How to Visualize Quantum Field Theory

[@zapphysics]

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

[@nomoregoodlife1255]

is there a name for the opposing "spring" remaining neutral and under what circumstances does this remain applicable? thanks c: i.e. 3:30

[@李辉林-z8p]

到底都是谁需要伪科学，封杀揭发伪科学的客观自然科学？ 18个量子比特纠缠是什么？量子计算机为何如此强大？李永乐老师讲量子的纠缠态与叠加态 738,479次观看•2018年7月6日 （量子力学被推翻了？并没有！量子跃迁需要时间吗？ 89,161次观看•2019年6月17日） （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 › ... Translate this page 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）]

[@zapphysics]

@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!

[@kaerlighe9]

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

[@misterlau5246]

@@kaerlighe9 if you know programming, take a look at the code for the animation.

[@theprofessor3684]

you know... you're a classic example of "I learned this better on youtube then I did in class"

[@lsdap1969]

Now we need at least 500+ of them to see the quantum example

[@brandonmckinzie2737]

seriously, i was about to say i've studied this formally and this just improved my intuitions so much!

[@dialecticalmonist3405]

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.

[@WeeklyUrbanWalks]

THAN

[@rv706]

He's a _quantum_ example 😔

[@kasperosterbye7883]

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!

[@DotRibhu]

Awesome video. Finally some visual representation.

[@yacinekunplays5876]

someone should reward this guy for such great animation and easy explanation

[@KB-vq6li]

Holy fing wow.. some things just clicked in my head watching this. Thank you so much. I love this

[@PrettyMuchPhysics]

Amazing visualization! Really well done :D

[@TibraAli]

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.

[@deepbayes6808]

One of the best vids I have seen so far on the topic. Thanks.

[@dialecticalmonist3405]

100% It's AMAZING. It's exactly what I was hoping to find.

[@ilkero1067]

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.

[@harwn999]

Exactly!

[@kinnaa1234]

The simplest and awesomely elegant way the QFT explained. Thanks a bunch.

[@JL-cy1ks]

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 :)

[@cesarjom]

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.

[@BorisNVM]

This is the most intuitive idea i've ever seen. Congrats

[@schmetterling4477]

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.

[@dialecticalmonist3405]

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.

[@vanpersie38]

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!!

[@MM-ei7xv]

mind-blowing! really amazing work, thanks for uploading

[@meadows124]

Thank you so much, this is the most simple and intuitive explanation on QFT and how it results in particles

[@Ryan_Perrin]

This is a great conceptual motivation for QFT

[@bob5476]

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.

[@leyasep5919]

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

[@WintersRampage]

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!

[@Raymond_Cooper]

The amount of hard work put in this single video is remarkable!

[@alighar01]

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!

[@suman.dey.s]

I learned this concept from the Classical Mechanics book by Goldstein for classical fields.. thanks for your nice explanation...

[@arghyamazumder4368]

Yeah bro

[@haushofer100]

Great video. It would also be nice to see this kind of simulations for 2D fields instead of rings. Thanks for your great work !!

[@wulfazwlkwos9019]

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.

[@zapphysics]

@Wulfaz Wlkwos that is a fantastic idea!

[@dogcarman]

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.

[@ManlioLoGiudice]

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

[@devlrn906]

Nicely explained the core logic. Thanks...

[@wizard7314]

Thanks for making this, it was great to hear this complementing perspective while reading a QFT textbook.

[@mbmurphy777]

Very nicely done. I haven’t seen things presented in this way before and it certainly gives a nice perspective.

[@brightsideofmaths]

Really nice visualisation! I like it :)

[@Myxinidae]

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.

[@zapphysics]

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.

[@adonaiblackwood]

Amazing topic & information! Wonderful video & explanation too! Thanks so much! Sub'd & Shared!

[@jimlbeaver]

Fantastic explanation and visualization. Thanks

[@g3mck120]

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.

[@erikpanzer8521]

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.

[@vaibhav1618]

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!

[@123cache123]

Finally wrapped my head around it!! Thank you so much!!

[@denestandary3372]

This material is marvellous. And a special thanks for the links below.

[@Roy.Abhishek]

Truly a great video! keep up the great work!

[@sumahuma6054]

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.

[@sumahuma6054]

@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!

[@sumahuma6054]

@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.

[@michaelcollins7738]

Superb effort and explanation 👏👏👏

[@Hahalol663]

This was amazingly well-explained and clear, excellent work!

[@ThomasGutierrez]

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).

[@ngodwi]

A great intuitive explanation of a non-intuative topic!! Well done!

[@reimannx33]

Beautifully explained and demonstrated.

[@jarofclay8900]

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.

[@ELB97]

Yes, I'm definetly subscribing.

[@andrewmilne9535]

Hey, late to the party, have a couple of questions. (These are genuine questions, not challenges - I am sure there are good answers, I just don't know them!) (1) I understand what it means in the classical case to go to infinitely many oscillators - you can treat the mass as a continuous substance with a density and a spring constant per length, and displace some region, I guess. You spread everything out, as it were. But I don't have a clear picture what that means in the quantum case, where there is a minimum amount of energy per oscillator and you can't spread that energy over a region. (2) On the circle (or on any one-dimensional object) the oscillation is constrained - it can only go two ways. Isn't that what gives you the particle-like behavior? In any higher dimension, won't the spring mechanism be fundamentally dispersive? Thanks for all you have done - I've learned so much!

[@zapphysics]

Hi, these are very great questions, and looking back, I think I definitely could have done a better job addressing them in the video itself. I think the main points to answer your questions are around 6:36 and 9:58 in the video, respectively, but I'll try to answer both of your questions in some more depth, because they definitely deserve to be expanded upon. (1) This is a bit tricky mainly due to the fact that the same "intuition" for a ball on a spring doesn't really apply for a quantum harmonic oscillator. Probably a better way to think of a quantum harmonic oscillator is something like a piggy bank that only accepts dimes: it can only hold an exactly integer number of dimes, and since the hole is only large enough to fit dimes if you try to put in a different amount of money, it won't fit. In the case of a quantum harmonic oscillator, the dimes are the quanta of energy: you can only add or take away integer multiples of the exact value of energy accepted by the oscillator. Now, when we couple together multiple identical oscillators, any one oscillator can still only accept a discrete number of "dimes" at a time, but they are allowed to pass them back and forth between each other. When we increase the number of oscillators in the system, it gets easier and easier for neighbors to pass these quanta between each other, just like the neighboring masses respond more quickly to pushes and pulls in the the classical case, but you have to handle it a bit carefully to avoid things from blowing up (just like replacing the discrete masses and spring constants with a continuous mass density and tension). The end result is a line of continuous sites where these quanta of energy can live, but it is free to move from one to the next. The other key point is that, due to the uncertainty principle, we can't know exactly where these quanta of energy are living; we have to describe it by a probability distribution for them to be at any one site. The "spreading" effect that you are looking for an analogy for from the classical case is the spreading of this probability of the quantum to be at each site. However, it's very important to not get this probability mixed up with the location of the quantum: the unit of energy lives *at a single site* at any one time (remember, the oscillators can only accept/give up an integer multiple of this energy at a time, so if there is only one unit of energy in the system, it cannot be split up between sites), we just can't know exactly which site it is living at at any one time, so the best we can do is a probability distribution. (2) You're completely right that when we go to higher dimensions, the probability distribution will no longer "look" particle-like. In fact, in d-dimensions, instead of points, you would see the probability of locating the quantum in the system as a (d-1)-spherical shell expanding outward at the speed of sound. This is because we initially put the quantum of energy in a single site, so we have to have infinite uncertainty in momentum. Since the particle is massless, though, it has to travel at the speed of sound (or light in the case of a vacuum theory), and that is why you see a shell instead of a more "dispersive" effect where the probability spreads out over the full space. What you are really seeing is the natural Lorentz-invariance of the field theory! Again, I need to reiterate that the particle-like behavior isn't coming from the behavior of the probability distribution, and in fact this distribution looks very classical in higher dimensions: it is essentially a wave expanding at the speed of sound. The particle-like behavior is coming from the discrete nature of the quantum harmonic oscillators that make up the system. Consider we surround the site where we place the initial displacement (classical) or unit of energy (quantum) with a spherical detector. In both cases, the perturbation travels outward at the speed of sound until it hits our detector. In the classical case, the spherical wave originating from the displacement hits the *entire* detector, i.e. the full detector sees an excitation at once. On the other hand, in the quantum case, the chunk of energy travels outward at the speed of sound, but since there is only a single unit of energy in the system and this unit of energy can only live at one site at a time, the detector will only see a "hit" at *one, specific point*. Of course, we can't predict where that point will be, since all points have equal probability (the spherical probability distribution), but the main takeaway is that there is a fundamentally different behavior between the classical and quantum cases, and this "single-hit" behavior that we see in the quantum case is exactly what we expect from a particle! Hopefully that clarifies your questions a bit more!

[@andrewmilne9535]

@@zapphysics those are fantastic answers, and I so appreciate the time you took to respond! I am much clearer on the first question, and your answer on the second question covers my question well. The remaining questions I have is less about your video and more general questions about quantum field theory. I know it is a mistake to take the metaphors used in the visual depiction of a theory and overextend them, and I know slogans like "the electron is an excitation in the electron field" are gross simplifications. So the many KZbin videos of multiple interacting two dimensional fields with high (or low) points representing particles can only be taken so far. But they all rely on there being "particle-like" localization of the probability density field that endures for some duration of time, and for an unconstrained excitation, I don't understand how that is possible. Everything gets smeared out at the speed of sound. (The other question I have is about how you START with a localized distribution, but that is just the preparation end of the measurement problem, so also not a question directly related to your video!) I am also confused about the actual quantum field - is there THE electron field for the universe, or separate ones for each system/preparation? How many dimensions does it have in multiple-particle systems? I guess I don't understand what entanglement looks like in the field picture. Don't feel obligated to respond, but if any future videos come down the pipeline addressing these kinds of issues... put me down as excited!

[@zapphysics]

@andrewmilne9535 Yes, I certainly took the easy way out in this video by doing a non-interacting QFT :) I think one must always be extremely wary of anyone trying to present a "true" visual representation of an interacting quantum field theory. The main issue is that, outside of extremely special theories (e.g. superconformal field theories), it is not known how to find exact solutions for these probability distributions, whereas non-interacting QFTs are actually quite straightforward to solve, though they aren't really all that interesting for describing nature. In fact, it isn't even known whether or not interacting quantum fields in general are consistent mathematical objects (if you're interested in learning more, this is a good place to start: en.wikipedia.org/wiki/Quantum_field_theory#Mathematical_rigor). What's typically done in particle physics is that one starts with the non-interacting case, which we can solve, and then add in small perturbations caused by interactions. In this case, one can get reasonable answers and predictions (though the convergence of the resulting series at extremely high orders is questionable), but the mathematics behind it quickly becomes substantially more difficult than the free case, so visual representations of these on KZbin, particularly of realistic scenarios like QED, are immediately going to be a bit suspicious. Not saying that you shouldn't ever trust these, but I'm just trying to get the point across that it becomes significantly more difficult to get the answer, especially beyond first order in perturbation theory. Going beyond, if someone is saying that the theory they are visualizing is non-perturbative, they would need some sort of lattice calculations, which are unbelievably computationally expensive, or an unrealistic theory with extremely high degrees of symmetry that is going to be somewhat difficult to extrapolate to reality. I have seen some videos of the sort that you are describing and some are honestly a bit horrifying that they are being passed off as true. One that jumps to mind essentially just took Feynman diagrams, spread out the lines and called them excitations of the corresponding fields. So they ended up with things like virtual photon field excitations in their visualization, which is just nonsensical: we know that everything must be described in terms of probability densities of some observation (in this case, it would be a position observation), and we cannot observe "virtual particles" because they are unphysical. In some sense, these virtual particles never even exist and are really an intermediate tool we use to do perturbation theory; if you were able to solve the theory exactly, you would never need to talk about virtual particles. I think that your intuition is good on the matter: if something is showing a completely non-dispersive, but point-like probability density in any spatial dimension higher than one (and even in one spatial dimension, you should at least see left-right dispersion like in the video), it certainly calls into question the validity of what they are showing. One could always start with some Gaussian distribution which minimizes both spatial and momentum uncertainty, but at the end of the day, there is no getting around the uncertainty principle if you have a quantum theory. Calling something e.g. the electron field only makes sense in this perturbative picture. Really, only in the free picture, but in perturbation theory, we assume that the fields are close to their non-interacting counterparts. In this case, yes, single units of energy that you add to the field will always result in particles of that type (really, they will be slightly different than the free cases, altered by the interactions). The fields themselves are infinitely expansive and fill the whole universe. That is why all electrons have the same mass, charge, etc. As soon as we go away from this nice, perturbative case, though, everything goes downhill: for example, if I try to add a single unit of energy to the Yang-Mills field, I won't end up with a gluon, even though the fundamental degrees of freedom that describe this field are the gluons. (I can't tell you what you would actually get, since again, nobody knows how to solve this problem, but the likely answer is that you would end up with some *massive* glueball which is uncharged under the Yang-Mills interactions.) If I'm honest, I'm not exactly sure how to answer all of your other questions unfortunately. I do, however, want to make a follow up to this video that addresses some of these points eventually (along with some other misconceptions that I am seeing a lot in the comments). I am even toying with the idea of actually trying to do a similar setup with some (perturbative) interacting theory, but like I said, it is a lot of work to make sure that it is done properly, so we will see.

[@andrewmilne9535]

@@zapphysics I'm sorry I didn't see this earlier, just to make sure I thanked you! You have just answered more questions in a few paragraphs and in a substantive way than the 2 QFT text books I am struggling through! You are a fantastic explainer, and as a teacher myself I really, really appreciate it! I avidly await anything you take the time to produce!

[@xenmaster0]

Outstanding. Really fine visualization that makes the math come alive. Bravo!

[@AtmosMr]

Nice animations and lovely explanation of the concepts. I'll browse the code with interest. Nice one.

[@stauffap]

This is what education should be like. From that point onwards one can try to figure out the math by oneself and convince oneself that the results are actually like this. I think, that a lot of teachers do not realise that abstraction and generalisation make understanding a lot more bothersome and difficult. It's much harder to follow and abstraction or generalisation then to follow an actual example. The reason is that concrete examples create clarity. It's much more likely that everyone knows what you're talking about. Which is why it's a good idea to start with examples and then generalise, instead of trying to generalise right away. Simplicity helps as well. Why start in 3D, when you can get away with 1D? Probably just time restrictions. A lot of the teaching at universities just does not seem optimal to me. In fact a lot of lectures are a waste time. They often make the subject harder then it has to be and it's not because they don't understand the subject, but probably because they do not have a lot of experience with trying to explain their subject to other people. Tutoring really is a great way of learning how to explain something. You very quickly learn what makes it easier for the other person to understand. Anyways, you've made this a joy to follow and it very easy to understand!

[@mansouryoutubization]

Brilliant!!! thank you for your efforts. very educational and insightful.

[@baganatube]

This is a million-subscriber video! Liked & Subscribed!

[@thomasneal9291]

great channel. not only is your content here excellent, but your participation in the comments sections of OTHER physics content video is very welcome as well. how do you have the time??

[@the_neutral_container]

Most intuitive video on the topic I've seen to date

[@rajvardhanvolugula8589]

Very good examples to understand the quantum system

[@Higgsinophysics]

Jesus you did this with matplotlib? :O

[@zapphysics]

Lol yes, but probably more due to my lack of knowledge of anything else...

[@SimulatingPhysics]

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.

[@nUrnxvmhTEuU]

It's been a nice video, but I don't see how the introduced concepts tie to the maths of QFT. It would be awesome to see a sequel that would tie the concepts of QFT (field operators, annihilation&creation operators, Fock spaces) to this visual analogy!

[@MrOvipare]

Yeah agreed. It's a nice video but in my book if you only quantize matter you get plain old quantum mechanics. His example is essentially a 1D crystal made of matter.

[@mbrv]

Awsome video ! Makes some concepts really clear and more intuitive! Great job !!

[@amraref8910]

It is really a great video, the animation is really nice thanks for uploading

[@folwr3653]

Hi there! Nice simulation. I missed however some interpretation at the end. I will try to sketch my picture of it: Since the end result of the classical and quantum field simulation are sort of visually identical, despite the completely different calculation, it seems to come down to interpretation of the ‘particles’ (localized sound waves versus phonons). So I wondered what the difference would be. You mentioned that in the quantum field description the energy quantum has a 50% of being in the top particle and 50% of being in the bottom particle, instead of half of the energy being in the top and half of it being in the bottom. But it seems that there is no real distinction between the evolution of the two systems as long as you do not interact with them. In the first simulation you assume to have two classical waves propagating around the circle, each carying half of the energy in the system. They could be detected individually by an observer. It is possible to harvest an arbitrary amount of energy from the sytem by interacting with one of the particles, even without disturbing the other particle. In the quantum field case you inject one quantum of energy in the system that creates two propagating waves, but you can only harvest the whole quantum by interacting with one of the ‘particles’, destroying both of them at the same time, even if they are miles apart! At least according to the Copenhagen interpretation (and others). In the many worlds interpretation you somehow split off a world branch when interacting with one of the ‘particles’. The other ‘particle’ lives happily in a diffent world that is forever out of reach. Both interpretations are hard to swallow, but that seems to be the conundrum of QM or QFT. I wonder how the QFT simulation would look like when you would have more than one quantum to play with? I assume you have to specify the chance for having one quantum and the chance for having two quanta in each point of the ring?

[@zapphysics]

These are all good questions. I'll start with the easiest one to answer. If we were to create two quanta in the initial state, I don't think there would be too exciting of a change since this is a non-interacting theory. I am not 100% sure because I haven't explicitly done the calculation, but here's how I think the story would play out: basically, if I create them at two different places, I would just get four dots running around the ring at the speed of sound, 2 clockwise and 2 counterclockwise. Each of these would have a 50% chance of being the true location of a particle (since I know I created 2 particles and each moves at the speed of sound). Now, if I create 2 particles at the same point, I think you would still see only 2 points, but each point would have a 50% chance of being the location of only a single particle and a 25% chance of being the location of both particles. Now for the more difficult question. The big difference is that in the classical case, I start by depositing some energy into the system to create the initial waveform and this waveform then propagates both directions around the circle. If I were to detect one of the waveforms, I would only detect that each waveform has half of the energy that I put in (unless I am on the far side of the ring where they overlap). In the quantum case, I put in a set amount of energy in a similar way, but whether I detect the particle on the upper half or the lower half of the ring doesn't matter: I always measure that either one I detect has *all* of the energy I put in. So, if I were to somehow absorb this energy, I could basically absorb energy twice in the classical case, but only once in the quantum case. I think that we have to be a bit careful when interpreting things in quantum mechanics. Especially in the Copenhagen interpretation. I don't think that it is quite correct to say that we destroy both particles at the same time because in a sense, the system isn't really physical until the wavefunction is collapsed into a single state. In other words, we can't assign a definite history to the system by saying something like "the particle was travelling both directions, then I made a measurement, found the particle to be in the upper half, so the one in the lower half disappeared." I think it is safer to just say that there is a 50% chance of measuring a particle at point A and a 50% chance of measuring a particle at point B.

[@folwr3653]

Thanks for the detailed discussion. I totally agree you should be cautious with the wording when interpretating QM. To quote Feynman: if you think you understand quantum mechanics, then you don't.

[@djelalhassan7631]

@@folwr3653 I understand quantum mechanics perfectly, there is a 50% chance of measuring a particle at point A and a 50% chance of measuring a particle at point B, and when I measure/observe the wave function collapse of a particle at point A then the particle is 100% definitely at point A. And the probability of tossing a particle of coin for heads or tales is the same as tossing a particle of electron, they both need a tosser, and there is no toss without the tosser, and the probability of 50% 50% chance is the objective possibility that not yet being realized. The Universe is the conscious living creation with ethics, purpose and free will and is interactive and participatory process of The Creator, and is not vise versa of the materialist nihilists people.

[@gcewing]

I think the two-particle case would be difficult to visualise in full detail, because if I understand correctly there's a separate probability for each _pair_ of particle positions. For N positions in the ring that's N^2 probabilities, which doesn't fit very nicely into a spatial diagram. The best you could do would be some kind of projection of the state space onto the ring, but then some nuances would be lost.

[@jakublizon6375]

QFT is the reason we are progressing technologically so quickly.

[@parsaoveisi5655]

Good job dude! Keep it up!

[@brihaspatiangiras9081]

That was really good explanation.... thanks man

[@frankreashore]

Amazing video. Huge thanks.

[@syedmasudali3250]

Great explanation and a very nice work indeed. Thanks a lot for the efforts. Best wishes...

[@johnnyutah7010]

Great video. Many thanks for putting it together

[@hossainpezeshki6964]

Thank you for sharing the knowledge.

[@swish6143]

Really impressive illustration, I looked through some QFT texts with hamiltonians and stuff and didn't get any intuition from it -.-

[@bryanfuentes1452]

of course

[@fernandohood5542]

Brilliant demonstration of how some can seemingly appear from nothing.

[@AndrewMacRae]

Awesome description, great video!

[@michaelm9710]

PLEASE EXPLAIN this next! Below is the description of how atoms came into existence. But if quarks and electrons are fields or strings, what really happened?! Need a visual please. Atoms were created after the Big Bang 13.7 billion years ago. As the hot, dense new universe cooled, conditions became suitable for quarks and electrons to form. Quarks came together to form protons and neutrons, and these particles combined into nuclei

[@gibbs-13]

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!

[@shashankchandra1068]

Do u hv fb account

[@jeancorriveau8686]

*EXCELLENT* video. I now understand a lot...

[@chintanjani6742]

This was awesome. Thanks!

[@misterlau5246]

Oh, nice! I'm just looking here, I see you have some years doing this! 👏

[@rwmcgwier]

A quantum theory,, despite its name does not mean discrete. A quantum theory has operators for observables which do not commute. But for the physical consequences the uncertainty principle is what tells quantum from non-quantum theories. The other important property of quantum theories is that you can have entanglement. Thank you for your video, without the incorrect discrete part, it is helpful. One more, the photons emitted by a black body do not have quantized energy levels and therefore frequencies.

[@bassamshehadeh7305]

This is so beautiful thank you

[@xandersafrunek2151]

This is epic. I am going to try it in Matlab.

[@anonym3214]

Awesome work!

[@TheJara123]

fantastic man, you did fabulous job, please make more QFT videos like this..to Feynman dias

[@antonykolarov9942]

Great work! Congratulations! Although I find a big mystery here. According to the Uncertainty principle ∆x.∆p ≧ ћ/2, if the particle has a known position, its moment goes towards infinity and the position becomes undefined. In the classical quantum mechanics that's related to the non-commuting position and momentum operators. In QFT that's given (somehow) by the non-commuting field operator φ and the momentum operator and momentum operator of the particle: [φ(x),π(y)]=iδ(x-y). Thus we could not know the field amplitude and momentum simultaneously and that would introduce the quantum uncertainty. The particle cannot be localized and their energy cannot be known precisely. To me, that part is somehow missing or is too much hidden in your video. Maybe You can create a next slightly improved version?

[@zapphysics]

@Antony Kolarov This is an excellent point, and I have been considering making a follow-up video, part of which would address exactly this. You are exactly correct that we cannot entirely localize the particle as well as knowing the particle's momentum. In fact, if we want to place the particle at a single location in the initial state, we have to have infinite uncertainty in the particle's momentum. This manifests in the mathematics as a summation over all possible momentum states to give the initial state corresponding to a localized particle. In the particular case shown in the video, the field is massless, so the particle must travel at the speed of sound/light, and so this "infinite uncertainty" appears as the two pieces travelling clockwise and counterclockwise, respectively. Also, as you said, we can't know the energy of the particle either since we have summed over all possible momentum states, which are also the energy eigenstates of the system. We could, of course, also see this as another manifestation of the infinite uncertainty in momentum since a massless particle's energy is entirely determined by its momentum. In essence, we know that we only put in a single unit of energy (i.e. a single particle) into the system, but we have no idea how much energy that unit has. I appreciate the criticisms, and I agree with you that this discussion is missing in this video! Hopefully in the future, I will have an improved discussion about this important point.

[@antonykolarov9942]

@@zapphysics That's maybe the best video in the world about revealing the nature of the particles, so one may hardly criticize. We can only admire and wait for the next part! Good luck!

[@anmolsahu2468]

Thank You!

[@Bronze_Age_Sea_Person]

Given your examples, Am I right to assume that different fields existing in the same coordinates in space would be as if the masses had more than a single spring attached, yet the properties of said springs(such as elastic potential energy) wouldn't interfere with one another? Like your example which had a red color for probabiliity of finding red energy packet in a given quantum oscilator. If it had a blue and a green packet, which are no different from red, save for being related to completely different springs which don't interfere with one another and only share the same coordinates in space(well, the probabilities the packet is in said coordinate), they would also oscilate, sometimes joining the same position with red, but not interfere with red's functioning. If that is right, and let's say this "particle" was a quark, which interacts with all four fundamental forces, and disregarding each field's particularities so they were like the red, green and blue examples, would this quark be a region where the "em energy packet", the "weak energy packet" the "strong energy packet" and the "gravity energy packet" all share the same "coordinates"(the probability is around in the same region of oscilators), each oscilating separately, but given they were around in the same area, it would be impossible to separate them from the quark?

[@IliyanBobev]

How would this work in higher number of dimensions? Would we need to introduce momentum to keep the location probability along a single path, rather than smearing in all directions?

[@lucasbaldo5509]

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 👍

[@zapphysics]

@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.

[@lucasbaldo5509]

@@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!

[@fredrickvanriler7986]

.Damn Sir! What ...Super-intellect you have there,💯 I would kill for ur abilities

[@christianthom5148]

Very nice simulation. From your description pdf in the git I believe you use a Hamiltonian designed for a massive particle. So I don't understand why the particle moves at constant speed ; I would expect it would just stay where it was created, or diffuse slowly due to the Heisenberg uncertainty principle. On a similar but more general topic, I don't understand why in QFT creation operators don't need an initial momentum for the created particle, but only a position, especially when more than one particle are created.

[@schmetterling4477]

Depends on what you are creating. You can just as well write creation operators for plane wave states.

[@christianthom5148]

@@schmetterling4477 Yes, but in this case they are not localized. It seems to me that the creation of one unique massive particle is a breach in the conservation of momentum law. At least two particle with opposite momentum should be created. So it shouldn't it exist the theoretical tool to do so ?

[@schmetterling4477]

@@christianthom5148 None of the physics books on the topic that I have pretend that creation operators are physical. They are mathematical tools, not formal representations of physical processes. You can also not prepare a delta function in classical physics, it's still a good mathematical tool for all kinds of problems. If you can't understand the difference between math and physics, then you need to walk over to the mathematics department and apply for a job there. You will never be happy in physics.

[@Littleprinceleon]

The author of video claims he calculated for massless "particle" with a single unit of energy...

[@christianthom5148]

@@Littleprinceleon So maybe he did not use finally the Hamiltonian mentioned in the pdf in the GIT repository.

[@mustafaashry4310]

A master piece! Please continue making it

[@rbkstudios2923]

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

[@zapphysics]

@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.

[@lennartsenden1220]

This is incredibly well explained

[@DargiShameer]

Good explanation

[@TenzinLundrup]

I looked at the .pdf of your algebra. At the end you say that the probability density K(y) has to be between 0 and 1. However only its integral w.r.t. y should equal unity. Are the singularities of K(y) integrable?

[@barryzeeberg3672]

Great video! Can you tell me if the quantum fields are real things that exist, or if they comprise a mathematical model that is more or less a useful abstraction? What programming language did you use for your code in the git repository? I was wondering if a simulation that is based on a finite-size circular quantum field will generalize to an infinite size quantum field on a cube? That is, does the formation of "particles" depend on the disturbances being restricted and bumping into one another within a small region of a special shape? Is there any useful insight to be gained by looking at the Fourier Transform of the quantum field?

[@chrisbarry9345]

I wish he made examples showing how this turned into actual particles that make up an atom. Like the different fields moving to make an atom

[@Littleprinceleon]

Q-fields doesn't move 🤫😉

[@ARBB1]

Representing it by quantum harmonic oscillators seems reasonable at first, even Zee does it in his intro QFT book, but it is not very accurate considering the R^n models of space that it deals with, making it impossible to visualize.

[@zapphysics]

@Artur Renato B.B this is interesting, do you have a resource where I could read more about this? I have never heard that canonical quantization is not an accurate way of deriving QFT. Or maybe I'm misunderstanding what you are saying?

[@ARBB1]

@@zapphysics Well, I coincidentally had some academic curiosity about this subject some time ago, so I can direct you to some resources. "A New Way of Visualizing Quantum Fields" by Helmut is a useful summary of the difficulties and ways you can go about doing it. And there is no major issue with canonical quantization.

[@zapphysics]

@Artur Renato B.B thank you for recommending this paper. Perhaps since you have studied this more, you could clarify a point of confusion for me (which seems to be a main point of the paper!). I am not seeing how the wavefunction for a 1D lattice of N oscillators maps R^N->C. It seems to me that the mapping should be Z/N -> C (in the case of the ring) since the inputs for the wavefunction should just be the lattice sites, no? In the continuum case, this of course would just be R/Z->C (or just R->C for the non-ring case). Neither of these would be problematic, though. Perhaps I am being dumb an missing something obvious... Thanks again for sending the paper, it seems very interesting!

[@shashankchandra1068]

@@ARBB1 do u hv fb account

[@tmlen845]

does it also work if there is a 2D or 3D mesh of masses connected by strings? would a particle stay contained in a point and travel in a straight line?

[@zapphysics]

Great question. I did try this calculation explicitly a while ago, so I will try to remember the specifics. From what I recall, what ends up happening in higher dimensions is that the amplitude is given by Bessel functions in 2D and something like 1/|(x+ct-y)| in 3D. So there are a couple of things to note. Here, it looks like we have smeared out our point, but we have to be a bit careful since both of these functions have a pole where the amplitude diverges. Now, it doesn't make sense to talk about an infinite probability, so how I think the story works is that you have to properly normalize the function. Once this is done, the only place where you have a non-zero amplitude is at the location of the pole and you get your particle-like behavior back. But remember that we had to sum over all possible momenta to get this peak in position, so we have essentially lost all information about which direction the particle moves (and in fact, the exact energy of the particle). So, what you would see is a shell of highest probability moving outward from the source point at the speed of sound/light. But again, please take this with a grain of salt as I quickly did the calculation for higher dimensions a while ago and I may have missed something.

[@Theo0x89]

I'm not sure I understand what's happening here. Doesn't the limit N→∞ correspond to quantum field theory, which doesn't have a discrete set of oscillators but still a delocalization of probability for particles over time? If this is correct, then why do the probabilities do not smear out?

[@franks.6547]

I struggle with the same thing. First: the finite dimension of the string and not the individual oscillators would be the actual reason for discrete energy levels in the continuous case. Second: In the continuous case, you have to build localised (e.g. gaussian) wave packages out of multiple frequencies/wavelengths, and there are no local oscillator properties that limit the frequencies in that superposition, if the string is infinite. Then the dispersion in the continous case stems from the frequency/wavelength (=energy/momentum) relation that makes the group velocity dω/dk different for different frequencies in the wave package (Fourier) mix. Now, I struggle to relate this to the shown discrete case (which I'm sure has merit, too). The stability of spacially isolated excitations could have to do with the relative closeness of the frequencies present in the excitation - because classically, we have many coupled oscillators here, so when combined, they should feature more possible frequencies than just the ground frequency of the free oscillator (5001 frequencies for a system of 5001 coupled oscillators?). But I'm confused, too...