The Biggest Ideas in the Universe | 17. Matter

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 Idea #17, "Matter." The matter of which we are made can be solid because electrons are fermions, meaning that they take up space. We talk about that and the closely related spin-statistics theorem. Complete with demonstrations using visual aids!
My web page: www.preposterou...
My KZbin channel: / seancarroll
Mindscape podcast: www.preposterou...
The Biggest Ideas playlist: • The Biggest Ideas in t...
Blog posts for the series: www.preposterou...
Background image: www.publicdoma...
#science #physics #ideas #universe #learning #cosmology #philosophy #matter #fermions #spin

[@ofridagan]

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.

[@nujuat]

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

[@navidazadi4280]

And we must thank him immediately, because such a cultured person and great scientist takes his time and does a great attention and service to our understanding of the world and physics and truth. Thank you very much dear Sean. (I'm a human being somewhere on an earth in a galaxy in this world )

[@Kage1128]

Go to bed and watch tomorrow its not worth messing up your sleeping schedule

[@edithseichter4857]

Try to go to bed at the same time every day and sleep at least 8 hours. Care for your health.

[@ticklemeandillhurtyou5800]

Honestly I wish this would never end its kind of addicting

[@ericsvilpis1635]

tickle me and I'll Hurt you Only kind of??

[@Canard712]

Rewind & replay.

[@albertfeuerstein8773]

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

[@lpt369]

"...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.

[@nujuat]

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

[@rc5989]

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.

[@BertrandLeRoy]

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.

[@ba0cbmft]

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

[@dougg1075]

“ fieldness makes up nature “ that should smoke everybody’s minds

[@mobaby1979]

It did mine!! It's a neat and weird fact. I definitely feel more cozy in a world made up of 'nature-ness' compared to fieldness

[@whynottalklikeapirat]

@@mobaby1979 My head is full of "WHAT??!!o.O-ness"

[@rhondagoodloe3275]

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

[@etienga]

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

[@barissannan2731]

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

[@ErnestGWilsonII]

First let me say thank you very much for making this video series and sharing it with all of us. I realize this series cannot go on forever, I hope you can find time to do another series after this series. A few thoughts, if our species goes to Mars for any reason, this series should come along for the ride and be part of the archive of things we would like to have saved (backed up) on a different planet. Additionally, it has been an extreme pleasure to have access to one of the greatest minds on Earth. It is particularly rewarding and enjoyable to have Sean Carroll reading comments, following up and doing Q&A videos as part of this series. I am grateful to be able to watch this series as it progresses. This series and or one like it hosted by Sean Carrol would be on national television picked up by a major network if I had my wish. The content is fantastic, the delivery is perfect, the interaction is excellent. I am of course subscribed to this KZbin channel with notifications turned on and thumbs up!

[@spiritmonarch]

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

[@asolarasolarasolar]

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

[@papsaebus8606]

Asolar I hope he begins new video series after biggest ideas is done.

[@stephenbryant7873]

I think I could watch them again and learn more the second time around.

[@Animuldok]

Its physics, it will probably asymptote rather than reach a limit :D

[@Ryo-sd9rx]

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.

[@paulc96]

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.

[@markweitzman]

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

[@stephenbryant7873]

If you are watching the 33rd lecture in this series, I doubt you're an ineffective person in your area of expertise.

[@renaudkener4082]

I believe this serie of videos will reach the same status as "The Feynman Lectures on Physics" for the next generation of undergraduate students. Lucky guys :-)

[@barefootalien]

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!

[@user-sb3wh3dd4v]

Dear Sean, You are a GREAT communicator. Over the last few years, and throughout this series. I have learned SO MUCH from you. Things that I have been curious about for over forty years, you explain so clearly. If I were a president or king, I would appoint you as one of the important communicators of important subjects. How much better would this world be if only we had more real scientists, engineers, doctors, nad other well educated ETHICAL people in government? The answer is simple. The world would be a MUCH better place. Thank you for all you do!

[@jonnysee2948]

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

[@ericsvilpis1635]

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

[@menecross]

I finaly understand the property Spin. Thank you!

[@esperancaemisterio]

New video! Stopping everything and watching!

[@gilbertanderson3456]

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 ! )

[@ColbyNye]

Sooo sad to hear we are nearing the end! But thank you so much for doing these videos!

[@MoshkitaTheCat]

You amaze me, Dr. Carroll.

[@qclod]

These videos matter a lot to me!

[@iczemi]

Thank you your lectures (vlogs) are simply fascinating.

[@venustus100]

Thank you!!

[@rohitpandey3151]

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

[@TheMemesofDestruction]

33:00 - Thank you Professor!!

[@LuciFeric137]

Thank you professor Carroll.

[@ThalesF75]

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

[@wlegna18]

Thanks for the video! I just bought your book and I look forward to reading it.

[@jaschoudhury18]

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

[@margaritahernandez7459]

I love his lectures. Physics has always amazed me.

[@JohnDlugosz]

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.

[@Hulksterx]

Ahhh matter, something I can get a grip of.

[@mezza205]

but can you ?

[@oliverwinters1406]

Very good

[@luckabuse]

ideas can be matterial

[@davemojarra2666]

But not grammar, apparently.

[@ctixbwi]

I can’t grasp everything equally well. What elementary particles contribute to that soap is slippery?!

[@alexandeur]

Amazing! Thank you so much, Sean!

[@fsmvda]

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.

[@felipereyes8922]

In one dimension, that is a row of particles constrained to move in this same row, the particles can't go around each other, so you can't actually tell if the particles are bouncing off each other or going through. In this case bosons and fermions are in some sense equivalent, and there are techniques to map systems of one dimensional fermions into bosons.

[@MadScienceWorkshoppe]

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.

[@youtou252]

Absolutely brilliant

[@Cooldrums777]

Very satisfying explanations of spin and wave function interchange. I have to admit that coffee cup example of 720 rotation was extremely satisfying. I definitely would not have grasped the concept without that example. Of course we are still missing an explanation as to exactly what object or abstract quantity the quantum wave function is rotating 720 degrees in relation to ( I presume it's not a Planck length version of Sean) but I accept your assertion that it's just too complicated to discuss here. The ribbon was excellent as well, and once you demonstrated the interchange and rotation it made sense immediately. This was an excellent lecture overall. A nice selection of big ideas were covered. Thank you Professor.

[@viewer3091]

Thanks Sean.

[@Steve-xh3by]

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?

[@jeannieh3661]

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

[@bikashthapa7316]

thank you so much

[@bretnetherton9273]

Awareness is known by awareness alone.

[@nostradamuscat1131]

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

[@larryboulware6483]

Excellent !

[@robertshirley2645]

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

[@rsablosky]

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?

[@Petrov3434]

An amazing lecture. Once again -- Sean Carroll's lecture made our day !! A question: In book reviews of Roger Penrose's "The Road to Reality" several reviewers, who apparently understand more than I, made surprising comments which I don't understand -- a la Penrose delivers the knock-out punch: --- Conservation of energy/momentum/angular momentum in General Relativity is non-local !!! What such comments really mean? What is their significance? Many thanks

[@projectmalus]

My guess is the effect from the field moves away to another "level" where it can play a part in the formation of another field.

[@jankareaustinat310]

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

[@tizza963]

Amazing thank you so much

[@TheyCallMeNewb]

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

[@alachance2010]

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

[@tonydarcy1606]

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

[@tomasnemec5680]

Not many people out there still get this I am afraid ...

[@zebrawien]

​@@tomasnemec5680 Based on your data of the universe? - I guess. Why not break the ice and have the people participate? :) Simplified: 33, 45 and 78 is the number of spins per minute of standard vinyl records. The record is a circle. Pi is the ratio of the circumference of a circle to its diameter. :)

[@henryD9363]

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!

[@tookie36]

Thank geometry for Sean!

[@annwwar]

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?

[@marcsmerlin]

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?

[@trucid2]

One way to get around the exclusion principle is to get rid of the particles. For example, if a star is supported by electron degeneracy pressure, at high enough pressure you would merge electrons with protons to create neutrons.

[@Bill..N]

@@trucid2 Indeed friend..A temporary respite for physics... Add enough additional matter to the neutron star tho, and ALL our descriptive abilities DO fail us..

[@Bill..N]

@@trucid2 Which brings up a simple concern.. GR tells us that the singularity produced by an efficient collapse of just a 10 solar mass object results in an INFINITE gravity field..The event horizon would be about 30 kilometers, AND surrounding a very mysterious "Object" of perhaps 200 mm that somehow exits outside our spacetime while LEAVING its infinite field behind..Does this expose a defect in our understanding of matmatiical descriptions, ot the theory, OR even our inability to understand reality itself? Inquiring minds would like to know...Peace.

[@dankuchar6821]

@@Bill..NYes, General Relativity predicts infinite density. Physicist don't like infinities. We assume it means there is something incomplete about general relativity.

[@Bill..N]

@@dankuchar6821 And yet GR has passed EVERY challenge to its legitimacy.. It doesn't play well with QM, (Mans greatest theory) which has its OWN renormalization issues..but both theories function incredibly well.. Peace friend..

[@rickharold7884]

awesome. So cool. Thx !

[@ags5377]

One small correction: the example of the electron going through the Stern-Gerlach experiment is not correct. As it is a charged particle is it subjected to the Lorentz force which will distort the clear separation in 2 discrete states. The experiment is usually done with charge neutral particles such as silver atoms.

[@henryD9363]

Planks constant is used as a measure of spin, as you have described. Planck's constant has units of angular momentum. If you fire a beam of up spin electrons at a target will that target gain classical angular momentum? (It might be too small to measure experimentally, but...)

[@baogiangsongque5507]

Thank you Professor Carroll, Sean for the excellent lecture. how ever, keep in your mind that 10% is a part of true and the rest 90% is just a story. we are waitting for your next part of true physical lecture. 8:00 why one atom can not stack on top another one. 1. Because the atom want like that = thinking = a story =? 2. Because the matter have 2 forms: order energy mechanic and none order energy mechanic. After big bang all form of none order energy mechanic (FONOEM) transform into the particles. then all all form of order energy mechanic transform into the atom. 3. Matter have 2 mains state mechanic: state of lower order energy mechanic order energy mechanic and state of higher standard energy local reference mechanic. all atoms are usually standard energy local reference mechanic which called earth or solar space mechanic. Imagine if an atom outside of milky way or solar system enter into solar space. due on this atom motion creating a different energy vector and so on. We call anti-matter or none unique reference energy frame. Here the experiment: on the car running at constant speed as the car energy reference frame is the same. You must use force or energy to used the knife to cut the apple base on they are in the standard order energy mechanic and the same order energy mechanic. If the knife is being in the car running and the apple is being outside of the car. You can cut easy or can not cut the apple at all base on they are same form but in different state of vector energy. These explain clearly how chemical reaction and so on by physical term. May be no more rocket era enter into the space.

[@alachance2010]

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

[@Destrolll]

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

[@Toocrash]

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

[@kx4532]

I don't know about 1% but you can squeeze piezoelectric crystals to create a voltages and apply voltage to deform the piezoelectric crystals.

[@haydarmasud635]

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.

[@dougg1075]

Let’s get to the matter

[@barefootalien]

So a question for the Q&A if it's not too late... in the Stern-Gerlach experiment you drew the possible quantized values for measurements of particles for particles of spin-0 having 1 possible result; spin-1/2 having 2 possible results, and spin-1 having 3 possible results. But how does that pattern continue? Would a Gravitino with spin 3/2 have 4 results, and a Graviton with spin 2 have 5? Or does it just alternate back and forth with the results getting further and further apart, so a Gravitino would have 2 results at 3/2 and -3/2 while a Graviton would have 3 at 2, 0, and -2? Could this point to any insights we might get about the graviton through other kinds of tests, despite not having detected them?

[@briancannard7335]

Thank you for the 360 degrees user friendliness. It adds a lot of charm to your way of explaining. I wish you to not talk and write at the same time more often. I'm curious how do you manage to keep your eyebrows calm when that happens? Have you trained to keep friendly facial expression so your student keep listening? :-) One of the greatest teachers in the world! For sure. Thank you for your Mission!

[@briancannard7335]

OMG Feynman's mug 720 degress!

[@WEPayne]

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.

[@Petrov3434]

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)

[@BT-kf4kx]

Hi Dr. Carroll, can you plesae do a video explaining about the myth of "warp speed" that we keep seeing in movie such as star trek and such? I am very curious what's the correlation between gravity and electrons?

[@LiamHaleMcCarty]

What’s the simplest argument that atoms exist? How would you convince a non-physicist if they were skeptical and didn’t have much background knowledge?

[@swoop8047]

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

[@louiscohen]

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,

[@callycraig3132]

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

[@sagmilling]

New video! Popcorn time. Question, valence electrons must be separate "shapes" to have different psi, but the quantity of valence states increases with atomic number. What is actually changing?

[@felipereyes8922]

The tl;dr summary is that pauli exclusion is still followed because even though you have more electrons in the same valence energy level, there are more distinct quantum states that yield this result. In more detail, higher atomic numbers have more electrons. These start filling up the available energy states, beginning with the lowest, innermost states. Each new energy level is like a shell around the nucleus. Valence electrons sit in the outermost shell, and since they have the highest energy, they are the ones that bond with other atoms. The thing is, each shell can hold a different number of electrons. Although they share the same energy, the electrons have other properties that are different and so they can sit in the same shell without violating Pauli exclusion. The actual property is angular momentum, as you increase the energy there are more distinct angular momentum states that yield the same result.

[@phukfone8428]

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

[@valrossen]

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?

[@barryzeeberg3672]

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?

[@wdacademia2329]

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?

[@whynottalklikeapirat]

The universe is full of "doesn't matter"

[@NFLbeatster]

This video will forever go down in infamy 🤣

[@Dudufi1]

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

[@barryzeeberg3672]

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)?

[@nathanokun8801]

The "Spin" up or down at a fixed amount, no matter what increment of magnetic field is used gives a two-value-only "quantum" (stepped results) effect - how "Quantum Mechanics" gets its name - and not an incremental value, as :Classical" Physics would predict. I would assume that such a quantum effect also works with the double-slit experiment or all other quantum test results. The reason would be that to have different random results that all parties looking at each test agree to, no matter where or when they are (using Special Relativity to determine this), the values have to be stepped like in the smallest possible form of infinity, the countable or "Rational Numbers" infinite set (Cantor's Aleph-sub-zero infinity). Only this infinity has discrete, completely separate values with sharp boundaries separating them. The next higher known infinity (to my knowledge) is "c', the infinity for all the points on a line, which is the one used by Classical Physics (the "Real Numbers", I think), but these have no such discrete, separable values and the blurring of one result into the next would make different, slightly-offset (in the Special Relativity sense) observers IN THE SAME UNIVERSE (assuming Everett's Multi-World view of Quantum Mechanics is true) see SLIGHTLY DIFFERENT results. Thus, for Quantum Mechanics to be able to follow Everett's concept (which it can, though this may not be the only correct concept of how Quantum Mechanics works), ALL final results have to be stepped in the manner of Aleph-sub-zero discrete results and this can only happen when ALL quantum INPUTS (Spin and so forth) to the experiment are also stepped, not incremental. It looks like Quantum Mechanics is DESIGNED to create discrete results that allow the Everett-style "Multiverse" to exist...

[@sebastiandierks7919]

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.

[@Cooldrums777]

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

[@anilsharma-ev2my]

Space time conservation according to energy dilation contracts remain the same

[@sebastiandierks7919]

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?

[@Dongufo15]

i'm not sure about a purely GR explanation, but taking into account the Bekenstein entropy formula every time you add a bit of information to the BH the event horizon area increses by one Planck area, so you don't realy need stuff to go beyond the orizon to make it grow from the outside prospective.

[@johnp1]

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.

[@ausblob263]

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