Erratum: As a couple of people have pointed out, there should be an additional factor of the complex conjugate of the wave function in the expectation value formulas 48:00. See e.g. en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)

When he does "silly things" is a reminder for us that he's human after all. Love from Chile. Thanks for being such an amazing educator.

Drawing a rough oval shape and saying "so, here's reality" is probably the coolest move a person can make.

A little after 4 pm here in Wales, and I just got back from a visit to the Dentist. What better way to take one's mind off sore teeth & gums, than a new episode of Biggest Ideas with Doctor Sean. Thanks once again Prof. Carroll, for making the World a better place - or one of the Worlds, anyway !!

Yay! Thanks, Sean. You absolute rockstar.

"Something Deeply Hidden" Dr. Sean Carroll, will be in my book collection, thank you so much for training us. ❤

Sean Carroll is really a philosopher who does physics!

Sean "never makes a talking mistake" Carroll. Perfect diction, tone & intelligence consistent over time in many, many informative cutting edge physics videos. Many thanks

I really wish advanced undergrad physics class include information like this. I think it's almost always worth it to have a basic understanding about how the subject of interest fit in to a bigger framework of physics

Thanks for the latest video --- I guess you must consider penning a book entitled "The Biggest Ideas in the Universe", with each video being a chapter, or series of smaller books with each book covering a single video!

I believe it was on an episode of Veritasium that a theory proposed in a peer reviewed paper says that, and I'm paraphrasing here, that life if an emergent property of entropy. The idea being that in the aggregate, entropy is more efficiently increased in the presence of life as opposed to the absence of life. If we look at the floor of a forest, the immediate impression is one of disorder, or to rephrase that, in a state of high entropy. Where as if you review the photographs sent back from mars via the various rover missions. The surface of the planet seems to be in a relatively low entropic state. For me this was a very important revelation as I've been wondering for several years now as to what property of the universe it is, that provides the needed systemic or environmental pressure so that life might emerge naturally upon a planet where the building blocks are readily available. We know also that our universe is expanding. And that this expansion is accelerating. Is it possible, that entropy is a naturally emergent property of that expansion? Measurement of that expansion has been rated at so many meters per megaparsec per unit of time. However, it seems to me that the only measurement we could actually produce a quantifiable acceleration is the acceleration experienced by normal matter we can observe. It seems only natural that spacetime, the fabric in which all matter resides, must be expanding and flowing past all the stars, planets, galaxies, etc. At a velocity that enormously dwarves the velocity we observe galaxies travelling outward from the center of the universe. An analogy to this would be a large object being moved slowly down stream by the rapid waters of a river. With only the compression or deformation of spacetime via the presence of celestial bodies of matter. Creating a kind of drag upon spacetime, that naturally transfers some of its kinetic energy to the normal matter of the mass in the universe. If this is true, then we have an answer to what dark energy is comprised. Additionally, we know that when massive objects travel through spacetime that the greater the difference in velocity the more massive the objects become. This is general relativity at work. So if spacetime is flowing past us, then does this not also suggest an answer to dark matter? As spacetime flows past galaxies, so to do the mass of neutrons and protons increase in a corresponding measure. This increase in mass being explained via the manifestation of quark/antiquark pairs within the structure of matter. Thus while locally the differential would be too miniscule to effectively measure, in the aggregate it all adds up. Thus making dark energy, dark matter, and entropy emergent properties of our spherically expanding universe. And yes I am aware that certain assumptions are in place in this description upon which we as of yet lack clear consensus. And there are additional ideas I've been kicking around lately concerning the interior of black holes, the big bang, our eventual heat death, and the ways in which multiple verses (as opposed to a universe. Differentiated from the multiverse idea by way of other verses not overlapping our own) eventually interact via massive gravitational waves which might be described as spherical shockwaves traveling outwards for all time. Eventually, if any other verses do, or have existed and have also experienced heat death, might not the interaction of these shockwaves produce ring verses of much smaller scale than our own universe? In other words these shockwaves intersect each other, and if in the aggregate there is sufficient energy, then perhaps torus shaped verses are the predominant form of verse formation. If this were true, and there were a sufficient number at a high enough density, then the overall universe might be something far more akin to the patterns we see produced on the floor and walls of a swimming pool when light shines through the waters surface and there are enough waves to produce seemingly random peaks and valleys. If this view of the universe at large is correct, then it also suggests an answer to the nature of the big bang. Within our uniformly expanding universe, newtonian laws of physics provide a means for the limitation to the amount of material any given black hole has access. This model however would be invalid in the swimming pool analogy. Suppose if you will that we have the presence of a black hole, in the relatively chaotic system of peaks and valleys, such a black hole might rarely have access to incredible amounts of matter upon which to feed. Presuming that such a black hole could feed until approximately an equivalent amount of energy to that present in our current universe. Then perhaps, via some mechanism this could produce an event such as the big bang. Just my thoughts and ideas on the larger picture of the cosmos. I hope you enjoyed reading this narrative. #endhatrednow

Your self-criticized writing while talking has improved over the course of this series. It shows here especially. Been hooked since the beginning, and I'm always looking forward to new releases. Keep em comin!

Your opening remarks, about how having a certain complexity causes things to happen that you never would have guessed, is a perfect explanation of why software is so difficult. And it also provides analogy to your vocabulary shift to a chunked-state representation: we discovered "metafunctions" in C++ templates, which were designed to provide parameterized types for making strongly-typed collections and the like. Turned out to be a Turing-complete language that developed its own idioms. That's an extreme example of how we strive to *tame* software: make it in layers, to produce a hierarchy of complexity. It's so hard to explain how to write "good" functions that express a _single_ level of complexity, and what we're trying for is just why "gas" is not wave packets: once you abstract over it, you need to stick to the items within the emergent description.

24:11 - Category Theory sneaking in, at least heuristically

This Buds for you SEAN!

Thank you Prof. Carroll. Your Mysteries of modern physics - Time, is one of the most mind bending audiobooks I've listened to. This feels like a good supplement to that. Learning physics is very motivating when trying to connect the big ideas to everyday reality and clearing up misconceptions.

*Love these series of Videos. Absolute masterpiece*

Dude is the finest science communicator out there, period. This Biggest Ideas series is absolutely phenomenal. He's in the absolute sweet spot of communicating these concept at just the right level of detail and sophistication for people who are huge fans of the natural sciences, but don't have the math/science backround to read and comprehend actual papers on this stuff. My top three: Sean Carroll, Sabine Hossenfelder, Jim Al-Khalili. I see anything by them I'm dialed in.

I love watching and learning this stuff. Really appreciate your videos my man!

Another super-duper video ;-) Love all that you do Sean!

Some people use the term 'reality' for that which is realised, i.e. within a 'mind' - and 'actuality' is what is actually 'out there' (outside of a mind) irrespective of the various perceived 'realities' of conscious beings.

Sean, thanks again for do this series!

Thanks for doing these!! Wonderful!

Simply beautiful...Can't be any better!!

This is such a great series and this episode is very very helpfull. Thanks a lot.

Great video!! Thanks Sean 😁

Okay prof. You're too dang fast... and i love every second of it ... im okay thinking "this week im going to get this one in" boom another one and im like "shit! Im dumb, im dumb, im dumb... hurry up this is basic shit get on board its one hour" ... lol this series has taught me more with out being to over my head than anything else ive ever come across... honestly thank you for taking the time out of your day to make these... it means alot to ppl like me who were never brought up with science and never pushed to see how amazing it is ... so many times in the middle of it i realize i need to learn advanced things but i have my own life and so many times i feel i get the gists so thats good enough?!?... then here you come bridging the gap... it may be nothing to those who know but to me its a perfect balance ... idk if you will read this but you have taught me so much, just wanted to say thank you 🤷‍♂️... youre a good dude

Hi Sean! Love the idea of emergence.

Your didactic is superb, thank you Sean!

Very, very exiting, impressive and inspiring! If only i could keep up..... will need to get your books and papers and watch all the videos again and again. Thank you for carrying us to the edge of the known reality which we once would have thought was well over the horizon. Kind of like the 'Beginning of Infinity' heh! We are all in your debt even if not anywhere close to your depth. Down Under

The centre of mass example being precious and the idea of being able to distil a massive amount of information to one small bit not being understood deeply is very interesting. These limits to understanding are never talked about in undergraduate physics.

Hi Sean, thank you so much for your lectures, I don't understand some but when I read books some of your ideas click and make more sense.

Hi Sean, I've said it before but you are a legend for doing these, they have really helped me through this difficult time and I'm sure I'm not the only one.. I haven't been able to afford to pay yet but am buying your books 🙂

love your "who cares?" approach to the semantic arguments ppl love to get lost in

As a physics (master) student in Leiden, I'm so sad I missed your Ehrenfest Colloquium in 2018. At the time, as a bachelor student, I only seldomly attended these because most of those lectures went far over my head. I've just watched the recording online, and I can conclude the same would have probably happened with your lecture. So in the end I'm kind of glad I have listened to it only now as a master student, after a QFT course and a whole lot more physics experience overall. It was definitely a great introduction to emergent gravity from quantum field theory, and I now also have a greater appreciation for Everett's 'Many World' interpretation. (If anyone else is curious, you can watch it here www.universiteitleiden.nl/en/news/2018/09/livestream-sean-carroll-gives-ehrenfest-colloquium by clicking on the livestream link at the bottom) I've really enjoyed your last few lectures of 'The Biggest Ideas'. Especially the one about Entropy gave me new insights and a more formal firmer grasp of the concept. In the past, I've mostly viewed Entropy as the Boltzmann entropy, with other versions as 'things that are the same, but different in interpretation'. Although I knew this to not really be true, I've never really looked into it and therefore never understood the other forms of entropy (nor, as it turned out, the importance as the concept as a whole.) I hope it can help me communicate the topic in a better way to students in the upcoming semester as a student teaching assistant for the 2nd year bachelor Statistical Mechanics course.

Are you going to talk about fractals and the feigenbaum constant in one of these videos?

This is one of the only physicist I have ever heard admit that theories they hold could be wrong. Honestly refreshing.

Amazing, fantastic

awesome, just awesome!

Awesome. Love the video! Thx

I'm sure this video is great but the gases/gasses thing just blew my mind. makes perfect sense now that I know but I don't think I had ever thought about or encountered that before.

Thanks for explanation ❤

Are you going to talk about Fractals???

You might want to call the "higher level" rules/laws/theories as "Meta-Laws/Rules". This is much like in chess: The rules governing the initial placement and movement of pieces is your "micro" laws and the basic concepts of strategy and tactics to actually play the game are the Meta-Rules. This keeps the two separate, since the Meta-Rules can vary in complex ways while the low-level rules are usually fixed/constant (speed of light, etc.;), as in chess.

So the mumuration behind you would be many to one (course grained) ie lots of birds into one mummur. And I guess in that case heterostructural because the mummur has emerged from the starlings? I love your talks Sean. They help me sleep as well as fascinate me when I am awake. I love the pace and the tap tap tapping of the pen. On so many levels - thank you. Also, as someone who has been run over by a non-dual realisation, I find your talks very meditative. cheers mate. (:

Interesting ideas. Good video

I once played of MIT game 'space-wars' at Stanford coffee house in which there was a bug -- the force law was 1/r (measured it using ruler and watch) instead of 1/r^2 and one could not establish a stable orbit making the game unplayable. Orbits failed to 'emerge'.

If you could talk about emergent gravity ( in reference to E.Verlinde's paper) in the Q & A session, that will be really great. Thanks in advance!

I notice the murmuration behind the professor. As an undergraduate TP student, emergence or how novel properties emerge from their lower counterparts (the sum greater than the parts) is something that has intrigued me for several years.

awesome video，compare to other too mathy ones, this one relatively easier to understand and very interesting

Thank you Professor Carroll for a wonderfully informative series. My question is (I have many but I'll settle with this one): Are there any hypotheses down the lines of the reason for emergent properties/theories being possible because of the necessary fussiness of quantum mechanics (QM) measurement? Or put another way, are there hypotheses that map the apparent necessary ambiguities of QM to existence emergent properties or theories? Or, in the broadest sense, are their any proposed ideas (from scientists, I'm sure philosophers have many proposals) at all on reasons for the existence of emergent properties?

This MT theory is so much more intuitive than the standard explanation for fermion behavior. Can I get some links?

I love the fact that, because of a worldwide disaster (Pandemic), we all get the opportunity to hear lectures from Nobel Laureates and people who are really at the cutting edge of their particular disciplines. There was previously no chance that AT THE SAME TIME, people like Sean, Brian Greene, Roger Penrose etc would be able to produce videos about their respective fields while the general public ALL have the time to take it in (whether we understand it or not is a different matter!!) So now, we have the "Perfect Storm". The experts have the time, the public have the time AND the technology is sufficiently advanced and available to allow this to happen. Thanks to the Coronavirus, those of us well enough can gain a whole lot of information. (Imagine if this had been the case in Einstein's time or even Newton's time!)

I am waiting for a video where you lay out the frontiers of large scale experimental and observational physics like LHC, extremely large telescopes, James Webb telescope, ITER, etc and what questions they will try to answer.

You can take approach to it as if classical definition was superior to quantum almost as classical cluster was a sum of all orders of magnitude. Then the clasical potencial describes reality that only matters and you treat wave even without intercepting the classical limit as a sort of partial integral of everything happening under the classical curve. I am sure you know how complex one must be to comprehend so much data at once. The classical limit is where we are rather we like it or not. The point is to eliminate all ignorance related to entropy but still be able to derive consequences of all this knowledge to fit to the classical potential slope and support it. Easy to say probably. With every next part of this series I see more clearly the awesomeness of the whole concept and I deeply appreciate it. Sadly it looks like we are very close to applying infinitesimal to this series. Therefore one must admit that much entropy was consumed over this grat treat marking the genius of its creator. Many thanks for that time.

The Blind Men and the Elephant by John Godfrey Saxe (a poem). Also, the four stages of scientific acceptance by J.B.S. Haldane (not a poem).

@Sean Carroll Love your stuff. What program are you using on the iPad to do the chalkboard. I need that for my channel. Also ever heard of Linea Sketch?

I like this episode Carol.

Question for Q&A: Regarding emergence, is spacetime something that needs to emerge from quantum gravity, or can it be skipped as long as you can describe its results?

Prof. Sean Carroll please make the next episode of 'Biggest Ideas in the Universe' on String Theory and M - Theory

Heres hoping Sean sees this lol Thanks!!!

Quasiparticles and theories which are using them are good examples I think. How the lack of an elektron could act like a partical and simplify the description of the system. Or an excitation could act like a partical. Or the excited electron and the empty lower energy state could act like a partical-antipartical pair.

A question: As quantizing both the classical theories of Sine-Gordon and Massive Thirring gives rise to a relationship between fermions and bosons in a single quantum theory, would there be any sensible connection to be made with supersymmetry, given that supersymmetry also reflects a relationship between fermions and bosons?

Hi Professor Carroll - I'm not sure if you'll see this seeing as it's an "old video", but I figured I would ask. Would you be able to add reference textbooks (your favourite, or "the best", books on the subject) to your descriptions at some point? These videos will be invaluable resources for people interested in these topics for a long time, and a comment (from you especially) indicating where people could go for more info, whether more formal or otherwise, would be incredibly useful. Incidentally, it would also be a way to plug some of your books (thinking Spacetime and Geometry for your videos on GR). Thanks again for these amazing videos!

With respect to bosonization, the kinks and anti kinks seem to represent particles, but also excitations (at least in sine gordon where particles are changing state). Is it then useful to think about the kinks as quasi particles like phonons for example? And is this a different kind of emergence, when the collective behavior of interacting particles seem to create excitations that also look like particles?

I didn't fully get the interaction between quantum and chaotic behaviour for Hyperion at around 1:01:00. I always just assumed chaos and quantum indeterminacy were separate realms but this is very interesting

In the Q&A video, could you talk about the difference of "throwing away" information vs "compressing" the information? As an example, is calculating the center of mass of the earth not compressing the information of all the individual particles? (vs. throwing that information away)

I'm always wondering how QFT approximates (in the limit) F = ma, F = kq1q2/r2, etc. Does it actually work out, or are we thwarted by infinities in the calculation? Also, how can you even have r2 when the positions are uncertain? And is it possible to derive V(x,t) from a wavefunction in a coupled field? E.g. I know psi of electron, can I then calculate V(x,t) for the photon field, or vice versa?

This is the second time I've awaken from a bizarre, science heavy dream, to find Sean Carrol on my TV.

Given the correct combination of atoms and molecules plus the right energy conditions in normal space, a pizza could strongly emerge from an oven ? Whether it is allowed pineapple or not remains a deep mystery.

great, can there be a theory which suggests why 'real patterns' may exist? under which conditions ?

luvin the hair :)

Thanks

I thought Emergence was essentially a phenomenalogical proposition. 'As above, so below' Co or mutually generative. So, the big question is: what emerges? A better model or concept for reality.

Question: If theoretically there are a semi- infinite number of 'spectacle-like' theories through which 'reality' can be faithfully observed BUT each have individual limitations, will it ever be possible to see the total of reality except by somehow discovering and then combining all such theories? Would this not be a semi- infinite or infinite venture? Or are we nearly there yet? Thank you for your amazing work.

thoughts on Deutsch's constructor theory?

WHERE DID THE ENERGY FOR THE UNIVERSE COME FROM ???

Is ehrenfest’s theorem why in a bubble chamber, a particle leaves a trail that appears to be a particle on a trajectory? NVM, right after that you answered it

1:18:58 Vamoooo Juan Martín viejo y peludo!

Is it possible to quantify or rigorously define how “simple” or “efficient” a theory is, maybe in terms of information? You didn’t explicitly mention Occam’s Razor but this seems implicit in the fine-grained, homeostructural category and maybe for the others too

The last few diagrams put me in mind of something that is maybe not the same as Strong Emergence, but looks a lot like it, and (IMO) does happen: your micro theory is incomplete, its domain is not all of reality, and you have a macro theory that works for some parts of reality where your micro theory doesn't. Then the macro theory might make accurate predictions that the micro theory can't, but only because you are in a situation where you can't, or shouldn't, use the micro theory anyway.

I like his audio-only podcasts because there's none of that blackboard writing things down business.

I hope I'll understand all these amazing things by the time I'm 500.

I thought you'd talk about emergent gravity at some point.

What about General Relativity as an emergent theory of gravity where the standard model or an expanded GUT would be the micro-theory. Think of Sakharov's ideas on this. This gets around the pesky problem of quantizing GR by consider it as an emergent theory analogous to thermodynamics compared with statistical mechanics. The gravitational constant G would be derived from this micro theory and they gravitational field would be distortions of the quantum vacuum. In this concept gravity doesn't exist and the level of particle physics but emerges at the macroscopic level.

Thanks Sean , perhaps maybe.

At 1:00:05 you talk about Hyperion not spreading into a blob of probability due to decoherence. I'm with you there. Then you go on to say specifically that it's being bombarded with photons all the time that are constantly observing it / branching the wave function of the universe. What about its own internal interactions? Thermal motion of its internal atoms, for example, or the constant electromagnetic forces caused by its various chemical bonds? This is something I've never quite gotten hold of with my mind... I've seen you answer this question several times, at the Royal Institution for one, and in a couple of other lectures Q&A sections, and what you said, to paraphrase, is roughly, "Not all interactions cause branching of the wave function, but there isn't time to specify which ones do and don't and why." Well... the upcoming Q&A video would seem to be the perfect opportunity! :D Did you just omit Hyperion's own internal observations of itself? Or do those interactions (or at least some of them) genuinely not cause splitting/collapse because of reasons? (Entanglement, maybe?) In either case, when *exactly* does an interaction branch the wave function of the universe, and when doesn't it? Or is it simply not well-defined due to something like quantum relativity? I seem to recall a passage in Something Deeply Hidden that mentioned that... but I think it was in the roleplayed conversation between father and daughter and less than perfectly clear. Still, something about what branches the wave function depending on frame of reference, maybe?

I am developing an emergent, mostly mathematical theory of cognition that is applicable to seemingly different portions of reality: nervous systems (of course), microbial life, genetics and epigenetics in the tree of life, immune systems... About consciousness and qualia, maybe they are emergent properties of cognition. I still don't know and have to think a lot more unless I get the kind of insight I had about cognition.

Question: Are our bodies composed of fields and wave functions on the most basic level?

Prof Carroll, you keep emphasizing structure, mapping in your videos. Are you secretly a physicist that uses category theoretical thinking in the background?

What a coincidence, two days ago I was talking to some friends about the nature of consciousness; arguing that I truly believe it is an emergent property of living matter. You mentioned consciousness briefly in this video but do you have any further thoughts on this?

Certainly the different domains need to match at their mutual boundaries.

Two things. First, as somebody who doesn't believe in reality, I usually phrase it by saying that "reality is hypothetical"; this can be formalized. Second, starting at 26:30 or so, you're drawing *commutative diagrams* in some category! I approve but wish that you'd have said something.

I spotted a small mistake in minute 48:16. The formulas given for the expectation values of position and momentum (x-bar and p-bar) are missing the complex conjugate of the wave function inside the integrand (for p-bar, the derivative applies only to the wave function, and not to its complex conjugate). Also, not sure if hbar has been set to 1, but if it hasn't, p-bar should have a factor of hbar.

12:35 Lenguaje 22:34 Maps entre teorías. 38:30 Universality! 46:55 Ehrenfest Decoherencia 1:03:00 ! 1:14:15 Ads/CFT correspondence

“Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.” - Arthur C. Clarke I feel the same sentiment towards Strong Emergence - which happens in reality or does not. Either way, it boggles my mind. To believe, understand, and possibly know that each of us is only a smattering of nougat within a colossal wave function and derivable from a quantized, basement-level particle physics seems irreconcilable with our subjective conscious experience. But what is the alternative? Invoke some goofy analog of the luminiferous aether?!? Science peters out around the edges (presumably because we're not done yet), but its core principle of reductionism is not soft around the edges - it's as crisp and well-defined as the monolith that mesmerized our ancestors in Clarke's 2001: A Space Odyssey. I'm particularly taken by the example of the 3+1 dimension Conformal Field Theory (CFT) being the boundary condition of a 4+1 dimension Anti-de Sitter (AdS) space. Makes me wonder if there's a philosophical analogy to be had - like abstract objects being a lower-dimensional boundary condition of the concrete. For example, many philosophers believe that number is the essence of quantity - that numbers are mind-independent objects and that a description of reality would be incomplete without their inclusion. Perhaps this so-called essence is profitably thought of as a lower-dimensional boundary condition. But so far, going from AdS to CFT seems more straight-forward than the other direction. It feels far easier to agree that gravity in AdS doesn't imply any contradiction within CFT, but I don't quite see how gravity is to be inferred from CFT - and it must be inferred if the emergence is to be weak, right? (It feels even stranger to suggest that an abstract object infers a concrete object. What's next - inferring an ought from an is?!?) Finally, is there any limit to the chain (or web) of inference? Is the 4+1 AdS just a boundary condition for a 5+1 Something Else, with another spectacular reality like gravity popping out from it? It's like turtles all the way up - like we could synthetically generate a never-ending progression of knowledge. Anyhow, I think it was essential for Dr. Carroll to broach the topic of Strong Emergence and I'm so glad he did. As a scientist, he's properly committed to naturalism and reductionism but also properly open to investigate a purported counterexample. He's making both science and philosophy better in the process.

36:35 I'm not sure if emergent macroscopic behaviour is the phenomenon, or a certain reduction of extant configurations is the phenomenon. You can abstract the Earth as a point mass because mass tends to clump not in every possible way but in spherical bodies. Decoherence is another vast reduction or configurations that can be seen. So emergence as well as Dennett's patterns may be clues to that vastly compressed reality where only a tiny subset of the mathematically possible configurations actually exist in some sense. In a sense the job of physics is to map that reduction at every scale.

This clock has no moving hands. It is still a true clock describing real time, it is just that its domain of applicability is only noon. If you can make a correspondence between a particular sand heap and a mathematical theory of physics does that mean that the sandheap is a a theory of physics. How much of emergence is property of clever mappings between otherwise unconnected abstractions. Is reduction in the eye of the beholder?

27:14 that diagram is very category theory. I wonder if it would make sense to take a categorical limit and find the "least" theory that ecapsulates special relativity and Newtonian mechanics.

Isn't the measurement effect pretty much strong emergence? More accurately the Born Rule, which is not covered by the Lagrangian, that in principle applies to particles in mass via probability?