The Biggest Ideas in the Universe | Q&A 10 - Interactions

[@sambo7734]

wow. mindblowing. no wait .. mind expanding!

[@minaghavimi4843]

I absolutely love these videos, exactly what I was looking for, explaining laws if physics to non-physicists. Thanks Sean for taking the time to educate the public, I have read all your books. Not saying I understood them all well, but From Eternity to Here completely changed my perspective about the universe and how it works.

[@simkintube]

I love these videos. I learned some math on my engineering degree but not enough to read QM for myself without being overwhelmed. I'm very curious about the general ideas behind "real life" physics but I don't really have time to learn all the math. In practice these means that most of these ideas are behind a math "paywall" for me. Luckily these videos allow me to make some headway into these subjects and that makes them very fun and interesting. This type of content is very difficult to find elsewhere. I know the DrPhysicsA channel which uses a very similar format and is a little more heavy on math, sadly he isn't active since 2014. Khan Academy also uses this format for more elementary stuff. What makes these videos different from the usual divulgative content is that they include a small amount of math, Nowadays I find I'm rarely able to learn anything new from the normal content that is 100% based on verbal analogies.

[@barefootalien]

Depending on what flavor of engineering (Aerospace for me), you might have closer to the appropriate level of math than you think. If you did Differential Equations to some degree, and understood and enjoyed them, and you're comfortable with trigonometry and complex numbers, you should be able to follow a more advanced discussion on QM just fine, and get a feel for the math involved without necessarily taking the time to learn it to the extent necessary to actually solve problems. The only math in QM I'm a little shaky on after a good engineering education is linear algebra, but as I understand it, that's really purely optional for QM, as Matrix Mechanics is precisely equivalent to the Schrodinger Equation. If you want to take a crack at a deeper understanding than even Sean can give, I recommend MIT OpenCourseware's lectures, specifically by Dr. Allan Adams, who I found to be a very informative and entertaining lecturer. kzbin.info/www/bejne/oouWk4OLgNRosMU

[@andreybashkin9030]

A chuckle at "uninteresting infinities", full blast of laughter at a "simple minded QFT". Love the whole series!

[@6614990]

Thank You !! Please keep this as an ongoing series. You give understanding to the once unknown; again heartfelt thanks.

[@briancannard7335]

"Eventually we will figure this stuff out!" Thanks Sean, keep inspiring next generations!

[@ritemolawbks8012]

Dr. Carroll can neglect the pandemic hairdos and vanity like Einstein did during the _1918_ _Flu_ _Pandemic._ His level of knowledge and incredible teaching skills gets all of the attention. I don't see how anyone could retain this much information and effectively communicate it to all audiences.

[@jimsmindonline]

QM feels very much like an emergent phenomena from some more elegant theory we haven't fully conceived of yet. I think Einstein's concerns about it are still valid today. I sometimes think some of the maths put us on the wrong track of understanding, although it works, the implications are difficult to come to terms with. Enjoyed the series so far and wondering where it goes next.

[@barefootalien]

I very much agree. In fact, this is my one objection to Everettian Mechanics remaining post "Something Deeply Hidden" and Sean's brilliant analogies and lectures that neatly parry almost all objections I used to have... QM is clearly "not finished". It's not even approximately finished. We love to quote how it is "the most spectacularly successful and precisely verified theory humans have ever devised", but then (never in the same breath, mind you) we'll also admit "Oh, except when it disagrees by a factor of 10^120, which is actually just the low estimate of a factor of infinity, and there are many other examples where it completely falls apart and doesn't describe reality at all." If, as a theory, Quantum Mechanics _in general_ is incomplete and obviously flat-out *wrong* in many ways, then how could its simplest, leanest, meanest version possibly then be "the one"? Many Worlds may be a promising frame of thought, but to my mind as well, there's clearly "something even more deeply hidden" out there, which the simplest version of QM definitionally _cannot be_ .

[@sorinstroe6156]

I have a weird concern that i've never seen addressed. If we have entangled particles A and B, and we delay reading B for 5 minutes, where and how exactly does B keep the information gained instantly from the collapse of A, and how is it any different than if it had that information from the moment of creation instead of just for the final 5 minutes of its life? I've been taking it for granted for 20 years that there is a real debate about "action at a distance", and only these last few days did i realize there's no debate, "action at a distance" fails at the very thing it was invented for. If hidden variables are magicalExplanation1, "action at a distance" is magicalExplanation1 + magicalExplanation2, because it requires hidden variables, but also an unexplained mechanic for action at a distance, and breaks special relativity. So we better just keep magicalExplanation1 and deal with the consequences.

[@barefootalien]

@@sorinstroe6156 Ah. This actually has been addressed in this video series, but it's a pretty subtle point that it's easy to gloss over. When you have entangled particles, barring an explicit hidden variables theory, there is no need for either particle to "store" anything. That's still thinking in an anthropomorphic manner and attributing things like motivation to them. Your concern, if I can paraphrase illustratively, seems to be something like this: "Entanglement means if I measure some property of Particle A, then instantly and non-locally, Particle B 'knows' what was measured in Particle A, and changes its wave function in response. How does it 'know' to do this unless there is either 1: instantaneous transmission of information from A to B that violates locality or... 2: something about Particle B that somehow conspires with A to store the information about what to do in every possible circumstance of their measurement. Even worse, since you can delay measuring Particle B, even if it is 'action at a distance' transmission of information, it still has to have some means of 'storing' the result until it's measured." But that's exactly the paradox that makes the Copenhagen interpretation involving measurement-triggered 'collapse' of the wave function so absurd. There are, predominantly, two 'flavors' of QM that are worth any real respect and consideration, as complete, scientific theories about how reality works. 1: Theories / "interpretations" that take the wave function to _be the thing that is real_ about reality, and... 2: Theories / "interpretations" that take the wave function to be something other than traditionally 'real' and thus require something else to be reality, i.e. "hidden variable theories". In 2, the answer to your quandary is trivial. In these theories, there is, quite literally, something about Particle B that (I don't want to say 'knows' or 'stores', so I'll say...) encapsulates what will be measured at any given place and time in conjunction with any corresponding measurements in Particle A. In 1, which includes Many Worlds as well as spontaneous collapse theories, which necessarily take the wave function to be real in order to apply physics-based reasons for collapse rather than woo-woo based reasons, the answer is more subtle, and I think this is the point on which you're understandably losing track of what's going on. The answer is that in "real wave function" theories, there is _no such thing_ as "Particle A" and "Particle B". There is only one wave function, technically of the entire universe, but since what we really mean by "entangled" is more like "isolated and not significantly entangled with the rest of the universe", it is useful and 'okay' to talk about one wave function _of the entangled pair_ of the vibration in the appropriate field that we interpret to be 'Particle A' and the entangled (i.e. not in any way separately defined) vibration that we interpret to be 'Particle B'. It is _not_ okay to talk or think about the separate wave functions of Particle A and Particle B like they are two independent objects, because _they are not_ two independent objects. That's what we *mean* by "entangled". Because there is only one wave function of the entangled system, at the moment at which Particle A is 'measured', by which we mean "becomes entangled with its environment in a macroscopically amplified manner" (synonymous with 'decoherence'), what is _actually_ happening is that *the wave function that is the entangled system of A and B* becomes entangled with its environment in a macroscopically amplified manner, which doesn't just "tell B what to do if it's measured in the same way", it _actually changes what B is doing_ in a very real way, regardless of the distance between them. You are at that point free to choose your favorite "wave function is real" flavor of QM to describe what, exactly, that means "really happened"... whether B's wave function "collapses" or decoheres at that instant, or whether the wave function of the universe branches into every possibility of what could have happened Yes, this means that these theories require us to accept non-locality... but it does _not_ require any hidden variables capable of *storing* anything, because, again, there is no such thing as Particle B to have stored anything in the first place... only one wave function to describe the system of A and B. All that's really happening is that we used to have a part of the wave function of the universe that was isolated enough from everything else that we could usefully talk about it as a pair of entangled particles, and then once we measure one part of that wave function, decohering it, "collapsing" it, whatever you want to call it, we very quickly lose the ability to talk meaningfully about that entangled pair any longer, as that part of the wave function becomes hopelessly entangled with the overall wave function of its environment (the universe). Because we knew that the two 'particles' were entangled in a certain way, _at the moment of that decoherence_ (our measurement in this case), we know that the part of the isolated wave function that was "Particle B" had a correlated value. What is often left out at this point and left confusingly implicit is that Bob will only measure Particle B to be correlated to Particle A (i.e. down if A was up, if they were correlated inversely in terms of spin) if he both: 1: continues to keep Particle B completely isolated from the rest of the universe (which he was already required to do in order to maintain the entanglement as he moved to his arbitrary distance from A), and... 2: measures the same property of Particle B that Alice measured in Particle A, along the same axis that Alice measured it, *as the very first interaction with anything that Particle B has ever had since becoming entangled* with Particle A. If he does _anything_ else-if he measures another property, if he measures it along a different axis, if he lets a stray photon interact with Particle B by failing to keep it in a perfect vacuum and total darkness, or if a random neutrino he can't possibly stop just happens to collide with it-then Particle B immediately decoheres and will no longer be correlated with Particle A. As soon as either particle is interacted with in any way, the entanglement is essentially destroyed, and we only know something about the other particle in that instant and then for so long afterward as its wave function remains undisturbed and does not itself decohere. Imagine if we had a pair of incredibly delicate crystal sculptures, one of a dog, and one of a wolf. They're so delicate that to keep them safe, they need to be encased in a special protective box and treated extremely carefully. If the boxes are jostled too much, or if they are opened, within seconds they will shatter into completely indistinguishable dust. It is impossible, even in principle, to peek inside the box in any way without opening it and thus destroying the sculpture just after seeing what it was. We then give one box to Alice and the other box to Bob and have them travel (very, very carefully) to Atlanta and Boston respectively. Once at their destinations, Alice opens her box and, in the brief seconds before the jostling of the air in the room she's in disintegrates it, she sees that she had the wolf. In that instant, she now knows that Bob has the dog, even though he's far away in Boston. Bob doesn't know this yet, though. And the dog doesn't _need_ to 'know'... it just _is the dog_ since it's the other half of the entangled pair of [wolf+dog]. In order to find out that he has the dog, Bob has to have not jostled his box, and he has to open it in the same orientation (right-side-up, say) that Alice opened hers. If he dropped the box at some point, or if he opens it upside-down and it shatters on the floor before he can see what it was, then he doesn't find out what he had. Alice could call him and tell him what she had, and thus he'd know what he had before he dropped it, but that happens at sub-light speeds, so that's okay. If, on the other hand, Alice had dropped her box, and opens it in Atlanta to find only a pile of dust, then she knows nothing about what Bob has. That doesn't mean they weren't 'entangled' (i.e. one dog and one wolf, in unique combination) at some point... just that the entanglement broke before she got to find out which one she had. Likewise, if someone snuck into Alice's train car late at night, and carefully replaced her sculpture with one of a pineapple, then she'd also have no idea what Bob had. If nobody messed with Alice's box, but someone replaced Bob's sculpture with a rutabaga, then it doesn't matter what Alice finds when she opens her box, as it no longer has any connection to Bob's; he's always going to find a rutabaga. Alice could still call and say, "Hey, I have the wolf, so you must have had the dog at some point," but it no longer affects Bob's sculpture, because the entanglement is broken/decohered. Not sure if any of this made sense or not. I hope so. I tried to explain it several different ways in case any one way didn't help. :)

[@JohnDlugosz]

@@sorinstroe6156 The two particles are "at the same time" in _some_ reference frame. Five minutes apart in yours, but so what? To someone else, B was measured first. Point is, for spacelike-separated events, you cannot set an intrinsic time ordering. The "spooky action" is *outside of time* .

[@dermotapower]

Barefoot fantastic thank you. I”ve been struggling with this for months (I know, ‘months’ is nothing this stuff takes years). Sean did a great interview with Rob Reid on his After-On podcast. Rob asked a lot of questions that mere mortals like myself would love to ask and teased out some of the conundrums and paradoxes in Sean’s Many World viewpoint. I’ld recommend it to anyone else who needs story and metaphor to clarify the maths and physics. This explanation of ‘spooky action at a distance’ is really great so thanks! Glass wolves and dogs in boxes- that’ll will stay with me .

[@las97531]

I start to understand more thanks to this extremely good explanations 😀

[@PACotnoir1]

Thanks from an old one (near 70), that follows (after having read your last book) those videos since the beginning of september, trying to listen one subject each day. One suggestion: if you kept it, it would be useful to be able to download your writing of the virtual blackboard for reviewing.

[@esperancaemisterio]

Great video Sean! I've watched nearly all the videos for nom physical graduates in the KZbin and yours are the best ones, by far!

[@adithyaaanand7061]

12:31 [e+'s arrow] Thank you for clarifying that. I was worried you might deem that question dumb enough to give a clarification to...

[@osman2k]

thanks for these lecture, you are awesome!

[@StumpyMason_]

Thank you again for another great episode

[@rc5989]

While enjoying every episode and the companion Q&A, I am also interested and observant of the curiously effective method of teaching being employed by Sean Carroll. In my opinion, these videos should be regarded as the 21st century social media Feynman Lectures. If there was homework and smaller groups with graduate assistants working with the students, then this would be functionally equivalent to an undergraduate overview course in physics. All my opinions of course. While I truly love to learn physics, I also love to learn about learning. This is a perfect storm.

[@musicalcacti]

Love the KZbin content professor!

[@ToriKo_]

21:00 when does the wave-ness of the Fields matter; when can we not use particle language and stop pretending they’re particles? When the interactions are not feeble but strong. 25:00 Feynman showed us that that language of having a Free Field, doing some stuff to it and then talking about it as a collection of particles, and then turning on the interactions a little bit, still works. 35:20 “If we weren’t locked into our Classical intuitions...” I think I’m having some trouble with this. I think the notion often conveyed is that the wave function, or the fields, are vibrating all of the time. But I think the correct notion is that they are vibrating all the time only for systems that are not yet entangled with ‘our system’. And when we observe the unentangled Field we get a particular answer. Which is to say when the diverging configurations of the WF become highly consequential to us, (entangled), the WF decoheres for us, with emphasis on the fact that we are part of the system that it decoheres for. Which is all just to say that this picture of Fields in superposition of vibrations isn’t happening all around us, it isn’t the fundamental nature of day to day reality, because we’re already entangled with most of the reality we usually think about. Instead these Fields in superposition occur for systems that are not yet, or only just becoming entangled with us. Which begs the question, are my assumption correct: 1)we are mostly entangled with the world around us, 2)that pockets of unentangled systems within that are rare and self contained, made in labs or smth, 3) that unentangled systems occur mostly at the edge of our light cone (this is prob really wrong, this use of ‘light cone’ is probably confused in a lot of ways, ‘our’ too - referring to the earth? The entangled system we live in?). And so this picture of Fields in a superposition of different vibrations is actually more fundamental than our day to day reality, (than the physics that goes on in the entangled system we are apart of), while not really being a description of it. And it’s crucial in understanding the physics that plays out in the wider universe beyond us. Reminder that I still don’t understand how an unentangled system can ‘interact’ with an entangled system (DSE, as a model of the world around us) and not decohere. What does our entangled system ‘look like’ for an unentangled WF/system?? Can it even ‘tell’ it’s unentangled? 37:00 locality 55:00 I still don’t understand how each mode can have an infinite number of energy states. How can there be different energy for any particular wavelength? Maybe something to do with the amplitude? What is the amplitude referring to in this picture? “What we do know about black holes is that they’re not simple perturbations of flat spacetime, black holes are probably not even described by QFT at all.” I’m really struggling to piece together how QFT is THE best theory we currently have of the way nature works, and that QFT is probably not the way nature works. How does it fit the data really really well when it doesn’t fit data like black holes etc etc? Things that seem like they should be covered. Why are we pushing for math that seems to be absurdly more powerful at the cost of being more abstract, while at the same time brushing off relatively simple cases where the powerful math fails to be powerful?

[@pigdog126]

Why is the Hamiltonian integrated over space and not spacetime, or does such a Hamiltonian exists which is integrated over spacetime?

[@JohnDlugosz]

52:40 "My box is getting worse and worse" That's what happens to my Amazon deliveries sometimes, too.

[@akumar7366]

Love the haircut, your a star 🌟

[@michaelsmith935]

Haha. I feel the same exact way about my hair. Still debating if I should get it cut.

[@dk6024]

Thanks for the late post; I needed to get some work done, today.

[@KaiHenningsen]

I'm sure he already said that in another video, but there's an important _conceptual_ difference when thinking about "spooky action at a distance" in the field context. Remember, in that context, the wave function is not about particle states, but about field configurations. Now, the superposition means that we have several different field constellations (One with, say, A up and B down and one with A down and B up). When we measure that field at one point in space, we effectively select one of those configurations - it then follows immediately that measuring at the other place now must have a pre-determined outcome. You can't measure two different configurations. (Or in many worlds, measuring different configurations can only happen on different, non-interacting branches.) No longer quite so spooky, in my opinion. Also, just wanted to say _"lockdown mullet"._

[@ghytredstillghytred7617]

But communicating that 'configuration choice' instantaneously to Bob *is* spooky action at a distance.

[@KaiHenningsen]

@@ghytredstillghytred7617 But you don't, in that view. Bob is part of the configuration you select, so you selected the Bob that measures the particle configuration you selected. If you want spooky, then call it "you select the configuration of the whole universe".

[@remogaggi82]

I liked the long hair! Either way you are awesome Sean.

[@eliezerjosedasilvarios719]

If Feynman diagrams can add more than 1 how can I be sure my below one adding is correct ?

[@JDLuke]

At about 31:46 as you drew electron number, I started to become one with the universe. Then you apologized for making it too complicated, but that little addition of colored flows to the diagram was a brilliant insight for me. I could suddenly intuit (and I am very much an intuitive thinker) more about quantum fields and the various values flowing through them far better than I ever have before. Thank you.

[@aaronwatson808]

I've always heard that total energy E is given by: E^2 = p^2*c^2 + m_0^2*c^4. Can you explain why you write E^2 = p^2 + m^2? I'm assuming your m is rest-mass energy and your p is some clever energy variant of momentum? Where does this come from?

[@aaronwatson808]

@@michaelsommers2356 Yeah, I posted the question before I have watched the video all the way through! I'm an engineer so I've never seen that before. I understand now. Thanks!

[@blaganger5]

Loved your longer hair, was very 70's-ish!

[@d.glasby5117]

Darn, I was hoping Sean would apply for membership in the Luxuriant Flowing Hair Club for Scientists.

[@ssshurley]

“Backyard Einstein” 😆 that’s why I love you man! I was dying! Never cease to amaze me!!!

[@jainalabdin4923]

Different modes with infinite number of energy states contributing to the vacuum energy being infinite seems analogous to the Ultraviolet Catastrophe problem for a black body emitting an infinite amount of energy? Maybe we need to quantise a further level for modal energy states? Are different energy states from modes across different fields interacting and are in some form of superposition, and when the vacuum energy is measured, we get the expected value?

[@markweitzman]

Sean seems to skirt over the fact that the perturbation expansion is in fact an asymptotic expansion - but they are still useful even though they don't converge even for electrodynamics.

[@longcastle4863]

7:48 ... Do each of the different quarks have their own field?

[@JoeTaber]

What if the *only* real locality is measurement locality, entanglement, and dynamical locality is an *emergent property* of measurement-locality? Maybe entanglement would "prop up" space into three dimensions and be "propagated" by entanglement with and in the quantum vacuum.

[@JohnDlugosz]

I don't see how that would work. Entanglement emerges from the amount of freedom in Hilbert space. Measurement Locality is an axiom that the fundamental interactions occur at a common point in spacetime. How does imposing Measurement Locality cause the apparent nonlocal description of entanglement to occur?

[@seandimmock5813]

When’s the quantum textbook coming!!!!!

[@ToriKo_]

@@mark_huisjes thanks for the rec

[@lenhorn9170]

you’re explanation on cutting your hair is the first thing i’ve half understood in your series

[@ToriKo_]

Hahahah

[@msanguanini]

Is it possible that vertical particles pop up due the result of space inflation?

[@iruleandyoudont9]

one thing I didn't understand, aren't there still infinite possible wavelengths even if you set a minimum scale? aren't there an infinite number of wavelengths BETWEEN any two wavelengths?

[@Ni999]

Mathematically, yes. In reality, no. If it were possible then your kitchen oven would not only be capable of generating infinite energy, it would be required of it. That's a simple answer, you can find details on the full problem by looking for _the ultraviolet catastrophe,_ as that's the common name that we called the problem. It was solved by the discovery of quantum mechanics. If I understood correctly, Sean is going to cover the Planck constant next and that will probably contain a detailed answer to your question.

[@ravtastic9802]

For the same reason as having a confined area means the maximum wavelength is the size of the box and no larger and all others are integer divisions of that... On the other side all must be multiples of the smallest wavelength otherwise you would have noninteger wavelengths inside any box and there's the infinity again. If you have a largest and smallest size and must have integer divisions then there can only be Large/Small number of possible frequencies without violating that all boxes must have a 1 2 3 4 etc... waves in them.

[@DApple-sq1om]

True in general, bur not true for STANDING WAVES.

[@eefaaf]

I was so hoping you'd say "I'm 110% sure you can't have a probability greater than 1"

[@johnbach3144]

Just finished 'Something Deeply Hidden', I made it to where you mention the reference to the title of the book! It's a perfect quote for the title (I feel good in spotting it since I suspect many readers would either have missed it or not gotten that far). For your next books, please make the references to the titles even more Deeply Hidden - I will enjoy the challenge of looking for them!

[@GETMEASTRAITJACKET]

I doubt you could do slob you're far too cool.... and no offence but thank you for helping me wind down and sleep in the evenings. Love from the UK XxX

[@barefootalien]

Okay, I actually do have a question on this one... If "electronness" as we're calling it in our simplified code, (lepton number in the real world) is a preserved quantity, and an electron neutrino can carry "electronness", what happens when the anti-electron neutrino spontaneously changes flavor? Obviously the answer is "lepton number is only approximately conserved, and neutrino oscillation is exactly one of the things that violates it", but... if it is violable at all, in a way that, it seems to me, in no way involves an external influence that would explain that violation, then why is it conserved at all, even approximately?

[@JohnDlugosz]

No, all the different neutrinos have the same lepton number. Likewise, the electron, muon, and tau all have the same lepton number. All leptons have the same lepton-ness: electrons, neutrinos, and quarks of all three generations. Don't be confused with his use of the word "electron-ness" as that (electron/positron and it's matching neutrino only) is not a thing. Lepton number is conserved absolutely in the Standard Model. Gravity doesn't count, and processes beyond the Standard Model (like Supersymmetry) are completely unknown and have never been observed, although it must have occurred shortly after the Big Bang.

[@barefootalien]

@@JohnDlugosz Ah, right. Yeah, I'm pretty sure I knew that somewhere buried in my brain, and was confusing it with lepton _flavor_ rather than number, and it's lepton flavor that is only approximately conserved, with neutrino oscillation violating it. As I understand it, though, the possibility still exists that neutrinos may be their own anti-particle, in which case would they be considered to have a lepton number of both +1 and -1?

[@ExcretumTaurum]

Internal pressure? You’re sure Jennifer didn’t have some influence?

[@Progameroms]

thats probably what he meant...

[@bobdole57]

I still haven't gotten my hair cut. I look like Paul Mccartney from Let It Be

[@Petrov3434]

Degrees of freedom --- Penrose uses them as his argument that "string hypothesis" is -- mere fashion.... I don't understand anything here ;-))

[@Saitama62181]

The equation for the "mass shell" appears to be analogous to the Pythagorean Theorem. What's that about?

[@Ni999]

It's the result of setting c to 1 (as in 1 light_second/second instead of 299,792,458 meters/second) for computational convenience and then just leaving the c off because it takes more work to write down term than is convenient - especially when it can be a distraction. Strictly speaking it was wrong but it's a common wrong that we don't care about in terms of some bigger context. Physics is full of that as practiced. Here's special relativity - E² = (mc²)² + p²c² You might say that the first term is potential energy and the second one is kinetic energy just to help get your arms around the bits to follow. The squared part of E² came from Dirac and led to a concept of antimatter that surprised everyone by being a real thing. Remember, √4 can be either 2 or -2? Already the equation goes places that surprise us. Take a thing that isn't moving - it has no momentum or velocity, so that second term goes to zero because p=0. That leaves - E² = (mc²)², or E = mc² If it's massless like a photon, the first term goes to zero because m=0, so you get - E² = p²c², or, E = pc Light has energy without mass so momentum isn't based on mass and velocity for it. For light, p=h/λ (λ is the wavelength) and with algebra - E = pc = hf And that's the Einstein or Planck-Einstein equation for the quantum energy of light. For a normal anything else that has mass, it does have momentum but the classical p=mv (mass × velocity) isn't good enough for relativistic speeds so then we get a thing called γ (gamma - same Greek letter we use for the photon because we have all the letters re-used and physics tests need to be hard (lol j/k)) and - γ² = 1/(1-v²/c²) E² = (mc²)² + γ²m²v²c² Which believe it or not (I can show you if you want) using some tricky algebra (and nothing else) leads to the popular and easier version for - E = γmc² That leads some people to claim that mass is relativistic when it's not (and Sean mentioned early on that it wasn't and that point would be important) but it's just γ (gamma) describing time dilation and length contraction when necessary. So what it really means is that - E² = (mc²)² + p²c² E² = m²c⁴ + p²c² And that takes a lot explaining so Sean just said in parentheses that "c=1" and that was important to mention or the units wouldn't work out. After all, 1⁴=1²=1 so it's easier to just skip the whole thing and just say that the mass shell is in - E² = m² + p² Even though it's technically a lie really is just physics shorthand. That it looks Pythagorean is coincidental but we may yet see him using it in a Pythagorean way. Just remember that E² = (mc²)² + p²c² is a Swiss army knife in physics. What may really interest you, and you may already know this, is that you can use the Pythagorean theorem and the fact that c is a constant regardless of your speed and follow in Einstein's footsteps to not only see that time and space are relative but actually quantify by how much by deriving γ. My favorite video on that is from Sixty Symbols, I'll post the link... _Why is time slower in rockets?_ kzbin.info/www/bejne/eanUm6yibJmcq5Y The other big lie that's also just shorthand is when we describe mass in _electron volts_ which is an energy term. If - E = mc² then m = E/c² And if c=1 and we're among friends, then E=m. ¯\_(ツ)_/¯ PS - please excuse the typos and the length of the answer.

[@Missle636]

If you want to make the true analogy to Pythagoras, then you should write it as m² = E² - p². That might seem strange at first because now there is a minus sign... But remember: spacetime is not Euclidean, it is Minkowski. The mass-shell equation is really nothing else but the spacetime interval s² = t² - x², written in terms of different physical quantities. Now the link with Pythagoras is most easily seen. The Pythagorean theorem d² = x² + y² tells you how to measure distances in Euclidean space, while the spacetime interval tells you how to measure distances in Minkowski space (a.k.a. spacetime). The minus sign in Minkowski space is essentially there to make the speed of light constant.

[@ToriKo_]

@@Ni999 appreciate the thorough comment

[@Ni999]

@@ToriKo_ My pleasure. 👍

[@ToriKo_]

@@Ni999 I’m curious what was ur path in learning physics? Do u have a degree?

[@novalongclaw5215]

I need you to take 12 steps back and start again.

[@JohnDlugosz]

@@PetraKann Yea, looking at isolated sample frames, one might have thought that they could be put into order based on follicle length, but now we find it's a cyclic function like a wave, rather than a continuously increasing function. Although I can well imagine that mathematicians don't like haircuts because the discontinuities makes them queezy.

[@quantumzoflyne]

I like the interaction part about the haircut 😂🖖🏻

[@raymondluxury-yacht1638]

Surely you could pull off the "mad professor" look with your hair!

[@rljpdx]

less hair more science ;) just kidding, just started another one of my favorite shows...i know grade a content is forthcoming ;)

[@rljpdx]

oh no the hair slob bit got me (i need a hair cut)...

[@twinnerNet]

Quarantine hair growth is irrelevant if you've been growing it out for years already like me.

[@bmoneybby]

You have to fight through the shitty part of growing your hair out. Then after 1 year, the same people who thought it looked like trash will tell you how good it looks. It's empowering you just have to see it through, see yourself how you really look. Which is sexy my friend haha. Think like a rock star. Cause you are haha

[@MrPlatonist]

Looking like a slob here, but then again, i probably did before the lock down as well. lmao

[@randylamonda460]

Why isn’t the Higgs bozon the same thing as a graviton

[@JohnDlugosz]

Why isn't a banana the same thing as a potato chip?

[@randylamonda460]

@@JohnDlugosz Well actually, I've had banana that was like potato chip! LOL

[@voges1001]

Uhh what?

[@nmarbletoe8210]

Energy and matter both cause gravity, so Higgs doesn't change anything in relation to gravity.

[@deeprecce9852]

Hahaha..we dont give a damn about your hair Professor, its what inside your head that we are all here to learn and be WoW..🤭🤭🤭

[@ssshurley]

Yea we do... lol

[@ssshurley]

He’s a ⭐️ ✨🪐⚡️🌜🌛

[@arlenestanton9955]

TFTST

[@joshua3171]

pause and google.........

[@Valdagast]

Internal pressure? You mean dark energy causes haircuts?