Why Relativity Breaks the Schrodinger Equation
ฝัง
- เผยแพร่เมื่อ 4 พ.ค. 2024
- In this video, we look at why the Schrodinger equation is incompatible with special relativity, specifically through the lens of Schrodinger plane waves, and the energy vs. velocity curves for relativistic and classical physics.
Stay tuned for the next videos, in which we will derive relativistic wave equations, explore the four-potential and gauge symmetry, and eventually will return to hydrogen with a relativistic treatment of the electron! :)
For further reading, please check out Introduction to Elementary Particles, by David Griffiths. That book provides a ton of insightful context around the ideas in this quantum physics playlist.
Chapters:
0:00 Intro
0:50 Schrödinger Free Particle
2:00 2nd Order in Space, 1st in Time
2:52 Schrödinger Plane Waves
5:03 de Broglie Relations
6:55 Relativistic vs. Classical E(v) Curves
13:00 Ultra-relativistic LEP Electron
14:34 Returning to the Plane Waves
15:44 Concluding Remarks
#physics #quantum #math
Hey everyone, thanks for checking out this video! :) Just wanted to pin a couple of minor corrections here, based on your feedback:
1) I should have put “keV” instead of “KeV”. It’s like how kilogram is kg, not Kg.
2) I should have clarified that typically (Laplacian) ~ (d/dt) is called the heat equation or diffusion equation, whereas the term “wave equation” typically connotes (Laplacian) ~ (d2/dt2). *However*, that’s because we often use real-valued functions; when working with complex-valued functions, (Laplacian) ~ (d/dt) does indeed allow for wave solutions, because of the phase degree of freedom in the complex plane. The plane waves shown in this video are examples of that. But instead of just saying that S.E. for a free particle is a wave equation, I should have talked briefly about how the first time derivative requires that psi be complex, at which point this thing that looks like diffusion can actually get wavy. I hope that explanation clears things up.
Please let me know if you have any more corrections for this video. I’m trying to always get better over time! :)
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
The classic wave equation derived from Maxwell equations is relativistic invariant, but the quantum mechanic Schrödinger eqation is not.
Einstein’s Relativity is garbage science. It's physics is based off of Acceleration. Anybody that references it as real science is still playing with toys in a sandbox pretending that they are real.
Can you explain what exactly means by "particle has slower all oscillating things"? Exact experimental observations, pls. While concept of asymptotic E(p) curve fits well with my understanding of reality, I cant get rid of feeling that mass increase and time slow might be some correct mathematical backside of wrongly interpreted phenomena.
@@hyperduality2838 How did the word salad taste?
You are the 3blue1brown of physics. Some of the highest quality videos on youtube. Thank you sir
Thanks for the kind comment! :) Grant is definitely a role model, his videos are amazing.
This comment is very accurate
He even kind of sounds like him, just with a deeper voice.
Great comment, but I'd say Grants content, while thorough, is a little more accessible to a general audience that remembers some stuff. While these videos are a little more technical without having to draw out the analogies to death, just a solid technical overview, which I prefer.
Imo better than 3b1b
First rate pedagogy - always love learning from experts who are totally at ease with their topic.
Somehow you are hitting this magical sweet spot where every time you explain some profound result I feel like “yeah, this makes perfect sense”.
Ok: Then please can you explain it so that I can understand also.
@@terjebauge6248 explaining it means to explain whole quantum physics from start 💀...
you should first study highschool course and then some basic things
..
As someone with a chemistry background I mostly knew about relativity's effects on electron clouds as the reason heavy element chemistry stops making sense and just sorta does whatever it wants.
0:08 intro
0:50 free particle
2:00 2nd order space
2:52 plane waves
5:03 de broglie
6:55 curves
13:00 lep electron
14:34 return to plane waves
15:44 conclusion
Huh, he added it to the description now but it's still not giving the video chapters. Anyone know why?
Studied advanced physics in high school and just did vector calc in university. I’m so happy to finally understand this stuff!
I just want to say that I appreciate this so much. This is the level I'm at, and its hard to find content that doesnt hold back from the whole truth, while still giving a good intuition and not falling back to the math alone pretending that understanding the math is the same as understanding the thing itself.
Thanks, I’m glad you’re enjoying the videos! :) And I agree, there’s a difference between knowing the mathematical procedures, vs. seeing what the math actually means.
Only when we have the math, do we the thing itself.
@@RichBehiel I think too often the assumptions underlying the mathematics are dogmatically defended without recognizing when the predictions of the math do not necessarily depend on all of those assumptions.
Math is law
Absolute truth (universals) is dual to relative truth (particulars) -- Hume's fork.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
Much that most in this video is right on-the-spot, there is a tiny detail that is not. In the metric system, all the dividing prefixes use a lowercase letter: d for deci-, c for centi-, m for milli-, etc. And, all the multiplying prefixes, an uppercase letter: D for deca-, H for hecto-, ... and K for kilo-. But it is not KeV, Km, or Kg that are written on the graphics in the video, but keV, km, and kg instead. A little detail but it should be corrected.
Anyway, thanks for the video. Very educational and interesting.
You’re right! Thanks for the correction :)
The SI prefixes for kilo, hecto, and deca are k, h, and da, in lowercase. So it is keV, km, kPa etc.
Now I shall learn
Me when I see a notification for this channel
This is exactly what I've been looking for. I need to see the math. General concepts don't satisfy my curiosity anymore. Well, they do but in some areas I really crave a deeper understanding and linear algebra helps with that.
cant wait for part 3!!!
I'd love to actually see a video about DIRAC's trick to form a 1st order equation and how it automatically predicts both spin and antiparticles.
Will do! :)
Thanks for another great video. Quickly becoming my favorite educational physics channel. Amazing amazing explanations, great content, def deserves more attention.
Great video!
U obviously a PRO!
Please share in the description the relevant academic bibliography for further reading.
ThX!
Great idea, thanks. I’ve updated the video description with a reference to Introduction to Elementary Particles, by David Griffiths. That book is a wonderful summary of the standard model, and is where I’m getting most of the ideas for this quantum physics playlist.
Really well done! Looking forward to the follow up!
The Schrödinger equation is actually no wave equation but a diffusion equation (Laplace operator proportional to 1st(!) time derivative).
For real-valued functions, I totally agree. But for complex-valued functions, the first time derivative allows for wave solutions because of the phase degree of freedom in the complex plane. I should have clarified that in the video, because you’re right that typically “wave equation” connotes 2nd order in time.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
im always so excited to see your posts. you by far have the most informative content on youtube about quantum mechanics and WHY things are the way they appear. thank you for doing what you do, and once again illuminating a topic that's well known but whos facets are rarely seen.
Thanks for the kind comment! I’m glad you’re enjoying the videos :)
My exact sentiment! Amazing content
I very seldom subscribe to new channels on youtube, but I'm currently taking Particle Physics, and while our notes cover the mathematics in some detail, the conceptual understanding is often much more of a struggle to get. I get the sense that your videos are going to be very helpful here.
Really nice video, I'm already excited for the next one 😁
The legend has returned
I am so glad, that TH-cam algorithm recommended me your channel. Super interesting quantum and relativistic stuff, that I slept through my lectures in university!
Thank you for such quality content. I wish you could upload more often.
PS I am sure you will get to 1mil subs
Thanks for the very kind comment! :) I’d love to upload more often, if I could find the time. Making videos is a lot of fun.
Fantastic explanations! Thank you!
I love your content since its not just your typical edutainment physics shit with diluted details and simplified explanations. Instead you present actual physics with real equations
I was sitting here wondering why there was no third video in the series. It was just uploaded! Good work! Subscribed.
Thanks! :) The next few videos are actually kind of a detour from hydrogen, laying out the basics of relativistic quantum mechanics, so when returning to hydrogen in part 3, we can treat the electron relativistically.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
this channel is a godsend!! coming from a pure maths background your videos are a perfect transition into physics
Thanks, I’m glad you’re enjoying the videos! :)
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
very interesting video topic and I like how you put your videos together, thanks
Thanks for another great video. Quickly becoming my favorite educational physics channel
I’m glad to hear that, thanks for watching! :)
You have a great voice. It took me about 90% of the video before I realized that it wasn't that I only got 10% of what you were saying, but rather that I was getting 0% of what you were saying. Also, great visuals!
Such an amazing explanation which reaches the fundamental reasons of the theory! Thank you for that!
Thanks, and I’m glad you enjoyed the video! :)
You're such a tease :)
All of your videos are so good but they always leave me wanting all the things you hint at. Maybe one day you'll get to spin statistics and I'll finally understand why QM forbids particles that arent spin n or n+1/2
We’ll get a glimpse of that while looking at it the differences between Klein-Gordon and Dirac. I’ll also do a vid on the Proca equation, not sure whether it’ll be before or after hydrogen part 3. But then we’ll have seen relativistic scalar, spinor, and vector fields. At that point it’ll be natural to get into Wigner’s classification, and we can start building toward the idea that all the particles are irreducible representations of the Poincaré group - that’s where the answer to your question is ultimately found.
Amazing amazing explanations, great content, def deserves more attention
Thanks! :)
Great video. I started watching your videos recently and they are very inspiring! 💚
Thanks, I’m glad to hear that! :)
That was a GREAT explanation!!!! Very nicely done!😀
Thanks, I’m glad you enjoyed it! :)
Great stuff!
I'm in grad school for physics as we speak. I look forward to your upcoming videos
The stubborn-German joke (13:50) made my day! :-)))
Zero point stubborn German.
That number equals 1 in the limit as German stubbornness approaches infinity.
I am really looking forward to the next videos
You are a hero
Relativistic Schrodinger's equation. (static):
Y= Function wave
d²Y/dx² + (1/c²h²)[E² - (mc²)²]. Y - (mc²/E)(2m/h²)U(x).Y = 0
E = Total energy (relativistic)
h = Planck tilded constant
That was an interesting video to watch! (even though I don't know anything about the topic, except for some basic concepts)
I absolutely adore your videos! Thank you!
Thank you for watching! :)
Awesome physics content.
Great video! I just discovered this channel. Thank you for doing this!
Thanks! :)
Great video! I almost understood some of it.
very interesting, thanks for making the video
Wonderful video. Great explanation skills.
Thanks! :)
Ty for explains it so well
A nice didactic exercise Richard. I would say that from a top down view, which the physics student must develop in due course, the concise point IS made by about minute 4 when you indicate that the time operator is first order while the space operator is second. This only shows that the S equation is not "obviously covariant" , but neither are the nineteenth century Maxwell equations, although they turned out to be be so to the surprise of early writers. I think that a very important point missed is that there is no scale factor to the S. equation insofar as velocity, such as c, though h-bar appears to set a size scale. That c must appear in the relativistic kinematic equation you later display, and in the "SI version" of the KG relation, is key, and is roughly how any material particle is "aware" of a universal speed limit.
best regards, D. Barillari
Sometimes i want to make a research web learning academy , in that case i tried and found people don't hace 2 dollars to donate. This video make me the memory of nostalgic projects. Great video xd.
These really are some high quality videos.
Thanks, I’m glad you enjoyed them! :)
Your videos are such a blessing for someone like me who thinks visually and graphically. Im not the biggest fan of physics usually but content like this makes me second guess. Do you have a book set that you suggest with emphasis on graphical intuition? I have taken all the way up to engineering physics 2 (maxwells equations and elementary optics)
Honestly I’m not sure about a book that focuses on graphical intuition. Unfortunately most of the physics books I know of are pretty dense with equations. But one book that stands out is Introduction to Elementary Particles, by Griffiths. He writes with such wonderful prose that the ideas become much more accessible, and there’s a good number of insightful figures in there too. It’s one of my favorite books of all time. If you’re already familiar with Maxwell’s equations and elementary optics, you’ll have a good mathematical foundation for learning the topics presented in that book.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
uh oh who decided to mix relativity and quantum in the same bowl. Great video as usual!
Mixing relativity and quantum mechanics, hey what’s the worst that could happen? 😅
Hi, and my compliments. As you are so talented with animations, I make the following suggestion, if you ever consider making an updated version of this video or one that discussed the relativistic version of the relation between E and p. I suggest you animate the right triangle showing how the mc^2 side stays constant while the pc side and the hypotenuse E change accordingly going from newtonian regime to ultra-relativistic to a massless particle (photon) with E = pc.
Excellent job! Please make a lesson how to calculate the Lamb shift, we all are very anxious 🥰
i love your videos so much!!!
Ocean waves with longer periods carry more energy and travel faster.
In contrast, light maintains a constant speed; the shorter the period, the more energy it exhibits during collapse.
Therefore, it cannot be described as a wave, but an alternative term may be utilized.
Good point! It would certainly be wrong to say that light is the same as an ocean wave. Whether the term “wave” is broad enough to encompass all wavy things, is a matter of semantics. The great thing about math is that the equations specify the behavior of the waves, so there’s no semantic ambiguity when doing calculations.
There is no such thing as collapse.
super. thanks again
I am amazed at your knowledge of nuclear physics.Your knowledge of elementary particle interactions is tremendous.Let's break down in detail by theta or pico seconds the process that occurs in a uranium or plutonium nuclear explosion.
My layman understanding of the development of relativistic quantum mechanics has been that Dirac took the Schrodinger equation and made it relativistic. Boy am I surprised how oversimplified my understanding was.
Well if it makes you feel better, this subject took many years for the geniuses of the world to figure out!
Btw funnily enough, Schrodinger came up with a relativistic wave equation (that we now know as the Klein-Gordon equation), before Klein and Gordon. But Schrodinger, genius that he was, realized that the Klein-Gordon equation didn’t give the correct fine structure for the hydrogen energy eigenstates, so he fell back on his nonrelativistic equation since at least it was a very good approximation. Then Klein and Gordon published on the relativistic Schrodinger equation (which is what it’s sometimes called), so they got the credit.
Problem is, KG predicted negative probability currents in some circumstances, and also requires a time derivative term as boundary conditions (these things are related). This went against the spirit of quantum mechanics at the time, which prompted Dirac to break geometry and take the square root of the energy-momentum-mass equation, thereby giving us a mathematical basis for interpreting spin and antimatter. We’ll go through that process in the upcoming videos.
@@RichBehiel It's been my observation that the difference between a good problem solver and a great problem solver is that a great problem solver cheats by changing the problem into one that can be solved.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
Out of my depth here but re the non-relativistic Schrodinger equation is really more like a heat equation?
Yes, it’s very similar to the equation that governs the time evolution of a temperature distribution in a uniformly-conductive medium. That’s also the equation that runs through scale space, in image processing. These are all examples where the rate of change is proportional to the Laplacian.
Excellent way of presentation. If you can connect plane wave solution of Maxwell’s equation with that of Schrödinger equation it would bridge EMFT and wave function / quantum mechanics.
Feynman did all of that in 1948/49, but it doesn't get you very far. The problems that you are looking at here are physical, not mathematical. There is no self-consistent quantum theory of the electromagnetic field. There was none in the classical case, either, we are just not talking about the problems very much when we are teaching classical electromagnetism.
Got an msci, really enjoyed this
Amazing ❤
Thank you.
Please look up zig-zag particles (Penrose), from which you can derive a relativistic Schrodinger equation with absolute ease (a Telegrapher PDE). It’s honestly a neat trick! 😉
Very cool!
that is any amazing proposed question. thank you and ill let ya know what i think afterwards
Excited to see future videos. I remember seeing a lot of this stuff in my head during my studies, but to see it animated like this is a treat. You're doing great work
Actually I recognize the Schrodinger equation more as a heat equation than a wave equation. The model in my head had the wave equation with a second time derivative as well as a second spatial derivative but I sort of see how complex numbers might make the Schrodinger equation a wave equation too. I had to think about that one though and still do.
You’re right, the Schrödinger equation is kind of an ambiguous mix of both. I should have clarified that in the video. If psi were real, then it would be a heat equation for sure. Because the rate of change of the field would equal the laplacian, so the thing would diffuse out and settle down over time. But the complex phase and the i in the derivative, the SE has wave solutions because of the way the laplacian of the real part affects the imaginary part, etc., and that can go on waving forever. That’s actually why the SE must have a complex-valued psi.
awesome quality material
Thanks! :)
Amazing stuff
Thanks! :)
This is very well explained. It was a fantastic companion while I painted my basement.
"Saying that number makes me sound like a stubborn German" - made my day
Very good video 👏👏👏
Thanks! :)
11:55 normally shouldn’t m be on the diagonal and E be vertical because it’s x^2-y^2 instead of +y^2: mass is the magnitude of the momentum four vector
I’m showing a Euclidean triangle here :)
You’re right about the magnitude of the four-momentum. The next video is starting off from that point of view. But it’s tricky with the Minkowski metric, because the magnitude of the four-vector is smaller than what the hypotenuse of a triangle would graphically suggest.
So cool!! Thank you
Thanks for watching! :)
love your videos!
Thanks, I’m glad you’re enjoying the videos! :)
Is the video on Klein Gordon and dirac equations up? I can't find it on your channel? I enjoy your videos.
Yeah, I’m working on them now :) Sorry if it takes a while to post, life is quite busy these days but I try to find time when I can.
What a good video!
Thanks! :)
@14:30 We have pushed matter really, really hard and can't exceed c. *But you could look at an external push like that in that terms of Doppler Shift, and see that as v approaches c, the force of the push approaches zero. This is like pushing a car with just your own body: When it is stationary, you can brace yourself and push really hard, but when the car is going as fast as you can run, the force of your push goes to zero. So have we **_really_** pushed particles that hard? **_No!_*
We are pushing the particles with electromagnetic waves travelling lengthwise down waveguides, so of course the particles cannot go any faster than the waves pushing them.
Now, if the waves were propagating _transverse_ to particle velocity, we might see something quite different. In that case, _there is _*_no limit_*_ to the speed at which the wave crests will appear to propagate sideways, from the perspective of the particle!_
At this point, somebody will probably say something to the effect of 'But in the reference frame of the particle, electromagnetic waves always travel at exactly the speed of light.' Yes... and no. This gets into murky territory, where the *assumptions behind our theories* do not necessarily hold true, and we must resort to experiments to determine *what nature really says.*
I see where you’re coming from, and it’s an interesting thought experiment! The only thing is, the energy of the electron increases and increases the more it’s pushed. In the example of pushing a car at running speed, there will come a point when the speed stops increasing, but so too will the kinetic energy stop increasing. So if the problem is just that light is not fast enough to push something faster than the speed of light, then we would expect there to be not only a speed limit, but also a kinetic energy limit, of about 255.5 keV in the case of an electron. The fact that electrons have been accelerated to half a million times that energy limit, is an indication that the electrons do indeed continue to be pushed with a tremendous amount of force.
Underrated
Hi! I love your videos.
I was wondering if you could give me some insight on whether the path of least action influences the evolution of an electron in a 1D potential.
Yes, the principle of least action applies universally. Quantum physics can be formulated concisely by defining the Lagrangian density of a field, then applying the principle of least action to derive field equations as the conditions that minimize the action when integrating the Lagrangian density over spacetime. That’s another way of deriving the Schrodinger equation (although the Lagrangian approach is often used more in QFT, for the Klein-Gordon, Dirac, or Proca equations).
That’s all coherent with the kind of quantum physics where we start with the Schrodinger equation and calculate wavefunctions. But it’s much easier to calculate wavefunctions than to work with path integrals, for example. So, often the principle of least action is invoked only implicitly, as something that gives rise to the conceptual machinery that we take for granted.
@@RichBehiel Thank you, I'm really happy to hear this!! It helps give me a much better sense of the actual actions at play :)
The equations of motion minimize the action in quantum mechanics -- least action.
The equations of motion are predictions -- syntropic.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
subscribed!
This would have made a great #some3 entry, plus your fiber bundle video.
Oh man I should have submitted it! Totally forgot 😅
Very cool
Some of my thoughts: Would Einsteins general relativity work in 4+1 dimensions? Could an uniform accellerating universe along the 4th dimension (near the speed of light) lock and shrink that dimension into place? Could you measure a uniform gravitational pull of a 4th dimension, if that dimension is curled up to near 0 length? What would schrodingers equation's say to those curled up dimensions? Would that curled up dimension's energy leak into the other dimensions by quantum particles or would they only be virtual?
Fantastic
Spectacular video.
Got a small question. The wave equation is second order in both time and space. I'd say the schrodinger equation is a heat (or diffusion) equation. Wouldn't you?
Great question! If psi were real-valued, then yes, because the rate of change would be proportional to the laplacian, so the wavefunction would flatten out and then stop moving. But since psi is complex, the phase provides a degree of freedom, which accommodates wavy solutions.
You bring up a good point here. That’s actually why the Schrödinger equation has to be complex-valued.
I should have clarified that in the video tbh.
If those numbers are right then the electron was moving only moving 4 mm/s slower than light!
Wow, when you put it like that, that’s wild! 🤯
Regarding 4:25 is it possible for uncertainty in X to be different that uncertainty in y? ie if x momentum is tightly known then x position is loosely known, at the same time y momentum is loosely known and Y position is tightly known.
And therefor in a crystal temperature in one direction can be different than another direction
Certainty is dual to uncertainty -- The Heisenberg certainty/uncertainty principle.
The Schrodinger equation is used to make predictions about the behaviour of matter and energy -- a syntropic process, teleological.
Making predictions to track targets, goals and objectives is a syntropic process -- teleological.
Teleological physics (syntropy) is dual to non teleological physics (entropy).
Syntropy (prediction) is dual to increasing entropy -- the 4th law of thermodynamics!
Alive is dual to not alive -- the Schrodinger's cat superposition.
Being is dual to non being creates becoming -- Plato's cat.
Thesis (alive, being) is dual to anti-thesis (not alive, non being) creates the converging thesis or synthesis (becoming) -- the time independent Hegelian dialectic or Hegel's cat (Fichte's cat).
Schrodinger's cat is based upon Hegel's cat and he stole it from Plato (Socrates).
The scientific method of asking primary questions to get answers is based upon the Socratic dialectic, which is also the Hegelian dialectic.
Questions are dual to answers.
"Philosophy is dead" -- Stephen Hawking.
Stephen Hawking accepted the Schrodinger's car metaphor which is based upon metaphysics or philosophy, hence metaphysics is allowed in physics.
"Antinomy (duality) is two truths that contradict each other" -- Immanuel Kant.
"Always two there are" -- Yoda.
Enantiodromia is the unconscious opposite or opposame (duality) -- Carl Jung.
Legend
So good, so beautiful, so excellent.
With regards
“Okay saying that number makes me feel like a stubborn German” was hilarious
Damn this is amazing but this is too much for me... I might have to rewatch when i actually have enough maths background
For different observers you will get different values for p of the paricle. So particle can have different values of psi at the same time which is absurd. 😅
At first glance yes, although this paradox can be accounted for when one looks only at the phase gradients, rather than the absolute phase. The phase gradients track coherently with each observer’s p value (in the nonrelativistic limit).
Fantastic video as always. Keep up the great work! Just as a heads up, de Broglie is pronounced closer to “de broy” than “de BroGlee”. There’s an audio prononciation as well as an IPA transcription on Wikipedia if you’re interested. No worries if not, I’m sure everyone knew what you were talking about.
Thanks for the correction! 😅 I’ll be sure to pronounce it correctly next time.
When the sequel?
I can't wait for it............ 😉😉😉
As soon as I can! :) I work on these vids in the evenings and weekends, but lately my schedule has been busier than usual so the next couple videos might take a little while.
Time space is a dimension, do the other dimensions have an analog for black holes or are Black holes the product of all four
Hi Richard, that was great! But I'm wondering, could we not just bung a factor of gamma on the momentum and walk away with a relativistic Schrodinger equation? I'm sure they would have tried this and failed and then switched to Dirac, but ??
thanks
D
Great question! I’ve never thought about that. Hmm. Well, gamma and momentum are interrelated, so if we put in a factor of gamma, it would implicitly be a function of momentum, so then momentum would be nonlinear. At that point we might as well go with Klein-Gordon (which btw is sometimes called the relativistic Schrodinger equation, because Schrodinger came up with it first, but was unsatisfied with it because it didn’t account for the fine structure of the hydrogen eigenstates). Dirac fixed that problem by linearizing the energy and momentum terms, which brought spin and antimatter into the equation.
Anyway, another interesting feature of relativistic waves is that their phase oscillates, rapidly, even when the particle’s momentum is zero. The mc^2 rest energy term is twice the Newtonian momentum of a particle traveling at the speed of light, for a sense of perspective. So relativistic waves are oscillating super fast, while the Schrodinger equation for a particle at rest is just a constant, inert, lifeless complex number. So even far from the speed of light, there are qualitative differences between the two models.
@@RichBehiel Magic! Thanks again 😃
The issue is not the equation, the issue is the attempted solution by separation of variables.
Separation of space and time is asked too much when things get relativistic.