Your Daily Equation #13: Generalized Schrödinger Equation

[@ky-effect2717]

This is absolutely great! We need more hard core math and physics in open media. Everyone keeps "dumbing" down scientific explinations of everything but we'll never grow up if we get to ignore all the magnificent equations and mathematics that help to explain our universe. Keep up the good work

[@markrobertson6664]

Brian, please keep going with these!

[@LearnedSome]

I just love the way Brian can break down the most complex concept to everyday language like this. Really makes physics a lot less tedious. Keep up the great work!

[@Dr10Jeeps]

Thanks again Brian. I really appreciate your taking the time for these daily equation podcasts. You, sir, are a gentleman and a scholar!

[@mu.makbarzadeh2831]

"One for all, all for one." is one of the greatest quotations. My ability is teaching math for children and high school students who are in quarantin and can not use from their time to continue their studies. I think each of us can be capable to help at least one other person. It's time to run and do somthing toward happiness and give gifts for anyone. Thank you dear professor!

[@wailingyeoh6882]

Thank you so much, Brian, for The Daily Equation. I enjoy them very much even though I am only at Algebra level now. Please keep them going and also please keep these videos on KZbin for a long, long time because I am learning Mathematics and as I go higher level, I want to be able to come back and listen to you again. So PLEASE do not remove The Daily Equation from KZbin. Thanks!!!

[@jamescurtis1226]

Brian Green, You turn my brain to MUSH....I want MORE!!!

[@marioursin8539]

Dear Dr. Brian Greene. My question is in regard to "SPACE" or the "ETHER": Could you please explain, why physics doesn't pursue the research for the ether anymore? The Michelson Morley experiment has not been able to prove the existence of the ether. This raises to me some if not THE most fundamental questions in Physics: 1. Can we conclude from the experiment, that the ether doesn't exist? To my understanding, the lack of proving the existence is not equivalent to the proof of its nonexistence. 2. Is it not more proper, to interpret the negative outcome of the experiment that our theoretical concept of the ether was and still is incomplete? 3. Why has the research in the field of the ether been stopped just because Einstein recommended that we shouldn't bother about it?- (after all: Einstein was also proven wrong in his dispute with Bohr) 4. I saw your excellent documentation about "What is space". To my understanding, this is the best documentation on this topic so far! But it raised serious questions: if in the phase of inflation space expanded faster than the speed of light, and even now galaxies are drifting within the expansion of space apart from each other, are we not escaping the real questions by replacing the word "ether" simply with the word "space"? In other words: If space can move Galaxies how can we measure the speed of space relative to the own speed of the galaxies pushed by space? To my understanding, the Michelson Morley experiment had the intention to measure the speed of the ether or space relative to the movements of celestial bodies (like the speed of water may differ from the speed of the ships sailing in their own direction and speed). Why Physics has stopped to do research in reference to those questions:? What substance is pushing Galaxies? How we measure the speed of space? What medium is space to move as a wave of light? To me these questions are unsolved. A greater mystery even is, why these questions are not researched anymore in physics. …or have I missed a point here? I would appreciate very much your answer because these questions have remained unanswered for decades. So far teachers and professors have answered: "the medium of light is space, and that answers the question" but does it?

[@madavanraja3636]

I had a dumb question. If each particle is in the 3D space, then the coordinates of each particle are also multiples of the 3D space (x, y, z or r, l, phi or r, theta, phi). So won't the dimensions of the wave equation also be 3 as all the x coordinates of the particles will be the same and similarly for y and z? Why are there extra dimensions?

[@douglasstrother6584]

One can think of these higher dimensions similar to the concept of phase space in classical Hamiltonian mechanics in which each particle has position and momentum coordinates.

[@louiscorprew7970]

Thank you! Fascinating perspective on the wave function, I have not thought of it beyond the three dimensions we exist in.

[@rickmorrisrigar]

Professor Greene, You are an excellent teacher, I just love this, so glad you are doing it, although it hurts my brain, I want MORE 😁😁

[@ashheralikhan]

Loved these episodes ♥️💫 Thanks for uploading .

[@Meow_yj]

I have so much respect for you professor! :) Thank you.

[@toddvolyn9137]

Love this series! Maybe some of the classic physics equations like the laws of motion?

[@bluefinance153]

Dear Brian Greene, can you please explain the Renormalization in Quantum Field theory?

[@frun]

Yes, and can renormalization group flow be reversed ?

[@bluefinance153]

@@frun 1 I think the answer to the question is that not only the flow itself cannot be reversed, there is no flow which could take you in the reverse way, no matter what is the suggested path. Since there is a decreasing function characterizing any flow, then any RG flow violating this decreasing form is forbidden. In that sense the flow is irreversible - in the sense that a flow has a direction, and flowing in the opposite direction is impossible. since the flows are non-local, they can either increase or decrease the central charge of the CFT. In fact, given any local renormalization-group flow within a certain general class which leads from a UV theory (CFT_1) to an IR theory (CFT_2), we show that one can find such a non-local flow in which the endpoints are interchanged: the non-local theory flows from CFT_2 in the IR to CFT_1 in the UV. We work at large N, but the flows we consider involve quantum field effects in the bulk, corresponding to 1/N corrections in the dual theory.

[@kelvinlu8885]

I love this channel and thank you Dr Greene

[@bkkfootball]

Professor, just thanks!!

[@007myzorro]

AMAZING WORK Brian. Thanks a lot !!!!

[@robertdalziel165]

Brilliant session. Really enjoyed this. Now going to try and work all that through without referring to the video!

[@mcconkeyb]

It seems to me that the equation is more of a state equation as opposed to a dimensional equation. If it truly is a dimensional equation then it should lead to testable conditions for all of the higher number dimensions. Have any of these testable conditions been tested?

[@althomas6045]

I like when your quick videos are 30 minutes.👍🍺

[@AMATEURTUTORIAL]

Thank you so much sir .

[@kingoffire9373]

These are great!

[@mapeandrews3951]

If you still have space for requests I would love you to do the Wigner’s hypothesis (named after Eugene Wigner, the physicist who discovered universality in atomic spectra) Thank you.

[@interVULife]

I'm so excited to join the class 😁

[@mikebell4649]

Thanx Brian ! I’m on this module this year at uni’

[@fatherpig]

Hi Prof. Brian, first of all I would like to thank you for the videos. Secondly, what is your opinion of existence of higher dimensions and could you please introduce us to how to "visualise" these higher dimensions and how to work with them? Many, many thanks in advance.

[@jonnymahony9402]

He's pro string theory, so I think his opinion is, that they somehow should exist.

[@BarryKort]

At about 11 minutes into the video, where you take up the case of a cloud of particles distributed in space, it occurs to me there is a caveat about keeping a single shared value of time for all of them. Time-keeping is local, so if the cloud is confined to a local neighborhood, then it's not unrealistic to assume that they all age in unison according to a single shared local clock. But if you consider the case (e.g. as in the EPR scenario), where the distance between the particles can become arbitrarily large, then each particle ages according to its own independent local clock. So, for example, if there is a gravitational gradient present, particles ascending the gravitation gradient will age faster then those descending the gravitational gradient. The one place where this caveat is especially crucial is not so much for Schrödinger's Equation, but for derivations like those found in Bell's Inequality. In that case, by assuming a universal cosmic clock, it's possible to exactly cancel out any time-varying model for the states of the particles as they speed apart. But if you admit that time-keeping is local to each particle, then instead of perfect cancelation, you would end up with a non-vanishing "beat frequency" term that survives to the bottom line. To my mind, that's why Bell's Inequality does not hold in our cosmos. We live in a cosmos where time-keeping does vary from one spacial location to the next.

[@aBigBadWolf]

I wish Brian would address comments like those! Interesting thought.

[@remcoy1825]

This is the non-relativistic version of the equation, so it assumes that space-time is Newtonian, i.e it assumes that there is one absolute universal time.

[@BarryKort]

The (Newtonian) assumption of one absolute universal time is perhaps the most startling and important distinction between QM and GR. And it is in the EPR scenario where this disparity comes to the fore (especially in the derivation of Bell's Inequality). Time itself is the not-so-hidden variable, and "spooky timekeeping at a distance" is one of the features of GR that QM calculations must not ignore. There are gravitational gradients all over the cosmos which perturb timekeeping from one spacial location to the next.

[@dechou8921]

That was effing awesome. Thanks

[@robertbonitz6325]

An example of how one comes up with a wave function for a particle with an actual example would be useful.

[@mikaeltalgretarsson3437]

Woooooww you blew my mind. Never heard this n-dimensions interpretation of Schrödinger before. Why do number particles increase number of dimension? Why don't they just interact im 4D? Something missing???

[@mrigankasandilya7720]

Professor, make a video explaining about using Ramanujan's mathematics on Black Hole..

[@retepaskab]

Quantum physics (at least in the media) only talks about a few particles at once. Are there known quantum systems with a high number of particles? Is it somehow mathematically explainable that high number of dimensions in the wave function space collapses the wave function?

[@shouvikmondal1977]

SO, HOW MANY DIMENSIONS ARE THERE IN OUR UNIVERSE ? IS IT INFINITY ? OR, IS THERE ANY DIMENSION OF TIME AS LIKE THE SPATIAL DIMENSIONS ?

[@ky-effect2717]

My understanding is time and space is the same, similar to magnetic and electric fields there's only based on a perspective distinction. The term Spacetime is supposed to represent this concept of intimate integration.

[@martijn130370]

Great lecture. I have seen the definition of i = sqrt(-1) pop up many times here, but the only proper definition is that i^2 = -1, since otherwise if I remember correctly you get the possibility that i = - sqrt(-1) as well as the plus counterpart, since x^2 is not a bijective function

[@rlsfrny]

martijn130370 tears why it’s normalized with the absolute sign.

[@lautarokinalczyk838]

Does this have anything to do with the dimensionality of Hilbert space?

[@frun]

Yes, this IS a dimensionality of Hilbert space

[@goodsamaritan6401]

Best mathematician

[@venkateswarlumanti9427]

please explain FERMAT'S LAST THEOREM

[@NyteRazor]

Off topic. Anyone watch Devs? Finale is tomorrow. Anyway, multiple dimensions just reminded me of the TV show that is about multiple universes. So fascinating trying to figure out REALITY.

[@prayogdash3564]

professor Brian Greene can you please explain in the upcoming videos about STEPHEN HAWKING's equation on identifying the area of event horizon by the entropy of the black hole.

[@ShailendraKumar-ug4tn]

Are you talking about bekenstein-hawking entropy equation.

[@prayogdash3564]

@@ShailendraKumar-ug4tn yes

[@prayogdash3564]

it is a mixture of hawking's radiation and bekenstein's conjecture

[@muerpa]

I love these

[@davidhand9721]

This is why the Dirac equation and QFT are better. Among other reasons like eliminating double counting and so on.

[@neonblack211]

an now we will generalize the schrodinger eqution from one particle in one spacial dimension to multiple particles in multiple dimensions... and that's really quite simple! Ok Brian

[@kevinjamescreed]

Its that little piece of resistance... the difference between what knowledge is understood and that which is yet to be mastered... mwah, its been an experience 8 )

[@sayanpramanik6393]

Sir will you please tell us what is quantum entanglement?

[@Epoch11]

Why can't these particles/waves occupy the same dimensions.....or at least the same dimensions can be used to describe them? Also about the consciousness of atoms question I see the atoms ability to know what to do as some sort of awareness, because how does it know it should repel or move closer to another atom.......perhaps when you put a lot of these atoms together the sense they have is greater and allows for spacial awareness and then for more abstract concepts................just a thought.....

[@salesmoduna1070]

MIND BOWLING VIDEO.........

[@azwaryusoff662]

Can we move form here to Relativistic case?

[@nikko_301]

Help me get this please! Could the waves overlap each other in our three dimensions of space in such way that they add together and cancel each other out? If so, isn't this equation a little simplyfied in a way where the waves aren't added nor subtracted to/from each other - yielding the same mathematical result but without going through the hassle of adding and subtracting. I hope my english is understandable. And I promise to stay humble receiving feedback on my question, I realize I'm criticizing one of the greatest mathematicians our known human kind has encountered :-) Thanks for great content!

[@rhesarozendaal6551]

I'm not an expert, but the way I see it is that you need to account for the interactions between the particles, and that is why you end up with an equation that depends on all spacial coordinates.

[@frogz]

thank you again professor greene, i still would like some commentary or even a video on fibonacci in nature if you have time or know about the subject

[@frogz]

also, you hurt my brain every episode...please dont stop once this corona madness is gone, i am enjoying your videos too much and would LOVE to see this become a regular thing

[@ajeethkumar3569]

love you ❤

[@Domispitaletti]

Can i ask a dumb question? When you solve that equation, how you know you are correct in your probability? Can you tes it with some experiment?

[@dankuchar6821]

It depends on the answer, but generally that's the goal. Some answers we are incapable of creating experiments because we just don't have the technical expertise yet.

[@jonnymahony9402]

sure, these are results of experiments and QM makes very precise predictions. Without QM modern computers woulnd't work.

[@veruskapaninforni6439]

Do you mean that a wave function for two particles has 6+1 variables because we have to consider a single wave function represent the status of the two particles in the same time?

[@dankuchar6821]

As far as I understand, you have stated that correctly.

[@sarmadnajim4839]

Amazing

[@ismaeleye]

Sorry for my ignorance but, could anyone tell me how I can get a good definition on internet about dimensions...?? I only can see in the explanation .........different location for the particules in a single 3D space. Thanks.

[@frogz]

1d, you have 1 axis of freedom, left and right, 2d you have left right up and down, 3d you have left right up down in and out, 4d.... left right up down in out and back and forth in time, 5d... add another axis of movement/freedom, you can actually replace the time dimension with a spacial dimension and call it it's own thing and have as many axis of movement as you wish

[@wimukthihashan5]

thank u sir

[@Goldslate73]

Sir... With all due respect.... I didn't get the part with 6 spatial dimensions

[@wavenature3180]

The wave function is the complex square root of the multidimensional probabilities of the changing spacetime positions of many particles. Fun to ponder. The math definition is much easier to follow and more detailed than the word definition.

[@captainandthelady]

This isn't for the faint of heart...is it.

[@michaelwhalan9783]

Exams would be printed with a number of equations, so students did not have to work through this and panic. Teachers would show the working out knowing students would need further course in this.

[@dabrownone]

The d's in the integrations look like two's!!!! lol. Thanks for the videos. Very interesting

[@kevinwencel1485]

These are the symbols for partial differentiation. They are not normal d,s they are curly d,s, more like a backward number six. if you have a function such as y = 2x + x^3 then you only have one variable so correct symbol for differentiation would be dy/dx. However if you have a function such as y = x^2 + 3x + 3t^2, then you have 2 variables and you have to carry out partial differentiation on each variable separately and the symbols would be curly d/dx or curly d/dt.

[@jthompson120db]

the widely known troubles of things popping up on the computer when you´re trying to do something is all too familiar for most surely

[@827supriyopramanik2]

What does it mean for the wave function to be imaginary??

[@adamadiallo845]

In the double-slit experiment, what's interfering? A single wave-particle with itself?

[@joshuapasa4229]

Its the wave function of the particle interfering with its self.

[@frogz]

virtual particles?

[@gleannemarie]

So.... I don't even have words. Can someone point me to a beginner's guide to understanding what all of this means? Waves of what? Particles? What is the practical application? Is this always only theoretical?

[@jonnymahony9402]

Look at the other daily equations videos.

[@stevenyee8967]

Love this explanation of Schrodinger Equation.! Other lectures never brought up the point that multiple particles exist in 3N multiple dimensions. I always thought that a particle(s) can exist in many places at the same time but within our 3 dimensions of our universe. Does multiple particles mean they can exist in multi Universes or multi worlds at the same time or are the 3N dimensions in our own universe where these dimensions are unreachable to us or imaginable??

[@erwinmarschall8879]

You yourself argue that the idea that "a particle can exist in many places at the same time" is nonsensical! The wavefunction is your (observer's) private personal information about the probability of detecting the particle at a point in space (and time).

[@rlsfrny]

That isn’t what Prof Greene said. He said the probability wave of N particles “lives” in a 3N dimensional space. He also said that this does not mean that a 3N dimensional space is a real description of reality. It is a mathematical construct for the probability wave.

[@stevenyee8967]

Erwin Marschall, I agree that ‘particles can be in multiple places at once’ is nonsensical but this is the quantum realm played out with quantum mechanics rules where two or mor particles can be entangled and affect the others spin instantaneously regardless of distances. Quantum tunneling where particle can go through barriers all seems crazy by classical worlds we all live in. The Heisenberg uncertainty principle show that a particle can be in multiple places by the probability that it might be more likely to be in one position than another position but it is in all places before we try to observe it thus affecting the outcome. Just as the spin is in superposition until it is influenced by the measurement it is in all states of spin which is why Schrödinger’s cat is both dead and alive before the measurement is made.

[@mickeybrumfield764]

Our reality appears to be an incredibly vast place.

[@davidbarnett1740]

Does any of this have anything to do with Schroedinger's cat?

[@michaelsommers2356]

Go back to the previous equation and look at the bit about linearity. Since the equation is linear, any linear combination of solutions to the equation is also a solution. Thus if cat-dead and cat-alive are solutions, so is cat-dead + cat-alive.

[@piotrabunski5885]

Maybe next time something about General Relativity and Einstein's equation :D

[@informationparadox387]

That would be too Hardcore!

[@amogh5427]

Sir U look like Einstein with neat hairstyle ✌✅

[@neiln62]

This 3n dimensions don’t make sense because all we need to do is look at the amplitude^2 to get the probability of where the particles are which would be a measurement in only 3 dimensions.

[@warren64216]

Oh to be a hyper-dimensional being, capable of seeing those mathematically perfect orbits so eloquently described by Prof. Greene, on whatever scale they might exist. After listening, I find myself travelling back in time to the 1970's and a lecture hall with 25 other students, revelling in all of those unique solutions for wave functions of varying radius, energy and amplitude. It's ironic how contemplating the very small makes one feel so very small. I remember thinking the famous Beatles tune "Strawberry Fields Forever" should be renamed "Quantum Fields Forever".

[@ricardodelzealandia6290]

Well that didn't help my headache at all.

[@willpoolman2204]

Ok, so maybe I'm a dummy, but if you need to introduce the concept of imaginary numbers to derive an equation that will describes reality, it seems to me to be saying something of the sort like "not really but just imagine if". brings me back to the paradox of the map versus the territory. We can make better and better "maps' that describe reality but none of them are the actual territory. I get lost down the rabbit hole every time I go there. Help, Said Alice !!!!

[@trevormugalu3797]

Man Schrodinger was on steroids

[@shaunhumphreys6714]

thankyou for the non dumb downed explanation. im not good at maths-though i love topology. , algebra i would be beaten by a ten year old, explaining what physical quantity each algebraic symbol represents and its relationship to the next symbol thus defining the term plainly makes university level physics accessible to us. ive self learnt the concepts of relativity, and the standard model, and the electroweak unification, quantised field theory- quantumelectrodynamics, chromodynamics from books , online university resources, reputed physics channels especially PBS spacetime, reputed online tutorials like brilliant. im but i glaze over the equations, without digesting them , without having taken courses in the maths to catch up to the level of conceptual physics though if the equations are taken apart and explained like this then i do digest them fully. and i like being able to engage in that part of the physics. i hate not understanding and having to skip two paragraphs of a physics paper that are just equations. though i have to say, compared to papers from early twentieth century and before, modern physics papers are too crammed with maths equations. i think they are hiding a lack of ontological insight, i.e. physical interpretation. I d.find the Schrödinger equation now abit redundant. The dirac equation perfectly accurately describes particle evolution of the spin type matching fermions e.g. electrons, plus is relativistic. and its ontology further confirmed by the manifestation of anti-matter in the four component dirac spinor. so then you just need another equation for the bosons as they have spin one e.c.t. The schrodinger is non relativistic which immediately makes it inferior. Plus it deals with state vectors, which can only describe pure quantum states and are thus less general than density matrices, which can describe mixed states as well. I feel we should be using the Lindblad equation, and the shrodinger is a special case of the more general lindblad equation. The original motivation for the linblad equation was that in the schrodinger and similar equations, the system's time evolution is governed by unitary dynamics. This implies that there is no decay and phase coherence is maintained throughout the process, and is a consequence of the fact that all participating degrees of freedom are considered. However, any real physical system is not absolutely isolated, and will interact with its environment. This interaction with degrees of freedom external to the system results in dissipation of energy into the surroundings, causing decay and randomization of phase. These effects are the reasons quantum mechanics is difficult to observe on a macroscopic scale. The concept of cohherence and decoherence, and linking that with the wavefunction phase, greatly improved and made the many world's a far more robust ontology of quantum mechanics, making me take it seriously. However many world's is still far too dependent on the schrodinger equation, i would need to see it connected to the dirac and a generalised equation for quantum mechanics like the lindblad. I've yet to see anyone attempt this, rather as roger penrose pointed out, there is a religious like adherence to ''there's the evolution of the schrodinger equation and nothing else''. The Lindblad can describe incoherent processes, which represent environmental interactions. The density operator has the property that it can represent a classical mixture of quantum states, and is thus vital to accurately describe the dynamics of so-called open quantum systems. We have differential equations for a set of probabilities (which only constitutes the diagonal elements of a density matrix), But maybe we should be using quantum master equations which are differential equations for the entire density matrix, including off-diagonal elements. A density matrix with only diagonal elements can be modeled as a classical random process, therefore such an "ordinary" master equation is considered classical. Off-diagonal elements represent quantum coherence which is a physical characteristic that is intrinsically quantum mechanical. This links with heisenberg's derivation of quantum mechanics in his matrix mechanics which came before schrodinger tried to make a realist derivation in terms of pure waves. which he never intended as probability densities, that was born and bohr who hijacked his equation. I am also still along with many worlds, drawn to schrodingers forgotten realist interpretation after he rejected the whole quantum jump approach of bohr, which means im drawn to completely opposite ontologies. i kind of want the many worlds to be right, as i see it as the only route for time travel to the pasT, at least time travel where you could hsve free will in the past to change things without violating causality. time travel can result in a brand new copy of the desired time era, which being out of phase, totally causally disconnected from the world you came from, you can create a brand new history. But then schrodingers realist zitteberung interpretation where the wavefunction is like a fast moving fan, with a trembling motion where there are slight differences in the speeds of the particles following a fast slow slow type trembling motion feels more grounded, more likely to be true in a way. the slow is only a tiny bit slower than the fast but this variation reproduces the probability density, i.e. places where the probability density is more strong. imagine the fan moving near light speed you cant see anything and if mapping it it would reproduce a probability density, and not be able to identify definite positions, but when stopped you get a definite position-the stopping is akin to the measurement which interferes with the fan like wavefunction allowing you to latch on to one definite particle. further more recent work has identified the zitterberrung as a circulating charge which is a physical interpretation for quantum spin. this physical spin interpretation still has not been disproven. in a sense the wavelike property is only seen when you allow a free particle to evolve over time, then i think you get an illusion in seeing the peaks and troughs of waves. whereas fundamentally a particle is a discrete androughly spherical charge -spherical because that shape obeys the universal law of least action.which appears both at quantum and macroscopic levels. in the case of a photon, you have a discrete sphere of influence of an oscilating electric and magnetic component perpendicular to each other, and that oscilation would have a circulating characteristic i.e. following rotational degrees of freedom.

[@vvgman]

God, i thought i was smart, no i can see how much of a loser i am!

[@douglasstrother6584]

By the time Maxwell was my age, he'd been dead for nine years.

[@drdhwhitney]

Not dimensions Brian, degrees of freedom. You are adding unnecessary confusion; it is all still in our real world of 3/4 dimensions, just complicated.

[@jayeshraut341]

Degree of freedom of a particle is also Movability of parties in dimensions so what is problem with dimension

[@joshuapasa4229]

Can you not say Ψ = Σ Ψ_i ?

[@johnstfleur3987]

"KOBE BRYANT'S RESURRECTOR."

[@lastnamei]

Your equations can not replace God ...

[@rlsfrny]

Dheeraj Verma Then dont bother coming. There’s plenty of other places you can go if you’re looking for god.