An Introduction to Quantum Field Theory(ribbonfarm.com)
ribbonfarm.com
An Introduction to Quantum Field Theory
http://www.ribbonfarm.com/2015/08/20/qft/
5 comments
Into the rapid hole??
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.
I wish I could write like that.
An interesting and surprising fact about Feynman's books is that he never _wrote_ any of them, as such; he famously disliked writing. QED is essentially a transcript of a lecture (although I don't know how much polishing and editing was done by Feynman himself; probably some). Same with his collection of physics lectures. His most popular book, "Surely You're Joking, Mr. Feynman", was transcribed from a series of interviews, pretty much verbatim.
Relativity: The Special and General Theory by Einstein would also fit that description, I think. (Though I haven't read Feynman's book so I may be misunderstanding you.)
It's a marvelous book, but a little frustrating as well for not quite explaining enough to calculate with, even super-inefficiently. Can't we get a correct formula for the propagator, including the four spin components? When I tried to fill that in from other sources I was snowed under by all the formalism or prerequisites -- yes, it's probably a short step if you already understand it or you're smarter than me.
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.)
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.)
It would be nice to have a version that uses complex numbers and linear algebra instead of spinning arrows. A little bit more math would make it easier to connect with the "grown up" version of the theory.
Anthony Zee's book on QFT (http://www.kitp.ucsb.edu/members/PM/zee/QuantumFieldTh.html) might be what you're looking for.
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.
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.
Thank you! :)
It's been a while but I'm pretty sure the spinning arrows are Phasors. Ironically the spinning arrows might make more sense than the math that describes them.
https://en.wikipedia.org/wiki/Phasors
https://en.wikipedia.org/wiki/Phasors
Much less famous than Feynman's Messenger Lectures at Cornell (or his real "Lectures" that got turned into the books) are the lectures he gave in New Zealand that became QED: The Strange Theory of Light and Matter.
The good news that they're online!
http://vega.org.uk/video/subseries/8
Enjoy!
The good news that they're online!
http://vega.org.uk/video/subseries/8
Enjoy!
This is a great article. One thing I don't understand: the author says:
> 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?
> 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?
Not a physicist, but that actually happens. Depending on the coupling strengths between the various kinds of particles respectively fields and the amount of energy they have, different particles get created with different probabilities. That is why the Higgs is so hard to detect - for every Higgs you produce billions and billions of other particles that are easy to create and you have to look for the one Higgs in all this mess. Physicists calculate the expected amounts of other particles with incredible precision, subtract that from the experimental results and if they are successful they end up with a tiny amount of unexplained stuff.
When particles are created in the LHC, a huge number of particles are created when particles are collided. This is why physicists have to sift through mountains of data to find the one higgs boson in the flood of every other particle.
In addition to the fine answers already posted, it's also worth noting that it's not the Higgs itself that is detected but rather the decay products - shortly after production, the Higgs boson decays in one of a finite number of different ways, with associated probabilities, and this is what the scientists look for in the (presumably vast) data.
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? Does somebody know? (My current understanding seems to suggest that fields are just a tool.)
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.)
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 high energy processes.)
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
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
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.
This took way longer than I imagined. I won't repeat the argument here in detail but it essentially boils down to the argument that fields theories are just an effective description of long distance behavior ignoring what is really going on at short distances, that fields are just a convenient tool to make locality manifest and that field theories contain a lot of redundancies due to this.
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.
https://m.youtube.com/watch?v=tnA7bh7dTqY
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.
https://m.youtube.com/watch?v=tnA7bh7dTqY
Ohhh no! Just when I thought I got the answer. Just skimmed it and I draw some hope from the fact that the author uses the unconfirmed Unruh effect and wave function collapse, which is as far as I know not a thing because it is not unitary, to explain the double slit experiment. So maybe it is the author who is confused and not the others he is complaining about and I won't have to change my mind once again but I will have to read it way more carefully before drawing any conclusions.
The people that I tend to respect most in these areas tell me that (at least in fundamental physics/particle physics) fields are reality, and that it's our perceptions of particle behavior that are an illusion. (Just for example, an accelerating observer will count a different particle density than an inertial observer for the same underlying field state: that's known as the Unruh effect.) So at its deepest level, reality appears to obey the rules of field theory: the fields themselves are the fabric of the universe.
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.
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.
I'm just an physics enthusiast and my knowledge is solely based on popular literature, but it seems to me that either (1) the mechanistic, computational, discrete view is the foundation and everything that appears continuous and field-like comes just from averaging over myriads of particle interactions, or (2) real-valued fields are the foundation and discrete structures appear at certain thresholds. In some sense the former possibility appears to be safer, because in the latter case we could just find ourselves in some meta-stable configuration, where some parameter of our universe could be sweeping through the parameter space in an unfortunate way, such that the threshold for matter to exist might get out of reach and everything could easily dissolve into a different structure.
> averaging over myriads of particle interactions
But you can have partial wave collapse through things like lack of particle observations https://en.m.wikipedia.org/wiki/Renninger_negative-result_ex...
But you can have partial wave collapse through things like lack of particle observations https://en.m.wikipedia.org/wiki/Renninger_negative-result_ex...
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 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-...
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-...
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?
My intuition for it is that there are fields at all points in spacetime (the fields of the standard model: a tiny vector of sorts), and excitations - certain patterns in these fields - behave as particles.
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.
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.
Fields are real because perturbation theory (Feynmann diagrams) is unable to describe solitons, vorticies, monopoles and bound states.
Sounds like the best argument I've heard on this thread yet.
Could you link some experiments? Sounds super interesting.
Depends, if you are a realist, then there is a field; if you are a anti-realist then the electron is not real but only a convenient shorthand in the first place.
Compare http://plato.stanford.edu/entries/scientific-realism/ (and references therein)
Compare http://plato.stanford.edu/entries/scientific-realism/ (and references therein)
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.
It depends on what constitutes 'an element of reality'. Are photons an element of reality?
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.
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.
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 could probably reformulate the question as whether fields are an abstraction of particles or particles are an abstraction of fields.
So I could probably reformulate the question as whether fields are an abstraction of particles or particles are an abstraction of fields.
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 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.
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.
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?
If you haven't read it already, you might enjoy this:
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.
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.
There is no need for abstractions to have a strict hierarchy. they're all abstractions -- They employ some measure of indirection -- and thus neither are fundamental or 'real' if you think about it. The words "physical" or "real" won't help you to understand physics at all.
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.
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 would be careful making analogies with temperature, it can be important when actually making a judicious choice of how to calculate observables! cf. https://en.wikipedia.org/wiki/Thermal_quantum_field_theory
That's a non-issue. Everything you've ever experienced is mapped through your perceptions, and thus it's all illusory. Physics is about coming up with language that describes our experiences accurately, not distinguishing between meaningless philosophical inventions.
Everything we know about the world has at some point to go through our senses but it is still a reasonable assumption that there is a real world outside and independent of our minds.
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.
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.
You're not asking what the world is really like, you're asking about whether or not a model of reality is a fiction or not. Physicists model reality. Every model is a fiction. Some are just more useful fictions than others.
> Are quantum fields actual elements of reality
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.
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.
In the meantime I looked for a lecture I watched some time ago and where I remembered that it suggested that fields are not real.
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.
https://m.youtube.com/watch?v=tnA7bh7dTqY
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.
https://m.youtube.com/watch?v=tnA7bh7dTqY
What exactly makes something "not real" and only a tool? Is relativity "just a mathematical tool" because planets don't have differential equation solvers in them?
Real is probably a bad word and I can't really give a sharp definition but I can provide an analogy.
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.
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.
Quantum physics is not about a game of soccer. It's about phenomena that do things that actually do look strange when just looking at particles.
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.
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.
If you haven't yet watch the first half hour of the lecture I linked to - this makes the point way more clear than I ever could in a few comments. And it essentially settles the question. Besides the fact that there are so many people claiming that fields are real but at least for the moment I will assume that they are just wrong or until I hear a convincing argument that this point of view is wrong. There are some hints in some of the comments here that fields are really necessary in some circumstances but they are not specific and I am not knowledgeable enough to judge them. Will have to do some research on that.
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.
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.
"Good old quantum mechanics" is quantum field theory.
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.
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.
I wouldn't call it Ether, since that would imply some absolute reference frame.
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).
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http://theoreticalminimum.com/