How to use the einstein energy-momentum relation to derive the Klein Gordon Wave Equation. I go over four-vector notation, Four-gradient, and writing the equation in terms of the D'Alambertian.
Пікірлер: 165
@michaeljburt5 жыл бұрын
I've met many physicists in my life. Many with PhD's or working on them, both theoretical and experimental particle physics. I can say very confidently that you are the clearest physics communicator I have ever seen. I hope you're pursuing a professorship. It really takes a brilliant mind to both be able to execute the theoretical mathematics and physics, and discuss it while doing it.
@AndrewDotsonvideos3 жыл бұрын
Thanks so much!
@KRATOS-dq6sd3 жыл бұрын
@@AndrewDotsonvideos did you really just reply an year later
@jakwhyld44063 жыл бұрын
@@KRATOS-dq6sd did you really just reply an eight months later
@mevnesldau84082 жыл бұрын
@@jakwhyld4406 did you really just replay a month later?
@Epyriel2 жыл бұрын
@@mevnesldau8408 Did you really just reply a month later?
@saarausmaan Жыл бұрын
Now I found one of the clearest concepts about the Klein Gordon wave equation . Thank you so much
@mrnarason6 жыл бұрын
Do one for the dirac equation
@mohannadislaieh30096 жыл бұрын
I agree
@kanhaiyalal-kv2vg5 жыл бұрын
Please make video on dirac equation
@D-baller5 жыл бұрын
I concur
@boriscrisp5185 жыл бұрын
yeah.. get on with the dirac eqn, you beardy hipster
@Mr-xf9me3 жыл бұрын
Done
@MyTBrain6 жыл бұрын
“Klein - Gordon in under 15 minutes? “ **cracks knuckles** “Watch me...” Stellar Job Andrew!
@namanvats76443 жыл бұрын
I spent all day trying studying form books , wikipedia ,detailed lectures but this video help me get rid of my every single doubt about the topic in just 14 mins.
@RVN_198 ай бұрын
i watched this video when i was just about to start uni. and i didnt understand anything. now that i am taking QFT, holy moly you are amazing at explaining things
@alapandas63984 жыл бұрын
Everybody is saying about the box notation. But I saw in Feynman Lectures box square was used.
@theflaggeddragon94726 жыл бұрын
You're going to want to start at the top left when presenting, split the board in two and DON'T ERASE. Don't worry I did this all the time when lecturing and have only recently corrected my habits but it really helps students/viewers on the other end. Great video ;)
@AndrewDotsonvideos6 жыл бұрын
I'd like to start at the top left, but my light has a terrible glare around there! That's why I have a black outline in the corner in all of my math videos. So I know where not to write.
@tracyh57515 жыл бұрын
It's not too important for videos as we can rewind when needed. As long as you are careful in the classroom you should be okay. :)
@garybarbourii82744 жыл бұрын
I will not be satisfied until I understand every bit of this, and more.
@JoeHynes284 Жыл бұрын
i am on a two and a half year journey so far, i am 44...
@kamehamehaDdragon6 жыл бұрын
If you don't know quantum physics like me, this looks super crazy. If you do know physics, I bet it still looks super crazy xD. Good video.
@renatolucas3120 Жыл бұрын
I'm in a IC(scientific initiation) of symmetry break and this video clear a lot of things that I wasn't getin. Waiting your next video !!
@CarlosKoji876 жыл бұрын
What's interesting about the Klein-Gordon Equation is that it gives the wrong fine structure for the hydrogen atom and also gives negative probabilities. Not only that, it allows for negative energy states! I think a video on deriving the Dirac Equation would be really cool. It would be a great transition as it remedies some of the issues in the Klein-Gordon Equation.
@teodoranirmala31636 жыл бұрын
Carlos C Imho, Klein-Gordon equation actually only work for bosons. Electrons in hidrogen atoms are fermions, so these can be handled by Dirac Equation. May this helps.
@angelmendez-rivera3514 жыл бұрын
Carlos C Yes, it gives the wrong results for those particles because the equation is not applicable for those particles. The Klein-Gorden equation is a boson equation, since, by having a scalar wavefunction, it assumes integer spin.
@theicemancometh54926 жыл бұрын
I love how you write your 'a' the same was as the d in a partial derivative
@WaveSound1236 жыл бұрын
I've never seen the d'Alambertian writen with a square, only the box XD
@AndrewDotsonvideos6 жыл бұрын
Hmm. Griffiths uses the squared version. I guess as long as you define what you're saying it means.
@angelmendez-rivera3514 жыл бұрын
Liviu Stoica Box, square... eh, really minor difference
@cyrilvidal53954 жыл бұрын
David Tong Quantum Field Theory lecture notes www.damtp.cam.ac.uk/user/tong/qft/one.pdf => box only but both usages are allowed
@lPlanetarizado4 жыл бұрын
first time I saw d'Alambertian I thought it was an error in the file lol
@WaveSound1234 жыл бұрын
@@lPlanetarizado Good one😂😂😂
@ashmindersingh4347 Жыл бұрын
Finally someone explained d'alembertian in form of 4 vectors
@esorminihaz82694 жыл бұрын
This equation was derived by Isaac Kleiner and Gordon Freeman. Using this equation instead of the Dirac equation caused the resonance cascade
@ghicheon95402 жыл бұрын
Thank you very much! I was looking forward to finding the meaning of /d myu d myu/, I found it here!. I'm studying physics as a hobby. You're videos help me study physics alone because it's not easy to find lectures that teach from the scratch. I appreciate it so much! ^^*
@danielbachour99874 жыл бұрын
Great man! Enjoyed the video! i'm going to catching up with all your videos! You know, to refresh things up! Keep it going!!
@KhoaNguyen-os5zv6 жыл бұрын
I wonder why Caltech didn’t give u at least an email. You’re so mathematically gifted. I’m an error asian.
@robertmorrison16573 жыл бұрын
People there are extremely intelligent. Like sheldon cooper type people. Fine okay, maybe just leonard intelligent. However, I would suspect that to get into that university for physics, you would need an iq of like 160 at least. This guy might be very smart, but he is not a genius. He still probably has an iq from 140 to 150 though.
@heavennoes3 жыл бұрын
@@robertmorrison1657 I don't think Caltech judges people by IQ.
@robertmorrison16573 жыл бұрын
@@heavennoes Not exactly. They don't have you take an iq test to see if you will do well in university. What they will do is see your grades, scores on SAT's, and other things that show how smart you are, plus maybe some extracurriculars just to see how driven and committed. So they kind of see what your iq is like, whether it is high enough or not. So they sort of do judge by iq.
@Onegod40-v4h4 жыл бұрын
That's fantastic demonstration.Really appreciate it
@thephysicistcuber1755 жыл бұрын
I've never seen the D'Alembert operator as box^2. It's always been just box :p EDIT: I've scrolled through the comments xD
@TheBaluchiterium4 жыл бұрын
It's usually given as \Box which, however, is strange. It is more logical to make the transition from "nabla" to "quabla" (quadri-nabla) and to denote the latter as \Box which for contravariant components is equal to \partial^{\mu}. Then a Minkowski-space scalar product can be written as \Box^2 = \partial^{\mu} \partial_{\mu} which is just the d'Alembertian. I think this is the reason why some authors disagree with the more widespread convention of d'Alembertian = \Box. And I do, too.
@petriklelel4 жыл бұрын
@@TheBaluchiterium Thank you for the explanation, as I was only familiar with the \Box notation for the d'Alembertian. Also, I really like how you wrote it with latex code :)
@organicolympic17292 жыл бұрын
Highly impressed in your presentation😊🙂
@angelmendez-rivera3514 жыл бұрын
I think another, perhaps better way, to explain the significance of contraviant and covariant indeces when working with vectors and 4-vectors is to talk about the conventions of matrix calculus and to consider ordinary vectors as single-column matrices. Their components are expressed with a covariant index. Then, an expression with a contraviant index is simply a single-row matrix, or a "row-vector," also known as a covector in some contexts.
@onderozenc44703 жыл бұрын
At the end, this relativistic wave eq. comes down to expressing the probability of a particle including the photons making tunneling through a potential field acting on them to express the observability of the black holes' thermal radiation within the large wave length micro wave spectrum.
@AstroPC963 жыл бұрын
This guy should have been my QM professor!!
@xnick_uy5 жыл бұрын
For the sake of keeping a more consistent notation, I would have written the abbreviated 2x2 metric with an overbar on top of the zeroes (since they stand for (0,0,0) ) and use -Id for what appears as a -1 with the overbar on top (since it actually stands for the minus 3x3 identity matrix).
@ThePremez6 жыл бұрын
Hey Andrew, what whiteboard are you using and where can I get it from? I'm a Physics/Maths student in the UK and I've been wanting to get a good whiteboard for a while now, but when I googled it I found there's a whole quality scale based on things like erase-ability, whether it's magnetic or not etc... Only thing I care about is good erase-ability. Which yours seems to have. Thanks in advance! Great content btw, really like this sort of higher level stuff.
@zokalyx6 жыл бұрын
ThePrimebrook same problem here, ive used 200+ pieces of paper to do problems and that is wasteful IMO. I really need a whiteboard, but I don't know which
@agnaldojunior5538 Жыл бұрын
Very clean, thanks.
@thephysicist55196 жыл бұрын
You are genius I liked u plz continue up and I will share ur vedios
@lemniscatusofficial4 жыл бұрын
3:50 why did you use a scalar field?
@kanhaiyalal-kv2vg5 жыл бұрын
Please make a video on dirac equation thanks
@Leonlion03055 жыл бұрын
I only have crippling intro quantum knowledge but I finished both the Schrodinger Equation @ relativistic speed and this one. I understand ~50% of these but I understand it. Pls be my physics prof lol
@natepolidoro45655 жыл бұрын
what an intelligent sasquatch!
@Alolyn10 ай бұрын
The d’alembertian square symbol makes me imagine that the guy who introduced the equation typed it up on an iphone with an emoji for an operator, and traveled back in time to give it to physicists in the past but the emoji turned into that box with a question mark on it and they just rolled with it Or they used a japanese ロ “ro” (which makes it seem related to rho) cus they got tired of using the greek alphabet
@AndrewDotsonvideos10 ай бұрын
I feel completely the same
@ionlyazir36626 жыл бұрын
Nothing better than quantum mechanics at 3 a.m. btw im only 15. Thats probably the reason that i have no friends -.-
@ionlyazir36626 жыл бұрын
Francisco Russo thx for support :D
@arkkaushik2642 Жыл бұрын
Hey if row vector is covariant terms shouldn't the last term should also be row vector?
@abacademy4186 ай бұрын
Thanks
@jazzani953 жыл бұрын
Thx! Very clear. Can you motivate the Sine-Gordon Equation? It has solion solutions. Understanding solitons is important when comprehending the solutions for the Kosterlitz-Thouless transition.
@havefun44935 жыл бұрын
thank you very much!
@darioolmos7480 Жыл бұрын
Does a tensorial field have gauge symmetries if it follows this equation?
@AndrewDotsonvideos Жыл бұрын
Global but not local. You always need to replace derivatives with gauge covariant derivatives if you require local gauge invariance. But yes it does still have a global phase invariance and a corresponding conserved charge
@darioolmos7480 Жыл бұрын
@@AndrewDotsonvideos thanks for your answer!! And such a nice video 💯
@laneellisor71136 жыл бұрын
Love the video! Do you think you could do a video on college labs and any tips or advice for them?
@chymoney16 жыл бұрын
Can you explain what the metric means conceptually??
@AndrewDotsonvideos6 жыл бұрын
It tells you how not-flat the spacetime you're working in is. If it is flat, you get a diagonal of 1's (with some minus signs) which basically just tells you a^2+b^2 = c^2 still holds.
@mohannadislaieh30096 жыл бұрын
U are genius, I likef that
@thephysicist55196 жыл бұрын
Mohannad Islaieh u are right
@fermiLiquidDrinker3 жыл бұрын
What if I just _don't like_ natural units?
@bonchiengooddog37912 жыл бұрын
What is this equation trying to achieve?
@theultimatereductionist75924 жыл бұрын
Since the Klein Gordon & Dirac equations combine relativity & quantum mechanics, then why do physicists say we are still struggling to combine the two?
@angelmendez-rivera3514 жыл бұрын
The Ultimate Reductionist You are wrong in several aspects. Firstly, the Klein-Gordon equation and the Dirac equation are incorporations of *special* relativity into quantum physics. There is no *general* relativity involved. Secondly, quantum field theories DO *mostly* combine general relativity with quantum physics. In fact, the only real conflict between both theories is that the Einstein field equations are classical field equations, not quantum field equations, but unlike all other field equations that we have worked with, Einstein's field equations in particular cannot be quantized by any methods currently known. The problem lies with quantizing the metric tensor, which yields singularities upon singularities. These are non-regularizable and non-renormalizable.
@theultimatereductionist75922 жыл бұрын
@@angelmendez-rivera351 "Firstly, the Klein-Gordon equation and the Dirac equation are incorporations of special relativity into quantum physics. " Ah. Oops. Rookie mistake.
@drbeanut Жыл бұрын
@@angelmendez-rivera351 why need to quantize spacetime curvature? what if just let it operate on wave-function continuously?
@angelmendez-rivera351 Жыл бұрын
@@drbeanut You cannot have wavefunctions without quantization.
@drbeanut Жыл бұрын
@@angelmendez-rivera351 How so? A wave-function merely assigns a continuous probability amplitude distribution to some arbitrary field.
@zokalyx6 жыл бұрын
One little question Andrew, or anyone else (who knows)... At 3:50 (dx/dt)^2 = d^2/dt^2 ??? I don't see why... For example: y = x (dy/dx)^2 = 1 d^2y/dx^2 = 0
@x17exeventien796 жыл бұрын
Its not an algebraic product, it's an operator manipulation. The linearity of derivatives allows you to get away with notation tricks like that for some things even though its not strictly correct.
@zokalyx6 жыл бұрын
x17 Exeventien yes, i saw this in papa flammy videos, it is just using the operator twice
@TomDixon894 жыл бұрын
(dy/dx)^2 and d^2y/dx^2 are not the same. What he did was the squaring before applying it to wavefunction. E=d/dt i.e E as an operator which you apply to a function. an operator applied to an operator is an operator. i.e (d/dt)(d/dt)y = d/dt(dy/dt) = d^2y/dt^2 BUT (dy/dt)(dy/dt) is a function on a function ie d/dt = operator dy/dt = function. So grad^2[y]+m(y)+E^2[y] represents d2y/dx2 + my + d2t/dE2 square brackets indicate operator acting on y and regular brackets are functional, or even numeric. The important part is that the operator (the derivative operator in this case is squared not the function). The way I remember it is: if Im a function and you give me a number I can tell you the resulting number. If Im an operator and you give me a function I can give you the resulting function.
@angelmendez-rivera3514 жыл бұрын
Francisco Russo He never wrote (dx/dt)^2. He wrote d^2(φ)/dx^2. They are different.
@souvik93053 жыл бұрын
I saw in a landau book that four vector transformtion are all positive sign,so why is there a minus sign in your video(-Sinhx)....plz can you clear thr doubt....what am i missing
@invisibules2 жыл бұрын
I think the sign of the potential energy term is wrong in that schrodinger equation at the beginning ... isn't it?
@AndrewDotsonvideos2 жыл бұрын
Yup you’re right, sorry about that
@MultiDaniella146 жыл бұрын
Thanks. Help alot
@MultiDaniella146 жыл бұрын
helped*
@arifsarkar73283 жыл бұрын
Cool man!! this is 👌
@soerser24283 жыл бұрын
Why is there no minus before the V in the Schrödingerequation?
@frankmoscatelli45552 жыл бұрын
Students are so used to seeing an arrow as denoting a 3 vector that when I teach 4 vectors I use it, not a bar, to represent the 3 part of the 4 vector. Otherwise, great video.
@MM-ei7xv3 жыл бұрын
god! you're great thanks a lot
@as.n42446 жыл бұрын
As far as I know, N=4 supersymmetry has spin zero s-quark, s-lepton, and LSND-neutrino :)
@as.n42446 жыл бұрын
And for non-SM, there’s the axion pseudoscalar for charge parity violation, all I can think of off the top of my head
@theultimatereductionist75925 жыл бұрын
Why does nobody ever show the Klein Gordon Equation applied to 3, 4, 5 or general N particles? I want to see exact solutions for SYSTEMS of particles. NOT just 1 particle.
@zoltankurti5 жыл бұрын
Qft is all about that. But you automatically get all integer particle numbers and even their superpositions.
@waqarali91664 жыл бұрын
I enjoyed 😍
@TheApostleofRock4 жыл бұрын
bold of you to call me a smart person
@archi1245 жыл бұрын
why can the klein gordon equation used to describe scalar bosons if it leads to a negative probability density?
@angelmendez-rivera3514 жыл бұрын
I do not believe it does that if you work with bosons, only with fermions. That is because the equation only works with bosons.
@tony_narchuk2 жыл бұрын
Isaac Kleiner - Gordon Freeman equation
@chymoney16 жыл бұрын
For the “ wave function” in your Klein gorgon equation you said I.T was as a scalar field. A probabilistic scalar field? What is it??
@TheDutchPhysicist4 жыл бұрын
For the schrodinger equation you have the wave function whichs depends on space and on time and moves through space and time seperately, here you get a field that propagates in space-time. So its like the wave function, except now its a field in space-time.
@angelmendez-rivera3514 жыл бұрын
Sebastiaan van Rijk Yes, but he is asking what does the field stand for. The answer is that it is a probability amplitude.
@akokJ6193 жыл бұрын
The metric tensor is it always necessary to use the + - - - convention?
@oni8337 Жыл бұрын
nope you can use - + + + instead if youd like but keep it consistent
@akokJ619 Жыл бұрын
@@oni8337 didn't know 2 years ago. I know now XD
@sidddddddddddddd5 жыл бұрын
Correct me if I’m wrong. That box shouldn’t be squared. No?
@AndrewDotsonvideos5 жыл бұрын
It's just a definition. You could define a smiley face operator to equal the right hand side so long as it's consistent with what you're using it for. But, Griffiths also uses the box squared for what its worth.
@sidddddddddddddd5 жыл бұрын
Andrew Dotson Yeah, I get that. But it’s always convenient to have some kind of a universal notation. It’s like the metric, you can use + - or - + notation. There should be some SI equivalent of such stuff. Anyway, keep it up, Andrew.
@miguelamaral96425 жыл бұрын
I don't think the d'Alembert Operator should be squared, it is simply equal to exactly what you derived
@caterinacevallos98225 жыл бұрын
I'm a bit confused when you say something is Lorentz-covariant? Does it mean that the "form" of the equation stays the same? What would it mean for a transformation to be then contra-variant? (Do you have an example of that?)
@thephysicistcuber1755 жыл бұрын
Caterina Cevallos I'm pretty sure in this case covariant refers to the form of the equation. Indeed there are no indices in the final form of the KG equation. I don't think "contravariant equation" is a thing
@AndrewDotsonvideos5 жыл бұрын
Sorry I'm just seeing this now. When I say Lorentz-covariant, I mean it transforms properly under a Lorentz transformation. The equation will still change, but under the prescription given by the L.T.
@zoltankurti5 жыл бұрын
@@thephysicistcuber175 maxwells equations in vacuum are covariant, and they have unpaired indices... Covariant in this context means the equation is tensorial with respect to the Poincaré group. In other context covariant and contravariant just refers to tangent vector and cotangent vector components.
@thephysicistcuber1755 жыл бұрын
@@zoltankurti I wasn't implying that there must not be unpaired indices, I was just saying that in this case the equation is obviously covariant because of the absence of such indices
@zoltankurti5 жыл бұрын
@@thephysicistcuber175 many not invariant objects have no indices. Pressure, energy density, and I don't need to go on because I'm sure you can list a bunch of these too.
@ahmedkarrar254 жыл бұрын
I still don't understand why did u write phi instead of psi? (4:11)
@navneetmishra32083 жыл бұрын
Phi usually represents a complex function that is not a scalar field.
@zoltankurti5 жыл бұрын
It's interesting... On what basis do you call this quantum mechanics? You don't even have one operator in association with this classical Klein Gordon field.
@angelmendez-rivera3514 жыл бұрын
Zoltán Kürti What is your definition of quantum mechanics? Because my understanding of the term is that there is no obvious reason this should not be called quantum mechanics. It can be derived from the axiomatic postulates of a quantum theory, so it is quantum. And, there is an operator called the d'Alembert involved.
@angelmendez-rivera3514 жыл бұрын
d'Alembert's operator is the 4-wavevector operator squared and multiplied by a constant.
@Excidium966 жыл бұрын
In the beginning, you talk about not being comfortable with non-relativistic quantum or special relativity then this video isn't for you. Buuuuuut I still watch all your math-deriving videos even though I don't even know calculus yet......It's just interesting to see what mathematical skillsI could potentially have If I just study as hard as you have....And that's what I am aiming for with my physics degree :)
@soulsilencer18642 жыл бұрын
I entered an "AP physics practice test" today and they asked me fucking relativistic quantum mechanics
@Riteshbachhar5 жыл бұрын
why here we have scaler field instead of wavefunction?
@angelmendez-rivera3514 жыл бұрын
Ritesh Bachhar The wavefunction is a scalar field.
@angelmendez-rivera3514 жыл бұрын
Smit Shilpatul Yes, but the Klein Gordon equation is only valid for spin 0 particles, so your point is moot.
@Salmanul_3 жыл бұрын
Idk why but the box notation looks a bit uncomfortable, it feels like I have to write something inside it. Like fill in the blanks questions haha
@mastershooter642 жыл бұрын
I want that beard :(
@non-inertialobserver9465 жыл бұрын
Pi=e=3
@miguelaphan585 жыл бұрын
how natural units works..?,...besides...nice job
@alexbaykov92215 жыл бұрын
Basically, it is just measuring velocities in fractions of c and measuring action (or angular momentum) in hbars.
@samgeribo6 ай бұрын
Ben Affleck
@PetraKann4 жыл бұрын
Physics is the least complicated and simple of all the scientific disciplines. Complexity increases markedly when moving from the field of Physics to Chemistry to BioChemistry to Biology. The level of complexity increases once again when doing Psychology and economics. That's one of the advantages of Physics - it's simplicity.
@DeltaXGamerPT4 жыл бұрын
In what sense is physics simple? It is extremely complex... Even compact equations, which are certainly not the rule, are notation heavy and many are notoriously long even with compact notation. And to be honest, although great mathematical prowess is absolutely necessary, I think the greatest challenge - and also beauty - of physics is gathering a sensible intuitive interpretation of said mathematical jargon to explain the world around you. I really don't understand where the triviality begins.
@PetraKann4 жыл бұрын
DeltaX Gamer PT physics is the most rudimentary and least complex of all the scientific disciplines. It’s the pre-school of science. Basic idealism and simple assumptions. Nice geometric forms and convenient system behaviour. Even when you examine Quantum Mechanics, it’s mathematical foundations are simpler than Newtonian Mechanics. I am not trivialising they field of Physics just stating an obvious fact about its nature and the functional limits. The predictions made by theories in physics are orders of magnitude easier to validate than all other scientific fields Ever wondered why? Physicists often take it personally which is the wrong attitude. Their field is a basal fundamental footing for other scientific disciplines to build upon.
@DeltaXGamerPT4 жыл бұрын
@@PetraKann It is that way because it is our own interpretation of the language of our universe. I understand where you are coming with this and agree with most of it. I just don't like how you say it is not a complex field. Its assumptions and implications are far from the whole truth of the theories, which is why it so rare to find someone who can communicate them diligently and in a simple manner. It is simpler in the sense that it is the science where you skip the least logical steps apart from mathematics. It is still, however, one of the hardest sciences to be able to grasp.
@Prxwler3 жыл бұрын
Yeah, because it's more difficult to learn a bunch of long and complicated names than learning how to reason.