An Introduction to Quantum Field Theory
ribbonfarm.com
ribbonfarm.com
It starts off with a spring mattress analogy (like the one in the linked article, but with more math) and goes on to more advanced material from there. I remember it requiring little background besides LinAl and multivariable calc.
I wish I could write like that.
If someone made a clear-but-impractical QED simulator using, say, lattice gauge theory, I pledge to sing its praises. (You'd expect this to be possible for general relativity too.)
The good news that they're online!
http://vega.org.uk/video/subseries/8
Enjoy!
> If you want to create something heavy like the Higgs boson, you have to hit the > Higgs field with a sufficiently large (and sufficiently concentrated) burst of > energy to give the field the necessary one quantum of energy.)
So when the LHC creates a spike of energy at a point large enough to create a Higgs boson, why does that energy interact with the Higgs field and get "used up" by other fields? In other words, if Higgs requires 100 units of energy and electrons require 1, why do we get 1 Higgs boson and not 100 electrons?
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? Does somebody know? (My current understanding seems to suggest that fields are just a tool.)
Depending on the field of science/engineering and the specific application, one might choose to work with electromagnetic fields, photons or a combination of both.
In the QFT framework, a photon is merely a quanta of the electromagnetic field. So photon based or EM field based approaches are just two ways of dealing with problems. Neither is more or less 'real' than the other.
So I could probably reformulate the question as whether fields are an abstraction of particles or particles are an abstraction of 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 hold for the case of particles and fields. Given a set of field frequencies and amplitudes, you could describe the positions of particles and probabilities of observing them. Given positions and probabilities of observing particles, you could compute the frequencies and amplitudes of the associated field.
We can describe any given set of particles (however big or small, however fast or slow) in terms of fields, and vice versa.
I like this comment :
When I studied quantum mechanics, my professor advised that I avoid the question "which is more fundamental?" and replace it with "which is more useful?".
From this stackoverflow link (http://physics.stackexchange.com/questions/122570/which-is-m...)
My QFT knowledge is rusty, so please correct me if I'm wrong.
http://www.amazon.co.uk/Decoding-Reality-Universe-Quantum-In...
The question of whether or not something is 'real' is a slippery one at the scales we're talking about.
It's like you're asking if numbers are more fundamental than operations on them when you can't possibly have one without the other.
I don't know how to answer the relativistic questions of fields yet. For that one would need to learn a lot of Quantum Field Theory.
For the layman, however, these two links are very informative:
http://www.symmetrymagazine.org/article/july-2013/real-talk-... http://www.pbs.org/wgbh/nova/blogs/physics/2013/08/the-good-...
Compare http://plato.stanford.edu/entries/scientific-realism/ (and references therein)
Combinations of excitations can be interpreted as different excitations, and by 'can be interpreted' I really mean "can spontaneously transmute into" according to the probabilities of quantum mechanics. Since all interactions occur in discrete units of these fields (except for the photon field), referring to these units as particles is a convenient and compelling approximation - but it doesn't tell the full story.
Basically, it very much seems that fields are the more fundamental concept.
Quantum fields are REAL because certain phenomena like solitons, vortices, monopoles and quark confinement can only be understood properly in the full field context. Quantum field theory cannot describe these phenomena in terms of Feynman diagrams. Feynmann diagrams and scattering cross sections/lifetimes were once considered fundamental and fields were believed to be a tool to derive them. Physicists now understand (the competent ones) that Fields are more fundamental than the diagrams. The Fields are also real in the sense that the do much more than just represent particle states, field symmetries are fundamental symmetries of nature, e.g. the strong force has SU(3) symmetry, electroweak SU(2)xU(1) etc.
Steven Weinberg gives a very strong argument for the necessity of fields in his vol. 1 QFT book. It's very technical but a brief summary is... QM + relativity + cluster decomposition principal (which more or less says the results of distant experiments should be unrelated) --> fields
The statement I was referring to comes 28 minutes into the lecture but you probably have to watch everything up to that point for the full context.
So after watching this again the answer to my question seems pretty clear - fields are not real things. I am still left a bit confused because you very often read and hear that fields are real things and actually more often then the opposite.
In condensed matter physics (and thus in most familiar many-particle systems), I tend to give the opposite answer. Field theory is a great tool for describing or approximating many condensed matter systems, but my sense is that it's less fundamental there. But that's also less my area of expertise.
But you can have partial wave collapse through things like lack of particle observations https://en.m.wikipedia.org/wiki/Renninger_negative-result_ex...
When we collide particles in an accelerator and then look at the results on a computer screen you can hardly argue that our vision disturbs what the experiment tells us about the world out there in any significant way. The whole goal is to learn things about the world out there in a way independent of us and that is certainly possible.
Relativity taught us that space and time are really different from what they usually look to us not withstanding that we may have a hard time developing an intuition for them.
So I disagree, that our senses and minds have limitations does not imply that it is pointless to ask questions about what the world out there really is like.
Yes. Just as Schroedinger/Heisenberg quantum theory describes the behavior ("reality") for particles on a small scale, quantum-field theory describes the behavior of fields on a small scale.
This lecture leaves no doubt that fields are not real but just a mathematical tool. The relevant part are the first 30 minutes. I am still not absolutely confident about that but just because it is so often suggested, including the people in this thread, that fields are real. But I am now at least almost convinced that particles are real and fields are not. Really worth watching.
Take a soccer field with two teams and a ball on it. I would prefer to describe that as 23 particles of a few different kinds (ball, field player, goal keeper) and different properties (team membership, mass, fitness, whatever).
You could certainly invent a ball field and a field for both teams that are zero everywhere except where the ball or a player is located but you certainly wouldn't suggest that there are ball and soccer player fields in the universe even if they perfectly describe what happens on the playing field. On the other hand we could certainly agree that there are really players and a ball located somewhere on the field with specific masses, velocities and so on.
Maybe you can look at it from a point of redundancy. If you describe ball and players as particles with locations and momenta you get a description that naturally matches what is going on. If you use a field description you have to place a lot of constraints on what is allowed and what not, players disappearing, a second ball appearing and so on. The field description has just a lot more degrees of freedom than the particle description and you have to impose a lot of constraints to suppress field configuration that are not physically possible. So it also a kind of Occam's razor argument to pick a simple and minimal description.
I don't see how a "natural" description is any different from the word "real" here- fields describe things particles can't, especially when trying to use your "natural" intuition.
And by the way I am in no way suggesting any classical particle model, even without fields you still have the entire quantum mechanical machinery and there are certainly non-classical things going on. The question is whether you really need fields to describe some aspects of nature or if good old quantum mechanics is good enough and quantum field theory just makes things mathematical more accessible.
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.