Particle States in Quantum Field Theory: Local vs. Global Approximations

[Fra]

My comment here is taken out of a context which is my personal vision towards a solution to several open problems in theoretical physics, here is an attempt.

I guess it would be very hard for you to explain me how one can measure the probability of an event which happens only once. I just don't get it.

To first contrast: the frequentist view means that you can only determine the probability of an event in retrospect by simply noticing the continuum or "large-n" limit of relative frequencies. Clearly to conclude what the relative frequency was in the past is of no survival value unless you can use this also to infer the relative frequency also in the future. Also we have the problem that the continuum probability seems to also be an idealisation, since it makes no sense to actually consider the continuum limit to be physical.

To clarify what the purpose of the probability concept is to me, my view contains a reconstruction of the probability concept and information theory from a discrete scenario of counting information

Probability of a given future event is the an observers measure of the degree of expectation of something. This measure has great utility when it comes to choosing an action to prepare yourself for the future. The observers future persistence and survival depends on it. Ideally the preferred action is the one that maximises the observers benefits.

This is a conjecture I make, that I use as a constructing principle that onw can call the "rational action conjecture". This conjecture does not mean that observers always behaves rationally - it rather means that a second observers best single bet, is that the observer acts rationally as per the construced measures of expectations.

So probability to me, is not really something you measure, it is an acquired expectation you have, that by the rational action conjecture determines your actions. So as I see it, the measures of expectations and the corresponding "probability spaces" and state spaces are coded in he observers past. And thus the probability is simply an expectation of the future. The expectation can be real and rational, even if the actual future later proves to be in contradiction to the prior expecations. Because this is the non-trivial case where we have non-trivial interactions, which revises the expectations.

To me, the case where past expecations where are in line with the actual futures is what I call equilibrium because nothing happens apart from confirmation of expectations.

This is why, in my view that observer is always active, there is no such thing as a passive observer just collecting information. The observers actions is effectively the perturbations that we call "measurement", so the CHOICE of the measurement is actually constrained. Some "choices" are simply "less likely".

The state space is my view, is then not timeless, it's spanned by a recoded truncated part of a subjective history. This acquired state eventually codes the expectations of the future (in a sense quite similar to thermodynamic arrow of time), but with the difference that evolution will favour clever datacompression, this should give rise to non-commutative state spaces, so the actual microtructure of the observer contains several sub.structures whose states are not commuting.

The ideas I have aims to find out if these relations follow from these principles, if they do there will be plenty of predictions.

But it's a completely new way of thinking of probability and information. I think it's best thought of as actual expectation of the future. In this sense, the probabilities are actually "subjectively physically real", but not objective. So in my view, the corresponding state vector, is actually subjectively real, in the sense that it's encoded in the microstates of the
observers internal structure. But this also is the key to allow for the state spaces to evolve.

Also in my view, the unitary evolution, is just an "expected evolution" that is valid in differential time - not globally. It follows from this thinking that each observer "sees" a spaces of possible differential changes, and on this space there is a measure defined. This becomes the action measure and by this one can calculate a correspondence to the feymann transition amplitudes. But this entire amplitude is really just an expectation.

The case where some of these expectations are in fact in perfect match with the actual future, is just a special case of we beeing close to equilibirum. Each observer "expects" a unitary evolution, and this is reflected in this observers action. This is the rational action conjecture. Howver, when such observers, that are not generally previously tuned, their expectations will be scattered, and they are forced to revise this expectations and action patterns. This is my view of what happens when systems interact in a way that they deform, destruct or severely change appearance.

/Fredrik

 

[Fra]

a bit more:

In the normal scheme, we have acquired initial information - a state; and we have a rule of deducting from this the future state (ie. hamiltonians and wave equations). This information about hamiltonian and the equations are no subject to any observability constraints, they are considered in a realist sense.

In what I picture, the information about the inference rules (includin hamiltoniain) is treated on the same footing as the initial state. And instead the inference of the future state follows from the rational action conjecture which is more to be seen as a induction rather than deduction. And instead of the falsification/corroboration abstraction, the feedback from the environment takes part in constantly evolving the current "state" and the statespace.

It's like a more advanced analogy of simple diffusion, the rational action conjecture is like a form of "diffusion" but taking place over non-commutative structures, which effectively means we get far more sophisticated dynamics an not just simple heat/information transfer.

I demand information about initial conditions, and information about the inference rules (laws of physics) to be treated on the same footing and both are subject of information bounds and measurement constraints. Ie. it makes as little sense to talk about what physical law is, unless it's inferred by a real process, than it makes sense to talk about where the electron "really is" in between measurements. All we have are expectations of where the electron is, and what the laws are.

/Fredrik

 

[Studiot]

As a general rule the world is not made of particles, it is more correct and less confusing to say that it is made of fields. Unless I'm mistaken all or most of us at the Forum realize this?

Aren't they complementary ideas?

You could say that a particle is in some sense the smallest volume/unit in which the field or action of interest can operate.

 

[tom.stoer]

If you look at the formalism of QFT you have the choice:
either the world is made of states in an Hilbert space created from certain field operators;
or the world is made of fields in a path integral;

The "old" duality according to the Kopenhagen interpretation of QM does not carry over one-to-one to QFT.

 

[Studiot]

Tom I think you have misunderstood my comment. It was not about duality.

 

[tom.stoer]

Really? In Germany we call it "Welle-Teilchen-Dualismus", so perhaps this causes the confusion

 

[Studiot]

My answer to what is a particle goes right back to Dalton (and perhaps even the ancient Greeks).

A 'particle' can be as large as a cup of coffee or a planet.
Or it can have zero dimensions.
It all depends what we are talking about.

From the point of view of chemical bonding, molecules (if you allow single atom molecules) are the 'particles' - smallest elements - that can participate.

From the point of view of fluid dynamics ( and indeed any continuum theory) we take a
'control volume' and in the limit shrink it to a point. These are the Fluid 'particles'.

From the point of view of Finite Element Analysis the 'particles' are the mesh spaces. These always have real defineable size.

From the point of view of the coffee trolley the 'particles' are the cups of coffee brought into the office...

What I am really saying is that the concept is about divisibility - What is the smallest element within which a subject or model of interest can operate such that if I divide it further my model is no longer valid. My subject can be material (mass, volume etc) or it can be non material (gravity) or even just a concept.

There are many unresolved questions in this area of enquiry.

What is the smallest element of charge for instance.

Hope this explains what I mean.

 

[tom.stoer]

Hope this explains what I mean.

Yes and no. It explains a lot on the conceptual level. A particle is the smallest entity which is involved in a certain process (at a certain scale). But it does not explain what the particle "is" in an ontological sense. And I think this is the question here in this thread.

But I guess that you are aware if this and that your answer is probably the best possible. Most discussions regarding particles are contaminated with classical ideas of particles and how to rescue these ideas on the quantum level. Unfortunately this is hopeless.

So perhaps an ontological answer is not possible and one must step back and take the positivistic view that a particle is some entity which appears as a particle ...

 

[Studiot]

But I guess that you are aware if this and that your answer is probably the best possible. Most discussions regarding particles are contaminated with classical ideas of particles and how to rescue these ideas on the quantum level. Unfortunately this is hopeless.

Yes I would agree with all this.
So perhaps what I am saying is that to be of use in the modern world the idea of a particle must move on, like everything else.

So perhaps an ontological answer is not possible and one must step back and take the positivistic view that a particle is some entity which appears as a particle ...

If it looks, like a bear, smells like a bear and bites like a bear...

 

[Physics Monkey]

I think that the notion of a particle is one of those concepts that's just too useful to give only definition. One needs to be flexible. It can be a little classical ball bouncing around or a quantum particle that sniffs out its surroundings or a little packet of energy or a representation of the asymptotic poincare group or the quanta of a field or any number of other variations on the theme. Even virtual particles can have a place. Each point of view has its own intuitive advantages and each points to different forms of generalization.

For example, the field point of view is quite useful. Unlike the concept of representation of the poincare group, the concept of a quantum field is easily generalized to situations without poincare symmetry or even without crisp particle-like excitations at all. In my opinion, it pays to understand as many of the points of view as one can, within reason.

It's like a tapestry (or manifold!) where you patch together a global understanding of the concept of a particle from lots of little pieces that each capture some of the intuition and meaning.

 

[czes]

How to explain Vacuum Polarization
http://en.wikipedia.org/wiki/Vacuum_polarization
and spontaneous gamma rays emission
http://en.wikipedia.org/wiki/Spontaneous_emission
if the virtual particles were not real ?

 

[Demystifier]

How to explain Vacuum Polarization
http://en.wikipedia.org/wiki/Vacuum_polarization
and spontaneous gamma rays emission
http://en.wikipedia.org/wiki/Spontaneous_emission
if the virtual particles were not real ?

By calculating these effects non-perturbatively, without referring to Feynman diagrams.

This is analogous to the following. If you have 1 apple, you can mathematically represent it as
1=(-1)+2
However, neither -1 apple is real nor 2 apples are real. They are virtual apples. Only the total result, i.e. 1 apple, is real.

 

[Naty1]

Thanks czes...

That vacuum polarization article in Wikipedia is quite interesting...don't believe I have seen such a description previously:

This part I knew:

According to quantum field theory, the ground state of a theory with interacting particles is not simply empty space. Rather, it contains short-lived "virtual" particle-antiparticle pairs which are created out of the vacuum and then annihilate each other

So the vacuum state HAS some energy...ok, we knew that.

In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron-positron pairs that change the distribution of charges and currents that generated the original electromagnetic field.

Are they talking here of an externally (artifically) induced electromagnetic field...or one that occurs naturally as part of the vacuum? I assume the former...and I think helps answer my former question regarding this:

...virtual particles are also excitations of the underlying fields...detectable only as forces but not particles.

And

Vacuum polarization was observed experimentally in 1997 using the TRISTAN particle accelerator in Japan.[1]

is pretty cool...is this generally accepted as "observational proof" of virtual particles? A more direct "proof" than the Casimir effect, for example??

 

[atyy]

It's like a tapestry (or manifold!) where you patch together a global understanding of the concept of a particle from lots of little pieces that each capture some of the intuition and meaning.

Any black hole like things in the manifold? Those are particles aren't they? A particle of particle.

 

[tom.stoer]

According to quantum field theory, the ground state of a theory with interacting particles is not simply empty space. Rather, it contains short-lived "virtual" particle-antiparticle pairs which are created out of the vacuum and then annihilate each other

Wikipedia is talking about perturbative effects in (almost) trivial vacua. That's nice, but unfortunately useless in many cases:
- el.-weak symmetry breaking via the Higgs
- quark-condensates an chiral symmetry breaking
- confinement and chromo-electric Meissner effekt in QCD
- QCD theta vacua
- instantons / instanton liquid
are all non-perturbative vacuum effects which completely escape any perturbative treatment based on virtual particles.

 

[qsa]

I think that the notion of a particle is one of those concepts that's just too useful to give only definition. One needs to be flexible. It can be a little classical ball bouncing around or a quantum particle that sniffs out its surroundings or a little packet of energy or a representation of the asymptotic poincare group or the quanta of a field or any number of other variations on the theme. Even virtual particles can have a place. Each point of view has its own intuitive advantages and each points to different forms of generalization.

For example, the field point of view is quite useful. Unlike the concept of representation of the poincare group, the concept of a quantum field is easily generalized to situations without poincare symmetry or even without crisp particle-like excitations at all. In my opinion, it pays to understand as many of the points of view as one can, within reason.

It's like a tapestry (or manifold!) where you patch together a global understanding of the concept of a particle from lots of little pieces that each capture some of the intuition and meaning.

Obviously present day theories model “particles” that way. But the question was is that really satisfactory. It is bad enough to swallow the particle-wave duality, but the interaction picture and all of its associated concepts make one really wonder, even the working scientists themselves don’t feel easy about it.

What is needed is a theory that describes entities just like QM i.e. probabilities in space, and when interaction happens entities mesh and form new probabilities in space. And when they separate the separated probabilities look like the usual entities. How can that happen? I think we must explain how the typical entities form a stable structure. This is a very old question, started with Lorentz, and people are still working on it. It is called the ”electromagnetic mass”. Moreover, the particle sniffing the entire universe is real, that is how you should get the gravity. That is already been postulated by the holographic principle.


Both above concepts must be unified in one coherent theory. I know it is possible(very). Reality is very weird, but not QFT weird.

 

[Demystifier]

..is this generally accepted as "observational proof" of virtual particles?

Of course it isn't.