How to Visualize Quantum Field Theory
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- Опубліковано 30 сер 2020
- Quantum field theory has made incredible advancements in physics and technology possible and is arguably the most successful theory in all of physics. But what exactly is it? How can we visualize a quantum field theory? Let's run some simulations to see how we can interpret this complicated subject in a simple way!
Link to github repository: github.com/ZAPPhysics/QFT_Sims
If you do cool things with the code, let me know in the comments! I would love to see it!
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This one was a ton of fun to make! If you want to play with the code or read about the math behind the animations, check out the git: github.com/ZAPPhysics/QFT_Sims
is there a name for the opposing "spring" remaining neutral and under what circumstances does this remain applicable? thanks c:
i.e. 3:30
到底都是谁需要伪科学，封杀揭发伪科学的客观自然科学？
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（量子力学被推翻了？并没有！量子跃迁需要时间吗？
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（耶鲁科学家验证量子跃迁确属连续过程，并成功开发量子跃迁 ...www.sohu.com › ...
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Jun 15, 2019 - 在研究中，研究人员通过特制的高速监测系统，成功捕捉到了量子跃迁将要发生的起始时间，并以此在量子跃迁进行到一半的时候人为逆转量子态 ...）李辉林注：这是我的论文“动力学基础理论的提出及应用原理示意”发表9年后；“宇宙物质结构动力学”网络公开（国内7年、国外5年）后，看到的第一篇国际论证“物质非能量转化”地足以推翻杨振宁“量子伪科学”为封建专制服务，及抢劫、剽窃“宇宙客观真理”否定欧美文明地权威佐证报道。
李辉林评论：总书记高呼“要发展量子科学”。就将几年前被我驳斥得体无完肤的陈词滥调又都重新放于网上。上Google网上去查看原文，却只有标题没有内容了。看来都是被那些科学巨骗们忽悠的（大陆伪科学的癞蛤蟆们一叫，台湾的伪科学癞蛤蟆们也都跟着一起叫。当然首要的不是为了某个政治人物。而是只有维护文化精神领袖，才能巩固不劳而获靠嘴巴成就生存“真理”的伪科学、文化、知识垃圾精英的荣誉、地位、利益。）！想用“电子光”物理作用，人为地设计一个“量子”伪物理概念替代 [本来想用“电子跃迁存在不连续的突变”来解释存在“物质与能量交换的量子过度现象”。被耶鲁大学的科学实验证明“电子跃迁是连续的”而破碎：薛定谔的“猫”从来就是鲜活的“电子”，是被人类所谓的科学精英们自己始终坚持近百年装死制造出地幻觉“量子”彻底死了。就想干脆用“量子跃迁”混淆、取代占有“电子跃迁”回避掉其“物质变能量地不连续性”。]。设计出“量子”的原始定义是“物质与能量地相互转化”。那么它不论作为物质还是作为能量都应该是可以实际收集储存（存在）的。可它与“光”一样只是在电子的“得”或“失”时地物质结构力地一种反应现象，电子平衡时“光”就没有了踪影（此时的元素没有电子成对地一入一出，而“量子兔成对出现就纠缠无踪影”了？），所以是不可收集储存与直接使用的臆造物质与盗窃物理现象，仅仅只是将“控制储存的基本物质电子运动，引起物质结构能量反应出的光现象及利用其物理特性，进行比特（状态）再分解（光的路径、偏振、角速度还可以做若干地分劈）获取更多的计算机运算、存储的开关单元。但是最终必须还是要还原成电子物质才能进行有效的存放。”。如“有光”（1）与“无光”（0）的计算机存储，只能靠电子的“得电”（1）与“失电”（0）来实现的。其讲解中除了将“量子”当做佛祖的名号供奉于神坛，就没有介绍出任何其具体有地实际作为。所以其“量子”没有任何实际意义，只是盗取、占有了“电子与光的物质结构与能量变化反应”的关系地“伪科学概念”。如果没有电子运动，“光”就不可能存在，“量子”更完全是垃圾科学家们脑袋里多余的“狗屎”。以你们的这种“科学理论思维”：高锟先生的“光纤技术理论”，还有“光碟信息技术理论”就都应该脱离“以电子为基础技术理论”而归依你们臆造的“正统”，作为“量子计算机的辅助材料理论”叫“量子科学技术理论体系”了？如果再对计算机追根寻源，其人类发明的第一台计算机就是使用“电子管”靠其发光运行计算、存储的，不就已经是你们这种欺骗逻辑的“量子计算机”了吗？逻辑理论上就是“挂伪真理的狗头，卖科学的羊肉。”，盗用一些成功的实用科学手段，去“证明伪真理”主观意志。将自然科学主观复杂诡异化，成为被主观封建专治说教控制地典型教义。（国内外都统一地封杀我的个人网页上的科学论文、评论、《证据》，只允许我做些时事评论，不允许做揭露伪科学的评论与论述。预示着“人类社会的专制与“民主”从意识形态上正在接受、效仿伪基础科学欺骗性地思想认识方法，用主观搞乱客观而趋于统一去专制、奴役人类！”。2020年12月7日）
牛顿第二定律，当加速度等于0时，物体要保持原来的运动不变，就必须要克服其物体继续运动的阻力反加速度，平衡这个反加速度的一个相等的加速度存在。爱因斯坦的“能量”也只是抄袭了工程力学缺失了阻力能量、极不准确的：“E（能量）等于m（质量）乘以c（速度）的平方”地物体做功公式，以为这个物体运动公式产生出的不等式，是因为“能量与质量可以互相转化”！所以就假设其中间存在一个转化媒介“量子”使其能够“被平衡”？完整的能量公式应该是“E等于M平方乘以C平方”。质量可以影响速度，速度影响不到质量。能量“消耗”的只是物质地结构（如分子结构、原子结构），没有消耗任何基本物质（电子、质子、中子，“能量”只是在改变这三种基本物质的排列组合时地“结构动态反应”动力现象。）。自然中不存在量子，宇宙不是产生于大爆炸。这不是质疑大师们的数学能力，而是其眼界和思想广度与深度的客观逻辑性地积累没有达到能够包罗宇宙所有事物。
F=ma 0=m0 ? （加速度等于零时，物体运动不需要动力？）
F=mv=-a'm=F' （物体做匀速运动时，加速度等于阻力加速度。）
我在国内（包括网络上）如此讲了十多年，又在国际网络上讲了五年。没有一个专业科技人员肯公开出来讨论，甚至辩论。其一些被我点名的中国国家权威们面对他们的虚伪、欺骗、抢劫，也全都始终选择保持静默？而不是被诽谤？名誉受到攻击？却只能动用权势，在国际网络上对我提出的“国家伪统治体制事实”进行全面封杀！认为我在此种情况下（得罪了东西方文明，遭国内外共同封杀。）不敢回国去。可是我还是于2019年9月至12月回国呆了3个月，有惊无险地回来了。因为我说的是纯粹的自然科学与客观经历、无党无派独往独来，他们不敢轻举妄动并不会是害怕李辉林，而是害怕其潜规则强盗科学与真理在全世界曝光？或者在欧美的态度与其一致的情况下，他们仍然还不坦然地害怕？
【爱因斯坦晚年信精神，怀疑物质！】那是因为爱因斯坦只知道宇宙中的所有物质都是在“相对性”地不断变化，由存在到“消失”的。却不知道他们全都是由“绝对性、客观真理似的”不可被消灭或创造的基本物质：电子、质子、中子地相互关系（只存在万有引力与万有斥力地物质结构能量关系，。）与排列组合（能量只是改变物质分子结构或者原子结构所产生出的，并没有消耗任何基本物质。）而成的。以至于整个宇宙地不断变化却又永存地存在。如果爱因斯坦还健在，他看了我的“论证”，他还能如此为自己提出的“能量与物质相互转化！（并引起人类基础科学界半个多世纪虚假地猜想、臆造、欺骗。）”而迷茫吗？或者也会像整个中国的科学、文化、知识分子们及那几位华人诺贝尔物理学奖获得者那样地不敢面对，却又觊觎将其中拆零分散而获得一个个“重大科学突破”立可见成效的客观事实？
上帝从来不现身于人类，只是为人类创造了一个“三基本物质”组成的客观世界，出了一道“客观宇宙”题，如果人类还不能正确认识、解释这道客观题的结构与运算，怎么有文化、资格谈论与见到上帝？靠什么去描绘、解读上帝？难道上帝也是个希望见到什么都不会表达，只会编造花言巧语吹捧他，表示愿意为他做奴才的那种人类？人类有史以来只是我首先提出了“宇宙客观真理及关系”，就是基本物质电子、质子、中子地性质、结构、运动、变化关系组成了整个宇宙。宇宙中所有的事物，包括人类自身的物质结构与运动变化，及思想、意识、行为都是这种基本物质地运动变化所产生的。在这宇宙整体客观真理面前，人类所有的先知先觉、文化圣人们，所有所谓的科学、文化、知识都只能算是其中主观臆造或者片面客观的认识；所有的自然科学家、劳动生产创造者的知识成就都只是其构成中的沙粒、砖瓦、基石。其区别仅仅只是存在阶段、局部、相对性地优劣。人类所有科技、文化、知识累积到现在，都连面对、探讨这个客观真理的知识能力，甚至态度都还基本不具备。[在Google网络点击或键入“李辉林”，查找“动力能量学之宇宙物质结构动力学”（演变论）]
@nomoregoodlife good question. This is purely a result of the symmetry of the system and can be seen as the finite version of an interference effect. Since the initial state of the system started with adjacent springs compressed and extended, you can sort of think of it as the "compressed piece" traveling in the opposite direction and at the same speed as the "extended piece." They then meet on the opposite side of the ring and effectively cancel each other out at that spring!
In the numbers from 11 - 5001( 7 digits), there is one 7, three 6 and three 2. ( 2 7 6 2 6 2 6 )
Will this repeat itself in the following numbers ?
Could you please tell me how you found the order of the numbers
Thanks
@@kaerlighe9 if you know programming, take a look at the code for the animation.
you know... you're a classic example of "I learned this better on youtube then I did in class"
Now we need at least 500+ of them to see the quantum example
seriously, i was about to say i've studied this formally and this just improved my intuitions so much!
The amount of value per unit of production cost must be off the charts.
It's one of the most amazing videos of ANY type I have ever seen.
THAN
He's a _quantum_ example 😔
I have seen many youtupes on QFT, but this one is clearly the most illuminating. In my minds eye I can see a two dimensional version, I can visualise the double split experiment. I can even imagine how different fields can interact and get boson like behaviour. Best!
Amazing visualization! Really well done :D
someone should reward this guy for such great animation and easy explanation
One of the best vids I have seen so far on the topic. Thanks.
100%
It's AMAZING. It's exactly what I was hoping to find.
Amazing video. I like how you don’t get bogged down in mysterious statements about how QFT is the marriage of special relativity and quantum mechanics. I think more physical intuition is to be had from the condensed matter point of view.
Thanks a lot! I'm used to this theory from books but seeing how you applied this knowledge (e.g. propagators) in your code is really exciting. Keep it up!!
mind-blowing!
really amazing work, thanks for uploading
This is an outstanding demonstration of a step-by-step emergence of behaviour from discrete elements, thanks for your work !
Oh, and sharing the code is the cake on the other cake :-D
The simplest and awesomely elegant way the QFT explained. Thanks a bunch.
Thanks for making this, having code and resources to look at makes this video that much more amazing!
A series surrounding this would definitely be interesting. I'm sure the algorithm will roll 20s for you someday in the future!
The harmonic oscillators (HO) connected together in a circle (closed string) is a great visualization of how QFT works. You can imagine extending this to a 2D plane of HO joined together to show how a fluctuation may travel through the field (system of HOs) thus revealing the familiar particle representation.
Thanks for making this, it was great to hear this complementing perspective while reading a QFT textbook.
This finally helped me visualize anything quantum related after so many articles and videos failed and it is the best simplification of something complicated I have ever seen
Excellent video, simple, clear. I really appreciate this kind of videos and i do appreciate you are also making the code available to others. You really are giving added value to the Internet. Thanks
Very nicely done. I haven’t seen things presented in this way before and it certainly gives a nice perspective.
This was amazingly well-explained and clear, excellent work!
Very good video! I am taking qft right now and this touched on everything we’ve done so far but Noether’s theorem. Thanks for making this.
Great video. It would also be nice to see this kind of simulations for 2D fields instead of rings. Thanks for your great work !!
Awsome video ! Makes some concepts really clear and more intuitive! Great job !!
I seen some videos about QFT and it was not very clear how exactly particles are viewed as field excitation, so I glad I saw this :) I hope more people in future will ask themself same question and with some luck end up here :)
Nice animations and lovely explanation of the concepts. I'll browse the code with interest. Nice one.
Truly a great video! keep up the great work!
Holy fing wow.. some things just clicked in my head watching this. Thank you so much. I love this
Most intuitive video on the topic I've seen to date
Awesome description, great video!
This is a million-subscriber video! Liked & Subscribed!
This material is marvellous. And a special thanks for the links below.
Amazing topic & information! Wonderful video & explanation too! Thanks so much! Sub'd & Shared!
Thank you so much, this is the most simple and intuitive explanation on QFT and how it results in particles
Finally wrapped my head around it!! Thank you so much!!
Really nice way to visualise periodic boundary conditions of a finite spring by a ring of oscillators!, I’m doing a (many body non rel) qft couses atm and this really helped seeing where particles come from, rather than just creation operators!
A master piece! Please continue making it
Really nice visualisation! I like it :)
Fantastic explanation and visualization. Thanks
This was awesome. Thanks!
Great video. Many thanks for putting it together
The amount of hard work put in this single video is remarkable!
Great explanation and a very nice work indeed. Thanks a lot for the efforts. Best wishes...
Outstanding. Really fine visualization that makes the math come alive. Bravo!
Good job dude! Keep it up!
This is a great conceptual motivation for QFT
Brilliant!!! thank you for your efforts. very educational and insightful.
Quantised does actually not re,ate to “the number of particles”, it’s a discrete distribution of energy with the (h.v) as the smallest possible energy chunk,. It makes it confusing for newbies but it’s cool!
Thank you for sharing the knowledge.
Beautifully explained and demonstrated.
This is the most intuitive idea i've ever seen. Congrats
Yes, because he was cheating you. He made the claim that you are looking at a system of quantized harmonic oscillators, when in reality you were looking at a classical harmonic lattice with periodic boundary conditions. This was classical physics, not quantum mechanics.
Very helpful, thank you!
I wonder if this can be extended to show how fields interact and the role of bosons virtual and otherwise. Another case might show how two particles repel each other.
Very helpful. Thank you!
This is incredibly well explained
A great intuitive explanation of a non-intuative topic!! Well done!
Nicely explained the core logic. Thanks...
Love this video I appreciate it!
Amazing video. Huge thanks.
This is so beautiful thank you
Awesome work!
*EXCELLENT* video. I now understand a lot...
That was really good explanation.... thanks man
It is really a great video, the animation is really nice
thanks for uploading
This is amazing!
I learned this concept from the Classical Mechanics book by Goldstein for classical fields.. thanks for your nice explanation...
Yeah bro
Very nice. It's cool the way "particles" emerge from a continuous field. I'm looking forward to seeing how you add relativity to this model.
Also, since it's circular, I wonder if rather than imposing quantization "arbitrarily", you would get it by fixing a single node to zero, which my intuition says would create reflections and standing waves, and get the antisymmetric wavefunctions of fermions by fixing another point to 1, possibly representing the singularity at the big bang, and an anti-singularity at the "big rip" at the end of time.
Video went perfectly until you introduced discreet energy levels and probability at the same time. Would be much better if you introduced discreetness and showed its effects and then introduced probability and gave us a sense of how the probability is calculated. We went from "ok here are connected dots with springs" to "things are discreet in a way that we dont know and there is a magic proability" all the intuition went away.
Exactly!
Very good examples to understand the quantum system
Superb effort and explanation 👏👏👏
Excellent simulation 👍👏
Beautiful vid!!
Great stuff!
Do the different color regions (compressed and stretch) correspond to particle antiparticle pairs?
Nice
I want to see a whole series about this
How did you get the million dollar list? It was so cool. I I didn't know that P vs NP is there too
PS: I don't see a speed changing option in this video. Just to point out you know.
Have I said it already that I want more content on these
@RBK STUDIOS, thank you! I'm glad you liked it! The list of the millennium prize problems can be found here:
en.wikipedia.org/wiki/Millennium_Prize_Problems
I will look into the speed changing option on this video, thanks for bringing that to my attention.
My God. Are you kidding me?
This is the best physics video I have EVER seen.
I feel like I understand it better than ever.
Great job. Thanks.
🤘great content, thanks
If you have not done it, I think it would be brilliant to take famous equations in physics (Maxwell, Schrodinger,etc.)and explain the Math symbols and what they say in an intuitive way.
@Wulfaz Wlkwos that is a fantastic idea!
Seconded, thirded and fourthed. I was dragged through this in uni (part of CompSci was 3 semesters of basic science, including biology 🤯) but never really got it.
fantastic man, you did fabulous job, please make more QFT videos like this..to Feynman dias
Loved it 🙏
Jesus you did this with matplotlib? :O
Lol yes, but probably more due to my lack of knowledge of anything else...
When it comes to deal with simulations instead of simple animations matplotlib is really useful because is embedded with other python libraries like scipy and numpy which makes numerical treatment less tedious.
I also use matplotlib for making animations of my simulations.
Thanks for this video
Thank You!
AWESOME!!! I just got it!!! TY :P
Very nice!
Deserves way more views
Thanks for the video! How did you set the interaction between the separate harmonics oscillators? What's the form of this potentials?
@Sergey Gladchenko Good question! I used the standard interaction potential for coupled harmonic oscillators in both cases, assuming all oscillators are identical. So, for the nth oscillator, the potential is given by k/2*(q_{n+1} - q_n)^2. The details are all in the PDF on the github linked in the pinned comment!
QFT is the reason we are progressing technologically so quickly.
The masses on the linear chain aren't harmonic oscillators. You can rearrange the expression for the energy of the system (the hamiltonian) to be in the same form as an equal number of harmonic oscillators, but these correspond to normal modes of the system, not individual sites. For the loop of string, the normal modes are standing waves. In the quantum case, these correspond to momentum states for the particle.
I'm not sure I entirely agree with the statement that these aren't harmonic oscillators. They aren't *free* harmonic oscillators, but they certainly are coupled harmonic oscillators. By that, I mean that each individual mass obeys the equation of motion of a harmonic oscillator (in this case, Hooke's law), it's just that these equations of motion can't be solved independently. Now, of course, when decomposing them into their normal modes, the equations of motion decouple and can be solved independently, but one can always form linear combinations of these normal modes to find solutions for the masses at individual sites (and that's exactly what I did to get the systems in the video!).
In a similar way, one can take the eigenstates of the Hamiltonian in the quantum case (the quantized normal modes) and simply Fourier transform the creation/annihilation operators which generate these states. This is exactly what is done to find field operators in QFT.
Go from a string to a disk; I'd love to see that. Then go one step further and make it a very thin cylinder.
@Ricky Upchurch Thank you for the lovely comment! So I'm in the middle of writing my thesis on QCD (en.wikipedia.org/wiki/Quantum_chromodynamics) so one's knowledge on more elementary topics becomes, well, wavey. At the moment I'm learning so much about the advanced stuff that the Quantum Mechanics you're talking about is difficult to reach! You should perhaps know, that waves are practically the breath of Quantum Mechanics. The Schrodinger equation gives rise to solutions such as wave equations and in 3D it gets more complicated, but it still remains waves: Probability waves to be precise. The non-wave solutions you mentioned come from looking at scattering problems. You construct incoming waves that scatters off of some potential (think of it as a force field) and stuff happens! Sometimes, when you get the incoming waves just right, they can become trapped in the potential. If the particle gets trapped there forever, we can identify it as a stable particle (like an electron). The solution is a Dirac delta function (just as you mentioned, this is not a wave). Then some particles may be trapped there from some finite time, and they will have resonance-like behavior and decay over time (these are usually associated with unstable particles, like a neutron which decays in 11 minutes, I believe). I will admit that I only recently looked into resonance scattering, because my thesis actually requires it. I am learning it from a book written by Semyon Dyatlov and Maciej Zworski called "MATHEMATICAL THEORY OF SCATTERING RESONANCES", which is freely available online. So don't take my word as gospel!
@Ricky Upchurch Happy holidays. Also, forget about the book; it's written for mathematicians so it's really difficult to read. If I find another source I will let you know.
Nice video!
A particle in a QFT in this analogy would be the quantized normal modes of the chain. In the usual treatment, single quanta excitations would generally be delocalized (where each delocalized mode acts as a decoupled quantum harmonic oscillator) because they excite an entire normal mode of the system. You can localize the particles to be more classically particle-like, but this involves superpositions of multiple energy quanta. More specifically, I wouldn't expect the the probability distribution of single mode excitations of the quantum fields to resemble localized propagating particles unless they were placed in a coherent states (which involve superpositions of many energy quanta).
Well done.
Thank you 😊👍
This is one I’ll keep coming back to. It closes some gaps of understanding books left out. What would this look like if it was 3d like an electron orbiting a nucleus? Would it be a fuzzy sphere with a small bump moving on rhe surface randomly? I would guess it would take a lot more computing power to code that as well.
Amazing , sabscribed
BRILLIANT!
I love this!
好厲害的影片，謝謝’
What model did you use for your phonons on the second part of the video? In the infinite N limit they seem to have perfectly defined trajectories, which shouldn't be possible for quantum particles because of the uncertainty principle... a finite trail should be developed.
Otherwise great video 👍
@Lucas Baldo This is just using the simplest QFT for phonons: a massless, non-interacting scalar field. The reason they have perfectly defined trajectories is due to the fact that they are massless, so they are required to travel at the speed of "light" (really the speed of sound in the case of phonons). This is just because of the Lorentz invariance of the wave equation. In fact, it would be quite problematic if they did develop tails because it would break this symmetry!
These do still satisfy the uncertainty principle in that they do not have a well-defined momentum (in fact, that's exactly why there are two dots going in opposite directions. In higher dimensions, this would be a spherical shell spreading out at the speed of light instead of just the two dots). It's just that with massless particles, momentum determines the energy of the particle, not its velocity. It's the same story with e.g. photons: they always travel at the speed of light, but they can still have different values of momenta.
@@zapphysics Thanks! Didn't know about that. I was looking at both moving dots as two separate particles, but by looking at them now as two probability peaks for a single particle things are making more sense!
Good explanation
Wonderful.
could you please make more of the example? I need a little bit more examples to intuitively imagine quantum field, especially together with the formula of quantum field which is a liner combination of many creation/annihilation operators multiplied by the corresponding wave functions respectively. Thanks!
Do u hv fb account