Ontological status of fields in QFT

tenzin

I am interested in the input from the physics community on quantum field theory. If each particle has an associated field of which they are manisfestations what causes a particle to arrise from a field?

pallidin

Good question.

jeff

This isn't the physics community.

tenzin

I guess you are this site's official spokesperson?

pallidin

Jeeze... come on guys. This is a serious question. I, for one, would like to know the answer. Can we dispense with the personal battles?

tenzin

I agree. too bad that when quentsions come that require some thought come up no one wants to comment. I guess unless you can show how much you know there is no need to comment. That is not surprising considering its the internet.

Pallidin, you have any input on my initial question.

pallidin

tenzin, I wish I did have some constructive input to what I believe is an excellent question from you.
But I do have an observation. If memory serves correct(and if it is even true) I heard somewhere that an intense electrical potential differance permeating a well-constructed vacuum aparatus produces short-lived virtual particles.
If this is true, then I believe a good place to start with understanding or developing a more advanced theory might be in this experimental arena.

General thoughts:
Obviously, SOMETHING specific must occur in a given field in order for the particle to arise. Very interesting.
Thinking of fields in terms of a piece of string, I wonder if enough agitation in a specific way might cause the string to "knot", yet not requiring the string ends to actually loop themselves, rather a disturbance in the "middle" sufficient to cause a "knot"
If the force used to produce this effect is not high enough or if not correctly implemented, perhaps the "knot" stays a part of the string and can be "pulled apart", hence a virtual knot
If the force is great enough, or perhaps if other unknown specific conditions exist, perhaps the field tension pulls the string such to were the string breaks, leaving the knot intact, hence a stable particle.
Probably way off-base, but just some thoughts...

Pallidin

tenzin

I know the way physicists look at a field is like a 2-D system of spring-masses. Each mass is connetect by a spring to another mass and each mass has for springs connecting it to four masses. The springs for a given mass are at right angles to each other. They then define a Lagrangian for this spring-mass sytem which determines the state of minimum energy for the system. They then extend this problem to one of a system of infinite masses. This is the Lagrandian density for the field. If you extend this example to 3-D you get a field with is defined everywhere.

So from the anaology the spring-mass sytem certainly has energy. Somehow particles arrise from this field perhaps by converting some of the field enery into mass which are related by E=mc^2 or something similar.

Your point on staring by looking at virtual particles soulds like a good start. My only question on the virtual particles is that do they violate conservation of energy? According the the uncertainly principle delta(E)*delta(t) >= h or something like that. 'delta' means uncertainty in the measurement of that quantity. To for set amout of time the energy can be 'uncertain' therefore they would claim there is no violation of conservation of energy. My whole question is why is there this uncertainty? Is it a property of nature itself or simply our inability at this time to make precise measurements. I think it is due to our inability. There is no reason to establish that the energy can be exactly known. It is exists they it should be knowable.

vanesch

First of all I don't know why this question triggered so much aggressivity! It is a good, basic question, and there's a good answer to it. In fact, the answer comes in two pieces.

The first part of the answer is: quantum fields. If you quantize a free field (meaning: changing the function: E^3-> R^n which is a classical field into E^3 -> operators over hilbert space), it turns out that energy eigenstates of the theory correspond to a set of natural numbers n1, n2, ... n_k..., which, energywise, correspond to the summed energy particles of mass m would have if there were n_k particles with momentum k. If you now calculate the momentum corresponding to that same energy eigenstate, you find that it corresponds to the summed momenta n_k times k, and the relationship between energy and momentum is given by the correct relativistic relationship E^2 = m^2 + p^2 (I put c=1 here).
So this strongly suggests that the field is made up of n1 particles of momentum k1, ... and n_k particles of momentum k !
And there is a quantum field solution for exactly each combination (at least for bosonic fields).

The second part of the answer, because we usually think of particles as localized lumps and not only as a strict energy-momentum relationship, comes from decoherence. It turns out that inevitable interactions of fields with the environment makes that any spread-out wave packet soon seems to collapse into a lumped wave packet. If you want to learn more about that you'd have to read up about decoherence in quantum mechanics.

So in all, quantum fields give rise to energy-momentum relationships which come in "packets of one particles" and intereactions with the environment make that they appear in most cases as lumped in space as well. So we really get the "particle impression" !

cheers,
Patrick.

Swamp Thing

In a sense, the field is by definition a measure of the particle's tendency to manifest itself. The probability of getting the particle is related to the field intensity.

jeff

If you want the state of the art this is the book

http://www.amazon.com/exec/obidos/tg...glance&s=books

I'll warn you that based on you're comments on renormalization in another thread, your kung fu isn't good enough to understand this book.

tenzin

I have this book. What I am tired of getting is people telling me to read books. That is because you have no ability to think yourself. I have many books I could recomend to you that would allow you to really begin to think but I don't. I rely on my own ability to reason. I don't care what some guy wrote in a book. He could be completely wrong. The problem is that you people and the physics world in general have no understanding of reason and what criteria are needed to establish something as existing.

lethe

so why do you say things like:

tenzin

this was before I got tired of writing to people who don't think.

lethe

wow! you ve been at this forum for all of 2 weeks, made 50 posts, in 4 or 5 different threads, probably even got 2 or 3 book recommendations, and already you are tired of all the people who don t think.

it takes most people at least a month to get tired of them.... but i guess that is because you are so much smarter than the rest of them.

and a paragon of patience. i can see how you would make a good teacher.

tenzin

but i guess that is because you are so much smarter than the rest of them.

Pretty much. If you keep up the effort you can be as smart as me someday too. Well maybe not you but most of you out there.

jeff

Yep

Most scientists feel that science can't prove the efficacy of such criteria or confirm proposed ontologies and as a result don't worry much about it (unless they're theorists who are really really stuck for good ideas).

The concept of field is more fundamental than that of particle in that the latter is an approximation valid only in situations where spacetime curvature may be neglected, as is the case in conventional QFT in flat spacetime. The reason is that the properties of mass and spin classifying particles depend for their definition on global poincare invariance which holds only in minkowski space. From this point of view, particles can be thought of loosely as local excitations of fields since classical curved spacetimes are always locally flat. In fact, the relation between the particle concept and spacetime geometry means that particles are actually an observer-dependent concept: Observers undergoing acceleration in minkowski space will detect particles not seen by inertial observers.

Speaking in terms of particles, a related question is what allows the interconversion of matter and radiation such as the creation and annihilation of virtual electron-positron pairs in the electromagnetic vacuum. The answer is, as you mentioned, mass-energy equivalence. Such virtual processes must by the uncertainty principle go on all the time so that unlike the classical vacuum, the dynamics of the quantum vacuum is nontrivial.

The uncertainty principle can be viewed as prohibiting experimental confirmation - and thus meaningful discussion - of violation of

On the subject of energy conservation, another phenomenon worth saying something about is the transformation of virtual particles into real ones by the action of external fields. The invariant mass m and 4-momenta p^μ = (E, p) of virtual particles by definition don't satisfy the standard relativistic mass shell condition p^μp_μ = m² that holds for real particles. However, if an external field contributes enough energy ΔE to a virtual particle of mass m, we get p²_virtual → p²_virtual +(ΔE)² = p²_real = m² converting it into a real particle.

What did you think of it?