The Man Who Saved Quantum Physics When the Schrodinger Equation Failed
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- Опубликовано: 27 май 2024
- The Schrodinger Equation regularly fails. In this video we look at two upgraded equations (including the famous Dirac Equation) that work in both quantum and relativistic environments.
The Schrodinger Equation is famous, and rightly so. It's the governing equation of a theory called quantum mechanics. It can very accurately predict how quantum systems (i.e. very small systems) will behave through space and over time. The basic premise of it is that it adds together a system's kinetic and potential energies and equates this to the system's total energy. This is seemingly pretty common sense, but the Schrodinger Equation is "quantized", meaning measurements on the system only give very specific results. We can also never predict exactly which measurement outcome we will get, but only the probabilities of each possible outcome. The Schrodinger equation also has "measurement operators", which are the math equivalent of making a measurement on the system.
Importantly, the Schrodinger Equation is not relativistic. In other words, it does not account for the strange effects we see when relativity is accounted for. We know that when objects move at high speeds relative to each other, that they noticeably measure distances and times differently to each other. Because these effects are not accounted for, the Schrodinger Equation does not always accurately predict the behaviour of small systems that may be moving at high speeds. It also treats time as a universal variable (i.e. everybody measures time in the same way), which is not how relativity deals with what it calls "the fourth dimension".
To save quantum mechanics in these high-speed scenarios, we need to look at some other equations that are both quantised and relativistic. The first equation of this sort that we'll look at is known as the Klein-Gordon Equation. To get this equation we start with Einstein's famous mass-energy relation (E = mc^2). But in reality, we start with the full version of this equation which also involves momentum. Taking this full mass-energy equivalence relation, we can then quantise it and derive the Klein-Gordon Equation.
The Klein-Gordon Equation accurately predicts the behaviour of spin-0 particles. In other words, it does not account for spin. But it is quantum and relativistic. It also has a "psi" quantity in it just like the Schrodinger equation, but here "psi" is charge density, not probability density. This is because the Klein-Gordon Equation allows negative solutions for the square modulus of psi, which previously we interpreted as probability. It makes no sense to have negative probabilities, and instead this equation deals with the behaviours of particles with positive, negative, and zero charge.
To account for spin, then, we need to look at yet another equation. Remember, spin is angular momentum that is inherent to a particle (without it moving along a curved path or rotating). The equation that starts to account for spin is the very famous Dirac Equation. It's highly complicated, but can be essentially thought of as the square root of the Klein-Gordon Equation. It has four complex degrees of freedom in its "psi" quantity. The first two of these look like the quantum wave function "psi", but the remaining two encode details for systems that are quantum and also relativistic.
When Dirac came up with his equation, he realized that some potential solutions allowed for particles similar to the ones we know, but with the exact opposite charge. For example, electron-like particles with +1 unit of charge rather than -1 were allowed. Dirac thought this was initially a mistake, but we eventually found particles like this to exist! We now call them antiparticles, which make up antimatter. In other words, what was initially thought to be an accident of under-constrained mathematics, actually provided a wonderful prediction for phenomena never seen before!
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Timestamps:
0:00 - Understanding the Schrodinger Equation
3:50 - Relativistic Quantum Mechanics
5:05 - The Klein-Gordon Equation
7:42 - The Dirac Equation
Videos in Cards:
1) • Schrodinger Equation E...
2) • Spin in Quantum Mechan...
Dirac was known for the scarcity, brevity, and precision of his speech. Dude was not a guy you'd go out with to have a beer.
He was once lecturing at a convention and had written several equations at a blackboard. When he was finished, someone raised his hand and said, "I don't understand your equation in the upper right of the board." Dirac sat down. After moments of awkward silence, the moderator of the convention asked Dirac, "Are you going to answer the man's question?" Dirac: "It wasn't a question. It was a statement."
Not so much on the small talk, Paul?" ... like the movie line.
Nooo waaay 😂😂😂😂
Well he is not a good teacher with that attitude then .
@@user-og9nl5mt1b Not sure it was an attitude as much as a symptom, or an expression of who he was.
How are you only at a little over 200k subs? This channel is great and deserves much more! The quality of video production to the information being given out and it's clarity, very much props! Thanks for another vid!
Nobody wanna learn physics, they are good with making cringe tiktok videos and busy being hipocrite on Instagram.
i was thinking the same thing.
@@AryanKumar-cj4gyto be
Yea let him become 1 million subs and become slave to yt algorithm
Parth been watching for a long time you are one of the best physics communicators I have ever seen I really love your videos keep it up :)
Thanks for sticking around and for the kind words!
You’re “wave of probability” description at 1:30 was a REVELATION for me
Hi, Parth!I have been studying physics for a while now. Thank you for providing these comprehensive videos. Your teaching style is brilliant. May your channel prosper.
Fantastic! Superb! I'm running out of words! I'm just going to seriously study QP and this video has equipped me with so much clarity!! Looking forward for much more!!
Excellent as usual. A pity we have to wait so long between vids Parth. Just finished The Strangest Man by Graham Farmelo on Dirac - brilliant book.
Thanks for watching! I'm hoping to create more regularly within a couple of months time :D
I've heard it's a great book, I'll have to check it out sometime!
Yep That's what I'm reading!
I can strongly recommend that book too. First because P.A.M. Dirac is a very interesting person, second the book is written in a very good style without being sloppy. The author is taking great care of the circumstances and context of different stages in Dirac's life without loosing the focus on his main subject.
Parth,
thank you deeply for your efforts - this presentation really shows how sincerely you thought about Dirac's groundbreaking achievements, and how to transport the message to a broader audience.
Highly respected! 👏🤓😎
a very good explanation in the discription box about the subject. Have been watching you since 2020 :)
👍👍
I really appreciate the PRECISE wording, even though this is all hand-wavy area. Very informative!
I agree. When most commentators on physics water things down, they say things that can easily be understood wrongly. Parth will say something followed by a clarifying statement. You might not understand the second part, but you won't misunderstand the main point. I am impressed with his clarity and precision.
Brilliant video, very clear and amazingly simple. Well done.
Just found the channel. Very sweet to have you explaining the meat of the matter so well.
OMG you are literally me (Science + Music)
Love it!
Science+ interstellar music
Dude ...Scary
literally who asked
This is a huge drill down of the most complicated formulas in science. Well done man
(I am interested in bose Einstein condensation atm - on yt level.)
Hey Parth, Great job on your video. You have a continuous bass frequency in your audio! take a look at your mic for the futrue
Excellent video as always! 😊
Thanks a lot! 👍1:58 ... then some interesting effects start to show up such as time passing at different rates from one object's perspective to the other and also distances being measured differently from each object the Schrodinger equation doesn't account for these effects it also treats time very differently to how it treats space whereas in relativity time and space are treated on a fairly level footing 2:18 in the sense that with some maths time can be treated as a fourth dimension to go alongside the three dimensions of space that we work with now 2:25 ... 6:31 ... that it doesn't account for a particle property called spin spin is a quantity that particles can possess just like charge and mass and it's a measure of how much angular momentum a particle naturally has 6:42 8:00 ... so how does the direct equation account for spin when it's square at the Klein Gordon equation doesn't and again remember I'm ... equation doesn't account for spin when the Dirac equation does is because the equivalent of squaring actually loses information this is the same way that the square of negative 2 and the square of positive 2 are the same value. 8:24
The clue about the DIRAC equation is that square rootsvof differential operators apparently make no sense, so DIRAC had to find a way to fix that problem. His idea was genius: He looked for coefficients that anticommutate so that mixed terms would cancel out, and each coefficient squared would yield unity. And there are such coefficients, it's matrices. Needing 4 of them, it had to be complex-valued 4×4 matrices so that Ψ had to be a 4 component vector which leads to the question what each component actually means. So, the DIRAC equation predicts both spin and antimatter.
the timing just could not be more perfect, I'm currently learning this for my final exams 🙏
Your explanations are crystal clear and in the days of preparing for my doctoral comprehensive exam, I really benefit from your channel! I really love the way that you give the fundamental idea of the basic concepts in physics. Thank you very much, Keep it up, please! :)
You would never pass a doctoral exam with this kind of bullshit. ;-)
This is tough
Please recommend a book for this topic
Bro...this video is very much informative, I'll be very much pleased if u continue upload videos on QM,during my Grad days, it's a nightmare portion of Physics for me 😂
Parth this is BRILLIANT!! I watched all of Jim Al Khalili's vids and loved what he said about Dirac but he didn't explain it! This totall does and PLEASE do a proper long in depth Dirac video! I've been reading the biography of him by Graham Farmelo: The Strangest Man, well worth a read for you and anyone who loves this unknown genius.
thank you for pointing out that momentum doesn't require mass! I will look more deeply into that.
Brilliant, but I really really want a video about QFT but not just an overview. Thanks for your effort.
And overview of QFT would be a 1,000 hour video.
Thank you very much a helpful documentary.
Parth, I love your work and the way you explain this quantum material. I truly understand how much time and energy it must take to do this work. Please note you are gifted in your ability to understand physics as you do, and in relaying this most complicated materials to us viewers; we all appreciate you. I've been an electronics engineer for over 45 years and pride myself in making complicated things easy for people to understand. Please note I look at your materials over and over as some of the material has to sink in, it finally does. And yes, I would love to have had a beer with Paul Dirac; deep thinkers are my kind of people. I was not able to locate your video for the Klein-Gordon Equation, did you ever complete this video? Thanks again!
Why are you telling us that you don't know the first thing about physics? ;-)
I'd emphasize the brillian idea of Dirac of eliminating square root. In this approach matrices appeared naturally, not because Dirac was a super fan of them.
Well explained. 👍
9:32 The +1/2 and -1/2 spins are the fourth quantum numbers for electrons in atoms which is why we are limited to two electrons per orbital.
I would like to put it differently:
as spin-1/2 particles only one electron would be allowed to occupy an orbital of a particular angular momentum due to Pauli's exclusion principle. But spin is providing an additional degree of freedom with two distinct states allowed to be occupied, ie. a two-fold degeneration of a state already defined by other quantum numbers. Hence I wouldn't say "limit" but rather "allow" two electrons to occupy a state of defined angular momentum.
Great video! A little bit more (mathematical) depth would be nice in general.
Best presentation of quantum mechanic
The way you explain things is amazing and I can make sense of it. Thank you.
@4:40 - 7:00 there is a very distracting oscillating bass distorting the audio and I can't even focus on what you are saying. I have enjoyed the video thus far though. You are a great speaker and presenter of the information. Perhaps, there is a way to reupload only this part somehow.
I am so curious about the Klein-Gordon and Dirac equations, but I have to wait at least a couple more weeks until the next video. Cruel universe! Why meeeee!?!?!?! Why.....*sob**sniffle*. This was a great video! Super eager for the follow ups!
Bro the video is wonderful
I love quantum mechanics
I would like to see a playlist from you which explains all the basic concepts needed to understand quantum physics
Nice work bro
Thanks very much! I have a playlist with all my quantum videos, but will one day surely make one with just the basic concepts. In the meantime, here's the playlist: ruclips.net/p/PLOlz9q28K2e4Yn2ZqbYI__dYqw5nQ9DST
@@ParthGChannel thanks bro
Nice video. Nice explanation. Your left eye blinks at a slower pace than your right one: this mean you are stressed and need to relax and sleep more. No burnout please.
The Dirac equation is in effect also a Schrodinger equation, i.e., of the form: i∂/∂t(Ψ) = HΨ. It's just not the most basic Schrodinger equation with H = p^2/(2m) + V.
The Schrodinger equation is a Dirac equation
Great content.
U deserve much more subscribers ❤
Hello Parth, Brilliant video! Thank you! You mention Schrodinger equation is not apt for quantum systems involving high speeds. Can you please quantify this statement? Do you mean sub sonic regimes should be ok?
The equation Schroedinger came up with is not Lorentz invariant, which means that it's not an equation that can describe relativistic systems.
Excellent 👍
Also on this topic, the Dirac equation explains, partially, why Gold is a gold color, and why Mercury is a liquid at room temperature.
Great communicator really!
Can the distribution have two peaks or maxima. If not then some spring like behaviour. Under no pressure the diameter like bell curve. But can tail end size can change because of some other factors not taken into account when measuring.
Parth G, you are doing great in all, as always. you are one of the right persons to ask the following.
when an atomic system absorbs a discrete energy of photon (say, the difference between ground and excited state), the electron cloud gets excited and relaxes back to ground state, after few nano-second.
On before and after this event, if the energy of the absorbed and emitted photon remains constant to preserve energy in time, then where do the electron cloud, get the energy to go against nucleons pulling for infinitesimal second.
is there any connection with Noether's theorem on time translational symmetry, might it be broken for that few nano-second?
I'm awaiting for your answer
Go ask @TerryBollinger
Interesting question! So if I understand your question correctly, then I think if we consider the total energy of the system then it stays constant.
Before: photon has some energy and electron cloud has ground state energy.
While absorbed: photon no longer exists / has been absorbed, and that gives enough energy to the cloud to rise to the excited state. I believe it is the photon's initial energy that gives the electron cloud enough energy to overcome nuclear attraction and go into the excited state. In other words, for those nano-seconds the photon has been absorbed and can be considered to not exist.
After: Photon is re-emitted, so total energy is once again conserved. I'm not sure whether it's technically more correct to say that the "same" photon as before is re-emitted, or whether a new photon with the same energy as the first one is emitted by the cloud.
Let me know if I have understood your question correctly!
@slowdown7276 Always a good idea!
@@ParthGChannel Thank you parth g for answering. My question lies on, the few nano-seconds of being in excited state of the cloud. where do the cloud gets the energy for staying in the excited state for few nano-seconds,not asking for the cause of excitation. Because, before and after excitation, energy of the closed system is constant. What is about, while in excitation state?
I think you're getting confused by the term "absorbed". It's not like water being absorbed by a sponge, where the water is still there inside the sponge. In this context, it really means "destroyed". As Parth said, after the photon has been absorbed, the photon no longer exists, and the energy it had is now possessed by the electron. When the electron returns to its ground state, a new photon is created which carries the energy away.
BTW, the excited state can exist for much longer than a nanosecond under some conditions. Phosphorescent materials, as used in glow-in-the-dark watch faces, etc., can continue to emit photons for a few hours after being exposed to light.
Very nice video!
Only a trivial comment: The "i" in "Ψ" is simply pronounced as "i", (like in "thin"), not as "ái". The same applies to π, μ, ν, ξ, χ symbols used in science.
Feynman effectively salvages the law of non-contradiction : nothing is it's opposite, in atomic physics, by sketching an opposite sub-atomic particle emmiting process, called beta decay, that restores atomic stability after some energetically disruptive event, like an electromagnetic light wave, providing technical apparatus for a consistent interpretation : opposite, inverse, or complement say, of electron and proton adjective antonyms negative and positive in the Rutherford and Bohr theories of an atom, dispelling the ubiquitous practice of including entities of general form xnot-x, where not means opposite, in physical formulae and models, for instance by concatenating non-number negative representative non-numeral, "-" , with number one numeral, "1", even though the geometric opposite of > pronounced "ir", reflected about a vertical straight line segment, is < said "ri".
Original note in french (translation below)
Votre remarque à propos de l'équation de Dirac permettant de prédire l'existence de particules de même masse mais de charge électrique opposée (positron etc) est applicable au signe de la masse.
Aussi, si la physique a du admettre expérimentalement l'existence d'une matière de charge électrique opposée à la matière conventionnelle suivant la prédiction de l'équation de Dirac, cette même équation permet de prédire l'existence d'une matière constituée de masse négative.
Concernant l'électron et ses alter égos, on en aurait 4 types: m+/e- et m+/e+ (électron et antiélectron de masse positive) et m-/e+ et m-/e- (électron et antiélectron de masse négative).
L'existence d'une masse négative, en appliquant la loi de la gravitation universelle en tenant compte du signe de la masse (force répulsive pour des masses de signes opposés et attractive pour des masses de même signe), permettrait de rendre compte de la fuite accélérée des galaxies à l'horizon cosmologique.
Note: la construction du phénomène théorique "run-away" ne respecte pas la relation fondamentale de la dynamique, contrairement à l'application du signe d'une masse à l'équation de la gravité.
Admettre l'existence d'une énergie négative (E=mC²
Tell me how to approach gamma matrices of Dirac mathematically and conceptually. It appears to be with too hard mathematics Dirac too admitted.
Yes, correct Formal Math, but "Precision is not Accuracy", and confirms that the information lost in quantization Quantum-fields cause-effect, is between line-of-sight density-intensity and linear-transverse logarithmic reciprocation-recirculation, or collation-collapsed alignment and holographic coherence-cohesion sync-duration resonance, two different forms of function like counting Numerical pulses and identifying shell-horizon envelope-shaping Calculus of Logarithmic Time Timing continuity. This is the basis of relative-timing vector-value mechanisms in holography, (about which I know nothing).
This guy does plenty of hand-waving. As a physics professor, I can talk without moving my hands.
i'm confused, is the modulus of the klein-gordon wavefunction negative? how does that work geometrically? Also, probability density can totally be negative, thats how nodes show up in the psi squared.
Good stuff
Welcome back Parth! I was waiting for your next video❤️
Thanks for watching and for your support!
How do the Dirac and the Klein-Gordon-Equation account for time diletation and length contraction?
By being invariant under Lorentz-transformations. That means that you can just apply a Lorentz-transformation on those equations as well as to the solutions of it. The structures remain the same but Eigenvalues will aquire the respective values of the frame of reference accordingly.
Currently reading Farmelo's "The Strangest Man," the famously comprehensive bio for Dirac, and this showed up in recommended 😍
Thanks for this precise and concise presentation!
Hi, nice video btw. How come we don't need to incorporate more relativity into quantum mechanics. Since don't most quantum systems involve electrons, photons etc that move at relativistic speeds?
So shouldn't these equations be used more than the Schrodinger equation? Or am I misunderstanding something.😅
Why would you need relativity for a 1eV photon? It's a very small energy compared to the rest mass energy of the electron and the rest mass energy of the proton in the atom that emits it. Now, if you want the spectra with extremely high precision, then you have to use relativistic equations because there are small correction terms that go with 1/c and higher powers.
How you animate equations
Thank you
Parth, dude, you got the time dilation backwards. If you are measuring from the frame of reference of the stationary observer, the moving person should measure less time since his clock ticks slower.
Would like a video on cp violation
please i want to ask. since no particle can move faster than light, how is it that this equation E=MC2 work? if the particle has to move to the speed of light squared.
The c squared in that formula is not the speed at which anything is moving. It's just a constant that's needed to make the units work out correctly.
Note: The fact that it resembles the Newtonian formula Ek = 1/2 m v^2 is just a coincidence and is completely irrelevant. E = mc^2 is actually the energy of an object that has *zero* velocity!
"if the particle has to move to the speed of light squared."
The equation says absolutely nothing about particles being required to move at the speed of light. The C^2 part is, simply put, just a constant, albeit one with units, which is the ratio of the energy equivalent of mass to its rest mass. The clue here is rest mass; it's not even moving in the relevant frame of reference (it's own of course). If we are to use so-called "natural units" where C almost often just 1, then the constant basically disappears.
MORE MATHS PLEASE PARTH
The Schrodinger equation is not "a wave equation", the wave equation is a hyperbolic PDE, whereas the Schrodinger equation is a parabolic PDE. It's much more similar to the heat equation, except over the complex numbers.
You're right that the Schrodinger equation is not the same kind of hyperbolic PDE as what we call "THE wave equation", but I have often seen the Schrodinger equation referred to as another kind of wave equation! This is because it can admit wave-like solutions :)
I think it genuinely is a wave equation. Although it appears to be only first-order in time, psi is a complex-valued function. In terms of real and imaginary components, it's a system of two coupled first-order equations, which is equivalent to a second-order equation. A such, it has solutions that are periodic in time.
@@gcewing That's an interesting argument, and I buy that the fact that it's a coupled system makes it second order in time, but having solutions that are periodic in time is surely not an interesting property: any PDE that has a constant function as a solution has a solution that is periodic in time. Furthermore, the heat equation with boundary conditions set to a function that is periodic in time and initial conditions set to a harmonic function compatible with the boundary conditions will have a solution that is periodic in time. There's a StackExchange post where this question is discussed, and the definition they use is that f(x, t) = f(x + vδ, t + δ), which seems a bit more restrictive.
❤ Very good 👍🏼
Dirac's equation has nothing to do with the Schrœdinger equation.
Dirac's equation is the Euler-Lagrange equation for _classical_ spinor fields. It's not a generalization or a special case of Schrœdinger's equation.
Do you know a relativistic version of Schrodinger's equation?
These are really good videos nothing "very" dumbed down what I normally see in Dr Brian Greene's videos and what I've encountered there is that by dumbing down these complicated ideas you destroy the essence . People are not that dumb how the physicists make them to be😅
I've tackled most of the topics in my masters (didn't do exclusive calculations using C-G equation) but yes all of what you said is technically sound also lived the spin analogy it did really make me smile listening to it
a cubed + b squared +c = 1 or -1. With the quadratic equation?
Do all Massless energies spread out?
At 1:45 you say it’s a wave equation. But isn’t it a heat equation?
My head is now spinning with integral momentum. Thanks.
Jar in space can realise space and time but a jar in space-time can only realise space-time ignoring almighty space and time
The d'alembertian operator has confusing notation in my opinion, it's like am I applying it twice or once
I am afraid, Dirac did n o t think that the extra solution was a mistake of the mathematics of his equation, but that he mistakenly identified it with the positively charged protons! (Later on it was correctly learned to represent the ''anti particle'' of electron, dubbed ''positron''.)
Dirac did try several interpretations (as did other physicists), but he was the one in 1931 that produced a paper interpreting the mathematical solution as a positively charged electron (which he called an anti-electron). When new theories are produced, the author doesn't necessarily appreciate all the aspects of it, just as Einstein didn't understand all the implications of the General Theory of Relativity. Sometimes it's other physicists that do, sometimes, as in Dirac's case, it's the author of the original equation that does so.
How does p^2/2m work for massless particles when describing kinetic energy.
It doesn't. That's the Newtonian formula for kinetic energy, which is only valid for massive objects moving at much less than c. Photons are massless and always travel at c, so you have to use the relativistic formula.
The fact that Schrödinger derived his equation from Newtonian formulas is the reason it's non-relativistic.
All this is way over my head. Yet I can't help but wonder that the Einstein equation at 4:26 looks a lot like the Pythagorean theorem.
So, spin is to angular momentum as rest-mass is to linear momentum? Have I got that right? I’ve never really understood spin before (maybe still don’t)
Spin isn't really understandable intutively. Need to allow your mind to undergo a paradigm shift by getting your hands dirty with lots of quantum math
Out of curiosity, what are some other ways antimatter has been observed?
We can produce antimatter from radioactive materials. A PET scan often used in medicine is 'positron' emission tomography, where a positron is the antimatter equivalent of an electron.
@@VenusianJungles Thanks for replying.
Shouldn’t the person moving at 0.9c speed show 30seconds and the stationary 68?
Thanks Dirac, I believe you a hero
Excellent and very instructive video. I have a question about Schroedinger's equation: what's the meaning of those symbols "^" over the momentum p and the potential V? Do they mean that we are dealing with measurement operators?
It simply means that we are dealing with operators, in case of p it's just a differentiation operator and V multiplies with a function V(x). The wave function is assumed to be a member of a well defined linear function space. There are a few mathematical complications with that that physicists are generally ignoring, but at the end of the day you are just talking about a linear partial differential equation and its solution theory in a slightly more modern (1920s) language.
@4:00 This equation was not 'Einsteins'. It was published earlier by one italian diletant.
|psi|^2 > 0 in Klein Gordon equation (where is the potential V? You describe only free wave equation... it is not normalized obviously). Psi should be related to the matter distribution of the electron, not only charge. Then how do you describe mass distribution ? I think that all of these assomption are to forbid negative mass (that can potentially save cosmology and QED by the way).
I have exam tomorrow but i'm still watching 🥶🥶 this curiosity will cost me a big thing 🙂🙂
shouldn't the first be what is the positional variable? Is this going to yield an XYZ position?
or just a single-dimension position? Saying its a wave first clarifies nothing
There are no positional variables in quantum mechanics. We can put a piece of matter (aka a detector) at position x,y,z and absorb energy from a quantum field at that position, but all we ever get back in terms of position is what we already know about the location of that matter... because we put it there deliberately. That position is therefor not a physical property of the quantum field.
@@schmetterling4477 Isn't the wave function assigning a probability
to each x position in space? So is the Schrodinger equation--is it single dimensional? Or 3 dimensional?
thank you
@@anzatzi The wave function does not describe a single quantum mechanical system. It describes an ensemble of that system, i.e. an infinite completely independent repetition of the same experiment. The dimensionality of the SE depends on the number of quanta we are modeling. For a single quantum it can be a three dimensional partial differential equation, but for two quanta it would be six dimensional, for three nine dimensional etc.. This is further complicated by the fact that fermionic quantum states of the same kind of quanta are antisymmetric and bosonic states are fully symmetrized. From that we can build sheer endless combinations and the most general case of an indefinite number of quanta is a direct sum of such product places (that's called the Fock-space).
Impossible to understand, but fun to watch.
Still waiting for the promised exposition on kg & dirac eqns
You can find it in basically every preliminary chapter of quantum field theory textbooks. Not sure why you think that advanced physics is on RUclips. It isn't. You can barely find decent basic physics on RUclips.
didnt you mess up around 10:50?
Schrodinger equation is NOT a wave equation, its a diffusion equation.
A wave equation has 2 space derivatives and 2 time derivatives.
A diffusion equation has 2 space derivatives and 1 time derivative.
One time derivative equations describe how things evolve in time.
Paul Dirac looks like Howard Stark from MCU
Plz talk some maths too in ur videos
5.15 A square squared? Is that a tesseract?
HEY WE HAVE THE SAME NAME AND THE SAME PASSION !!GREAT CONTENT
Great name!
impressive
From what I heard the only part where the Schrödinger equation is non-relativistic is the hamiltonian. So we can construct a relativistic Schrödinger equation although it’s not that useful in practice. The Dirac equation is also not that useful and just a steppingstone for quantum field theory.
QFT video coming soon ;) (maybe)
@@ParthGChannel great! Can’t wait
Isn't that like asking of what use is a baby?
@@charlesgantz5865 I’m not criticizing this video. I’m just adding some more information
Yep, as I understand, the Schrödinger equation works fine to give the time evolution of the system in QFT. All the relativistic stuff happens in the Hamiltonian (or Lagrangian if you're going that way). And the Klein-Gordon equation, Dirac equation, etc., appear as equations of motion for the various fields.
Dirac- Nice engineer 😊😊😊
In case of heat transfer specific heat is a parameter big part of heat transfer. What is the equivalent of that in shoriegndrr equation. Is it mass?
m.ruclips.net/video/LFC2HsT6Bh4/видео.html
String Theory was not a waste of time. Geometry is the key to Math and Physics.
What if we describe subatomic particles as spatial curvature, instead of trying to describe General Relativity as being mediated by particles?
Quantum Entangled Twisted Tubules: "A theory that you can't explain to a bartender is probably no damn good." Ernest Rutherford
The following is meant to be a generalized framework for an extension of Kaluza-Klein Theory. Does it agree with the “Twistor Theory” of Roger Penrose? During the early history of mankind, the twisting of fibers was used to produce thread, and this thread was used to produce fabrics. The twist of the thread is locked up within these fabrics. Is matter made up of twisted 3D-4D structures which store spatial curvature that we describe as “particles"? Are the twist cycles the "quanta" of Quantum Mechanics?
When we draw a sine wave on a blackboard, we are representing spatial curvature. Does a photon transfer spatial curvature from one location to another? Wrap a piece of wire around a pencil and it can produce a 3D coil of wire, much like a spring. When viewed from the side it can look like a two-dimensional sine wave. You could coil the wire with either a right-hand twist, or with a left-hand twist. Could Planck's Constant be proportional to the twist cycles. A photon with a higher frequency has more energy. ( E=hf, More spatial curvature as the frequency increases = more Energy ). What if gluons are actually made up of these twisted tubes which become entangled with other tubes to produce quarks. (In the same way twisted electrical extension cords can become entangled.) Therefore, the gluons are a part of the quarks. Quarks cannot exist without gluons, and vice-versa. Mesons are made up of two entangled tubes (Quarks/Gluons), while protons and neutrons would be made up of three entangled tubes. (Quarks/Gluons) The "Color Force" would be related to the XYZ coordinates (orientation) of entanglement. "Asymptotic Freedom", and "flux tubes" are logically based on this concept. The Dirac “belt trick” also reveals the concept of twist in the ½ spin of subatomic particles. If each twist cycle is proportional to h, we have identified the source of Quantum Mechanics as a consequence twist cycle geometry.
Modern physicists say the Strong Force is mediated by a constant exchange of Mesons. The diagrams produced by some modern physicists actually represent the Strong Force like a spring connecting the two quarks. Asymptotic Freedom acts like real springs. Their drawing is actually more correct than their theory and matches perfectly to what I am saying in this model. You cannot separate the Gluons from the Quarks because they are a part of the same thing. The Quarks are the places where the Gluons are entangled with each other.
Neutrinos would be made up of a twisted torus (like a twisted donut) within this model. The twist in the torus can either be Right-Hand or Left-Hand. Some twisted donuts can be larger than others, which can produce three different types of neutrinos. Gravity is a result of a very small curvature imbalance within atoms. (This is why the force of gravity is so small.) Instead of attempting to explain matter as "particles", this concept attempts to explain matter more in the manner of our current understanding of the space-time curvature of gravity. If an electron has qualities of both a particle and a wave, it cannot be either one. It must be something else. Therefore, a "particle" is actually a structure which stores spatial curvature. Can an electron-positron pair (which are made up of opposite directions of twist) annihilate each other by unwinding into each other producing Gamma Ray photons?
Does an electron travel through space like a threaded nut traveling down a threaded rod, with each twist cycle proportional to Planck’s Constant? Does it wind up on one end, while unwinding on the other end? Is this related to the Higgs field? Does this help explain the strange ½ spin of many subatomic particles? Does the 720 degree rotation of a 1/2 spin particle require at least one extra dimension?
Alpha decay occurs when the two protons and two neutrons (which are bound together by entangled tubes), become un-entangled from the rest of the nucleons
. Beta decay occurs when the tube of a down quark/gluon in a neutron becomes overtwisted and breaks producing a twisted torus (neutrino) and an up quark, and the ejected electron. The phenomenon of Supercoiling involving twist and writhe cycles may reveal how overtwisted quarks can produce these new particles. The conversion of twists into writhes, and vice-versa, is an interesting process.
Gamma photons are produced when a tube unwinds producing electromagnetic waves.
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Within this model a black hole could represent a quantum of gravity, because it is one cycle of spatial gravitational curvature. Therefore, instead of a graviton being a subatomic particle it could be considered to be a black hole. The overall gravitational attraction would be caused by a very tiny curvature imbalance within atoms. We know there is an unequal distribution of electrical charge within each atom because the positive charge is concentrated within the nucleus, even though the overall electrical charge of the atom is balanced by equal positive and negative charge.
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In this model Alpha equals the compactification ratio within the twistor cone, which is approximately 1/137.
1= Hypertubule diameter at 4D interface
137= Cone’s larger end diameter at 3D interface where the photons are absorbed or emitted.
The 4D twisted Hypertubule gets longer or shorter as twisting or untwisting occurs. (720 degrees per twist cycle.)
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How many neutrinos are left over from the Big Bang? They have a small mass, but they could be very large in number. Could this help explain Dark Matter?
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Why did Paul Dirac use the twist in a belt to help explain particle spin? Is Dirac’s belt trick related to this model? Is the “Quantum” unit based on twist cycles?
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Yes, that was a lot of bullshit. ;-)
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