consider a particle in a box and you measure its position. If there is no particle you will never - doesn't matter how many times you measure a position - you will never get an an answer. If there is a particle you will always get an answer. It modifies the usual idea of something somewhat - but most would say there is something there - we just do not know its properties until measured and can only predict probabilities. What's going on when not measured Copenhagen as far as I know from the various versions I have read says - we do not know - not there is nothing. Certainly the formalism doesn't say anything.

Thanks
Bill

That is my view and understanding.

 

[martinbn]

Mathematically it makes perfect sense to have a Hamiltonian as an object by its own. Physically, for a version of classical mechanics without particle trajectories see my https://link.springer.com/article/10.1007/s10702-006-1009-2

I might take a look, but I am already skeptical. You are switching between the notions. The point was whether you can have a version without particles (without objects no matter the name), now you are talking about a version without particle trajectories.

The Bell theorem says that if there is something, then this something obeys nonlocal laws. And yet, if I remember correctly, in other threads you deny nonlocality. My point is that it is inconsistent to accept that both (i) there is something and (ii) this something obeys local laws.

I have no problem with "nonlocality" except for the name. I also don't see how Bell's theorem says that if there is something it obeys nonlocal laws! It says that if those things that exist out there posses quantities that have values at all times then the laws are nonlocal.

How about the following quotes of Mermin, taken from https://en.wikipedia.org/wiki/Relational_quantum_mechanics#History_and_development :
David Mermin has contributed to the relational approach in his "Ithaca interpretation."[8] He uses the slogan "correlations without correlata", meaning that "correlations have physical reality; that which they correlate does not", so "correlations are the only fundamental and objective properties of the world".

That is more of the same. The fact that spins of two particles are correlated and the sipns don't have values before measurements doesn't imply that there are no particles.

 

[martinbn]

There is certainly nothing you are reading correctly.

There is your chance to clear things up.

 

[Demystifier]

I have no problem with "nonlocality" except for the name. I also don't see how Bell's theorem says that if there is something it obeys nonlocal laws! It says that if those things that exist out there posses quantities that have values at all times then the laws are nonlocal.

Then we agree more than I thought. Since you are fine with nonlocality, can you just remind me what exactly do you not like about the Bohmian interpretation? It's important for this thread because Bohmian interpretation is made precisely with the intention to say what is real in space.

 

[DarMM]

I have no problem with "nonlocality" except for the name. I also don't see how Bell's theorem says that if there is something it obeys nonlocal laws! It says that if those things that exist out there posses quantities that have values at all times then the laws are nonlocal.

Just for accuracy, that's not quite what it says. Possessing quantities at all times is the assumption technically called "Decorrelating explanation" in the assumptions of the theorem. One can retain it, but give up one of the other assumptions aside from locality.

 

[martinbn]

Then we agree more than I thought. Since you are fine with nonlocality, can you just remind me what exactly do you not like about the Bohmian interpretation? It's important for this thread because Bohmian interpretation is made precisely with the intention to say what is real in space.

I am fine with nonlicality in the sense in which QM is nonlocal. I am not fine with nonlocality when it means infinite speed of propagation. The main problem I have with BM is that it is very unclear (in fact quite confused) about the ontology of the wave function. Ah, and it is nonrelativistic.

 

[Demystifier]

I am fine with nonlicality in the sense in which QM is nonlocal. I am not fine with nonlocality when it means infinite speed of propagation.

In BM there is no infinite speed of propagation.

The main problem I have with BM is that it is very unclear (in fact quite confused) about the ontology of the wave function.

You can think of wave function $\psi(x,t)$ in BM as something analogous to the principal function $S(x,t)$ in the Hamilton-Jacobi formulation of classical mechanics. I think it reduces the confusion a lot.

Ah, and it is nonrelativistic.

That's a separate topic on which I was writing (on this forum and elsewhere) a lot.

 

[Lord Jestocost]

...but clearly there is something under what most would think as 'something'.

One should add, however, that this 'something' cannot be objectified, so it's of inscrutanable nature.

 

[stevendaryl]

The answer to the question in the title is clearly "No!" In general, a wavefunction is a function on configuration space, not physical space. When you have two particles, for instance, $\psi(x_1, x_2, t)$ is the probability amplitude of finding the first particle at location $x_1$ and the second particle at location $x_2$. In contrast, a physical field (such as the electric field) gives a value at each point in physical space.

[edit]This is a poor response to the original question, which was about fields, not wave functions.

What I would say about fields is that in QM they are operators, not values.

 

[bhobba]

One should add, however, that this 'something' cannot be objectified, so it's of inscrutanable nature.

Of course - it has exactly the same status as Weinberg pointed out but his critics forgot he carefully qualified - reality. Such fundamental things are notoriously hard to pin down. Its just most people would say if every-time you measured position you got an answer you would say something is in there - what is meant by something - blackout.

Thanks
Bill

 

[atyy]

The answer to the question in the title is clearly "No!" In general, a wavefunction is a function on configuration space, not physical space. When you have two particles, for instance, $\psi(x_1, x_2, t)$ is the probability amplitude of finding the first particle at location $x_1$ and the second particle at location $x_2$. In contrast, a physical field (such as the electric field) gives a value at each point in physical space.

The field has an operator-valued value at each point in physical space.

 

[bhobba]

The answer to the question in the title is clearly "No!" In general, a wavefunction is a function on configuration space, not physical space. When you have two particles, for instance, $\psi(x_1, x_2, t)$ is the probability amplitude of finding the first particle at location $x_1$ and the second particle at location $x_2$. In contrast, a physical field (such as the electric field) gives a value at each point in physical space.

That is true and got my like - but I think the OP was referring to the Quantum Fields of QFT which are quantum operators assigned to every point - not state AKA wave-functions. In QFT the state space is a fock space.

Thanks
Bill

 

[stevendaryl]

That is true and got my like - but I think the OP was referring to the Quantum Fields of QFT which are quantum operators assigned to every point - not state AKA wave-functions. In QFT the state space is a fock space.

Yes. It's sort of confusing in quantum field theory that the field operators seems like noncommuting versions of the wave functions of non-relativistic quantum mechanics. They really are not analogous. There more like the position and momentum operators of non-relativistic quantum mechanics.

 

[stevendaryl]

The field has an operator-valued value at each point in physical space.

You're right. The OP was not talking about the wave function.

 

[DarMM]

The wavefunctions in QFT are of the form (in the Heisenberg picture):
$$\Psi(\phi), \quad \phi \in \mathcal{S}^{'}\left(\mathbb{R}^{d-1}\right), \quad \Psi \in \mathcal{H} = \mathcal{L}^{2}\left(\mathcal{S}^{'}\left(\mathbb{R}^{d-1}\right),d\nu\right)$$
with $\mathcal{S}^{'}\left(\mathbb{R}^{d-1}\right)$ the space of tempered Schwarz distributions on a spacelike slice. Depending on the measure $d\nu$ the Hilbert space has a Fock decomposition. It doesn't for $d > 1$ for an interacting theory (without inifinite volume cutoff).