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An Introduction to Quantum Field Theory

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Re: An Introduction to Quantum Field Theory

#21
post #7

Ether is back! Well, somewhat. Now it's in the form of Higgs field. Unlike ether, Higgs field does not interact with uniformly moving particles, only those that are accelerating. Here's a great book I just recently listened: http://www.amazon.com/The-Black-Hole-War-Mechanics/dp/031601... It's by Leonard Susskind from Stanford. The thoughts experiments in the book are just terrific. Loved it.

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Re: An Introduction to Quantum Field Theory

#22
post #13
post #9

Earlier quoted context omitted.

The way I've understood it is, particles are localized excitations of fields. You know of the Higgs boson. It is the excitation of the Higgs field, which exists through all space. Similarly, an electron is an excitation of the electron field (not electromagnetic field), which exists through all space. Every single electron is a localized excitation of the same, single field. I don't know how to answer the relativisti…

I understand that, but is it just a neat mathematical model to treat particles as excitations of fields because it makes calculations especially easy or is there really a field out there?

Fields are real because perturbation theory (Feynmann diagrams) is unable to describe solitons, vorticies, monopoles and bound states.

Re: An Introduction to Quantum Field Theory

#25
post #11

Earlier quoted context omitted.

Compare it with temperature. If you run next to fast atom and you touch it, it doesn't actually feel hot. So temperature is not really a fundamental thing in nature but a higher level abstraction of the different moments of a large collection of particles. Temperature also becomes meaningless and the whole concept breaks down if you have only one or a few particles. It is of course a useful concept nonetheless. So I…

AFAIK the particles vs fields discussion is not the same as temperature vs fields. At the risk of straying into quantum info territory: - given all possible information about a collection of particles, you could compute the temperature. However, knowing the temperature doesn't allow you to determine info about particles uniquely (you can write down a density matrix, and not assign a pure state). - the above doesn't h…

Looking at what is more useful is certainly a really good idea if your goal is to calculate and understand a specific problem. But I think you would miss out on something if you ignored the question of what is fundamental. And I personally am absolutely not interested in specific problems, I want to know what really is out there. Realism? Locality? Space? Time? Particles? Fields? What is really fundamental, what are just emergent phenomena?

Re: An Introduction to Quantum Field Theory

#26
post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

Can you define what you mean by an 'actual element of reality'?

Re: An Introduction to Quantum Field Theory

#27
post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

Quantum Field Theory is really just ordinary Quantum Mechanics. It is necessary to use fields instead of "wave equations" because the number of particles can vary when the energy of a system exceeds a certain threshhold. (e.g. a single photon having an energy equal to or higher than the E=mc^2 energy of two electrons can transmute into an electron-positron pair. 1 particle transforms into 2. This is very common in hi…

Now I have to dig out a statement by Nima Arkani-Hamed where he says something like "[...] should bother you if you believed that fields are real." - I of course forgot the most important part but I still remember in which lecture series he said that. If my memories does not mislead me, he was really arguing that you should not think of fields as real things for very concrete reasons. Trying to find it.

Re: An Introduction to Quantum Field Theory

#28
post #3

Are quantum fields actual elements of reality or just a convenient mathematical tool to deal with many particle systems? One of the questions I am struggling to find a satisfying answer for for quite some time. Depends on whom you ask? We can't tell because both ways of thinking are completely equivalent? Fields are real! No, they are just a tool! Are there issues with real fields forming a preferred reference frame?…

Can you define what you mean by an 'actual element of reality'?

I guess it is not a really sharply defined term, but I mean some fundamental piece of the universe that is really out there as opposed to something that emerges from something more fundamental or is just a convenient model or abstraction. As I said in a other comment something like temperature which is just a nice tool to deal with the momenta of many particles where the motion of those particles is more fundamental. Not the best analogy as pointed out by another commenter but I think it gets the point across.

Re: An Introduction to Quantum Field Theory

#29
post #7

Ether is back! Well, somewhat. Now it's in the form of Higgs field. Unlike ether, Higgs field does not interact with uniformly moving particles, only those that are accelerating. Here's a great book I just recently listened: http://www.amazon.com/The-Black-Hole-War-Mechanics/dp/031601... It's by Leonard Susskind from Stanford. The thoughts experiments in the book are just terrific. Loved it.

There is very little in common between the old concept of "ether" and any quantum field. Analogies like the mattress model described in the article are helpful in some ways (like describing particles as excitations or ripples in the field, as here), and misleading in others (like making people think that there's some fixed medium for fundamental wave propagation).

Re: An Introduction to Quantum Field Theory

#30

This is a pretty good introduction. I highly recommend Feynman's book "QED: The Strange Theory of Light and Matter" as an excellent in-depth work that does not sacrifice accuracy for the sake of making difficult ideas understandable. It is both very clear to the layperson and accurate to the physics.

Wholeheartedly seconded. This book occupies a nearly unique position in the physics literature: it is neither a textbook nor a popularization. It assumes little more knowledge (of math or physics) than the typical popularization, but it explains what is very nearly the true, complete structure of its subject matter (quantum electrodymanics). Now, the methods that it teaches are absolutely unwieldy: it would be hopeless to do any real, meaningful calculation by drawing countless little arrows! But (as I think Feynman says) you can go to grad school to learn the efficient tricks. The underlying concepts will carry through essentially unchanged.

I wish I could write like that.

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