What is quantum field theory?

Mike2

The propagation of something, photon or particle, can have many possible paths, thus the Feynman path integral formulation of quantum mechanics. The initial position is relatively fixed and the final position is relatively fixed (compared to all of space). But it's path from beginning to end can be anything. So I wonder how far this concept goes. Does it apply to the first appearing of a particle (or particle creation)? Can the location itself of a particle's initial position when first formed also have many possible locations as well? Would this be quantum field theory? In otherwords, its intial state would be non-existence, its final state would be existence, and every possible path would be replaced with every possible location?

thanks.

AntiMagicMan

Hi, a quantum field theory is like a classical field theory only the field is quantised into discrete chunks. The electromagnetic field for instance is quantised into photons.

Mike2

I'm trying to develop an intuitive understanding of QM, and why it might be necessary from more fundamental principles (if possible).

Yes, I know that QFT is derived by making observables into operators and all that. But that seems to only be a trick to make the data fit the curve. But it does not explain the nature of reality such that quantization should be necessary in the first place.

So let me take a stab at it and see how far I get. Feynman's path integral formulation of quantum mechanics is valid where we must consider the possibility of every possible path from A to B, and the path integral considers the interference of every possible path from A to B which results in the most likely overall path from A to B. In ordinary QM, A and B are given (if I remember right). So when in second quantization, I suppose that even the initial and final states of A and B are the result of considering every possibility. Does this seem right?

Also, just considering the words, "every possible path", seems to indicate some mathematical formulation that is valid for every possible path. This sounds a lot like a formulation that is invariant (symmetrical) with respect to all possible paths. So is QM a way of handling broken symmetry, where some formulation is symmetrical wrt every possible path, so that we are forced to consider every possible path, and the path integral gives us the most likely path, or in other words... how the symmetry is broken?

Thanks.

Haelfix

We usually think of symmetry at the level of the Hamiltonian or Lagrangian, not necessarily the amplitude.

Still it is of course there. For instance, you want your physical laws to be invariant under the poincare group, that is rotations, translational invariance, and boosts.

Understand this, in most cases the number of different paths is infinite. In a sense our field is an infinite dimensional quantity, and is decidedly nonlocal.

We also are dealing with something that needs to be covariant, different observers must agree on the results of any measurement done, once a frame has been picked. So it should be apparent that this amplitude we are looking at is something very abstracted from physical intuition.

I don't like assigning to much meaning to the amplitude, or even the probability space. Its an aesthetic choice, but I prefer looking at real measurable observables (like laboratory frame cross sections) and giving that meaning.

A. Zee gives a nice little picture of what a quantum field is, in his book. The Mattress picture, where particles are identified as excitations of the springs. He belabors the point, that it is a harmonic paradigm, and could in principle be generalized.

AntiMagicMan

Hmm, if you don't understand why certain variables are quantised then you need to go back and relearn basic quantum mechanics before you can start doing Quantum Field Theory.

Remember the experimental evidence, photoelectric effect, blackbody radiation, all those experiments illustrate why certain quantities must be quantised.

Mike2

Your idea, here, seems to choose a preference as to what is meaningful. You seem to have chosen a classical interpretation of physics, and then are simply tweeking it with QM. But how do we know whether QM is a more fundamental picture of reality and our classical view is just an average taken from that. The question remains, what is the true nature of reality such that QM should be necessary?

I'm playing with the idea that the only thing we do know for an absolute certainty is that the universe exists. Anything beyond that must have probabilities associated with alternatives. We are working backwards to reverse engineer the universe from observables to principles. So first quantization uses Feynman's path integrals to produce a path from known position to known position. Second quantization produces particle position from fields of known initial to final states. So I suppose third quantization would produce fields from various possible configurations of spacetime.

But perhaps this gives us a clue as to the nature of reality. If all that is knowable for certain is that the universe exists and all else must consider probabilities of alternatives, then perhaps the nature of spacetime itself is derived from every possible alternative. Perhaps the overall size and acceleration of the universe is derived from every possible time of creation and acceleration speed.

Mike2

All this does is produce an equation (curve) to fits the data. All it is is curve fitting. But this only begs the question as to why things are as they are. And curve fitting is not capable of answering that question. You cannot "explain" observables if the basis of your argument is observables. That argument would be committing the logical error of petitio principii, a.k.a. begging the question. If we are ever going to find the true nature of reality and understand the limits of what is possible, then we are going to have to be able to derive physics from principle alone.

AntiMagicMan

That is pseudo-science, or at most philosophical gibberish.

Scientists do not explain things from first principles, they observe the world and describe those observations using mathematical laws.

Mike2

Yes, and this is called "curve fitting", wouldn't you agree? Some who have studied in great detail these curve fitting equations have deceived themselves into thinking that they understand reality when in fact they cannot explain anything. Their answer at best is, "Well, this is a generalization based on what we have seen so far". But that is not the same thing as understanding it. It is only a generalization. Yet, one of the criteria for a correct theory is that it at least be consistent, a purely logical consideration imposed on our curve fitting efforts. So in effect, we have already imposed our preference that reality comply with what is logical. I'm not suggesting anything more. What I am suggesting is that we may not be too far from being able to simply start with that logic and build a theory of reality that, oh by the way, does match observations.

But to suggest that it is impossible to derive physics from logic is to say that reality is fundamentally not understandable. It is in other words to suggest that the universe is a logical absurdity. But if the universe is not a logical absurdity, then prove that it is not. And the only way to prove that the universe is not a logical absurdity is to derive physic from logic alone. Simply deriving a theory for the existence of something on the basis of smaller somethings is just begging the question as to where the smaller somethings came from.

AntiMagicMan

Ok then, we curve fit. But we get physical laws that make sense. If you are not happy with it philosophically then er I don't really care.

ZapperZ

Do you have a single example of our present-day understanding that was "derived" from logic? QM and SR/GR were each built on their own sets of postulates which were not "derived". Classical E&M are nothing more than phenomenology (or what you called "curve fitting") - No one derived Coulomb's law. Classical mechanics? Translational symmetry of space, isotropic space, and time symmetry are all never "derived". The Standard Model in itself is phenomenology - no one derived that either.

It appears that all of our physics ARE essentially built on accepted postulates and phenomenology and not "derived". However, I disagree with your assertions that these are merely "curve fitting".

Zz.

Mike2

We are only now starting to consider the possibility of deriving physics from logic. The whole universe does not pop into existence instantaneously, since that would be equivalent to not having a basis (or argument or proof or logical derivation) at all for its existence. So the universe proceeded from a singularity. It must have been a growing manifold of some sort since the conjunction of protions of it are also included in it, and it can be described with coordinates, etc. Any object within this initial manifold must be submanifolds of it. Or they would not exist within the initial universe and would not be part of it. Symmetry requires that the universe must have grown without submanifold/objects before these objects appeared. For at the smallest differential level all points must approach the same value so that no distinction can exist to call an object. The only questions left are how large did the universe grow before objects/matter appeared as submanifolds in the universe? What topological considerations are there about spacetime that would hinder the initial expansion from being an infinite rate? And what conservation rules would apply? I suspect all these questions have logical answers as well.

ZapperZ

So in other words, you can't. You speculate that it can, but our history of science has shown that all that we have today have never been "derived". That was my question and that was all I require as an answer.

Zz.

Mike2

You are missing the larger picture. In fact we would not even be bothering today to achieve understanding of the universe (aka science) if we did not think is was logical. The very premise of science is that reality is logically understandable (as opposed to understanding it mythologically). Will you now deny the very premise of science and say that that reality is not logical. Of course it is logical. And all our studies and theories are steps in a direction to understand how that logic is expressed. Physics will not end until we can derive physics from logic alone. For the only alternative is just begging the question with incompleteness. But questions stop when it is realized that the answers stem from the principles of reason itself. For you cannot ask a legitimate question if you deny that there is a logical answer. But you can always question contingent matters.

I for one will not deny the premise of science, so I will assert that the universe is totally logical, which precisely means that physics can be derived from logic.

Stevo

Logic is a model of human reasoning, not of the universe.

How can the universe be logical?

Mike2

Logic is as valid to theories of the universe as existence and non-existence is. For it is either true or false that the universe exists or does not exist. Every theory about anything is subject to logic in that every theory is either a true representation or it is not, either it is valid or it is not. Logic governs which theories are correct.

ZapperZ

And you missed the point of my question. I asked for one, JUST ONE, example of what we know of today that was "derived" from pure logic. You were unable to give me any... at least, that's what I gather from hunting through your two previous responses to my postings.

There is a difference between DERIVING our observations via ab initio/First Principles calculations, and logically deriving results/observations/consequences based on postulates. You will notice that practically ALL of physics today is based on the latter. You are confusing the latter with the former. SR's postulates were never "derived". However, all consequences based on those postulates ARE logically derived! There is a difference!

Notice that in none of my previous postings in this string that I complete eliminate any possibility that we can obtain our knowledge of the physical world via other ways (logic?). I simply asked you for one clear example where this is possible. Since you can't, my whole point then is that what you are doing is nothing more than speculating, since you have zero physical evidence to based your opinion on. Now, is this not a logical conclusion also?

Zz.