Why The Schrodinger Equation Fails at Relativity

[@AndrewDotsonvideos]

A correct submission has been made!

[@K24_ej1]

Andrew Dotson How long did it take you to get to this point in your understanding of physics? My question comes from the fact that I am 27, but only recently decided to change directions in life to push towards my true passion of majoring in physics and seeing where it takes me. Anyways, just curious man. Thanks in advance.

[@possiblepilotdeviation5791]

@@K24_ej1 Romans, I can't speak for Andrew, obviously, but I can briefly tell you my experience. I decided to make a career change when I was 28. I was in a dead end job with no prospects, so I decided to start working on a Physics degree at my local University as a part time student (2 classes per semester). Bear in mind that I already had a degree (art related), so I did not need to take my General Education classes again, just the math and science courses. I kind of had to reshape my entire life. I needed to keep a full time job to pay the bills, so I applied for and finally found a full-time clerical position at the school I was attending. I was able to get a tuition discount from the school since I was an employee, use my lunch break for classes, etc. That was about 4 years ago. I'm almost 32 now. I graduate this coming May. I have a bunch of applications out right now to graduate schools to hopefully start my PhD work in the Fall. If you are dedicated, persistent, and perhaps a bit obsessive compulsive than anyone can learn the material. It's the whole "4 years of your life" thing that will stop most people. It's been a major undertaking, but worth every second for me, especially since I can finally see the light at the end of the tunnel. The material he is covering here is, truth be told, not overly complex. It's certainly not beginner material, but it's not the most complicated either. Good luck with whatever you decide.

[@K24_ej1]

Lyle Arnett, Jr Thank you for the reply Lyle. That definitely gives me a boost in confidence since we seem to be (were) living in the same boat. Dead end job. GE our of the way in college etc. I’ll take note of the things you said. I do appreciate it. 🙏🏻 thanks so much.

[@mikasaackermann8736]

Lyle Arnett, Jr What kind of art did you study, and why did it lead you to a dead end job? Asking 5 a friend

[@carlosvargas2907]

@@K24_ej1 You'll do well, man. Go on!

[@jibran8410]

Lvl 1 crook : Schrodinger Lvl 100 Boss : Dirac *THAT'S HOW QUANTUM MECHANICS WORKS*

[@arroyhondo]

Mike Warrecker that’s how mafia works

[@wotchadave]

What does that make Feynman?

[@ffggddss]

C'mon now, Schrödinger still did a very useful thing there! Just as we don't need even Special Relativity to do a lot of physics, we can still do a lot of QM with Schrödinger's Equation. It gives us quantized energy levels for confined particles, hydrogen wave functions, quantum tunneling, etc., etc. Fred

[@jibran8410]

@@ffggddss Yes I understand, it's just a joke going on around here on the internet with lvl 1 crooks and lvl 100 boss.

[@ffggddss]

@@jibran8410 OK, thanks for the warning. I'll be on the lookout for that ;-) Fred

[@marcusrosales3344]

Huh? Did I just get assigned homework?

[@EpicMathTime]

You are going to be an incredible lecturer and physicist.

[@krishnasimha8097]

Hey epic math time

[@alexp1113]

Do you hype yourself up before saying, “What’s going on smart people”? It’s always on point.

[@AndrewDotsonvideos]

I'm just naturally hype af

[@Shanksdan]

Glad to have stumbled upon your channel. Physics is really all about asking yourself why something is wrong/ right and actually calculating the answer by yourself (and of course, coming up with a hand waving argument before ).

[@dibidus6080]

Why am I watching Wolverine's lost brother talk about quantum mechanics at 1 am? We may never know.

[@sce2aux464]

And after this video, I watched...kzbin.info/www/bejne/a6imnZeNpM13f8k

[@hotlinkster123]

The first time a youtube recommendation has actually been good. Subscribed!

[@AndrewDotsonvideos]

Malcolm Hall awesome!

[@masoomladka5646]

@@AndrewDotsonvideos 😭😂😂

[@pwkn86]

Schrodinger did an OPPSIE!

[@jamestheotherone742]

But still hoodwinked a generation of mathematicians, physicists, sundry academics , politicians, and generals and made off like a bandit.

[@woofle4830]

Both the schrodinger equation and relativity work... so what point is anyone trying to prove here?

[@Nebukanezzer]

@@woofle4830 but not together.

[@woofle4830]

Ohok

[@juanjoserodriguezvera2405]

@@Nebukanezzer exactly and with this demostration we define one of the problems scientists want to solve

[@Ricocossa1]

5:06 This is why we often express vectors of the holonomic basis as ∂i , since there is really an equivalence between vectors and directional derivatives as well as how vectors and partial derivatives transform. In good old flat space this is just a curiosity, but this is crucial in Riemannian geometry where you want to define a tangent space without an embedding. The tangent space can be defined as some abstract vector space made out of directional derivative operators.

[@williamky8842]

The only explanation my lecturers give us was SE doesn’t treat spacetime on equal footing, KG and Dirac does Nice to see some more detailed explanations

[@WesSlEy954]

I’m proud of myself for being able to keep up with all the calculus going on here

[@ElSachinoo]

Nice! Another pre-maths observation: The Schrodinger equation (for a free particle) has a fixed mass value, which is also a relativistic red flag. Another decent exercise: Showing the Schrodinger equation is invariant under Galilean transformations - this also lets you see that mass defines a superselection variable in nonrelativistic QM ('Bargmann mass superselection rule').

[@HardHitnHstry]

I swear physics should also count as a second language.🐈🤯

[@ClayonTutorials]

Math is literally a language, and so is logic. Look up formal systems and formal languages for more information. English is a natural language (along with the rest of the spoken languages).

[@nosirrahx]

@@ClayonTutorials I was going to say something similar. Physics is a nation, they speak calculus there.

[@wolflarsen1900]

math, logic, geometrie are per definition languages. All Equations are sentences about quatitative or countable relations of individual elements of a defined universal set and so on. They all have the same structure as normal languages, they have a syntax, a semantics and a truth value and the only thing which can be true is a sentence (ok in normal language its utterances, which include context and sentence, because in normal languages there is also a context principle)

[@narata1541]

@@ClayonTutorials True, but I'd rather order my food in any other language than math. 😊

[@ClayonTutorials]

@@narata1541 But you should always "order" your internet using math: kzbin.info/www/bejne/kGSsgYmNg5JkodU.

[@Ohmau33]

I love coming back to these videos and understanding them a little more each time

[@thebigoeuph]

For my class that I TA'd for, we actually did that as an extra credit assignment...

[@materiasacra]

Instead of working out the coordinate transformation, one can glance briefly at the equation itself. It expresses the non-relativistic relation between total, kinetic and potential energy in the operator form required by Quantum Mechanics: E = p^2/2m + V. This is essentially different from the relation in Special Relativity. Done.

[@yenco4]

Grandioso encontrar un canal así y con tanta naturalidad

[@michaeljburt]

Extraordinarily clear explanation of the mathematics of both Lorentz transforms and how to apply it to an equation involving space and time. Absolutely fantastic. So many folks talking about these aspects of physics have never done the math. It is abundantly clear that you have, likely many times over.

[@argentinephenomenologist]

I like the initial explanation, and I love the fact that there's so much I'll get the chance to learn in some time to understand the following part. Greetings!

[@ThimbaDM]

My god this looks and sounds so tough. I going through high school, studying mathematics and physics and I'm about to apply for a university and try to get my masters in medical physics. Feels like I have a long way to go when I compare my high school material to this. Oh well.. I'm not afraid of hard work.

[@CaridorcTergilti]

Do not worry this calculation Is very easy, just standard derivation and substitution. You will understand It fully in a few years

[@DrGamez123]

doing quantum physics at uni RN, hyped to ask this question in class to make everyone roll their eyes, and for the lecturer to get slightly annoyed

[@sahilnaik3079]

Aha I love these videos. Tell me who doesn't want to watch that after waking up. Great video!!!

[@featherinescat]

In anime world, mentioning Schrodinger will make you smart

[@rituparnakundu2022]

Thank you Andrew for showing the rigorous calculation . I like to point out that without going through the long functional derivative part for the 2nd order term you can just square it. (d/dx)^2 = (rhs)^2. That will give the same result and a big time saver.

[@Wecoc1]

1:34 You know this is fucked up when even the Unicode missing letter square is a parameter on your equations

[@flaviusclaudius7510]

I was always confused when I heard that the Schrödinger equation was non-relativistic, when I knew you could just sub in a relativistic Hamiltonian and it just works (being identical to the Dirac equation); I didn't realise that 'the Schrödinger equation' and 'the general Schrödinger equation' were considered distinct, because I'd always only been taught the latter i.e. id/dt=H. I guess this makes sense now.

[@commaspace2196]

You could've made this way easier by approximating the whole thing to be 3.1

[@tapferetomate914]

If you say that the Schrödinger equation is i d/dt [e, t> = H [e, t> it totally works for a special relativistic hamiltonian. The familiar wave equation form of the Schrödinger equation is just it's representation in Position Basis with THE non-relativistic Hamiltonian: H=p^2/2m + V(x) In the case of a free relativistic Scalar particle: H =1/2m^2 * (pI * pI + m^2) where pI denotes the I-th element of Momentum, where I=2 or 3 This is so called lightcone quantization Add a potential V(x) and you're good to go. (you then obviously have a non-free Scalar particle)

[@dXoverdteqprogress]

There was a mistake in your proof. You assumed that the wavefunction is a scalar -- it is not. Let's take psy to be a Gaussian which, at it's peak, has the value p. In a primed frame the value at the peak cannot be the same as p because if you Lorentz contract a function that preserves probability, the peak will be larger. Taking this into account does not save the Schrodinger's equation from being non-relativistic, but people should be aware of this argument.

[@danielplacido8746]

But the wave function is scalar. Complex, but scalar.

[@dXoverdteqprogress]

@@danielplacido8746 Nope. It changes under a Lorentz transformation.

[@dXoverdteqprogress]

@MetraMan09 For a constant velocity, gamma is a constant; it only varies with time when you have acceleration.

[@colfrancis9725]

@@dXoverdteqprogress Wish I had seen this comment before I spent time writing my own.

[@alexbaykov9221]

Schroedinger started with relativistic equation, the calculations following this approach were inconsistent with experimental results of that time, so he did a non-relativistic approximation, which is exactly the Schroedinger equation we know. When the experiments became more precise, the need for relativistic approach became obvious.

[@brandonmartin9416]

I don’t know what the hell is happening, and I’m not a physics major, but I continue to watch anyways.

[@joaopedroaguiarfmatos1473]

i just saw partial derivatives at university,im feeling really smart for understanding ate least 10% of this video

[@bobbypederson]

I wish I was able to understand this video so I could do the challenge at the end

[@AndrewDotsonvideos]

What there anything specific that was unclear that I can work on?

[@bobbypederson]

@@AndrewDotsonvideos oh no, it's not your bad, just a bit of a lack of understanding on my part.

[@rufusapplebee1428]

@@AndrewDotsonvideos formulations in applications is algorithms. I am not smart enough to follow formulations, always. Takes me long time to get to the applications, then guess the algorithms and then look at the formulations and definitions of the universes and multiverses. The attempted long term goals of the algorithms is to change the definitions.

[@pushingpositivity518]

I like your videos. You definitely know your stuff. Also i like your shortcut videos an they way you do integrals & differentiating. Thank you.

[@Adam-pv4qn]

I'm so dumb I literally don't understand any of this but I'm still here to support.

[@LukeBurns]

It's worth noting that not only is the Schrodinger restricted to the non-relativistic domain, but it is also restricted to the description of electrons in a spin eigenstate! The Pauli equation is a non-relativistic approximation of the Dirac equation that reduces to the Schrodinger equation when in an eigenstate of spin.

[@mokopa]

3:25 It was at this point that i gave the video a like, and settled in for the long haul

[@noir935]

Do you struggle with Calc I-III,Differential Equations University Level Physics 1&2 Newtons Laws and Electromagnetism? If you are, make sure to >dotsontutoring.simplybook.me/v2/#

[@danielbachour9987]

Awesome man! I'm new here! Didn't know about your channel! it's amazing! And of course, already subscribed!! Keep the work going!!

[@christianfunintuscany1147]

Hi Andrew! Regarding the Schrodinger work and the process he used to find his equation it may be useful to read his article on Physical Review n.6 Vol.28 December, 1926. In pragraph n.10 he explains why he didn’t include a relativistic analisis.

[@emmanuelfchea]

I am proud of myself that I understood almost 96% of what was presented. I am a Physics major with minor in Mathematics. I still have more work to do. Kudos for the brilliant explanation.

[@addas1392]

Me too...🎉. I am really proud of myself. I did have to rewind on some parts. But I got it. Thank you Andrew. One thing I did not realize until now was how we could apply all the mathematical physics stuff into every derivation and understand that these are correlated. I am so inspired.🎉🎉🎉

[@heavennoes]

me to, I'm going 5th grade and I am proud of myself for finally getting what is going on after a lot of work.

[@worldedit8784]

I'm so happy I found this channel!!!

[@Sciencationelle]

I've got a real question. Love your vids, bringing some real physics on youtube, that's juste pure kindness and it is quiet satisfying to watch :) But in your video you said multiple time that "Schrödinger's eq. leads to wave equation" I'm not quite sure, this is what De Broglie said "stationary wave" but in fact all the Schrödinger's eq. solution's aren't wave, the solution are just "stationary state" without the proper form of a wave eq. Anyway that's what I've been told. I would to hear you on that one :) !

[@ActionPhysics]

On the same line of thought you will see that gallelian transformation doesn't keep SE invariant. But actually it does. While proving such invariance we can't simply take psi going to psi prime.

[@ActionPhysics]

We have to keep a phase factor then this problem gets super duper complicated

[@exegetor]

subbed. (decided by the 4min mark) Please keep doing this Andrew!

[@jeshurunluke5573]

Looks like ur daily upload schedule is always on the dot(son)

[@maxwellsequation4887]

Andrew Son cosθ

[@Zaalatrix]

Great video Andrew! One question though: Since v(x,t) = \frac{ \partial x}{ \partial t }, should't you also differentiate the v^2 terms when you Lorentz transform? Cheers, Henrik

[@marioangelov113]

No, he doesn't differentiate them, because v is constant, so that makes the whole γ factor a constant. Because v is the velocity of the moving inertial reference frame S'. If v was a function of t that would mean, that S' is not inertial, because it would have acceleration.

[@suryavasanth6893]

I love quantum physics after I saw ur lecture.

[@rafaelaguilar123]

Water is wet. Change my mind.

[@AndrewDotsonvideos]

you cant spell water without wet + ar because water ar wet

[@rafaelaguilar123]

*Galaxy brain*

[@waveexistence5742]

Water can't be wet. Wetness is a property of something with water on it. If water has water on it there is just more water, not wet water. You inherently need a second object in which to frame the state of wetness. So a bowl with water in it could be described as wet. But a globe of water floating in the vacuum of space is just water.

[@masskiller9206]

@@waveexistence5742 C-C-C-COMBO killed it lol

[@رضاشریعت]

Amazing!😂

[@YdarklifeY]

From the view of someone that is also studying physics that was very well explained ^

[@quTANum]

I think you can directly square the partial x differentiation operator? It'll be easier this way, since we don't need to apply the definiation of it again.

[@aram9167]

goddamn it you sound like an awesome teacher to have

[@AndrewDotsonvideos]

tysm

[@brianel-khoury885]

Love the medium level of rigour. I subscribed. Keep it up.

[@tuskiomisham]

we learned about the 2d wave equation in my semiconductors class. it's a beautiful thing, but it can't explain a lot of stuff

[@Calilasseia]

Nice and concise. I could think of a few lecturers who would do well to emulate this performance. :)

[@AdityaKumar-ij5ok]

1:36 why physicists always love to forcefully shorten their equation by using alien symbols

[@GeneralPet]

Operators are used elsewhere too

[@emmanuelfchea]

It gives you a better understanding of what happening as you solve the physical problems.

[@bilalhussein9730]

With that particular notation it has two nice uses: it tells you in a millisecond that the equation is Lorentz invariant and makes finding the Green's function extremely simple. It's a lot easier to remember the following: 1) No free Lorentz indices means Lorentz invariance 2) box +m^2 -> 1/(w^2-p^2-m^2) in momentum space. This is just a Fourier transform. Why write more down then you have to? General relativity can get tedious enough to work with using index notation/ differential forms. It would be an absolute nightmare without it.

[@doodelay]

Watching this I'm so proud of you bro, you understand this shit like it's second nature. And I know that took crazy effort. Will meet you at the top someday

[@peterwan9076]

Great work. Keep it up. Enjoy your video very much.

[@zhelyo_physics]

Fantastic video!

[@thelocalsage]

Really liked this video! Would like to see more like this.

[@mislavnorsic6681]

awsome video, try to add some mic to your place so that sound can be captured when you are not faceing the camera.

[@theultimatereductionist7592]

Which equations should we use for large systems of molecules?

[@ghanshamchandel1854]

Newtons. If wayy to big, then Einsteins GR.

[@vinirn]

I've subscribed to your channel at the first minute of the video.

[@katherinebolwellbyme]

I forgot how to do the chain rule, this was a great explanation/refresher. P.s. I never knew that a mu could be written as a little m.

[@katherinebolwellbyme]

Also it's not pronounced d

[@victorhakim1250]

Hey Andrew. Here's my main confusion: it looks like the Schrodinger Equation isn't even invariant under Galilean transformations! In particular, looking at the final equation you wrote, taking the limits as v/c approaches zero and gamma approaches 1, there still remains the rightmost term of the right side of the equation. Any ideas on why this lingering term appears?

[@victorhakim1250]

Ohhh I've figured it out. That "lingering" term actually needs to be there! (tldr: the Schrodinger equation is in fact invariant under Galilean transformations.) In taking the partial with respect to t', we're taking x' to be constant, not x. But in verifying the validity of the transformation, we have to start with the non-transformed Schrodinger equation, which originally uses psi(x,t) not psi(x',t'). In taking the partial of psi(x,t) with respect to t' (keeping x' constant, not x!), there is an extra term v(delPsi/delx) which is exactly what is cancelled out by the "lingering" term.

[@isaaccastro7853]

Glad to have just stumbled upon this!

[@camilosoares9132]

Do one on the black hole electron (simple math)...i stumbled across that by accident and would like a video and the hypothetical it can be. By the way i deduced it biologically (using physical limit and not mathematical limits). From what i understand that wasn't the first time black holes got over looked ;)

[@hbarudi]

Completed this entire major in physics, but still not much info is taught about equations being general relativity or special relativity besides the obvious such as Maxwell's equations and the E=mc2 equations. But I think Schrodinger's equation describes only the wave and simply gives a probability for where the particles is but does not tell the speed of the particle, just its energy and mass are involved. There is particle wave duality and Schrodinger equation focuses on the wave part.

[@qizhengli5685]

Very interesting video! Although I think it will be simpler to derive it if considering the relation of ∂²/∂x²=(∂/∂x)² =(γ∂/∂x’-γv∂/c²∂t‘)²

[@qizhengli5685]

which is to regard the partial derivatives as operators.

[@TheDarktsun]

I'm wondering if we should interpret this as the Schrodinger Hamiltonian is invalid at high energies, or that the energy is observer-frame dependent...Watching your Klein Gordon derivation next, thanks for the great videos.

[@philippjohannsen6217]

Great stuff with this homework thing going on. Looking forward to more challenges :))

[@linuxgaminginfullhd60fps10]

Some people say relativity and quantum mechanics are incompatible. I am new to your channel and don't know if you made a video about it. Yet you need relativity in any physical theory to properly describe magnetic field. In quantum mechanics you would need Dirac equation(which is relativistic!) to derive spin. Some people talk about black hole entropy paradox(as one of the reasons why they are not compatible). Wasn't that resolved years ago? Others talk about "quantum teleportation"... which does not transmit information, thus does not violate finite speed of information transmission(aka speed of light).

[@treborheminway1196]

Question:If entanglement is a defining aspect of QM,why would you expect relativistic terms in equations describing it. Isn't that essentially why folks like the whole " The universe is a hologram " idea? Doesn't entanglement mean there is no spacetime at the am level????

[@pipertripp]

Good craic. Enjoyed even if I have only the dimmest understanding of quantum mechanics.

[@alapandas6398]

I think the we should get psi'(x',t')=psi(x,t)(1-v²/c²)^(¼) to make the probability in the same region to be equal in both frames. Because probability should be invariant. And this psi' satisfies Schroedinger equation in psi does. By the way I got that equation you wrote but d²/dx'dt' terms vanished. I think I did some calculation mistake.

[@ThomasGutierrez]

Great content as always. However, \hat{H}\Psi=i\hbar\dot{\Psi} the "Schrödinger equation" does still work relativistically and is used in QFT (with the right Hamiltonian) to evolve the state vector in Hilbert space. The KG and Dirac equations aren't "wave equations" but rather best interpreted as "field equations."

[@OBGynKenobi]

Which brings up a question. Where is the line between relativistic and non relativistic. For example up to what limit does Schrodinger equation work? ie, what is the fastest speed an electron can go and Schrodinger still works?

[@AndrewDotsonvideos]

Go Mezant The answer is always “it depends on the error you’re willing to accept”

[@medexamtoolscom]

Isn't it weird that special relativity is automatically already built into Maxwell's equations, but not the Schroedinger wave equation? It's true, light travels at a constant speed by the wave equation solved using Maxwell's equations, it just naturally comes out that a wave is predicted to move at speed 1/sqrt(µ0*ε0), and like magic that happens to be c.

[@harrisonhutton]

When you would sit down for a lecture, how would your professor(s) introduce something like this?

[@geoffrygifari4179]

hey andrew, new sub here... i think there was a slight missed opportunity, for if you did cancel the gammas and show in the video the limit of v/c -> 0, you might retain the usual schro's eq with x' and t', thus showing that schro's work in the nonrelativistic limit

[@AndrewDotsonvideos]

Right but at first glance you don't recover the schrodinger equation because there's still the extra factor of d/dx'. You'd need to place more focus on the wave function itself to get everything to come out alright under Galilean transform.

[@geoffrygifari4179]

you're right! my bad

[@AndrewDotsonvideos]

Geoffry Gifari no what you said would totally work, it would just be a lot of effort😅

[@PrivateSi]

Certainly is a mind bender... I like this interpretation of quantum 'relativity'... Be interesting to see if the standard model could be derived. It's compatible with Bohmian mechanics. Liquid Crystal Space -- Bottom-Up Universe Thought Experiment.. Colloidal Crystal Multiverse Constraints: 3D, minimal base rules + parts. No singularities with the infinite possible -ve flux and +ve cell attraction = 2x repulsion. Balances as a close-packed lattice 1 Cell volume of flux -6, Cell +6. Pulls 6 opposites to light speed in 1 cell length Escape velocity = light speed (C) tied to the constant time light takes to move between cells Tunneling: stretched, faster than light front, light speed or slower rear Tunneling cells form in phase extrons+holons that often annihilate to regular='empty' lattice Tunneling particles reform elsewhere and their original space 'heals' as regular empty lattice Particles: Inflows repel. 6 equatorial and 2x3 polar flows (-6 if poles flow in, +6 if out) Extron: extra cell compresses the lattice, pulls flux (that pulls cells) that repel as rays Holon: flux-rich missing cell hole stretches the lattice, pulls in cells that repel as rays Dipolons: extron + holon.. Diextron: +ve + -ve extron.. Diholon: +ve + -ve holon Tempons: Cellon: lattice chunk.. Fluxon: holes.. heal to extrons+holons and/or/then annihilate 3D polar flows are more concentrated than flat equatorial flows so effect particles more Moving extrons push cells that -ve flux space behind pulls in with an inertia-providing kick Particles are surrounded by pilot waves that can diffract, interfere and alter trajectory Strong gravity may force (some) particle outflows to repel back to its inflows in a few patterns Charge Flow: -ve inflows, +ve outflows. Polar flow count. Lattice, extron, holon charge Flow has mass, gravity affects flow. Close flows attract or repel, outflows may join inflows Particles absorb charge flow force as they symmetrically accelerate cells to light speed anyway Dipolon / Matter-Antimatter: gravity shrinks matter, lowering charge emission phase resolution Close out of phase extron+holon pairs form dipolons, in phase annihilate and radiate excess flux A feeding black hole's core extrons+holons are forced in phase and annihilate. A universe grows Black Hole Universes / Recursive Conformity: Big Bang = black holes colliding and merging Gravity compacts extrons+holons, blurs phases, charge flow stops at light speed. Annihilation Total energy and matter potential is conserved. No fine tuning, universes follow the same rules Level n +/- particle lattice fields or other (joined) particle fields (+ free particles) feasible Mass / Gravity / Dark Energy: lattice charge balance, charge inflow, entanglement, universe shell Mass is (the number of) out of place lattice cells. An object's extron(s) + holon charge flow Mass pulls flux pulls mass. Lattice vibes up to 1 cell radius and light speed effect matter Outflows bounce in all directions, inflows lead to the center. Outflows tend to join inflows Mass uses up flux so void cells repel more. Universes trap cells so gravity shrinks the lattice Universes grow, shells thin, excess flux radiates, lattice expands. Shell gravity cancels inside Photon / Light / Time: relatively quantum.. particle vibes ripple charge outflows Transverse/helical waves concentrate charge flow mass to a point. 2D adds effective area Photons make lattice pilot waves that diffract in a slit but are overridden by a detector's fields Moves between cells in a constant time (+ universe expansion) as denser lattice takes more energy Gravity shrinks and acceleration compresses the lattice so both absolutely slow light locally Units shrink too and acceleration slows kinetic processes so local vacuum light speed measures C Velocity stretches kinetic processes in time as they travel more to complete. Clocks run slower The Standard Model: the possibilities are numerous. Some SM particles may be tempons

[@nahiakhan2135]

Thank you so much . Love from Pakistan ❤

[@fatematuzzohora5615]

you are a very good teacher you know that?

[@thiagotsutsui452]

Andrew, is there a way to do the same with Dirac's equation without using the relativistic notation?

[@largewoollybugger]

Andrew: I need more rigor Whiteboard: But, only (at most) 3 things are defined?

[@subramanyam2699]

Got so many connections in one video.. Tnx :)

[@acatisfinetoo3018]

I don't understand why the chain rule is used. My understanding is that it's used to solve composite functions, but i only did Calc one so this level of math is a bit beyond me...

[@bilalchughtai_]

Shouldn't you consider a multiplicative phase onto the wavefunction? When showing the Schrödinger equation is invariant under guage transformations for an electromagnetic potential we pick up such a factor in the wavefunction!

[@ゾカリクゾ]

Oh no... Your schedule will mess up with mine if you start doing these pbs-like competitions. You literally upload right after I go to sleep (I'm here now because it's saturday).

[@AndrewDotsonvideos]

Hmmm, actually, quantum mechanics forbids this

[@okmijnbhunji1316]

but lorentz transform is only for the special relativity right? should we work in functional form for the coordinate transforms, it would be more general i suppose.

[@tuskiomisham]

this is why processors above 6 GHz are not possible. a wavelength of light at 6 GHz is 5 cm. That's as big as the chip! you'd have to make the processor smaller yet, or decouple the ALU from time. currently the only time decoupling that is possible is with Q bits and observing Q bits. even then, the board and memory is still silicon, and subject to such limits. what im referring to is the early effect of a transistor. if you were to look at a cpu in ultra slow mo, the electrons would (most likely) look like ripples in a pond, with the epicenter being the clock itself

[@bryandepaepe5984]

Using liquid nitrogen the current maximum overclocked CPU frequency is 8722.78 MHz. The increasing electrical resistance from increasing temperatures is what limits frequency.

[@Dan-nh8nu]

Didn't have a scooby about what you were saying but watched it anyway :-)

[@wolframalpha8634]

You made my day !

[@arnoldbirkenhager1290]

Ha! You missed two primes :). Wouldn't have given you another result though, since you only forgot to write the primes and continued calculating as if they were there. Good job! Enjoyed the video and could follow along, but couldn't do it myself. A new Feynman in the making? Hope you aspire to be a teacher. Thanks!

[@steveagnew3385]

okay...the Schrodinger equation includes derivatives of space and time and relativity uses the equivalence of energy (or frequency) and mass to link space and time. So of course, there is no easy way out with the assumption of space and time. However, the Schrodinger equation in terms of matter and action is naturally Lorentz invariant and so the universe is made up of matter and action from which space and time emerge. Matter and action are the conjugates that link gravity and charge, not space and time...

[@xxyummyxx5]

Hi Andrew I'm about to start classical mechanics next quarter, any tips? Having anxiety and doubting myself a bit

[@chymoney1]

Thomas Marquez you can watch the whole class online so use youtube

[@ThisIsDjonathan]

I have no idea what’s going on.

[@animeshsah5843]

Can I ask for a book to study tensors intuitively

[@davisjohn-d6h]

Awesome video Andrew. Also I'm going to be taking my first electricity and magnetism physics class in a couple weeks, do you guys have any recommendations on good online resources to look at to help me in E&M?

[@corydiehl764]

walter lewin, and griffiths book

[@swish6143]

Definitely the Griffiths book. Greets from Frankfurt