An Introduction to Quantum Field Theory • Hacker News Board

Re: An Introduction to Quantum Field Theory

#41

Post by nerd_stuff » Sat, Aug 22, 2015, 5:08 AM UTC

peterfirefly wrote: post #8

timelined wrote: post #4

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.

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.

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

Re: An Introduction to Quantum Field Theory

#42

Post by furyofantares » Sat, Aug 22, 2015, 5:42 AM UTC

Steuard wrote: post #30

timelined wrote: post #4

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 hopele…

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.)

Re: An Introduction to Quantum Field Theory

#43

Post by danbruc » Sat, Aug 22, 2015, 11:07 AM UTC

danbruc wrote: post #27

MisterMashable wrote: post #20

Earlier quoted context omitted.

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.

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

Re: An Introduction to Quantum Field Theory

#44

Post by danparsonson » Sat, Aug 22, 2015, 1:30 PM UTC

613style wrote: post #2

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…

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.

Re: An Introduction to Quantum Field Theory

#45

Post by danparsonson » Sat, Aug 22, 2015, 1:41 PM UTC

danbruc wrote: post #25

toxikitty wrote: post #18

Earlier quoted context omitted.

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…

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.

Re: An Introduction to Quantum Field Theory

#46

Post by Retra » Sat, Aug 22, 2015, 2:07 PM UTC

danbruc wrote: 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?…

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.

Re: An Introduction to Quantum Field Theory

#47

Post by Retra » Sat, Aug 22, 2015, 2:11 PM UTC

danbruc wrote: post #11

toxikitty wrote: post #5

Earlier quoted context omitted.

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 proble…

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…

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.

Re: An Introduction to Quantum Field Theory

#48

Post by danbruc » Sat, Aug 22, 2015, 3:24 PM UTC

Retra wrote: post #46

danbruc wrote: 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?…

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.

Re: An Introduction to Quantum Field Theory

#49

Post by jpmattia » Sat, Aug 22, 2015, 3:24 PM UTC

danbruc wrote: 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?…

> 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.

Re: An Introduction to Quantum Field Theory

#50

Post by evanb » Sat, Aug 22, 2015, 3:41 PM UTC

timelined wrote: post #4

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.

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!