Everything, Yes, EVERYTHING is a SPRING! (Pretty much) with
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- Опубліковано 7 чер 2024
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Science Asylum video on Schrodinger Equation:
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RECOMMENDED READING:
Schwartz, "Quantum Field Theory and the Standard model" amzn.to/3HmWdYt
CHAPTERS:
0:00 The most important motion in the universe
1:08 How get energy and mental focus
2:20 A spring: Classical simple harmonic oscillator
4:48 QUANTUM Harmonic oscillator
6:00 Science Asylum - what is the Schrodinger equation?
7:30 Quantum Field Theory (QFT) uses spring math!
10:00 Intuitive description of what's going on!
12:37 What is really oscillating in QFT?
SUMMARY:
Why Everything in the universe is a spring (kind of). Why everything is a spring. Classical springs like you might have in your mattress have a harmonic oscillation. And this behavior has a quantum mechanical analog in what’s called a quantum harmonic oscillator. And this model of the motion in quantum mechanics can model the motion of all fundamental particles in the universe, as well as the forces mediating the interactions between them. In fact, the prevailing fundamental theory of all matter and forces, called Quantum Field Theory, is built upon this type of motion.
But what happens if we now go to the quantum realm? The equation of energy for a quantum particle looks almost identical to the classical case. Except, now it is expressed as, H, the Hamiltonian, instead of E, energy. The difference is that the Hamiltonian is an operator. It has to operate on something to determine how its energy is evolving. In the case of quantum particles, the Hamiltonian operates on the wavefunction, since the wavefunction shows how a particle evolves over time.
So how do we show that the same spring-like behavior applies to quantum fields? The astonishing part is if you write a quantum field theory for a simple field, then you get a Hamiltonian this is almost exactly what we have in the quantum harmonic oscillator or quantum spring. But now it’s for a particle field. What’s different is that in the case of quantum fields, since they extend everywhere in the universe, it has to be integrated over the three dimensions of the universe.
But unlike quantum mechanics, where the number of particles are fixed, in quantum field theory, the number of particles in the system can change. We can add particles by adding energy to the field, or annihilate a particle by removing energy from the field.
This aspect of quantum field theory is incorporated in the “a” and “a dagger” part of the equation. They are also known as the creation and annihilation operators. “a” is the creation operator and “a dagger” is the annihilation operator.
What the Hamiltonian equation shows is that quantum field theory is essentially an infinite collection of harmonic oscillators or springs, extending out to all of spacetime in all 3 dimensions. Because it’s quantum it will never be still, so there is always some small oscillation or vibration in the ground state, which is the lowest state. This minimal oscillation represents quantum fluctuations, also known
as virtual particles.
If we give the spring a punch on the order of Planck’s constant, it will excite the spring to the next state, the one particle state. The spring now has a higher amplitude to indicate the extra energy we have added.
We can punch it an infinite number of times to increase the state to equal to 2, 3, 4 and so on particles. The amplitude can only be integer multiples of the Planck’s constant. This is the quantum world; everything is in steps ensuring, we have a discrete number of particles.
We can now imagine that this mattress is of infinite size. We can have waves representing particle motion and some of the waves can collide illustrating particle interactions.
And if you can imagine 12 mattresses of infinite size, these would represent all the matter particles of the standard model.
Furthermore, we would have more mattresses that would act as intermediaries to exchange energy from one mattress to another. These represent the bosons of the standard model. So in quantum field theory, everything is essentially just springs.
#quantumfieldtheory
#QFT
#quantumharmonicoscillator
But unlike the classical springs, the energy levels of the quantum field oscillators are not continuous. They are “quantized”, that is, their oscillations are in discrete quantities proportional to Planck’s constant. These discrete units, when localized, manifest themselves as particles. - Наука та технологія
Great video, Arvin! I'm really happy with how both videos turned out. This worked out great!
Great collab!
Spoilers! 😂
Very cool collaboration. I wonder what the quantum analogue of Laplace’s equation would be.
Great complimentary videos; you and Arvin are my two favorite science content creators. I love the way you both make math and physics less intimidating. Looking forward to future collaborations between both of your channels.
Two of my favourite science channel s made a collab!!! What a day!
From string theory to spring theory we all grew up
I just took a dump that I thought would tear open.
@@Robin.Tussin That's hot 🔥
Haha, right
Different visual perceptions
String theory is spring theory lol.
SPRING THEORY!!! WOO HOO!
Yep, even inside a proton, this is what quarks are doing, stepwise. Thanks Arvin, I'm always trying to interest my students in springs. It's up and down frankly 😁
Glad to hear that you are promoting this to students! I did not have fun learning about the physics of springs either...but much later in college when I learned that EVERYTHING works this way, I was Hooke-d!
A proton is a collection of 1836 expanding electrons and add a bouncing expanding electron makes a hydrogen atom. “The Final Theory: Rethinking Our Scientific Legacy”. Mark McCutcheon.
A proton is like a pool of waves which have become swirling vortexes together making complex cyclic interactions we call a particle.
@@watamatafoyu Arnold Gulko spent- wasted- 70+ years on his “The Vortex Theory “ all to no avail.
@@ArvinAsh that was slinky 🤣🤣🤣
As a physicist myself, I've gotta say you guys are killing it with these excellent presentations! I love it!
An approximation is the most valuable part of what you said.
Some people get lost thinking you have described actual reality, and not just a portion of reality.
Love your work.
"All models are wrong. But some are useful."
This is a fairly advanced conceptual topic to be landing on a popular YuTub series! Add in the Lagrangian and Hamiltonian and you pretty much have QFT in a nutshell (but with 30 hours of lectures at University). Susskind was the first person i heard describe the workings of particles as harmonic oscillators, and it was (eventually) an "ah ha" moment for me. Especially when you consider harmonic motion is also a rotation that has been collapsed by one dimension (i.e. a 2D shadow of a 3D wheel, with one point going back-and-forth in 2D, or round-and-round in 3D.) I strongly believe there is much more to explore in the mystery that is ROTATION, a mystery that no-one, absolutely nobody understands.
Really liked this one. Keep up the good work tackling advanced concepts. Looking forward to more "jumping-off points" that these videos can provide.
Great comment regarding how Harmonic motion can be looked upon as a rotation collapsed by one dimension! Thank you.
@@ArvinAsh It kinda' makes you wonder about the Holographic Universe hypothesis; where everything can be looked at as either 2D or 3D, and the math works-out both ways. Are we, the Universe: a 2D subspace projection onto 3D space, or a 4D collapse into 3D space? Or some combination of fluid multi-dimensionality that selectively manifests itself just like "location"? (Or is our concept of "dimensions" itself incomplete? That would make physics a bit challenging! ...or clear-up some challenges?)
Two things seem to be consistent with the Universe: Harmonic Oscillation and Rotation. (The differences between those two may be less than we think).
I think this video will give people a lot to think about, which is job well done. Looking forward to the next one!
The 1D shadow of a 2D wheel, no?
@@patinho5589 Yes, to clarify:
You are looking at the wheel edge from above, ( edge-on), and shining a light down on it.. The rotation of a given point is exactly a Harmonic Oscillator. The same rate is observed, with the fastest change at the middle, and the slowing as that point reaches the extremes of travel. This is also the exact solution for kinetic and potential energy of harmonic oscillation. Same rate of change, same distance travelled. They are exactly the same.
@@onebylandtwoifbysearunifby5475yup. I was imagining a circle (2D) and a line (1D).
I suppose you could give them both an extra dimension(width) and therefore be talking about 3D and 2D :).
I note that the very beginnings of QM was formulated with the idea of harmonic oscillators in the black body thought experiments...i.e that the equipartition of energy assigned to the harmonic oscillators 'inside' the black body would lead to the ultraviolet catastrophe, which led Planck to suggesting that there was a quantization of energy levels. And so the the early forms of QM. So this idea was pretty much built into QM.
Great analogy man! It helps me conceptualize the quantum field state.
Thanks Arvin, you are so good at explaining the deepest scientific concepts. You really help those of us who can't grasp the complex equations involved, at least understand what they might mean.
Love the cross over with Nick! Two of my favorite science communicators.
Quite easily among your top ten videos of all time. Love every min. of it, especially the collaboration with Nick! God Bless You Both ❤
Love the colab with Science Asylum! He has a great channel as well.
Arvin, you continue to amaze me with your videos.
A great idea to see Arvin and Nick cooperating like this. If one presenter isn't working for you, the other might.
Thanks Arvin - for another excellent, concise video, which explains Quantum things simply & clearly. Your QM videos are some of the best and easiest to understand available anywhere. Thanks again.
Wow, thanks!
I’ve found this channel via nicks channel, and I wanted to say thank you for being a communicator of science to the world in a way that young kids can find you engaging and entertaining and adults can re spark their curiosity.
You’ve got a new sub in me 😊
from india?
Back during my physics undergrad I took a machine shop course and my teacher had put together his own theory of everything about how all materials have some springiness you need to account for. He called it: "Spring Theory."
Uh, this is basic materials science.
Everything had a young’s modulus
@@maalikserebryakovyea but that wasn’t as cool lol
AMAZING as always. I'm out of words.
that's what good science does btw.
removes assumptions and parameters.
simplifies everything until we run out of concepts, and words.
Thank you for this tutorial, Arvin. IMO it's much clearer than the spring analogy Anthony Zee writes about in his otherwise wonderful book, "QFT in a Nutshell." And yes, Schrodinger's "wave" equation is actually a heat (or diffusion) equation!
Marvelous explanation as ever!
Thank you Arvin!
This is such an elegant easy to digest explanation of this topic. Great thanks to these wonderful educators.
Love this video, not String Theory, but Spring Theory, which sounds incredibly apt to describe the universe. Springs vibrate too, so it’s vibrating springs, it’s all energy! Love the graphics in this video, absolutely fascinating.
Well, to be fair, strings can be harmonic oscillators, too, like with the example of musical strings. So, if some people find it easier to envision, they can imagine the universe not as complex-dimensional mattresses, but as the most difficult piano ever. Every field is its own set of keys, and each key can be pressed any which way to produce a uniquely different quality of sound, rather than just "press down". Also, there are probably about 42 pedals.
At least, those without aphantasia can imagine that...
Omg I love nick as well thanks for having him on. You guys should collaborate more often. My two favorite UA-camrs.
Awesome! Man, thank you. I understand my (usually confused) point of perception in 'The Big Deal' of our Universe more better. Seriously!
Fantastic video, you are the best Arvin!
Great video! Looking forward to watching it at least a couple more times :-)
This guy is great. Thank you for making these wonderful videos
Science Asylum and Arvin Ash!! OMG OMG OMG OMG 😱😱😱🎉🎉
Before you can blow a mind you have to open it enough. Arvin Ash is pretty good at this and I thoroughly enjoy these. 😍
Amazing animation. Really helpful in understanding the whole scenario Dr. Arvin Ash.
I am further curious about how will be the matter spring mattress and energy spring mattress would have interacted in the animation. Like in terms of Feynman diagrams style. It would be really great I can imagine.
Brilliant, love it! ❤
Great video! The visuals really help with understanding (general comment for all your video's). Thanks 🙏
Understanding that way is so much enjoyable.👌
If you make a PDF I will buy it, and probably I will not be the only one. This really associates the formal math and the intuition in a striking way. Well designed, brilliant accomplishment.
Great video !!! , So the Resonance in these can explain field interactions, which require right amount of conditions !❤
Arvin thank you now I got a good picture of quantum world I saved this video to decipher the equation need more
Damn, that's a cool concept. Thanks Arvin!
such a great explanation!
The universe is the most intricate musical instrument playing the most complex piece of music ever improvised
Good job! I wish this had been explained to me this way when I was an undergraduate. I didn't learn about this until graduate school and even then, it wasn't very clearly explained conceptually.
Your title makes perfect sense. If you take any wave and compress it the shape it will take looks like a spring and the same if you pull apart a spring it will look like a wave.
Arvin your videos are fantastic. Thank you
Glad you like them!
I've always loved (mechanical) springs since childhood. And now I know why!
Nice work. Thanks!
And then POOFph!, There's Nick! What a treat that was❣
I appreciate your modesty: understand the universe.
👽 Thank you so much Arvin for sharing your knowledge; Humanity needs full access to science.
We need more science video collaborations!!
These are great!
I've always said that literally everything in the universe is comprised of waves, from micro to macroscopic. So this vid is perfect!
COOL. Best explanation yet.
Science Assylum cutting in clears up a confusion I've had for a long time. How can something be both a first derivative in time (heat) and a second derivative in time (wave). The fact the wave function does not mean a wave equation in a Partial Differential Equation sense removes the contradiction.
This is why I leave so many questions on science videos asking if the way I understand a term as a mathematician is to be understood the same way in the science or if the term refers to something else.
Love the colab
Brilliant! Extremely lucid! 😉
This channel is marvelous
Wow. Wow wow wow wow wow. Wow. I'm glad I'm learning all this stuff before I die. Don't know why, but I'm glad.
Excellent
A lot to think about
Very nice and timely when VSL is catching up . Good we have seen many technical and technological game of science advancement.
It matches prediction upto 14 decimal point. Nature is indeed simple when you have an operator.
Thank you ASH
The Friend.
Excellent graphics!
Impressed with the animations and Nick appearance
This is a great video. Thank you!
Glad you enjoyed it!
@@ArvinAsh I have been following your content for a while, and I have learnt a lot from it, and has inspired me to grow up and become a physicist.
funny, I just received a couple of springs yesterday and also thought about the nature of the smallest things there are and that they are oscillations... nice!
Nick and Arvin 👍
what a surprize 🤩
Discovering your channel thanks to the Science Asylum, i'm thrilled :D
Beautiful and illuminating work, thank you! I know we're not to push visual models and analogies too far, but I'm curious; does the chosen grid spacing and the zone of spread around a local excitation in a field relate to any familiar or definable quantities? Regarding the "fields" themselves, would it be correct to simply think of them as allowed modes or symmetries of deformation "allowed" at all points in space-time rather than as actual entities unto themselves? I realize that this might be a distinction without a difference and therefore without a point, but somehow the "fields" give me ontological indigestion.
this is cool how both channels interact
Circular for motion includes spring motion toward both horizontal and vertical directions.
arvin you really do a great job man, cheers!
I appreciate that!
I love that creators are acknowledging each other, cooperating instead of competing. It bothers me when one creator, paraphrase the contents of another without acknowledging the source. After all it is not a zero-sum game, the audience does not need to choose which to watch, but instead can watch both. It is a win, win, win for the creators and the audience. More crossovers please.
This makes sense of why energy remains conserved over so many different situations. I want to call it "radical spring theory": everything is a spring!
Came here from Nick's video. Subbed, this is excellent stuff!
For those of us that don't speak math language your videos are very helpful in furthering our understanding of the mysterious world of the very small.
🤯
Love the analogy
I didn't understand everything but I really appreciate this kind of videos.
This was awesome and I love your head so much 🥰👍🏻
Great video! I am subscribed to The Science Asylum too!
Nice seeing Arvin and Nick in the same video! Does that lend itself to the "multiple worlds" theory?
No, it's more like Quantum Entanglement.
Gay
Jada Pinkett Smith entanglement
Thanks
That's quite a large donation actually, @ArvinAsh should be happy with that.
@@philipmurphy2 he deserves.
Bro its rupees not dollar
@@kkuj8314 it's still a big amount for me. It's a token of appreciation.
Great video.
Excellent video as always, thanks for your hard work! One question about the animation: in a real spring set up like that, the "particle" would propagate as a circle from the initial disturbance, rather than as a bump moving in a line (which you clearly did for clarity). Does your animation show the linear bump just to avoid "collapse" since it's not intuitive, or does the QFT particle sort of propagate linearly like the animation?
Glad I’m not the only one wondering that!
The bump is a 3d representation of the wave function. The bump is the highest probability of where the particle will occur, although it could occur anywhere in the circle you mentioned.
The example of pendulums: we see that pendulum in an array will eventually synchronise - during the early stages of this, they are transmitting information!
Given no prior constraints, any particle that's emitted like a photon from an atom, has an equal chance of going in every direction. Since the total probability has to add up to 1, the chance of finding it within a specific angle is the area of a circle on the surface of a sphere, over the area of the sphere. But if there is any information about the particle's position and/or velocity (within a degree of uncertainty), like shining a flashlight through a small hole, you can have a wave function that looks more like a bump traveling in a line. In that case you're basically ignoring all the particles that didn't make it through the hole.
not exactly. The "a" and "a-dagger" have a subscript "p", which creates/destroys 1 quanta in a momentum that is an eigenstate of linear momentum. A radiating ring (spherical shell) is not in a momentum eigenstate, and thus not created by "a".
The best channel for physics by far
For every action there is an equal opposite.
For nearly every word there is an antonym.
The spring theory hold up as a solid explanation of how the universe works, we need to also take into consideration that the springs are actioned by the cyclic behaviour of duality which is essentially two equal opposite rotating vortices moving through space and time. You can see example of the pair of vortices in fluids like under the waves at the beach, also solar flares, plants and trees which rotate out of the ground as they grow, the shape of electricity as it passes along a conductor and even the pattern our solar system makes as it moves through space.
What Schrodinger's equation does is square the Hamiltonian, turning a spring motion (back and forth) into a rotation (back and forth in two directions: forward-backward and side-to-side), representing a particle moving in a rotation. This is then mixed with the imaginary corollary to express the total wave, which is easily explained in the presence of two (not one) particles orbiting each other or a third particle.
The 4 resulting spring directions are then expressed as the quaternions that make up the Hamiltonian of a larger particle to which the orbits of the smaller particles lend to the spin of the larger.
Arvin can we see an animation with all the layers of the mattress including the bosons oscillating - interacting with each other to see a dynamic system?
See this video, where I show the different layers of fields in 2D. The layers of mattresses would be similar: ua-cam.com/video/jlEovwE1oHI/v-deo.html
Great video
It's great to see a video showing this underlying association with the quantum harmonic oscillator. I just think that one important detail was missing. That's the superposition principle and the theory of Fourier decomposition into harmonic modes. Any arbitrary wavefunction can be expressed in terms of a superposition of harmonic modes.
Otherwise, I find it remarkable just how ubiquitous the quantum harmonic oscillator is in quantum theory. Expressing the Hamiltonian in terms of annihilation and creation operators is termed "second quantization".
I love this channel
Arvin, your videos are brilliant.
Very cool to see Nick receive some love from you. Thsre cross pollinations are a great add on
Thanks. I'm glad we finally got to do it.
Love ir !
Thanks
If the only tool u have is a linear differential equation hammer, then everything looks like a spring.
I love the good exlanation in short
Dude.... I KNEW IT!! Haven't watched the video but I've always imagined the nature of the fundamental energy or substance of consciousness to have a quality of elasticity, like rubber bands, but a spring is similiar!!!
The rubber bands connected the springs laterally.
Very interesting. How would we conceptualize the quantum/discrete steps feature of these spring oscillations?
It's easier to visualize the quantization with a string rather than a ball on a spring. Get a slinky or a rope and tie it to something sturdy on one end, and hold the other end in your hand. Then play jump rope. That's energy level 1. Move your hand twice as fast, you'll notice 2 standing waves. That's energy level 2. See if you can get harmonics 3, 4, if you're good you can get 5, but you'll get tired pretty quick after that. That burning pain in your arm tells you that the higher harmonics take more energy than the first. ;)
@@DFPercush but adding a particle doubles the amplitude, not the frequency.
@@DrDeuteron Ok... is that a correction or a continuation of the thought? Because I wasn't talking about adding particles, just a single one. The nth harmonic in a string is analogous to the nth principal energy level of a particle. If you have 2 particles then I guess you're twice as likely to find one, so it makes sense.
Actually it just occurred to me, if you want to stick with the ball and spring model, I think there's a harmonic resonance there as well. If you attach the other end of the spring to a speaker you'll notice that certain frequencies will cause it to vibrate much more strongly. The lowest note where that happens is the fundamental frequency or energy level 1, twice that, 3x that, 4x that will also resonate. That could be another way to illustrate quantized behavior.
Well, the pendulum and swing are not the same as the spring and don't have the same motion. The pendulum motion gets arbitrarily close to simple harmonic as the maximum angle approaches zero. Just for those might assume simple harmonic motion in some other situation or on a test.
im really impressed how many times he can cut the same things over 10 multiple spots :) it just really gives me the suggestion, that the universe made from the same things like springs, because he uses the same cuts in the video every time too, so maybe this is the nature of things
Natural frequency of a spring is c=sqrt(E/M) ; Expressed for E, becomes E=mc2 ; Right? And continuum mechanics based on F = E*U becomes super computer (parallel computation) compatible, if us use strain space (not stress space) envelopes. And the work of P.J.Yoder, 1980 - derivation and implementation of strain space plasticity, provides all the mathematical proof that this "parallel spring system" is not only computed faster - but super compatible with nonlinear stiffness and thus... could help model things described in this video greatly :)
Arvin, I was told there would be no math. Anyway, the math part was over my head but your explanation was brilliant. Thank you.
The math was heavy in this one. I could not find a way to explain any details without it.
@@ArvinAshAsh. Don't stop what you are doing AND how you are doing it. You are killing, just killing it. Thank you
5:59 - “A Wild Nick Appears!” ^.^
"Hello Crazies!"
Hi, do you get the creation and annihilation operators defined the other way around?
This video is great but it actually available to everyone rather then members only right now.