We’ve talked about the quantum mechanics of particles, now it’s time to apply those ideas to fields. It requires a bit of effort to understand how a quantum field — which is really a wave on top of a wave, when you think about it — ends up looking like particles in the right circumstances. But it’s worth it.
The Biggest Ideas in the Universe | 9. Fields
And here is the Q&A video. I talk a bit about different kinds of fields, and why the Dirac or Klein-Gordon equations are not relativistic versions of the Schrödinger equation.
The Biggest Ideas in the Universe | Q&A 9 - Fields
Your videos are the best thing that has happened to me since March! Too bad it took a pandemic to get us here but, now we both have the time… I really appreciate your presentation style, easy to grasp but not “dumbed down.” It’s a privilege to finally be able to audit a class of yours. Dream come true.
P.S. I’m not sold on Everett yet… ; ‘ )
Dr. Carroll, love this series. It gives me something interesting to do while The Univ. of Arizona has gone online. I think
I am beginning to understand entanglement. Explained it to my wife and got no questions. Not sure what that means.
I have seen attempts to end run/explain “non-locality” e.g. ER=EPR. What do you make of them?
Also, if we there is no vacuum due to quantum effects; if there is a Higgs Field ; if there is “dark energy” all of which pervades all of space, are these potential media to resolve entanglement’s non-locality?
Or is this like Maxwell trying to invent interlocking cogs to transmit electromagnetic forces?
Thanks so very much for these talks!
Where does the Mexican hat shape for the modes of the Higgs field come from? How many possible shapes are there for different fields when comparing h to energy?
Does this suggest the possibility that the most fundamental description of nature has nothing to do with waves or anything wavelike, but rather wave functions emerge in QM because they are the simplest mathematical solutions to problems in field theory?
You have used the term “modes” to describe the behavior of waves, but I have been taught the term “nodes”. What is the difference between these two terms?
Hi,Sean! Was Democritus correct when he said that all matter is made of particles? Or is it more accurate to say that it is made of fields?
Thanks for the wonderful vídeos!
Please go more in depth as to how fields interact with each other. I have so many questions and I want to have more, this is great!
Can one speculate or consider that vibrations In fields are precursors to sentience or aliveness in the universe ? A not typical physics related question but I am curious
Hi doctor Sean! Thanks for the amazing video! I think it’s the hardest one in the series so far, but it’s really amazing that someone is explaining this technical things to someone without any proper training, like me! Please, keep the series and keep the explanations complete, even if it’s hard!
I would like to recommend that you talk a little bit more in the QA about fields of vectors and wave functions… Also a bit about complex numbers would be nice hehehehe! I (guess) I know what a vector is, what a field is, and what a wave function is (something that we square to get the odds of seeing an outcome)… So, the field theory is just that the wave functions is about vectors in fields?
I also would love to learn more about how fields interacts with each other!
Thanks!
Are there canonical quantization approaches in QFT similar to approaches in nonrelativistic QM? Are there equivalent conjugate variables?
Will you tell us something about particle creators and annihilators please? I never understood where boson and fermion commutation rules are derived from.
Thank you for this series. It is a pleasure to watch and learn. I just can´t find where to post questions for the Q&A follow up so I will post it here: Could you in the Q&A Follow up elaborate a bit about the false vacuum decay?
i want to thank you for these great videos and i have some questions for the Q&A: are fields expending with space time? if so,at what speed,and will this expansion eventually affect the wave functions?
and do the fields principles affect antimatter the same way as matter?
I’m almost at the end of your book, and I must say I now understand – and fully accept – the many worlds concept. I mean, here we find ourselves stuck (for the time being?) in an alternate universe where this character Donald Trump is running the show. If that’s not proof positive of the theory, I don’t know what is.
[sigh]
Dr. Carroll,
As Psi of Phi sub k of h squared looks like the probability that you will find that the field has the value h. Suppose you measure the field and you get some value, h, how would you know which state your field was in. It seems that any harmonic oscillator wave function has some probability of having any particular h.
As another question, you clearly explained free fields, as expansions of plane wave modes. I can see how you might deal with confined fields, such as the “field in a box” problem, or the hydrogen atom. Could you talk to us how these confined solutions might arise? I see pictures in texts that show Feynman diagrams for the hydrogen atoms with three wavy lines and virtual photons. I’d enjoy hearing your plain English consideration of these cases.
Thank you for these beautiful talks.
Bernard Leikind
University of Tampa
Thankyou for all of your videos,
Iam a regular follower of your running series, and it’s amazing the way you explain these hard rocky ideas to us, common man as soft rice powder in a plate.
Humbly request you to prepare your next book with this “biggest ideas” content, which is very useful for us like beginners.
Thankyou,
Johnson
The inset to the video 9. Fields says:
“Not quite right: the vaccuum is a product of the lowest energy state of all modes, not a superposition of them.”
Is this correct? I learned that it is the SUM of all modes in the lowest energy state.
Q: As the energy states (modes) of the wave function rise, the frequency of the modes (colored functions) also rises. This frequency rises in descrete steps as is described. Is this requency (of the colored modes) a somehow important parameter? For example does it somehow significantly correlate to the number of particles? Also is it correct to assume the requency (of the colored modes) somehow tied to the omega of the harmonic oscillator or is that not related at all?
And thank you, for the videos.
You said “the electron is not moving at anywhere near the speed of light”. Please explain. I thought electricity is the movement of electrons and they are just shy of the speed of photons.