The Biggest Ideas in the Universe | 9. Fields

[@chrismoon7758]

Dr Carrol I'd like to thank you for taking the time to make this interesting series of videos. I'm 70, a retired "blue collar" worker, neither gifted nor bright, nevertheless interested in the world and your lectures/talks have shed light on things which have fascinated me but were beyond my comprehension. Am also enjoying reading "Something Deeply Hidden". You have brought a lot of joy, understanding and pleasure to an old man. Thank you.

[@sunitasingh-oo9mz]

🥰

[@EvaTruve]

I have “From Eternity to Here” with me all the time while I am commuting. Life is about knowledge.

[@madrox4132]

I’d say they weren’t beyond your comprehension then

[@JRPLaw]

Mr. Moon, for what it's worth, I think you're an inspiration. I'm trying to encourage my mom to do exactly what you're doing.

[@JoeHynes284]

i am younger then you but never sat in a class room and have worked mostly "blue collar" jobs including my time in the navy. I agree with you 100 percent. I read the book and am no listening to it and these lectures when i drive to and from work, i think i am understanding more and more each time i listen...hopefully, but i feel it is time well invested

[@Emanresu56]

Sean, don't drown yourself! There are so many things to live for!

[@ExistentialistDasein]

This series is a great source of comfort during the current lockdown. Thank you for continuing!

[@Ron4885]

Very well said.

[@ExistentialistDasein]

@@Ron4885 Glad someone agrees.

[@Bill_Garthright]

_This series is a great source of comfort during the current lockdown._ It's also a great source of comfort during the current political situation in America, since it's good to know there are still intelligent people in my country.

[@Amir-vw6rk]

Sean, please, don't stop making this content!

[@waynebeard3163]

would someone help get out of the intuitive world I live in. If everything is waves and particles do not exist what is the organized matter such as trees, canoes, and human bodies. When I kick my canoe it hurts

[@vatsdimri3675]

@@waynebeard3163 I think simple ways to think about this is that even though everything is wave (or fields) those waves are not free, they interact with each other.

[@cazymike87]

Particles do exist ! You can feel all of that because you and evertyhing that makes you and objects you interact are localized. Localization is the answer to your question. Everthing that interacts is localized. That is why when something happens in a particular spot in time and space , will need time to reach to us to konow it happened. Interactions happens in a precise spacetime point.@@waynebeard3163

[@Director4Sciences]

Sean, thank you. What a beautiful balance you've established in this series between faithfulness to the current academic discipline and yet accessibility by the 'unwashed masses'. I find myself in what's probably the sweet spot of your 'ideal viewer profile' - limited but significant general academic background in math & physics + infinite curiosity and a deep & abiding desire to understand the physical world. As such, I greatly appreciate the (clearly sizable) personal investment you're making in synopsizing (and extending) your generous contributions to my cohort with Big Picture, SDH, Particle At The End…, et al. Please know that I am grateful! All the best. -b

[@EverythingQuestion]

"It's beggining to seem....hard" meanwhile I've been pretending to understand for a few videos now. lol. Love these. Great job.

[@ToriKo_]

Same here

[@schelsullivan]

Good job socially isolating. The middle of the ocean.

[@Ron4885]

Yeah, that really should work :)

[@fillemptytummy]

and good job doing the video even though TV makup isn't a thing in the ocean.

[@csababobalo8692]

Haha nice

[@tripp8833]

He’s not really in the middle of the ocean, that’s just a background

[@igorjee]

@@tripp8833 Thank you, I was worried to death...

[@xcq1]

This is exactly the intermediate cohesive introduction to these topics that I have sought for for years. The last time I've had such insights on new topics was probably in University. Thank you for sharing your knowledge in such an elaborate way.

[@Valdagast]

His hair field is expanding in value.

[@JohnDlugosz]

As long as it's non-interacting. We'll see later if it reaches its potential.

[@alangarland8571]

The grateful dead agree.

[@RooBot]

He's turning into a hippie. HI=(π)

[@lrrrruleroftheplanetomicro6881]

And it's growing much quicker than mine! and i'm 10 years younger. funny what we learn about each other these days.

[@brianziemba1910]

@@D1N02 lol!

[@alexd.alessandro5419]

May I say that though I understand little of the talk, I am enchanted by the utter humility and spirit of generosity of this beautiful person. Makes me think of Socrates. Thank you and all the best!

[@billg.7909]

Thank you. This is like a college physics course without having to actually do problems! I'm glad you don't shy away from the math, I want to see it, but don't want to do it.

[@achunaryan3418]

It's not a college course if you don't solve (not do) problems.

[@alvarorodriguez1592]

Thank you! No popular physics explanation has gone so far. Live long and prosper!

[@jeangatti9384]

Clearly the very best explanation I've ever seen for describing QFT principles, many thanks

[@Cooldrums777]

This video takes me back to my undergraduate days studying nuclear engineering. You even threw in a tiny partial diff eq (S wave eq). So much fun to watch this because QFT wasn't even covered in my graduate work. Thanks for this one Prof.

[@matthewkrellwitz8973]

10/10 best content on the interweb. Thanks Sean!

[@salvatronprime9882]

Thank you so much for this series. It's so awesome to get the most current date theory and details in a very concise and easily understood format!

[@matt_w]

Watching these now a year after they were published and they're exactly what I was looking for: a down-to-the-metal description of how all this stuff works without all the pop-sci fluff that surrounds these topics. Thank you so much for taking the time to make this series. It's a monumental effort. An interesting note: you use the word "quantize" to (I think) refer to taking a classical phenomenon and bringing it into the paradigm of quantum mechanics. This terminology is disorienting to an electrical engineer: "quantize" to me invariably means to take a sampled continuous amplitude signal and place each sample in an amplitude "bin" that can be labelled with a fixed-width binary number. We talk about quantization noise and various ways to mitigate its effects. That seems emphatically to not be what you're talking about here. You're talking about taking something with a single classical configuration and describing it as a superposition of configurations characterized by a probability function, all of which exhibit fully continuous behavior in space, time, and amplitude.

[@sdal4926]

Sean Carroll is a perfect teacher which is the best compliment I can say for who is doing this. And this is not only virtue he has

[@sandrasandra7593]

Dr Sean, you explain beautifully well, in a pleasant way, and speak very clearly, which is very important for those like me who are learning English

[@YoshiTatsu1]

Thank you for taking time to make these videos. I am a huge armchair physics nerd. I was a philosophy undergraduate and after I Graduated, I became completely obsessed with physics.

[@zicada7661]

I just have to say i love this thumbnail

[@royalbloodedledgend]

The Carroll Field

[@Ron4885]

Me too.

[@larryseabrook7089]

I have learned things from these videos that I missed entirely after previously watching more formal, mathematically rigorous presentations. Great job!

[@jorgefigueroa9652]

Sean, you are a terrific teacher, you make complicated things so easy to understand, you really have an special way of communicating, I’m enjoying every single one of your lectures. I do like your books, also, I recommend it to everybody out there who loves science.

[@JasonWalsh-q4z]

I love you're equations.

[@matiasreinoso3393]

As many already stated, this video series is amazing and so informative & intuitive, please continue it if possible!

[@pamelacollins1153]

I have no physics background; I have read a lot of lay person books on particle physics. Thank you so much for making these videos!!!! I’m starting to understand some of this, and it is so fascinating!!!!! And I love learning what these symbols stand for. Thank you thank you thank you 💕💕💕

[@bruinflight]

Sean you are so brilliant. No fault that I'm a layman, but I sure wish I could talk about these things with the depth of understanding and intuition you do. It's amazing to listen to you and there are parts I feel I understand more, but the math and subtleties therewith leave me behind. That's unfortunate too because I do love math! Great series, please keep your chats coming!

[@rc5989]

The biggest video yet on the Biggest Ideas in the Universe! I am just loving all the bigness including the big smile I get from enjoying these videos.

[@ronansleep]

Wow. This is hitting exactly the stuff I was missing when I did my physics course in the 60's. Really great introduction.

[@KieranGarland]

I absolutely love this series. Will be returning to them again and again. Thank you.

[@edwardlee2794]

To continue .. A layman, me, can't resist to follow it to the very end. Thanks for the efforts and keep up with the good work. From Hker worldwide

[@vinnyvdalidemonet8527]

@Sean Carroll, your video's have the feel of delivering individualized attention. I watch them with the appreciation as if you're focused on helping me understand these awesome lessons. Thank you so very much. For generously sharing your time, passion, lifes work with all your years of learned experience.

[@loriomyoreo8224]

This is my fav so far. I came for the voice and stayed for the knowledge.

[@sipplix]

The more physics I absorb and "try" to understand including, perfection in the mathematical description of our reality, speed of light limit, Entanglement, Super Position, measurement problem, wave function, dark matter, Plank scale etc. the more the Simulation hypothesis seems to explain a lot of things. Thanks for this very educational show, Knowledge Onward!

[@kevinevans8505]

I'm another one like Chris Moon. I have had it in mind for decades to understand this stuff and although I'm just making a start on listening to you, I can tell that you are the man that's going to do it for me.

[@TenzinLundrup]

The subject of this video is exactly what I have been wondering about, namely, what is a quantum field and how does one get particles from fields.

[@carolinaruivo3519]

Thank you Sean Carroll for this series and please keep sharing your knowledge! Listening to it while working :) Greetings from Portugal!

[@michaeldoughertyjr]

Thank you Dr. Carroll for making this series. I'm this far in, watching sequentially. This is the level of explanation and intuition that I have been waiting for from among the many of you that do similar work.

[@isabelab6851]

As I listen to this...it just feels like you are just making this up...and I mean that in the most respectful way! This material is so different than what I do that it is just hard to see how it is real. Thank you for challenging me intellectually...every time!

[@cloudvariable9910]

Thanks so much for this! For the longest time, I had no idea what the hell quantum fields even meant, but this immediately cleared up the conceptual debate for me! And I have to say, the formalism of it all just seems so appealing...

[@JustChrisNow]

I'd been doing ok with previous videos but I think I've hit my quantum comprehension wall. I'll see if the Q&A clears any of it up

[@samuelcharleshamilton-gree7328]

Thanks for this I am so glad you have taken the time. I enjoy seeing you get serious and taking us along for the ride. Also happy to take the pause outbreaks needed to keep up with you :) dont slow down

[@samuelcharleshamilton-gree7328]

These videos and www.preposterousuniverse.com podcasts.... Cheers Sean!

[@brunoprates862]

Hi Sean. Amazing video as always, thank you so much for sharing this knowledge. My questions: (first one is more important) 1 - If there is just one wavefunction for a given field, how come when we measure an electron in a experiment, it doesn't collapse the entire wavefunction of the electron field, therefore collapsing every electron in the world to a particular location? 2 - How many fields are there in QFT? I can't seem to find a consistent answer online... Are there one for each particle in the Standard Model? Do anti-particles have their own fields? What about different handed particles? 3 - Are there different fields for the different generations of fermions? An electron field, a muon field, and a tau field? Or is it just one field? If it is just one field, how does the difference between an electron and a muon appear to us when we observe the field?

[@alvarorodriguez1592]

1.- Go to google images and search for Gaussian Process. You will see parts where points are certain and parts where the probability extends. I’m sure the math is different, but at the same time similar enough to get an intuitive idea. If you have a lot of uncertainty/degrees of freedom, defining a part does not define all of it.

[@alvarorodriguez1592]

I will add to 2&3, how many Hamiltonians that make sense are there?

[@harishmurali8715]

As Alvaro hinted at, measuring the electron field at one part of the space does not determine the field everywhere. What you'll end up with is a superposition of all wavefunctions consistent with what you observed.

[@brunoprates862]

Just saw your answer now, thanks mate! The image was perfect to get an intuitive idea.

[@TheDummbob]

Regarding questions 2&3: as far as i know antiparticles have their own fields, aswell as right and lefthanded particles. For example the wave function of an electron is described in diracs theory (the relativistiv generalisation of schrödinger theory) by a four component object called a spinor (or a spinor field if your looking at the quantum field of electrons). these four components can be interpreted in the following way: the one is a lefthanded electron, one a righ handed electron, the orher two describe the right- and lefthanded anti-electron respectively. So each component corresponds to a quantum field in QFT. Also muons and tau particles get their own quantum fields in the same manner. To put it all toghether, there seem to be plenty quantum fields

[@franciscodiascoelho5954]

I appreciate these videos Professor Sean, thorough yet comprehensible enough for a layman like me. Thanks

[@edwardlee2794]

Great lecture. Truly heady stuff captivatingly presented. A layman

[@kj4242]

So far, this video is the most interesting but most complex of Dr. C's series.

[@wagsman9999]

Very clear introduction into fields, and quantum field theory.

[@CocoTheDiamond]

my degrees are in the humanities. i could NEVER qualify for physics and yet i am so interested!!! this makes it so accessible and lets us armchair science aficionados get some education from Dr Carroll! (who, let’s be honest, is a fucking rockstar of the science world) Thank you SO much!!!

[@mikeutube011]

when you’re at the beach and Sean pops out of the ocean to hit you with some intellectual pills. 👌 life is good!

[@lambda4931]

Thank you!!!! So interesting! How lucky we are to have this.

[@bernardloke1975]

Wow things are beginning to come together now! Thanks Sean!!

[@kagannasuhbeyoglu]

Prof.Sean Carroll. Thanks a lot for this series.

[@stephenbryant7873]

My mood brightened when this came in. Great background image too

[@perjespersen4746]

Man this video is good. Many of those dificult questions like particle tracks and the distingtions between the wavefunvtion and the field are answered... and I even passed a QGT course once.

[@kamiodd2873]

This man explains successfully in layman's terms some of the most complicated concepts in Physics, yet smiles like a child at Christmas when copy/pasting. "Can we keep him?" But seriously, thank you @Sean Carroll for providing these lectures and keeping our brains busy. Let me see if I get the gist of it at least a little: Quantum field theory asks "Is it possible?" It looks at different energies and wonders about the probability of finding certain energy states at any given moment in time and space or its potential. It does however not tell the actual scale of it? (I'm not a Physicist, can you tell? :))

[@chiphill4856]

Perfect level of mathematics! Thank you - I thought I would never get this far into quantum mechanics!

[@MrNjsteele]

Love this series, Sean! I have a general question about quantum fields. When ppl talk about unifying the fields, what exactly do they mean? Are we trying to prove that there is actually only one field that acts like different fields at low energy? Or there are many different fields that used to be one field at the time of the big bang?

[@harishmurali8715]

One usage of the word unification is that there are all these different fields at low energy which fit nicely into a collection which, at high energies, transforms a partucular way under some symmetry. It's called spontaneous symmetry breaking.

[@viktorbarkar8228]

Thank you Sean for your work. The voice of reason in this trying times 😊

[@Sasquatch4lifeX]

Listening to this reminded me I should review Fourier Series! It has been a while since I saw them in my Diff Equations class hehe!

[@vaibhav1618]

Sean, the thumbnails are amazing!

[@navidazadi4280]

Dear Prof. Carroll, I have a few questions, I would be most grateful if you reply; 1- Why you made each mode into "particles" and not a single particle? why this interpretation? For example, can't we consider excited energy state of n, corresponding to n paths/trajectories of just a single particle? instead of "n particles" interpretation. 2-When you take the potential of a field proportional to the square of field itself, we would have a stable vacuum; While the reality of the universe is that with being the Higgs field, the vacuum should be unstable to decay into a free parameter to produce Higgs boson's mass. So, Wouldn't it be better if the field potential is something other than the square of the height of the modes? 3-How can we have a static universe? Is that possible at all? You said that the cosmological constant entered to having the so-called Einstein static universe. The introduction of the cosmological constant by Einstein, however, was not entirely trouble-free and the solution is unstable, as this together with Hubble’s later discovery led Einstein to abandon the cosmological constant term. 4-In the early universe, for the inflation model in order to have the inflationary acceleration of expansion, the cosmological constant must be very large. However, the value of cosmological constant is very very small in the present universe. How is this contradiction justified in magnitude? (after all, there is only one Universe!) 5- Eventually, the reality of the world is field/wave or particle? The final reality of the world in QFT,in fact, seems to be the field, not the "particles" that are appeared from it. 6-Is it possible to present a kind of theory instead of the QFT in which the wave/field property has emerged from the collective behavior of particles? So that, it might even be possible to solve the cosmological constant problem! Yours Sincerely, M. M-Fard

[@허유선-y4m]

I don't understand all. But I think I can understand all in the near future. You are a good lecturer.

[@shinymike4301]

That opening...you did that on porpoise!

[@Cygnus__X1]

can't believe i'd ever be so excited even for the upcoming Q and A!

[@Jornandreja]

Are all particles entangled with the single wave function of the universe, even particles that aren't entangled with any other particle?

[@AllTheGoodNamesGoneReally]

As I understood it, in fact everything is entangled in the wave function and the main problem with measuring specific entangled particles is to reduce the entanglement with the rest. Can't express it better.

[@caribooland2906]

I just wanna thank you for this wonderful lecture, please keep that kind of content coming. could you make a video about quantum gravity? Quantization? String theory?

[@llaauuddrruupp]

These videos are so good!

[@russellblack4671]

Thank you for making QFT seem approachable. Very well explained. One minor correction at 35:30 - potential energy of a simple harmonic oscillator is proportional to k, not k^2.

[@igorjee]

This is my favorite episode so far. Thank you Sean! 42:49 Question. The string metaphor helped, but I still missed a few steps. Is there a better way to qualitatively understand why are energy levels discrete and equidistantial without having to go through the solution of the wave function of the modes? Looking forward to the part where you explain the interaction among quantum fields. I my naive mind they exist parallel to one another, in a kind of Descartian pluralistic way, which is obviously not realistic :) My guess is that they can be connected through spacetime or maybe mass or equivalent mass, as indicated in the potential energy equation. Waiting for the next episodes to see if I guessed right :)

[@ToriKo_]

I definitely can’t keep up these last few episodes

[@jimsmindonline]

This is getting to the limits of my maths, but you're done a great job explaining it in a way that makes it easier to understand than a lot of explanations I've heard. My question would be at some point could you talk more about the physical experiments scientists are currently doing, especially those on the cutting edge. For example I find it hard to visualise how quantum computers physically create entangled Qbits.

[@daydreamer05]

I'll not compare you to my teacher nor to someone else, because you are absolute 👌

[@alexcherfan7762]

Thanks for all this wonderful and informative content Sean. You're awesome for doing these. Plus, this is the fist time EVER and I'm not even kidding, that I've seen a youtube video with 0 dislikes. Congrats, even the trolls love you. Haha!

[@AZ-vy4gl]

Thanks for taking the time to do these videos

[@TetonGemWorks]

I am watching these so you CAN put ideas in my head! Thank you sir. If we watch all the videos and Q&A sessions, can we get a "Licensed Quantum Mechanic" shirt?

[@jacquessmeets4427]

correction: at 33.00 he states that all energies (kinetic, gradient, potential) per mode are proportional to the square of the height h. This is true for the graient and potential energy. The kinetic energy is proportional to the square of the time derivative of the height h. This is exactly what is required for a simple harmonic oscillator.

[@juanlizarazo2307]

Dr Carrol, thank you very much for this video series. I have a question regarding fields, and hope you could address it. If what we call a particle is a perturbation on a field, then the speed of the particle would be determined by the field, just like the speed of a wave is determined by the media in which it travels. In your lecture, you reconstruct the particle-like behavior by adding an infinite number of planar waves. Wouldn't the speed of those waves, and thus the particle they form, be determined by the media?. In this case the media is the quantum field. Could you give me some pointers of where can I find the answer to this. Best Regards.

[@AllTheGoodNamesGoneReally]

Yihaa! Home from work and a new biggest idea waiting! Nice!

[@Chris-bm5qd]

It's important to support the sciences to keep guys like Sean happy, or they might decide to turn the rest of us into dust.

[@camniv1234]

Thank you so much for these videos. I am ashamed I made it through a physics degree without this insight into the equations.

[@tomutube3138]

Fantastic series! I am really looking forward to every new video! Dear Sean, I have a few questions which I hope you'd consider addressing during the Q&A: 1. If I understood correctly, since each field mode is an element of a Hilbert space, we could as well described it in a particle number basis, i.e. a superposition of modes that have a definite number of particles. This alternative basis seems much simpler to me: no harmonic oscillator needed, no (absolute) energy for vacuum, and a countable infinite number of basis vectors instead of an uncountable number. Why do we complicate matters with the harmonic oscillator? Is my particle number viewpoint overlooking some aspects perhaps? 2. Since the Schroedinger equation is linear, am I correct in assuming that QFT is a linear theory (with a rather complicated non-linear potential 'landscape' but only involving linear operators)? If so, why don't we try to solve the system of linear operators instead of dealing with path integrals? Path integrals, while pretty, just seem to be complicate matters by turning an operator inversion into an infinite sum/integral which may or may not converge. 3. Since free fields don't interact, does it make sense to talk about particle number for free fields if we can't observe them? I always imagined the definition of 'quantum particle' to be intrinsically linked to a unit of interaction between fields. Am I misguided here? 4. In a previous video you mentioned that some people object to Everett's many worlds view because it is unclear where the (Born?) probabilities would come from. I didn't quite follow that point. Wouldn't the Born rule follow from the inner product in the Hilbert space as a posteriori probabilities? I surely misunderstood something. If I did, are there any (non-philosophical) limitations to Everett's many worlds? Many thanks again for making this series! The unique viewpoints that you bring to these big ideas is very refreshing. Tom

[@gilbertengler9064]

Just excellent! Thanks a lot👍 Please go on explaining the things so clear.

[@hippopotamus6765]

I'm completely exhausted just trying to keep up. I'll have a lie-down, a think and run it again soon. It's addictive..

[@samuelj5890]

yo this is a really good video, concise yet still a great explanation. i beg of you to bring out the next episode soon, my particle physics exam is only in a couple of days :)

[@kidmohair8151]

"languorously changing"; it is not often, I suspect, that "languor" has been used in QM btw I was quite taken by the mid-water thumbnail (as others have been) the tie-in is not lost... O, those languorous waves... until the hands disappear above, in a non-linear fashion 1:09:03

[@Walker-ld3dn]

Damn. He is sooooo good. Thank you, Sean.

[@iainmackenzieUK]

35:30 (Sir, I think the k is not squared in this equation: Energy of SHM oscillator = 1/2kx>2) It is not critical for your argumant of course, but just for completeness. (The omega IS squared later at 105:36) I am LOVING your videos. I look forward to them each week ( including the QNA sessions) Thank you so much for your time and energy. It is very much appreciated.

[@TheMemesofDestruction]

1:01:51 -- So in order to maintain our persistence, we require minimum existence?

[@pastrop2003]

Hi Sean, love your podcast, you should talk to Pascaline Lapeltier who is not only one of the best wine experts in the world but also a philosopher. You guys will have a blast...

[@roberthf1092]

Hi, I hope I'm not too late to ask a question about this video. Around 20 mins you start discussing a particular classical field and how to quantize it. What I didn't get from the discussion following is: how do you choose a classical field which, when quantized, will lead to a specific particle type? If e.g. the electromagnetic field leads to photons, which classical fields would lead to electrons, neutrinos etc? Do you e.g. have to "design" a classical field which has to have some set of required properties?

[@im_piano]

This lecture broke me. I was mostly keeping up before it.

[@petercarlson811]

How I have waited for this episode... XD

[@andyeverett1957]

Standing ovation, thank you.

[@Shalkka]

This pushes forward understanding of very important physics that is very valuable contribution. With the term "wavefunction" I have long taken the stance to maybe dance along and maybe I will get the meaning from context. But it seems digging down and still having a mysterious aura of qunatumness probably isn't appropriate. When does a function fail to be a wavefunction? I would imagine it involves things like being continous and not having corners. I have some incling it involves having an imaginary e exponent in it somewhere. So when a physicist invokes the letter psi and uses the term wavefuntion I am left wonering whether there aer some extra "magical semantics" I should read into that. Letters f and g are commonly used for properly unused "unknown/undefined" properties functions. So if I present "Consider the particle having wavefuction abs(x)" have I somehow failed to provide a wavefunction? It is somewhat hard to keep track of what the type signatures of various things are and they seem to changing a little. Getting it exactly concret would risk being stuck in technical details but when the subject area might no tbe intuitive it can be hard to separate out which is a hard unintutive turth that needs digesting and which is an obviously wrong interpretation that needs discarding. The term "Non-interacting" seems to have a meaning-option that is very different that seems to really go on. If have a pool of water what happens in one part of the lake affects what goes in nearby parts of the lakes and this could be called "self-interaction" water acting on water. And one could argue that such watermolecyle to watermolecyle interactions are how waves propagate. Howeveer water also has the property that if you throw 2 stones into it one at a time and record the wave patterns you get the same wavesum than if you threw both stones at the same time. In the context of where we go from wavesnapshots into two waves passing by each other we kind of need mechanics on how the next wavepattern is dependent on what the previous wavepattern was. One could think that "interactionless" version could include a scenario where each individual point did its thing without regard to its neighbours. "Neighbour going in positive direction, I am going to keep going on negative direction because that is what is part of my swinging". When doing a fourier transform into modes the imagination pointers can point to a wavepacket-like image. When a human things of a sound they probably think of a short shout. The modes are associated with frequencies that "constantly stay on", one keeps on shouting the sound. If you shout a short pulse early or late each will have a single unique correct fourier transform but there is no time dependency in those composite modes. A lot of listeners might implictly be adding position or timing information to what the total representation is. I am myself unsure how the same wavelength but different phase is handled. That is 10 hz starting from 0 and 10hz starting from top of peak are probably different modes but it could make sense to handle same hz modes in the same direction in the same "bundle". And this might happen via making "amount of frequency" complex where different phases correspond to how much that phase off-set is included (so 1+0i and 0+1i combine to some multiple of 1+1i which is a scalar rotated by only 45 degrees). Whether this is a connected or unconnected imaginarity source I can't tell. It is unclear how the energy of the modes realtes to the energy of the composition or superposition of the modes. If same formulas (kinetic, gradient and potential) apply to the actual wave and the modes and the mode decomposition preserves the wave then the energy shouldn't change just by decomposing it. Mathematically a function f(x)=0 can be expressed equally well as f(x)=sin(x)-sin(x). Even if wiggliness costs energy and sin(x) is undoutably wiggly it would be inappropriate to add the absolute values of the wigglinesses to get the total wiggliness. Antiwiggliness cancels out! I guess a more formal compaint woud be that psi^2+phi^2 is different from (psi+phi)^2. It is also not clear why that you can do fourier transforms means that you can only observe one mode. I can fourier transform a sound file and when a sound file enters my ear I don't have to pick a frequency to listen to I can use the full range of my ears. And the decoherence ideas could be employed in that the observation is not randomly picked. It is super confusing that the colored lines loan the x axis but do not loan the y axis form the white drawings (and the confusion of assuming x is space instead of h is hard enough as it is). The y axis is amplitude rather than energy. Or was the point ot say there were negative energies? The abstract hard things seems very interesting. Why would the amplitude need to spread out like that? But since it does spread out like that wouldn't that spreading define a number analogous to kinetic energy and gradient energy, say heigth gradient the amount of amplitude lost when moving over a small height difference (in the middle of and sides of yellow the height gradient would be low but where green and yellow intersect it would be high on yellow) There seems to be missing information why f(x)=0 is a dissallowed attempt to be a low energy state for a mode. Kinetic energy is 0, gradient energy is 0 and any number proportional to height is 0. I guess any other mode has a positive change to get a value for any x (minus some crossover points) . But if you don't pluck a string it's a perfectly fine string. Or does it mean somehow that any energetic entity touching truly quiet place will leave it echoing that is not proportional to the touching?

[@navidazadi4280]

Dear Prof. Carroll, I have a few questions, I would be most grateful if you reply; 1- Why you made each mode into "particles" and not a single particle? why this interpretation? For example, can't we consider excited energy state of n, corresponding to n paths/trajectories of just a single particle? instead of "n particles" interpretation.

[@lightningt12312]

Does the amplitude of the wave function have any kind of meaning per se, like displacement for water, or should it just be seen as a mathematical construct to square in order to get the "probability configuration" of observing particles at specific locations?

[@barefootalien]

That's pretty much exactly the question whose answer is the various interpretations of Quantum Mechanics. In Copenhagen, it is precisely that: it's a mathematical thing that you square to get the probability of a certain distribution of matter and energy. In Many Worlds, it is the weight or thickness of a particular branch of the wave function of the universe. In Pilot Wave theory, it's kind of like a description of the surface of a non-local version of water, with particles bobbing up and down on it, guided this way and that by the wave function as it moves, etc.

[@hattielankford4775]

18:58 let's acknowledge how huge that is that he had to clarify in the right direction.

[@vivekagrawal92]

Very nice introduction of field. I had one doubt the electron produces electromagnetic field. But electron is again particle of Dirac field. What produces Dirac field

[@BazNard]

Amazing videos. Thanks so much for making these.

[@rickcygnusx1]

Hello Dr. Carroll, as with many others, thank you so much for these lessons (actually, thank you is not enough!). I have a question on 14:15 , if we plug in a scalar field function into Schrodinger's equation and then square it to get the probability, should we get the same probability at all points in space regardless of the value of the field (because it's a function of a specific scalar field, or specific field configuration)?

[@joyfergie9532]

Thank you, Dr. Sean 🙏