The Biggest Ideas in the Universe | Q&A 9 - Fields
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- เผยแพร่เมื่อ 23 พ.ค. 2020
- The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody.
This is the Q&A video associated with Idea #9, "Fields." I go once more through why the simple harmonic oscillator has quantized energy levels, explain how the Dirac equation and Klein-Gordon equations are not relativistic versions of the Schrödinger equation, and mention entanglement and the Reeh-Schlieder Theorem.
My web page: www.preposterousuniverse.com/
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#science #physics #ideas #universe #learning #cosmology #philosophy #quantum #fields - วิทยาศาสตร์และเทคโนโลยี
Sean Carroll NEVER makes me feel stupid. He doesn’t patronize like so many others but he just elicits intelligence and critical thought from his students. This mans contribution to teaching and higher thought is historic and I believe he is at the forefront of conquering ignorance and lack of education in our species. LOVE THIS GUY!
Immediately clicked 'like' at the beginning when Sean said he wasn't afraid of using a bit of math to bridge the gap between fluffy discussions of physics and videos down-right dense with math. Thank you.
Just want you to know, Sean, this show is everything for me right now.
Same. This voice brings reason to all the insanity that is life
Mistake at 11:10, caught by Patric McHargue: it should be -b^2, not +b^2 in that expression.
If possible, please add a label to the video there. It's been a while and I just spent the last 10 minutes trying to prove to myself that I still remember how to square a complex number. Thanks!
@@ChristopherCurtis Time well spent.
School boy error
Raise your hand 🖐 if you caught that . 🚼
@@ssshurley 🖐
It has been forty years since abandoning an MSc for a degree in engineering. Thought I had forgotten it all, but Sean's delivery is as good as Feynman's. Retired now. Downloaded a bunch of maths and physics papers from my local university library and I'm trying to recycle myself back to the point I reached with the BSc. Funny thing is, the stage I bits were hardest to revisit. Sean makes it easy.
yes this "in between" level of presentation is much needed and very appreciated!!!
Thank you. Top 5 teacher list
Dr. Carroll please keep these coming. I love the perfect amount of detail and math you use for us normies.
I really like the pacing of these videos and the just right amount of information for me.
I have been interested in physics and been watching related videos on TH-cam. I got to the point where entry level videos by most science communicators are too easy for me, but outright college lecture VODs are too hard. This series has been the first stop gap that I have not been able to find.
And his way of explaining really help me wrapping my head around some of the more difficult concepts.
Thanks for explaining the inclusion of complex numbers in the wave function. What a cool method to keep the probability a positive value.
Thanks sean for doing the math (maths in England ) absolutely love it wish I understood it better but I have to start some where. Love these lectures I have recommended it to lots people. Thumbs up 👍
Sean please write quantum textbook, I am a physics undergrad and your GR textbook is the best
Quantum mechanics has great textbooks as is and great set of lectures available online!
QFT is so much cumbersome mathematically and worse understood and so difficult, that you really want to have someone teach it to you and go to university for it IMO.
He has mentioned in one of the last videos that he is in the process of writing an undergraduate Quantum Mechanics textbook.
@@randeepsinghmatharu9071 I hope Sean will continue with a textbook on qft afterwards.
Disagree
glad to hear, i just bought it. I am not in school, just reading for fun
Good to see you keeping your head above water there, Sean! ;-)
Thank you for these videos Mr. Carroll. You have really re-ignited my interest for physics.
Thanks for saying that the last video was hard, makes me feel a lot better about struggling to understand it...... :))
cat entering the room and meowing is adding perfection to perfection
Good on you for making content that educates during this time. Being productive during rough times is a good trait.
Enjoyed so much! "QFT is hard" You've done a great job of describing it in a way that makes it easier to imagine.
Thankyou for your time and passion and briiliance.. I love your emotion in explaining your passion
I'm a professional physicist, yet I'm learning so much from these videos! One confusion: how can the spatial modes of the field be entangled if you can write it as a superposition of momentum modes? Shouldn't entanglement be independent of basis? Thanks for all the effort on these! 🙏
What do you research as a physicist?
i like the explanation about the quantum harmonic oscillator in this video, very intuitive
Great series that goes into the concepts in greater depth than a purely popular presentation. Helps fill the gap, with Lenny Susskind's lecture series being the next rung up the ladder.
Wonderful work, thank you for hitting this note.
wow great content, thanks for all this work Sean!
If there is a positive to the pandemic it's that I can listen to podcasts from Sean Carroll, Brian Greene, and Lawrence Krauss. These sessions represent what is great about the internet.
I never heard of Laurence Krause. I am going to for out. thanks
@@davidjordan5175 Google "Origins Podcast, Lawrence Krauss. Also, before he retired from Arizona State University, he headed up the "Origins Project" and, much like Brian Greene's World Science Festival, it hosted many scientific discussions with leading scientists from various fields. Krauss is an American-Canadian physicist who completed his undergraduate degree at the university at which I am now teaching (although I am semi retired).
Dear Sean Carrol, thank you very much for this series. I studied physics and doing my PhD now and I'm realizing more and more how sloppy the quantum mechanics and quantum field theory courses at our university are. And I believe to know why many QM/QFT courses are so sloppy: Because they are immensely rushed to get to "applications" as soon as possible. Of course in this rush there is no time to think about foundations of quantum mechanics. In the end the university has produced many Master or sometimes even Bachelor(!) students who are able to do QFT calculations without understanding it on a deeper level. Of course, most students leave academia unsatisfied as a result.
It seems really confusing to me how people can do QFT calculations without understanding what’s really going on behind the math at a deeper level, especially at university level
@@ToriKo_ I mean this is basically the difference between engineering and math right? engineering is knowing that you can multiple both sides by dx, mathematics is knowing that it's a hack that only works in specific situations but both will arrive at the same approximate answer anyways
Sean you are SO right about the gap! Please continue with the mathy derivatives!
Awesome!
I'm studying physics at KIT and just started masters degree.
I've nerver heard of the Reeh-Schlieder Theorem and it just blew my mind.
Definately have to read into it.
Thank you very much sean! :)
3:00 There is indeed a gap, and you're one of the few who fill it!
Thank you for the big explanation at the end and answering my question. The end of the videos are always far out!
You go Sean Carroll!
25:25 Thank you for answering my question from the last video
Fantastic videos, I especially love the approach "do not fear of math", and indeed usually there are two kinds of materials to learn more about these for "the average guy": one is the "no math, it's the brain killer" one, and the other, which is more targeted people learning this in universities and such. But not too much between these two cases ... I love the kind of "middle way" approach of these lectures! :D
Dear Sean : thank for your good explanation, as you know I’m experimented physicists, and I explained, things in my own language, not mathematical language, so thanks for your hard work , hope to see you soon.mehdi
There's a theory that there's only one electron. This actually goes hand in hand with field theory. That is, the electron field is THE ONE electron and the appearance of a local electron is just a manifestation of local interactions with the electron field.
This is akin to the surface of a lake, think of it as THE electron field, now throw different size rocks at different strengths on the surface in different places and these are the other interactions. But it's still one surface, one field, one electron.
Am I crazy?
As an advanced arm chair physicist, this is the point where I remember that I don't know ish. Lol
I was with you all the way up to "Simply"
Superb!
We love you Ariel.
Sean, really enjoying this series, and Big Picture and Particle at the End ... Currently at ch 9 of Something Deeply Hidden. I'm wondering if MWI can do better (eventually) about the question of how many worlds exist? (for example, p163 talking about decoherence of a continuous event like the location of a particle hitting a screen, wasn't clear how the choice of how many divisions to make of the continuum should be up to us?). Also, p172 concept of how branches exist simultaneously out of contact with our own - I'm hoping eventually MWI can say more about this. Anyway, enjoying the book and hope to get to From Eternity to Here soon!
You're like a fuckin rockstar, you definitely play a role in my passion for physics! and had a big influence on what I chose to study. The coolest mad scientist in this day and age
2:30 Sean tells us how and why these last few vids have rushed thru and assumed knowledge of some of these new math ideas and physics concepts.
11:15 continued
26:00 “so the point of that was...”
27:30 hammering home the difference between Phi and Psi, and how to interpret E, element, maps
Before 49:00 I think was important too
49:00 entanglement, and reexplaining what exactly we mean by psi(x[vector]) - sum over phi [sub k vector] (h). How the modes are plane wave that stretch out over space, and how a QF is not a harmonic oscillator at every point in space, but a harmonic oscillator for every mode (wave vector) (plane wave that stretches over space).
1:04:00 criticisms of QFT
Okay so I’m going to say something that’s likely dumb because I don’t understand a lot of moving parts, but at least I’ll be able to have a written form of an idea that is forming in my head.
So it seems like we have a way of talking about the universe in QFT that consists fields in superposition? of different wavelengths and amplitudes?, and in 3D space it might be useful to think of these as plane waves. And the idea is that we are allowed to do this because we know we can represent any complicated wave (that the universe may be in at any one time) as a sum of sin waves, which we know from the Fourier transform?.
And this is why we can get ‘arbitrarily close’ to any psi (star) state, since we can continue summing component parts of the wave form to get diminishing returns
And I should add again that this is probably wrong in a million different ways, and I’m probably confused in a billion more different ways
OMG, I never understood before now the contribution of the gradient energy to the ground state. Why wasn't I taught this??? Thanks, Sean Carroll :))
Amen yes amen yes lots of us know some Calculus and are willing to use it!
wow, just great. had to take this vid in bite size chunks though
note for myself
11:23
28:18
49:27
19:09 replace x with h to get to modes from simple harmonic oscillators. Wave function can be constructed from perpendicular modes (like vectors). Modes are perpendicular if the sum of their overlap is zero. This combined with the restriction that the integral over h of the probability of being in any state has to be equal to 1 determines the shape of the modes, and the discreteness of energy levels.
Cool stuff
So I am watching this late at night. At 34:31 I hear a cat meowing outside my door. I press pause and go outside into the dark to look for it. After five minutes I find nothing so come back in, press play and at 34:34 I find out the meowing is from Sean's Cat, Ariel. doh!
Hahaha
I thought that was his baby😅
For SHO, V(x)=m(wx)^2 /2 = kx^2 /2. You tend to square the spring constant and to omit the mass.
Hi Shawn. Unclear how much you care to edit these old videos at this point but at 11:06 you made a mistake, it's -b^2 instead of +b^2.
Amazing series by the way, I'm learning a lot.
Amazing
16:50 yeah, I couldn't get what Hilbert Space is from Wikipedia. Decoherence is surprisingly a bit better.
Some book I read but don't recall explained that Hilbert Space is "inner product space". It simply has an inner-product operation defined on it, that follows the required identities of that operation.
@@JohnDlugosz Thanks. I know what that means in a basic mathematics sense, but it doesn't give me any intuitive understanding what that inner product means or why it matters. For example I'm not fluent in the math of Fourier transform but feel I understand quite well what that means.
Mathematicians denote complex conjugation by an overline ("bar"); the dagger is for matrices or linear operators (Hermitian transpose).
Thanks for this great series Prof. Carroll. I am a big fan of your lectures, Talks & books. But, I am now in my sixties, and although I am a (BSc Hons) science graduate, I do find some of the material pretty heavy going. This is probably because I never did advanced Maths, nor learnt Calculus, I'm sad to say. Explanations with words are always preferable in my case, but I always watch each episode twice anyway. Take Care & Stay Safe, with best wishes from West Wales.
It’s nice to hear I’m not the only one finding this heavy going
I want to make sure I understand this correctly:
1. In order to have "n particles" does every mode need to be in the nth energy state?
2. I'm not sure I understand how it connects back to "ordinary" QM. Do you treat a region of space that is supposed to have one particle as though it's a field with modes in the 1st energy state?
Professor Carroll.
I have a question about fields that apparently remains unanswered because is based on my own logic reasoning.
If there is a theory of everything or a grand unified theory, from a quantum field theory point of view, when all forces were still combined (if they were combined), then shouldn't whatever it was or still is, have a field of its own? I'm getting the impression that physicists think that when all forces were separated, that if it was indeed a field, that this field has vanished.
For a couple of months now, I've been asking around this question "Is quantum field theory missing a field? A field that determines at which temperature (combined with pressure?) and how much energy it needs, to separate other fields (gravity took a certain energy at very high temperatures and pressure to separate, the strong force a lot lower temperatures and perhaps already negative pressure, electroweak symmetry breaking a lot less temperatures and pressure, we already know the temperature at which the higgs gained its non-zero potential, but the higgs is very heavy, so I imagine the field itself separated before the strong force did, perhaps close to when gravity did, ... What if that field doesn't just do that for baryonic matter.... what if it does for transparent matter (dark matter) and energy? Physicists are looking for a theory of everything, I was just wondering on whether or not we are missing a field in quantum field theory, and yet both seem to have the same objective, solving another piece of the puzzle. Mine sounds really simple, i'm just wondering if the field still exists that may have been there when all forces were combined, and I postulate a function of that field. Not bad for somebody without a high school degree huh 🙂
Obviously the above is a question, but when it comes to that field i'm postulating, do you think it's also a scalar field?
Please continue to sow the show the Maths in detail.
50:00 thanks for clarifying that Φ as a sum of modes is not the same thing as a simple harmonic oscillator at every point in space. A lot of what's going on here seems to be about jumping between the frequency domain and the spacetime domain of a Fourier transform. When you talk about emergent spacetime, are you trying to define physics directly in the frequency domain?
Yes, that was great!
What makes the Schrödinger equation so difficult to make it Background independent, and do you think this points to it being a wrong direction to go for a TOE?
Thaaaaank you!
Could the Reeh-Schlieder theorem resolve the black hole information paradox?
Just as charge, mass, and angular momentum don't disappear when objects fall into a black hole,
if the information associated with an object is part of the global quantum field, then it wouldn't be lost when the object falls into a black hole.
Hi Sir, I have a simple question. Inside a factory at the end of the shift a supervisor and his co-worker are counting the produced objects, the objects are approximately the size of a tennis ball. It is their daily routine,the worker counts the objects as he takes it from the production lot and puts it inside a bag. The role of the supervisor is to keep watch so that there is no mistake while counting. One fine day, before starting the counting process, the supervisor looks at the lot and writes down some random three digit number as quantity of the produced items, in short he assumes that the actual quantity would probably match with that number. Now the question is what are the chances of that actual quantity matching exactly with that random number?
Has Sean covered how the Hamiltonian operator is defined and how it works? If not, what would be a good reference to read/watch on my own?
Found it. For anyone interested, he mentions it briefly in the video about QM, at about 30 min in:
th-cam.com/video/BJlkkOIFjx4/w-d-xo.html
But he skips the details, so for those of us keen on knowing more, I guess we should pick up a textbook.
I am a musician who watches this when I take a break from practicing. When I start. "Taking particleness seriously" I am going to tell everyone I know! I am not going to be holding my breath.
8:10 star is conjugate for scalars, dagger is conjugate of the transposition of a matrix
I think designing the nature in its basic concept as a field is great idea, but what is a field ? I think field is where energy is carried. As energy increases its density at a particular position we humans see a particle. Makes sense ?
Sean what about this Ken Wheeler guy(Theoria Apophasis)? What is going on with him?
Deravatives are simple and easy..even a blind mand can do them...and yea I am blind lol. So, shaun keep using the calc and other maths, I am currently a physic undergrad and would love to hear you teach calc, physics, and anything else you would be profficiant in those fields.
I had a bit of a problem interpreting the expression for phi(x) at 13:22 :
Sum(phi_k(h),k) (meaning sum over k)
Firstly, not sure how it depends on x,
Secondly, are the h values the same for every k?
Something like:
Sum(h_k*k(x),k) where k is phi_k with 'height'=1
would feel more explicit to me.
Or would it even be Sum(phi_k(h,x),{k,h}), where you also have to sum (or if h is continuous, integrate) over all values of h?
I am not sure, but i think that sum(phi_k(h)) is meant to mean sum( C_k(h_k).phi_k(x)) where there is only one weigth h_k for a particular mode (so no sum over h), but not all weights are allowed (C_k(h_k) = 0 if h_k is not a natural number)
are "fields " intended to be something intrinsic to reality? or are they just a mathematical construct/method/concept in order to perform calculations and make predictions?
and then he says, "lets invent a field ... "
Doesn't that theorum thing violate causality though? It's not possible to force stuff to do stuff is it??
When you "operate on Bob's spin," why does this not replace the entanglement between Bob's and Alice's spins with entanglement between Bob's and your spin? Why is this not decoherence of Bob's and Alice's spins?
wow. that made me want to give up work and go back and do maths. And the physics. And then quantum field theory. And then make Taj Mahals everywhere.. and then... and then ... and then ... :)
Why waves instead of saying these fields pervade every iota of space and all reality? Is the concept of the movement of waves fundamental in the math that was worked out?
10:42 can't believe a physicist doesn't know by heart the formula for the square of a complex number… there's a minus sign: (a + b i)^2 = a^2 - b^2 + 2ab i
OK. Alice might be able to prepare some system so that some spin is up, or prepare a whole bunch of them, and this has consequences for remote systems that are in entanglement with her lab equipment. The question is though in what way this is reciprocal: What if Bob "at the same time" (whatever that means), and not knowing what Alice is doing, "forces" some spin to be the way he likes it. Who wins? Or, how is it decided which actions determine which outcomes? The same question could be asked about "mere" observations: Alice makes a measurement and gets a certain spin state, and Bob also makes a measurement. The next day they compare their results and find out that they are always complementary. There seems no way to establish a direction of causality, if there is no real way to establish "objectively" a temporal order. Apparently a measurement or observation is also at its core an action upon something. The simplistic way out seems to be that everything included Alice and Bob's actions are predetermined (would that be super-determinism?).
An aside: Let's not even talk about magic of the kind: some action on some wave function - resulting in thunderclap, smell of sulfur smoke - and voila a Taj Mahal appears on the moon. I am fairly sure that this is complete baloney, and remains nonsense when you put the words "in principle" in front of it. Most things that we may dream up to be plausible and believe "in principle" possible (within some logically coherent theory) are almost certainly - in principle or not - impossible in reality.
Basically, you are expressing Einstein's objections to QM so you are in good company. QM is spooky action at a distance. If the moon is not measured by somebody it may not really there and on and on. Einstein all but said he would never accept QM. Dont even get me started on Many Worlds.
Is spacetime a field?
17:00 Did Sean Carroll just say that Wikipedia is too technical? I didn't expect that. :)
Seriously, I love these videos, but my brain turns off when you use math. In fact, I think I left my brain behind a few videos ago. I hope it can find its own way back home, someday. :)
how to define gradient energy and why do we want "reasonably" sized? I have solved S.E. for Eigenstates w/o regard for gradient energy and get ground energy Eigen state clearly exhibiting distribution he shows for ground state. I just want to understand this idea of gradient energy, I understand gradient but not gradient energy.
Was explained in his earlier videos - basically the change in any function with respect to position. (squared).
at 11:00 that should be -b^2 not +b^2
Hey, great series but my question is about the piece of equipment do you use to write like in a black board. What is it? (My wife work as a teacher and it would help her a lot) 👍🏽
I think in the Q&A1 he adress this question . Go check it out .
Ariel is meowing because she wants to be reassured she will not be used to demonstrate quantum entanglement
Help. Someone rescue Sean. He's drowning. :D Good thumbnail.
Perhaps there is another field that causes gravity. This could be where the dark matter is. Maybe there is a second field that causes gravity, where an excitation that doesn't require mass as a mechanism to warp it.
Alice can control spin
Alice signed up for a spin class at the gym?
Does Reeh-Schlieder then mean that any tiny little in guy somewhere out in space can cause a glitch so that the whole universe is destroyed?
So why we are not doomed yet?
Don't tell me anthropic principle.
I think, in order to be able to do so would require this guy the effort of creating a complete "anti - universe" to begin with, and let it collide with this universe. This is because this guy himself is also internally entangled in exactly the same way, so in order create a "localized" anti- universe, he has to create a complete anti-universe. This ignoring the complicating fact that guy himself would by definition be part of this same universe so this "actor" cannot be described independently. (Which by the way is the general cause of the general qm uncertainty/measurement issue; completly measuring something requires creating its exact anti-somthing, and that can never be acheived completely without loosing all entanglement (and therefore all future probing) of the system
It is hypothetical and cant be done. Dont worry about it and you can sleep in peace.
Ariel, Caliban... Does that make Prospero?
at 11:10 mark, isn't: (a + ib)^2 = a^2 + 2iab - b^2 (note minus sign before b^2)
Oops, you're right.
@@seancarroll Whew! (Pat stops shaking) I'm looking forward to the remaining episodes.
Brian Greene took down a whole episode of Your Daily Equation (#24), because of a v small mistake near the end. But none of the viewers spotted it before he took it down.
Why can't I think of quantum fields as one quantum harmonic oscillator per point in space? Sure, they are coupled and the math is harder, but why not? Will this not give me the right physics?
If you think like this , and then add up all the spacetime points in all the Universe to make a uniform spacetime then that means that you will add up all the harmonic oscilator per points. That will get you "a mode" of the quantum field , meaning a configuration of the quantum field. A quantum field is the sum of all "the modes" that a field can have in the entire Universe.
Simply put it: If you think like this , you will get a specific configuration of the quantum field. It will not be the real shape( configuration ) of the quantum field itself. One example of this view its wrong its the following :It is like seeing a circle ( because you focuse on a 2 d plane ) when in fact the object it's a sphere( if you see all the picture in 3 D).
@@cazymike87 Sorry, but I don't get this. Why should I get only a single configuration. The only difference between the cases (using one oscillator per mode vs one per point in space) is that the oscillators are uncoupled vs coupled. Right? I don't get the analogy either, better stick to the actual math.
Either you begin from a particle and moving to a quantum field or backwards from a quantum field to a particle you will still get just 1 mode of the quantum field.
For a particle and a scalar quantum field:
In space you will assign a position for a particle using a Complex number( a+bi) . Then you do (a+bi)sq2 to get the probability ( a Real number) finding on that spot. You make a plot with this Real numbers and what you get its a mode ( a plane wave, a mode of the quantum field). Why? Because of the probability . You only get one plot ( a mode , a harmonic oscilator ) because you considered the measured probability as a SINGULAR result ...and this its not the case. Bassicaly , your mistake is that you chose the "space point" by focusing on a given probability ( and then you plot it and get that harmonic oscilator).
--The same for a scalar Quantum field. You must decompose the Q. field into modes in order to have a SINGULAR position for a space point like particle. And then those modes( harmonic oscilators ) will have a SINGULAR position in space because you use the probability to capture a particle.
Quantum mecanichs is probabilistic at its core !
@@TheOneMaddin
This is no doubt the wrong time to comment ie I should have commented at quantum particles and not fields. In the delayed quantum eraser experiment, as it uses photons, and photons moving at the speed of light, is it therefore true that as the photons are traveling at the speed of light they experience no time. Therefore anything that happens to a photon would happen to it instantly (especially if it's some kind of distributed structure, something happening at point (a) on that distributed structure could be "communicated" instantly to point (b), because the photon experiences no time. Therefore it looks to us as if the photon has communicated backwards in time because it's instant and we're moving forward in time at unrelativistic speeds. (Like a train pulling out of a station, you're in another carriage in a stationary train, and for a moment you think you're going backwards, but it's the other train going forwards.) (The final) therefore there's no magic. Is any of that right ? Happy to know how this is wrong ! Hope y'all well
I have heard that if quantum tunneling occurs in the Higgs field and the boson migrates to a lower energy, we are done.
When you say that fields are not made of anything, that seems to be at odds with the opinion of other physicists. David Tong of Cambridge says that quantum fields are actual fluid/-like substances that fill the universe and that what we call particles are vibrations, or disturbances, of these fields. Prof John Spence also says that he doesn’t know what an electric field or magnetic field in a vacuum is made of, and nobody knows, since it’s a vacuum and nothing is there, or so it seems. Yet something is there.
I love this series....but I will never understand it in a million billion years x Pi
What I find funny/confusing: In the Schrödinger equation the part of the hamiltonian which is interpreted as the kinetic energy is the "gradient energy". Perhaps another case of physicist being bad in naming things. :-)
10:35 - You have an error, there should be -b^2
Overall great content, but I find myself wishing Sean would be clearer on math notation. He purports to give math equations, but as written they often are extremely ambiguous. Makes the whole video very frustrating even for people with excellent math background.
10:50 -b^2, no?
Correct. I'll let him off. It's a test to see if we were paying attention!
Anyone else listen to this while mowing the lawn?
5:00 and amplitude is height
11 people dislike that you’re not paying enough attention to Ariel.