Teuton wrote:

Teuton wrote:
What is the essential physical difference between "classical" fields and quantum fields?

"In very loose terms, the operator valuedness of quantum fields means that to each space-time point (x,t) a field value φ(x,t) is assigned which is an operator. This is the fundamental difference to classical fields because an operator valued quantum field φ(x,t) does not by itself correspond to definite values of a physical quantity like the strength of the electromagnetic field. On this background, Teller has argued in Teller 1995 that the field interpretation of QFT is inappropriate since the alleged fields in QFT are not to be interpreted as physical fields with definite values of some sort which are assigned to space-time points, like in the case of the classical electromagnetic field. Rather, quantum fields are what Teller calls ‘determinables’ (p. 95), as it becomes manifest by the fact that quantum fields are described by mappings from space-time points to operators. Operators are mathematical entities which are defined by how they act on something. They do not represent definite values of quantities but they specify what can be measured, therefore Teller's expression ‘determinables’. (Below it will be discussed why this talk in terms of a field at a point has to be refined using the notion of a smeared field φ(f).)"

(http://plato.stanford.edu/entries/quantum-field-theory/)

"[Operators] do not represent definite values of quantities but they specify what can be measured[.]"

Does this mean that operators represent the range of all possible determinate properties of a determinable quantity that can be possessed by a spacetime point? But how could an actual physical field be a collection of merely possible properties? Is it possible at all for there to be indeterminate physical properties in physical reality? For example, is it possible to have a mass without having a determinate mass?

I don't really speak philosopher language, but maybe the missing ingredient is the state. The field operator φ(x) at the point x can, if you're a philosopher, be thought as a determinable. The specific values of the determinable could be the allowed values <s|φ(x)|s> for each state s, or possibly the set of all expectation values you could construct from the field operator.

twistor59 wrote:

Teuton wrote:
What is the essential physical difference between "classical" fields and quantum fields?

A classical field assigns a value of some measurable quantity to each point in spacetime.
A quantum field assigns an operator to each point in spacetime (this is the heuristic version - the more mathematically rigorous version involves operator valued distributions as I alluded to earlier). This operator acts on "states" which live in an abstract (Hilbert) space and does stuff like changing the number of quanta.

Operators are mathematical entities which aren't part of physical reality. So the question is what is that which is part of physical reality and corresponds to or is represented by them.

No. In physics, an operator is more than a mathematical entity. For example, energy, momentum and spin are all operators, and are real quantities.

Teuton wrote:"On this background, Teller has argued in Teller 1995 that the field interpretation of QFT is inappropriate since the alleged fields in QFT are not to be interpreted as physical fields with definite values of some sort which are assigned to space-time points, like in the case of the classical electromagnetic field."

Nice, so Teller is an example of a quantum field non-realist, a point of view not being represented on this thread

Teuton wrote:Does this mean that operators represent the range of all possible determinate properties of a determinable quantity that can be possessed by a spacetime point? But how could an actual physical field be a collection of merely possible properties? Is it possible at all for there to be indeterminate physical properties in physical reality? For example, is it possible to have a mass without having a determinate mass?

Is your gripe here with non-determinism? Do you find it unacceptable that a physical quantity might not be thought of as a definite value, but instead as a range of possible values, each with a different probability?

Teuton wrote:

twistor59 wrote:

Teuton wrote:
What is the essential physical difference between "classical" fields and quantum fields?

A classical field assigns a value of some measurable quantity to each point in spacetime.
A quantum field assigns an operator to each point in spacetime (this is the heuristic version - the more mathematically rigorous version involves operator valued distributions as I alluded to earlier). This operator acts on "states" which live in an abstract (Hilbert) space and does stuff like changing the number of quanta.

Operators are mathematical entities which aren't part of physical reality. So the question is what is that which is part of physical reality and corresponds to or is represented by them.

The operators are the basic ingredients which are used to construct observables. An observable is a physical quantity whose value can be measured. The measured value obtained in a given instance depends, probabilistically, on the system state.

twistor59 wrote:
I don't really speak philosopher language, but maybe the missing ingredient is the state. The field operator φ(x) at the point x can, if you're a philosopher, be thought as a determinable. The specific values of the determinable could be the allowed values <s|φ(x)|s> for each state s, or possibly the set of all expectation values you could construct from the field operator.

In my understanding, the presence of a determinable physical property (quantity) at a spacetime point or region necessitates the presence of a determinate physical property (quantity) belonging to the determinable one in question. Or does there occur a random oscillation between various determinate properties had by a spacetime point or region such that there is a constant and quick change of determinate properties belonging to some determinable quantity?

In regards to observables, Operators are used QM in the same sense that functions of the state are used in classical mechanics.
For example, in a classical mechanical model, there would be a function E(s) which represents the energy of a system, and 's' is the state of the system.
If you wish to think that operators exist and are not merely abstract objects, fine, you can do so consistently, but then you should also consider thinking of mathematical functions as real in the same sense too.

hackenslash wrote:No. In physics, an operator is more than a mathematical entity.

Nothing can be both a mathematical and a physical entity.

hackenslash wrote:
For example, energy, momentum and spin are all operators, and are real quantities.

"Physical Quantities:
Hermitian operators in the Hilbert space associated with a system represent physical quantities, and their eigenvalues represent the possible results of measurements of those quantities."

(http://plato.stanford.edu/entries/qm/)

This means that operators aren't physical quantities (properties) themselves but mathematical representations thereof.

mizvekov wrote:Do you find it unacceptable that a physical quantity might not be thought of as a definite value, but instead as a range of possible values, each with a different probability?

For every determinable physical property/quantity there is a range of possible determinate properties/quantities belonging to that determinable one; and there is certainly nothing "unacceptable" about assigning different probabilities to the various possible determinate ones. But physical reality cannot be reduced to mere possibilities or probabilities. The real properties of spacetime points or regions must be actual determinate properties. There may be a quick random oscillation between them such no spacetime point or region has the same determinate property for longer than some fraction of a second; but for every determinate time t there must be some determinate property had by the spacetime point or region in question. (I don't know what it means to say that there is an indeterminate property present at t. I don't know what an indeterminate or "vague" property is supposed to be.)

mizvekov wrote:In regards to observables, Operators are used QM in the same sense that functions of the state are used in classical mechanics.

"An operator O is a mapping of a vector space onto itself."

(http://plato.stanford.edu/entries/qm/#Ope)

Mappings are functions, so you're right.

mizvekov wrote:
If you wish to think that operators exist and are not merely abstract objects, fine, you can do so consistently, but then you should also consider thinking of mathematical functions as real in the same sense too.

I'm an antirealist (fictionalist) about mathematical abstracta.
(A physicist who is also a physicalist cannot consistently be a mathematical realist.)

@Teuton
The post talking about operstors and whether they are real was directed to hackenslash
I am typing on a smartphone now, later when I am home I will respond to the other post.

Double post

mizvekov wrote:Nice, so Teller is an example of a quantum field non-realist, a point of view not being represented on this thread.

"Teller argues that ‘quantum fields’ lack an essential feature of classical field theories so that the expression ‘quantum field’ is only justified on a “perverse reading” of the notion of a field. His reason for this conclusion is that in the case of quantum fields—in contrast to classical fields—there are no definite physical values whatsoever assigned to space-time points. Instead, the assigned quantum field operators represent the whole spectrum of possible values so that they rather have the status of observables (Teller: “determinables”) or general solutions. Something physical emerges only when the state of the system or when initial and boundary conditions are supplied. Teller's criticism of the standard gloss about operator-valued quantum fields has one justified and one unjustified aspect. The justified aspect is that quantum fields actually differ considerably from classical fields since the field values which are attached to space-time points have no direct physical significance in the case of a quantum field. However, it was not to be expected anyway that one would only encounter definite values for physical quantities in QFT since it is, like QM, an inherently probabilistic theory after all and is equally confronted with the measurement problem."

(http://plato.stanford.edu/entries/quantum-field-theory/)

cavarka9 wrote:I was considering that a particle is a structure…

A physical structure is a group or set of relations between particles. The particles are the relata, i.e. the physical objects standing in relations to one another, and not the relations.

Teuton wrote:

hackenslash wrote:No. In physics, an operator is more than a mathematical entity.

Nothing can be both a mathematical and a physical entity.

hackenslash wrote:
For example, energy, momentum and spin are all operators, and are real quantities.

"Physical Quantities:
Hermitian operators in the Hilbert space associated with a system represent physical quantities, and their eigenvalues represent the possible results of measurements of those quantities."

(http://plato.stanford.edu/entries/qm/)

This means that operators aren't physical quantities (properties) themselves but mathematical representations thereof.

Still getting all your definitions from the dictionary of what colour is my lint.

http://hyperphysics.phy-astr.gsu.edu/hb ... moper.html

http://en.wikipedia.org/wiki/Operator_% ... _Operators

Teuton wrote:

mizvekov wrote:Do you find it unacceptable that a physical quantity might not be thought of as a definite value, but instead as a range of possible values, each with a different probability?

For every determinable physical property/quantity there is a range of possible determinate properties/quantities belonging to that determinable one; and there is certainly nothing "unacceptable" about assigning different probabilities to the various possible determinate ones. But physical reality cannot be reduced to mere possibilities or probabilities. The real properties of spacetime points or regions must be actual determinate properties.

Emphasis mine. But that is the very heart and soul of quantum theory. A system might or might not possess a definite value of such a quantity until a measurement is made. In the cases were it does not possess a definite value, quantum theory is not making definite predictions about individual systems, but rather about ensembles of systems.

Teuton wrote:
There may be a quick random oscillation between them such no spacetime point or region has the same determinate property for longer than some fraction of a second; but for every determinate time t there must be some determinate property had by the spacetime point or region in question.

It depends on the point of view you take - maybe the spacetime point itself is an abstraction ....

Teuton wrote:

cavarka9 wrote:I was considering that a particle is a structure…

A physical structure is a group or set of relations between particles. The particles are the relata, i.e. the physical objects standing in relations to one another, and not the relations.

That depends on how small can one consider a particle to be and how its intrinsic properties are. Perhaps particles can only come in groups, that too could be the case. Hence I used the word structure. Which could in other cases be used to consider say strings or other mathematical objects, they too are structures.

hackenslash wrote:Still getting all your definitions from the dictionary of what colour is my lint.

What exactly is wrong with the definition of operator as pointed out in the link Teuton posted?

hackenslash wrote:http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qmoper.html
http://en.wikipedia.org/wiki/Operator_% ... _Operators

Do you think these definitions support the notion that operators are not mathematical abstract objects?

Teuton wrote:For every determinable physical property/quantity there is a range of possible determinate properties/quantities belonging to that determinable one; and there is certainly nothing "unacceptable" about assigning different probabilities to the various possible determinate ones. But physical reality cannot be reduced to mere possibilities or probabilities. The real properties of spacetime points or regions must be actual determinate properties. There may be a quick random oscillation between them such no spacetime point or region has the same determinate property for longer than some fraction of a second; but for every determinate time t there must be some determinate property had by the spacetime point or region in question. (I don't know what it means to say that there is an indeterminate property present at t. I don't know what an indeterminate or "vague" property is supposed to be.)

QM/QFT are theories about probabilities from the ground up. The most common way to interpret it is that these probabilities are what describe best the system even in principle, and that it is not just the case that those theories present an incomplete description. They leave almost no space left for determinism.
But even then, you can say that in QFT probability distributions are what is "exactly determined", and that gets me to my second point that the difference between stochastic and deterministic is often overplayed.

I agree that properties must be determinate, and you can still maintain this position but with one small change: Instead of these properties being best represented by the abstract objects that are the real numbers, they are best represented by the abstract objects that are probability distributions (PD).
And really, I don't think there is anything fantastic or mind blowing about that. Deterministic variables (ie numbers) are a special case of random variables (which are represented by PDs). You can have a PD which assigns probability 1 to just one value, and zero to all others. This can be done even for continuous PDs (see the dirac delta function, or the impulse function).

twistor59 wrote:

zaybu wrote:

cavarka9 wrote:dont mind me but yes,what is a particle?.

hackenslash wrote:Probably a behavioural manifestation of the electromagnetic field...

What is a field?

It's an operator-valued distribution.

I'm not asking how it is represented mathematically, but what is its physical nature.

zaybu wrote:

twistor59 wrote:

zaybu wrote:



What is a field?

It's an operator-valued distribution.

I'm not asking how it is represented mathematically, but what is its physical nature.

I'm not sure if we can say that it has a "physical nature", at least not in general, and not directly, it's a component in a model. Using this component you can construct observables, with which you can make (probabilistic) predictions about measurable quantities.