8 ms·

An Introduction to Quantum Field Theory

126 points by simulate 11y ago

613style 11y ago
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?
- danbruc 11y ago
  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.
- xlm1717 11y ago
  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.
- danparsonson 11y ago
  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.
danbruc 11y ago
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.)
- toxikitty 11y ago
  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.
  - danbruc 11y ago
    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.
    - toxikitty 11y ago
      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-more-fundamental-fields-or-particles/122574#122574 http://physics.stackexchange.com/questions/122570/which-is-m...) My QFT knowledge is rusty, so please correct me if I'm wrong.
timelined 11y ago
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.
- peterfirefly 11y ago
  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.
  - toxikitty 11y ago
    Anthony Zee's book on QFT (http://www.kitp.ucsb.edu/members/PM/zee/QuantumFieldTh.html 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.
    - peterfirefly 11y ago
      Thank you! :)
  - nerd_stuff 11y ago
    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
- Steuard 11y ago
  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.
mudil 11y ago
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/0316016411 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.
- w0000t 11y ago
  I wouldn't call it Ether, since that would imply some absolute reference frame.
- deleted 11y ago
  [deleted]
- Steuard 11y ago
  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).
danbruc 11y ago
Obligatory link for those that want to go a bit deeper into the rabbit hole - The Theoretical Minimum, a collection of physics lecture by Leonard Susskind. http://theoreticalminimum.com/ http://theoreticalminimum.com/
- bostonpete 11y ago
  Into the rapid hole??
  - danbruc 11y ago
    Fixed.
    - bostonpete 11y ago
      OK, I thought maybe I was missing a physics pun or something... :-)

126 points by simulate 11y ago

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?

danbruc 11y ago
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.
xlm1717 11y ago
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.
danparsonson 11y ago
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.

danbruc 11y ago

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.)

toxikitty 11y ago
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.
- danbruc 11y ago
  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.
  - toxikitty 11y ago
    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-more-fundamental-fields-or-particles/122574#122574 http://physics.stackexchange.com/questions/122570/which-is-m...) My QFT knowledge is rusty, so please correct me if I'm wrong.

timelined 11y ago

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.

peterfirefly 11y ago
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.
- toxikitty 11y ago
  Anthony Zee's book on QFT (http://www.kitp.ucsb.edu/members/PM/zee/QuantumFieldTh.html 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.
  - peterfirefly 11y ago
    Thank you! :)
- nerd_stuff 11y ago
  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
Steuard 11y ago
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.

mudil 11y ago

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/0316016411 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.

w0000t 11y ago
I wouldn't call it Ether, since that would imply some absolute reference frame.
deleted 11y ago
[deleted]
Steuard 11y ago
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).

danbruc 11y ago

Obligatory link for those that want to go a bit deeper into the rabbit hole - The Theoretical Minimum, a collection of physics lecture by Leonard Susskind. http://theoreticalminimum.com/ http://theoreticalminimum.com/

bostonpete 11y ago
Into the rapid hole??
- danbruc 11y ago
  Fixed.
  - bostonpete 11y ago
    OK, I thought maybe I was missing a physics pun or something... :-)