The Biggest Ideas in the Universe | 17. Matter 

This series is going to be one of the most meaningful treasures of the world-wide-web. I wish some day humanity reach a point where everyone have a basic grasp on reality. These videos will definitely help get there! Truly a gift. Thank you.

Once again. Me: I’m going to bed now. Sean Carroll: Uploaded 3 minutes ago Me: new plan

Prof. Carroll, you are an extremely gifted teacher! Thank you so much for all your effort to put this series together.

“So the Universe does ultimately make sense, if not only for the reasons you might initially have guessed.” Amazing

"...just be inspired by it, don't lean on it in times of trouble ..." may be my favourite quote ever. But these talks are, for certain, my favourite series of physics lectures/talks ever.

This is the best video on spin I have ever seen, and it’s not even close. Amazingly, Sean Carroll is using earlier Biggest Ideas to teach us later Biggest Ideas. This is a lot of hard work given freely and I am equally excited and grateful to Sean Carroll.

Honestly I wish this would never end its kind of addicting

Sean, thank you for that explanation of spin as the angular momentum of the quantum field and for the discussion of spin zero, integer and fractional in the context of Noether’s conserved quantities. It has never been explained so clearly to me before, despite having a PhD in theoretical physics. What I like the most about this series is how it never takes the shut up and calculate road that so many professors take, and instead takes the time to explain what it all means, and calls out common shortcuts as inaccurate.

Sean, Thanks for your enthusiasm and patience in sharing your knowledge!

That spin 1/2 practical example... got me on the edge of my seat. You can totally sense the Feynman of it.

its a great pleasure listening to all that complicated stuff so beautifully brought down to earth. Thanks a lot.

Just got home and found a new BIitU video waiting. Ditto to Joao below - stop everything else. Get comfortable with a drink & a smoke - click on "Like" and starting watching for first time. Then watch again tomorrow, Brilliant. Thanks again Prof. Carroll.

@Professor Carroll, Sean you are so productive - its makes the rest of us look so lame :-).

"...this will be on youtube for a million years so I might as well make it pretty..." I love you Sean Carroll.

lol you just made my day, Sean! "Bosons vs. Fermions, that Classificashon..." XD Usually when you write and talk at the same time, it's the writing that dies a horrible death, but this time it was the talking, and I adore it!

I realized that this serie of lectures will end eventually. We need more bigger ideas.

Sean, these videos have been absolutely amazing. Exactly what I’ve wanted to know about the way these things work! Thanks so much!

You know what I love about physics is that you almost gain a sort of x-ray vision in a way, you see through things.

New video! Stopping everything and watching!

You’re so awesome Sean!!! Love you buddy!!! 💪🏽👍🏽❤️

I'm loving your relaxed presentation in this series. You've inspired a great many people; I'm sure wikipedia's servers have felt the burden. I've spent many hours in follow-up reading after GIitU videos, and since we, your viewership, matter, and this IS the matter GIitU: here are my questions. WOW, not only are Bosons bosons, but Fermions can be bosons too ! Cooper pairs of electrons are bosons. (What force do they mediate?) Mesons (composed of a quark and an antiquark, two Fermions) are also bosons. Pions mediate the transformation (decay) of quarks. Tritium and ⁴He are bosons. Who knew all these Fermion collectives could be bosons? 1) Why is hydrogen not a boson? Obviously it isn't or our sun would be a lot colder. 😡 But it is two spin ½ particles. ½+½≠1? This Wikipedia diagram en.m.wikipedia.org/wiki/File:Standard_Model_Of_Particle_Physics--Most_Complete_Diagram.png of the spin-0, spin-½ and spin-1 sectors before and after the spontaneous symmetry breaking of the Higgs condensation is quite fascinating. Is there REALLY an EM field, or is the overlap of (the crippled remaining half of) the weak hypercharge field and (the remaining crippled T³ component of) the weak isospin field what is reality. In describing the EM field are we in effect talking about the sun revolving around the earth (because obviously that is what we experience) ? 2) Would a super-advanced alien laugh at Maxwell's equations and rewrite them in terms of the underlying fields? (And what about strong hypercharge and strong isospin? And if isospin has nothing to do with spin, WHAT IS IT? You sometimes get a little casual in your wording ( the "electron field" ). Are the muon and tau separate fields, or is there a single lepton field with the muon and tau as extreme excitations ? (Recent muon results seem to call into question lepton universality.) Can you point us to a list of all the underlying fields of the SM? Come on Sean, give us ALL THE GOOD STUFF ! )

Best explanation for spin I have ever found. Thank-you!

Thank you your lectures (vlogs) are simply fascinating.

Sean, you touched on complex dimensions in the episode on topology, and hinted at the fact that two complex dimensions is not quite the same as three real dimensions. But, you didn't come full circle (so to speak) when you got to spinnor fields. Also, after explaining that angle is defined via inner product in Hilbert space, you can _show_ how rotating 360 degrees leaves the vector different from what you started with, mathematically.

You amaze me, Dr. Carroll.

I kind of like having my own space. So definitely more of a Fermion.

I hope we get to hear more about how the number of dimensions of spacetime affects the interchange operator. I can see how it would affect rotational symmetries and therefore angular momentum but I don't see how that argument about interchange causing us to have exactly two options could be modified.

I love his lectures. Physics has always amazed me.

Thank you!!

"of course it's the quantum state; what else could it be?"

Thank you professor Carroll.

I'm going through some health things right now and the drugs give me weird and intense dreams. When I listen to these lectures at night somehow that fades away and I have mathy dreams instead, sleep longer, and don't wake up as often.

First, thank you for doing these videos, Sean. Your ability to clearly explain complex ideas so that they are understandable to those of us who are not career physicists is truly unparalleled. That being said, my brain is hung up on the fundamental relationship between matter and “space.” Why do physicists refer to space as if it were a container or substrate that matter is “in” as opposed to just an emergent property of the matter itself? In other words, why don’t we just think that the structure of matter IS space rather than space existing as something independent from matter?

"Why aren't atoms squishy?"...ahhh...that exam question we all dread!!

Amazing! Thank you so much, Sean!

I have a question having to do with the Fermi pressure, specifically with the degeneracy pressure that keeps white dwarfs (or neutron stars) from collapsing any further. It would seem that the Pauli exclusion principle would, in some sense, be absolute: there's no forcing electrons (or neutrons) into the same quantum state. I assume that quantum mechanics doesn't break down, but somehow the Pauli exclusion barrier is circumvented for stars above a certain mass in both cases. How does gravity overcome this restriction?

Ahhh matter, something I can get a grip of.

Thank you for most interesting spin explanation I ever heard. I read before that matter is solid because of the EM repulsion forces between electrons. How does that fit in or compare to the Pauli pressure as the cause?

Absolutely brilliant

You talked about the Stern-Gerlach experiment, where instead being deflected through a range of angles, half of the silver atoms went one way, and half the other way. So, spin is quantized. But why??? Intuitively, I accept that electrons are constrained to discrete orbits because only a whole number of standing waves can persist within a fixed boundary. Is there an analogous consideration for spin? One website told me, “Half-integer spins are consequence of group theory.… The spin operators and associated Hilbert space of spin states are governed by Lie SO(3) algebra, with resultant eigenvalues of ±½.” But I object to the word “consequence” here. Properties of the real world can’t be a *consequence* of group theory; it’s the other way round! (Isn't it?) Can you explain in English why spin is quantized?

your the F**king man Sean!!! the man! I love you

Thanks Sean.

I need one of those schrodinger’s cup so bad :))

The only spins I understand are 33, 45 and 78. But they do involve Pi !

thank you so much

thank u carrol for beeing so consistent with us,this series will be like a sterter for a lot of peeps later on..thanks to corona too i guess

25:00 Fermions are described by spinor field, while bosons by tensor field

Today I learned the difference between "squashy" and "squishy".👍👍💙💯🔥

I hate to be the guy but the magnets in the Stern Gurlock experiment are a roof-like edge at the top, similar to the cross section shown, but the bottom is concave like the inside of the cylinder. The electron would move parallel to the cylinder axis (perpendicular to the diagram). Sean is not an experimental physicist!

One more question -- to which book do you refer when you say "it is in my book"? I have all your books (as well as from biologist Sean Carroll ;-)) ) -- in Audible format -- only two of your books have illustrations in PDF formats (Higgs and Big Picture)

Excellent !

Hello Dr, Carroll, thank you for breaking down such big ideas into the simplest form that even the dumbest people like me can understand. I hope you will make a lecture on tensor calculus and how to manipulate indices since it is at the heart of Relativity.

If and when is this series going to come out on a set of dvds?

A visual demonstration.. And then a second? This proved a different peregrination today!

When bosons gather in the same location, say the Physics lounge for the weekly wine and cheese, is the boson field value a superposition of all the bosons in that location? Is the field value ever ambiguous, ie, the same value could be a superposition of different bosons. Or will a Fourier transform always decompose the field vibrations into an unambiguous set of particles? Thanks, the series is great,

Vectors don't change under Bro°😅 - tis information is applicable to so much, it's distracting. Sean thank you!

To what extent is the non-squishyness attributed to Fermi-pressure rather than the electromagnetic force? I imagine that if the electromagnetic force was weaker, then Fermi-pressure would also be weaker. The "electron-wavefunction" around a nucleus would be larger and thus two atoms could overlap more before Fermi pressure really kicks in. Is that right?

Amazing thank you so much

Awareness is known by awareness alone.

What is the cause and what is the effect in the Pauli Exclusion Principle? Is the spin causing the minus-sign? Or is the minus-sign causing the spin? Or do the different underlying behavior of the fields cause both? Or are they all independently just different things that happen to correlate?

I am trying to get a more intuitive understanding of the quantum fields. (1) Say that, in the normal world, we had a macroscopic object like e.g. a finger. Would there be an arrangement of vibrations in the quantum field that looks like a finger, or would the finger be represented by something like a Fourier Transform? (2) Say that in the real world my finger pushes a small ball. What is the representation of that in the quantum field? Can I actually make something happen in the quantum field by something that I do in the real world? I would think that you need some special device (like a laser, etc, not just my finger) to manipulate a vibration in the quantum field?

awesome. So cool. Thx !

28:22 that bit of Jamaican Patois had me giggling ^_^ thank you for the teachings!

12:40 2 electrons are identical because they are vibrations is the same underlying quantum field. OK, but this begs 2 questions: (1) how did the quantum field come about so that it can be so uniform in making its particles, even when those particles are as far from one another as opposite sides of the universe, and (2) why is there a rule that the quantum field follows such that it know that it should make all electrons the identically (why should a quantum field feel obligated to follow any rule whatsoever, rather than just randomly doing whatever it wants at any moment and location)?

Is a monochromatic and coherent LASER beam composed of Bosons that are all in the same quantum state?

Thanks again for another great lecture. I'm wondering if we can use the field theories to explain how mater bends space-time, or the "bending" is just an approximation for graviton.

Believe you have made an error ~0:28. Speaking of Pauli Exclusion you say "2 hydrogen cannot occupy same space bkoz of electrons". Actually they can, but their spins must be anti parallel. If you add 2 neutrons to the 2 protons then the nucleus is happy too.

Are all atoms of a solid crystal entangled? if atoms in the same crystal are not entangled - where the entanglement breaks?

At 40:26 you say that "spin-1 really means spin of 1 hbar". I've heard this so often online and even in lectures and I'm still confused about this. A particle in the state |s,m> satisfies the eigenvalue equations S^2 |s,m> = s(s+1) hbar^2 |s,m> S_z |s,m> = m hbar |s,m> where S is spin operator (I'm not able to draw the vector arrow on top) and S_z is its z-component. s takes values of 0, 1/2, 1,... and for given s, m takes values from s, s-1,...-s+1,-s. That said, taking the first eigenvalue equation, shouldn't the absolute value of the spin vector of a spin-1 particle be the square root of the eigenvalue of the operator S^2? That would be square root of 1*(1+1) hbar^2 = sqrt(2)*hbar. Not 1*hbar. Similarly, the spin of a spin-1/2 particle would be sqrt(1/2*3/2) hbar=sqrt(3)/2*hbar. Of course, the second eigenvalue equation shows that a spin-1 particle can have a z-component of its spin vector of 1, 0 or -1 hbar. Or a spin-1/2 particle with spin up would have a z-component of hbar/2. But I think at this moment in the video you're talking about the absolute value of the spin, not the z-component.

5:30 doing my homework. Ionization energy of a hydrogen atom 14eV. Take an avogadro number of atoms, and convert to kWh, the answer is 0.37 kWh. A bit less than an atomic bomb

Mr Sean Carroll please can you recommend some books for learning general relativity assume that I know only 10th grade math?

I’m proud I guessed the relationship before I was told

I still have a question on the last idea of gravity, it's probably too late but I'll ask anyway. You talked about gravitational time dilation and even derived a formula for the eigentime from the Schwarzschild metric. The eigentime goes to zero at the Schwarzschild radius. So from Earth's point of view that means that it would take an infinite amount of time to see something fall into a black hole. Or from the object's point of view, the universe far away would have aged infinitely when it finally falls into the black hole. How is it then possible that anything ever in the finite lifetime of the universe falls into a black hole? We seem to observe that black holes e.g. in the center of galaxies grow over time, at least they didn't start out that big at the big bang, so stuff must have fallen into them from Earth's point of view. Where is the mistake in my logic?

At 24:07 you mention that "whether bosons and fermions are the only possibilities depends on the dimension of spacetime". Could you elaborate? I'm a physics master's student and in my QM II lecture we basically exactly followed your line of argument (of course more mathy and more detailed but still). So it's not clear to me how the argument that the square of the interchange operator is 1, i.e. having eigenvalues of 1 and -1 such that psi(X2,X1)=+ or - psi(X1,X2) but excluding the possibility of arbitrary e^(i*theta) phases, depends on the dimension of space.

Let’s get to the matter

Space time conservation according to energy dilation contracts remain the same

Is the fact that W/Z Bosons and Photons all have Spin 1 a result of the fact that EM and Weak Force are really the same force at higher energy levels? Or is it just an unreleated coincidence?

Please give a lecture on THE TIME.

On the incompressibility of tables or wood: a nice illustration but if it were really true, I'd never be able to build anything with squared-off corners.

Something I always wondered: why not other fractional values or spin? Like 1/3 or e/pi? Why only multiples of 1/2?

@Dr. Carroll, inside a black hole, right at the boundary that is infinitesimally close to the actual singularity, does matter take up any space?

So, I'm imagining gravity as a vector field, and it doesn't seem like it would have spin-2, because up and down are different. Is the spin-2 from the idea that, in 4-d spacetime you'd swap up/down and future/past? I mean, it seems gravity is symmetric that way. [I'm thinking and reversing all components of the vector _including time_ is the thing, yes? pi radians in all dimensions?]

Dont get too focused on ended these discussions, i think i speak for everyone that watched these videos in saying we all love to hear you talk about the universe and would rather you just kept making videos about it if you can find the time haha

In the Stern Gerlach experiment, if the electron was a classical spinning particle with negligible moment of inertia wouldn't that explain the quantized results? First the particle gets aligned with the field, then it gets deflected. Is that explanation obviously true or obviously stupid?

I agree that Satyendranath Bose's departed soul would not be very happy but then why not just call them pileon instead of boson?

So how would a gravitino behave in a Stern-Gerlach experiment?

Is there an actual energy gradient to Fermi pressure?

A Matter of Fact! 😆

Time to chop the wig! GWAN SEAN!

This video will forever go down in infamy 🤣

17:41 24:40 37:06 51:50 1:00:40

Would have liked a word on anyons. Moreover given recent experimental evidence.

Did you say 'bozzonic'?

Not absorbing as much as I would have hoped, while falling asleep.

Watching ...

Sean: it is something confusing the notation you used when discussing the particle exchange symmetry in your notes. You should have written \Psi(x_1,x_2)=+\Psi(x_2,x_1) for bosons [you wrote \Psi(x_1,x_2)=+\Psi(x_1,x_2)] AND \Psi(x_1,x_2)=-\Psi(x_2,x_1) for fermions [you wrote \Psi(x_1,x_2)=-\Psi(x_1,x_2)] . Otherwise, the particle argument is a bit nasty and unconventional.

What about the psychedelic synthesis ? So far i havent heard anything that could explain the psychedelic experience. Its a mindverse. Once you saw reality unfold and reconstruct around you and you experience being the observer and fall into other realities , lived episodes of other lifes ... well ... And then you see grown men and women like toddlers in a sandbox playing with toys pretending to have any clues about the universe , while you sit on the bench next to them , exhaling your dmt and a cosmic giggle is heard in the background ...

The brick is funny.

Can you do an Einstein hairstyle?

Nonscience question, does anyone know what app he uses for these? Would like to try it for some online lectures I'm going to be giving in the fall.