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If we ever want to simulate a universe, we should probably learn to simulate even a single atomic nucleus. But it’s taken some of the most incredible ingenuity of the past half-century to figure out how that out. All so that today I can teach you how to simulate a very very small universe.
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I retired a few years ago from a career in experimental particle and nuclear physics... and now I'm watching these videos and getting insights that had eluded me all those years. Thanks!
Vor 15 TageJohn Weiss [he\him]
@Gravoc The problem is one of _language._ Saying that it's being jealously saved by, "tight knit academic circles," is like you trying to read" The Epic of Gilgamesh "in the original Sumero-Akkadian with no knowledge of how to read cuneiform, nevermind Sumerian itself, then stating that there is no original "The Epic of Gilgamesh", just some bricks that a chicken tap danced on! The reality is: Quantum Electrodynamics is readily available in several textbooks. QCD is available through a combination of textbooks and physics journals. They're textbooks for physics grad students, however, and they're written in the language of Physics: Mathematics. Vector Calculus is needed for basic, classical Electricity & Magnetism. When you get into QED and QCD, you start needing subfields of Abstract Algebra. For anything involving General Relativity or Quantum Gravity, you need Differential Topology. This stuff isn't hard to _find,_ but it is hard to _learn._ If you majored in Physics, you already know how much work you crammed into 4 years. But even that isn't enough. You need another 2 years of grad-school courses, 2 years when you're working on physics every waking _and sleeping_ hour. I used to actually work on problems _in my dreams_ when I was in grad-school [not that it was any help!🤣] And that's what you need to build a foundation for … the first semester of intro Quantum Electrodynamics. Which not every grad-student even takes. I didn't, but my research didn't require it, so I had other courses I needed to take. Even if I hadn't changed careers after getting my PhD, _I would have trouble_ completely understanding this. Not because other physicists are locking it away. But because _I don't have the math_ to understand it. And any non-mathematical descriptions of physics are like reading the English translation of the Japanese translation of the Russian translation of a rather bad Persian translation of an out-of-date Arabic translation of the original Sumero-Akkadian text of "The Epic of Giglamesh"!
Vor 14 StundenSpotterVideo
@dondeestamanana Thanks for your kind response. That is an excellent insight into how this model might be expanded.
Vor 3 Tagedondeestamanana
@SpotterVideo Had the idea that the threaded rod and nut are also a good model for inertia. The more winding the more inertia and therefore mass. Pushing the nut is stopped bei rotation in a non classical spacetime. Photons would have no rotation. Therefore no mass and inertia. Agree that imbalance in quarks torsion system would then mean gravity in a microcurved spacetime which results in a "gravitational illusion" in macrocurved and expanding spacetime. No need to quantizise gravity or space or time. Just one additional dimension required as far as I can understand to this point.
Vor 3 TageuPtrade
it's all about consciousness solves the perpetual energy machine problem..
Vor 5 TageBobby Shaftoe
The ...narrow halls... of the elitist scientific economy attenuate even the most brilliant and optimistic people compelled to walk those halls.
Vor 6 TageStephen Manis
Kudos to the whole PBS Space Time team. It's information like this that keeps me coming back for more. I'm raising my 9 and 12 year old kids on your videos and despite most episodes being advanced for kids this age, it's sparked some great conversations with them about Quantum Mechanics and the nature of our reality.
Vor 15 TageConnor Mudie
Good on you for exposing your kids to this, you must really be sparking thier interest in the topic and if they choose to follow a path involving the learnings of these videos they will be so advanced in conceptual understanding and creativity.
Vor 9 TageLorp is
I wish my parents were like that and information that was as accessible and digestible as today. I would try to find answers at 6 and found the esoteric language of math both in its symbolism and written explanation. I still have a hard time internalizing it. Most of what I learned I figured out on my own and made the connection after.
Vor 12 TageHҽггØ ᬏᬏᬏ
I wish I had a parent like you.
Vor 13 TageDaniel Nash
That's great Stephen Manis. Starting you kids off not with the amazingly good explanations of space-time, may help them get into more difficult maths, and science earlier. That's what being a good parent is all about. Way to go my friend. 👍
Vor 13 TageDr Gamma D
the best part of this video is the death of the virtual particle. If anything shows YouTube science leads to confusion is the massive misunderstanding of the virtual particle, which is indeed just a term in a perturbation series that can be treated as a particle. with care. Likewise, all the twin paradox screw ups leaving people to believe you can travel near the speed of light, with respect to space. No. this is garbage. The only way to learn for real is doing homework problems that hurt. no pain. no gain. Once you crush the problems, enjoy the video.
Vor 14 Tagewilliam godfrey
I recently found this channel. It's absolutely brilliant. My background is in astrophysics and you definitely explain some of these concepts to the public far better than a lot of lecturers I had in the past.
Vor 15 TageSean Richardson
Lol
Vor 11 TageRepent and believe in Jesus Christ
Repent to Jesus Christ “Then he said to his disciples, “The harvest is plentiful but the workers are few. Ask the Lord of the harvest, therefore, to send out workers into his harvest field.”” Matthew 9:37-38 NIV J
Vor 13 Tagewilliam godfrey
@Entrepenumbra it really is excellent. I do yes.
Vor 13 TageEntrepenumbra
Do you have a degree in astrophysics?
Vor 13 TageEntrepenumbra
This channel is excellent
Vor 13 Tagei, booba
I'm so happy you addressed my comment in the last episode! I've been watching this channel for a few months now and have been very impressed with the content and the Q&A segments at the end of each episode. You're making physics as a whole a tangible thing to understand for a very wide audience, and I hope it goes without saying this is a very difficult thing to do. Thanks for all that you do, and I sincerely look forward to new episodes each and every week.
Vor 14 TageMatsuri fan
About your comment in the video, wouldn't it be enough to say that absolute zero being equal to no motion would violate uncertainty principle? Obviously your explanation is better and gives further explanation, but for a quick counter example would this be sufficient?
Vor 12 TageMad Professor
I lol'd at your correction. Well played, I Booba, well played.👏
Vor 14 Tageyour dreams
i burst out laughing when your name came on screen in the video
Vor 14 TageInvaderX32
I'm so excited to see the channel starting to slowly dip into the world of Quantum Chromodynamics. It's always seemed fascinating to me that there is a whole other level of particles and interactions going on inside the atomic nucleus, but trying to read about it on my own has always been daunting.
Vor 15 TageChaosKeep
Always amazes me how taking a step back and taking the time to examining the frame of reference we are trying to examine results in powerful new tools not understanding the universe, be it physics or geology.
Vor 13 Tagepobinr
Is it real or is it just maths ?
Vor 13 Tagecobb m
@Doug InOrlando https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageUche Powers
I am not anything close to a scientist, but I enjoy hearing things like this... It is so amazing to see how much human have observed the universe. It is all very complex but my heart wants to hear more. It makes me feel complete.
Vor 11 TageVogel Vogeltje
Human fee-fees are powerful.
Vor 7 TageGuillaume Couture-Lévesque
Those optimizations really seem like things that someone in the demoscene would've done for fun. I remember some hilarious hacks to get fluids working in realtime, or real time raytracing more than a decade ago. Quantization, caching, precomputation, and randomized sampling are pretty standard approaches to simplifying expensive problems.
Vor 15 Tagecobb m
@Brent Smith https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageGuillaume Couture-Lévesque
@dotnet You know that's a good point, I never thought of it that way.
Vor 14 Tagedotnet
The demoscene has similar constraints to scientific compute so it's understandable they end up with similar approaches. In both cases you're trying to fit an approximation of something very complex within as small and efficient of a data volume as possible.
Vor 14 TageSoken50
The fact it works so well almost leads me to believe in simulation theory :x Unlikely but certainly frightening.
Vor 14 TageMandragara
You'd be surprised how much of an overlap there is between people who do Physics and demoscene types
Vor 14 TageRenee M Carr
Out of all of the topics Matt has taught on here... this has to be one of the most mind blowing .. 🤯 it's unbelievable how any human minds have ever found ways to simulate these tricks as he called them. Lattice QCD... Unreal. It's amazing he's explained this in an understandable way for those of us who have no background in physics at all.
Vor 15 Tagecobb m
@Hyperduality https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageHyperduality
Mesons are dual:- quarks are dual to anti-quarks. Action is dual to reaction -- Sir Isaac Newton (the duality of force). Attraction is dual to repulsion, push is dual to pull -- forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Thesis (up quark) is dual to anti-thesis (down quark) synthesizes another up quark (proton) -- the time independent Hegelian dialectic. The 3rd quark in a proton is synthesized by conserving the duality or correlation of the first two quarks (up & dowm). The quark triality of a proton is actually duality -- the synthesis of the 3rd quark is a by-product of conserving duality. Energy is duality, duality is energy. Quarks are made out of energy hence duality! Duality creates reality. "Always two there are" -- Yoda. Atomic forces are dual -- attraction, repulsion, convergent is dual to divergent.
Vor 14 Tageim sleepy
I was so blown away by looking at that linear regression technique to 0 pixel spacing. Literally haven't felt this amazed in a few years. So simple yet so beautiful.
Vor 14 TageJohn B
I feel like everything in quantum physics is built on, "This is how it works, except its not how it works."
Vor 11 TageSystem BD
When talking about discrete elements of space -especially a regular structure of 3 or more dimensions-, I believe you should use the term "voxel" (a portmanteau of "volume" and "element"), rather than "pixel" ("picture" + "element"). It was once an obscure concept in computer graphics, but the popularization of voxel-based games like Minecraft has made this term rather common among young people, so you should not have any problem taking advantage of that.
Vor 15 TageDaCarnival
A four dimensional pixel (or voxel), shouldn't we have name for that? A tixel (time pixel)? What about a one dimensional pixel; maybe just a ixel?
Vor 9 StundenHand hdhd
Learned something new
Vor 13 Tagecobb m
https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageSimen
Since the model described in the video is 4 dimensional, wouldn't it be a hypervoxel?
Vor 13 Tagegeno
I believe the concept of what Matt said was using pixels to achieve the voxel? At least that's how i pixeled it even though i'm an old voxel.
Vor 14 TageMystixor
I started watching PBS Spacetime in 2016 (to my best knowledge) with the dream of studying Physics one day. Now, I have been in University for 2 years, and this is the first time I see a new video released on a topic I already learned about and it feels weird... but in a good way ^^ I hope Spacetime never ends
Vor 15 TageMark Watson
Best wishes!
Vor 5 TageNoName
@Mystixor so before this video you learned that lattice qcd existed, but not how it's done?
Vor 11 TageMystixor
@Lucas Möller Thank you for your kind words! It definitely can be hard getting up in the morning with a day full of work ahead, but you shouldn't feel down or unhappy about yourself because you might not always live up to some expectations you have for yourself. The last 2 years were very difficult for me as I realized for the first time I was at my very limit when it comes to... brain power. I just couldn't keep up with a lot of other people in Uni and to this day it stresses me out a lot. With every semester it's getting better though, talking with other people having similar issues, and always realizing you don't need to be the fastest with understanding stuff or get the best grades in every course. I know what you mean about reading books. I used to like reading, and now I can't even read books in my freetime which I know I would enjoy a lot, much less books I would be required to read for Uni (I'm just lucky our Professors don't really require us to read long texts or books). But I'm trying to battle it, I recently bought a book I will enjoy a lot and I also rediscovered a series of books I read (at least) 10 years ago and I am very much looking forward to experiencing again. I'm just reading a couple pages every now and then, baby steps now might just turn into fulfillment later, it's a chance I'm willing to take :)
Vor 12 TageLucas Möller
Bro had a dream and pursued it. I respect you and wish you the best of luck in university. I myself have been interested in chemistry and physics since my childhood and find looking at convoluted concepts like this very video described highly fascinating, yet I was never actually able to understand them on a deeper level. Can't even get myself to read a book, and it has frustrated me for as long as I can think. That's why I respect and look up to people like you who actually have the mental endurance to get up every day, motivated to learn. I wish I could, too. nngh why am I writing this much about myself what am I even doing snymore its way too late im sorry lolll
Vor 12 TageMystixor
I should clarify though, we did not yet learn about QFT, so I did not know the entire substance of the video :p
Vor 15 TageDanny Mcclenon
You guys did a great job with topic selection. It's above my redundancy threshold and I'm perpetually entertained. Stay creative!!!
Vor 15 TageLuis Sfeir-Younis
great video! Question: if 99% of atomic mass is caused by quark-gluon interactions, presumably such high energy interactions in the tiny volume of space that is a nucleon would have relativistic effects, no? Would be interested to see a future episode that explores these relativistic implications further, including potential links to updating theory of gravity, quantum gravity, GUT, etc
Vor 12 TageSB Dunk
I love your videos, but I often find myself getting lost midway through... However, I was absolutely gripped throughout this whole episode, and everything was explained exceptionally well!
Vor 15 TageRock Barcellos
I just nod and pretend to be understanding everything
Vor 14 TageSB Dunk
@Hyperduality Have you seen the film "The Number 23"?
Vor 14 TageHyperduality
The W+ boson is dual to the W- boson -- there are 6 force carriers not 5, the W boson is dual. Neutrons decay into protons & electrons -- the electro-weak force. Electro is dual to weak -- the electro-weak force. Mesons are dual:- quarks are dual to anti-quarks. Action is dual to reaction -- Sir Isaac Newton (the duality of force). Attraction is dual to repulsion, push is dual to pull -- forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Thesis (up quark) is dual to anti-thesis (down quark) synthesizes another up quark (proton) -- the time independent Hegelian dialectic. The 3rd quark in a proton is synthesized by conserving the duality or correlation of the first two quarks (up & dowm). The quark triality of a proton is actually duality -- the synthesis of the 3rd quark is a by-product of conserving duality. Energy is duality, duality is energy. Quarks are made out of energy hence duality! Duality creates reality. "Always two there are" -- Yoda. Atomic forces are dual -- attraction, repulsion, convergent is dual to divergent.
Vor 14 TageMaple Leaf
@SB Dunk that's a strong reaction but suit yourself
Vor 14 TageOlivia Neugeboren
Ive recently started thinking of fields and their particles as functioning somewhat like conways game of life. Stable oscilations are like particles, and unstable ones are like virtual particles. Theyre both made of fluctuations in the same pixel grid following the same rules, and the stable oscilations can generate unstable ones, which can influence other stable ones. These interactions can then lead to larger stable structures with new properties. Obviously the rules are very different so i dont mean its an accurate representation or anything, but its a concrete, visible, definable example of at least similar concepts, which to me forms a much better base for a mental image than saying "an electron spontaneously emits a virtual photon which is absorbed by another electron."
Vor 14 Tagealmighty.sapling
This viewpoint is just as much fun going the other direction: Conway's Game of Life is just some sort of operator on the space of {0,1}-valued functions over Z^2. It clearly satisfies many important symmetries (translation and rotation invariance). I doubt it's unitary, but it would be fun to see what properties it could be tweaked to satisfy. Other "rule sets" are just different operators on this space. You also might be interested in Sean Carroll's article: https://www.preposterousuniverse.com/blog/2013/02/20/smooth-life/
Vor 10 Tagecobb m
https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageDr Gamma D
interesting, but it is so classical that it implicitly introduces a gazillion quantum fallacies.
Vor 13 TageHigh Impact Sexual Violence
@Geoffry Gifari I've done some basic research into Conway's Game of Life and cellular automata, watched some videos and messed around with some myself. The Primordial Particle System is especially fascinating because of how closely it seems to mirror real particle interactions/basic life forms. Cellular automata often model natural systems, from physics to chemistry and even biology. It seems that they demonstrate a universal principle of emergent complexity which is mirrored across all levels of existence.
Vor 14 TageGeoffry Gifari
@High Impact Sexual Violence you've read about this before?
Vor 14 TageYves
Hi Matt, I'd really like to see an episode on what our options are if the James Webb telescope discovers advanced alien life on relative short distance
Vor TagE
Thank you so much for these videos, I wish I paid more attention to Physics in college and this content is the perfect level. Could dark matter be unentangled mass? I don't know why that isn't brought up as a possible explanation. My understanding is we do not know the gravitational impact of an unentangled particles like in a two slit experiment. Is one possibility that its gravitational wave spreads out just like the positional wave? If so, a lot of unentangled particles could explain the gravitational impact observed of dark matter. I guess there would then need to be an explanation why the wave function hadn't collapsed though.
Vor 3 TageShauka Hodan
As a layman, my mind went for the way you changed the calculation from particles to the fields themselves! It’s just genius. Thanks for the upload.
Vor 8 TageJan Pieter Cornet
Isn’t the decay of particles usually caused by weak force interactions? How do you add the weak force into the lattice QCD calculations? is that even possible?
Vor 15 TageTimmetry Gaming
The strong force is so extreme that the weak force has practically no effect on what happens within the realm of the Strong.
Vor 3 Tagecobb m
@Zack H https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageHyperduality
The W+ boson is dual to the W- boson -- there are 6 force carriers not 5, the W boson is dual. Neutrons decay into protons & electrons -- the electro-weak force. Electro is dual to weak -- the electro-weak force. Mesons are dual:- quarks are dual to anti-quarks. Action is dual to reaction -- Sir Isaac Newton (the duality of force). Attraction is dual to repulsion, push is dual to pull -- forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Thesis (up quark) is dual to anti-thesis (down quark) synthesizes another up quark (proton) -- the time independent Hegelian dialectic. The 3rd quark in a proton is synthesized by conserving the duality or correlation of the first two quarks (up & dowm). The quark triality of a proton is actually duality -- the synthesis of the 3rd quark is a by-product of conserving duality. Energy is duality, duality is energy. Quarks are made out of energy hence duality! Duality creates reality. "Always two there are" -- Yoda. Atomic forces are dual -- attraction, repulsion, convergent is dual to divergent.
Vor 14 TageDenys Vlasenko
Weak interactions should have a rather small effect in any hadron containing only light quarks. Adding weak interaction to QCD simulations would immediately increase already high computational requirements for negligible gains.
Vor 14 Tage꧁༒𓆩ꏳꉻꑄꂵꉻꉣꃬ꒐꒒ꏂ𓆪༒꧂
It's actually night here and I'm watching this amazing video! Special thanks for giving glimpse of every important video required to understand a certain topic everytime! I'm not a very old subscriber thus, this really means a lot to me! I've been watching old videos consistently tho! Excited for more upcoming videos!
Vor 15 TageNathan Wilson
I'm looking forward to the upcoming QCD episode(s)! This one was fascinating. It's astounding how clever dedicated mathematicians and physicists can be. Stay well out there everybody, and God bless you, friends. ✝️ :)
Vor 13 TageJase N
Love the way this man breaks complex things down. I would’ve love to have him as my Physics instructors
Vor 14 TageJosé Castillo
Excellent video, I'm interested in more videos about quantum chromodynamics and asymptotic freedom. I'm also interested in a in detail description of the 4 interactions in a string theory framework.
Vor 11 TageCrayvun
This episode is so amazingly cool, and surely one of the most complicated ones. Thanks as always, it's been an incredible journey watching you all these years.
Vor 14 TageBig Bowl Broccoli
Hey Matt, would the evolution of life contain a series of events containing the states or outcomes of future events, as life needs to continually maintain homeostasis and account for the state of its environment? Like, life needs to predict the future and operate on future events in order to survive and remain dominant. We need models and predictions in order to plan ahead. Then again, you don't need to predict everything, for example if a certain resource is abundant enough there's no need for predicting whether it is going to be there when you need it. You just keep doing what you normally do. Though I keep having this idea where in every life form there's information that's corresponding/symmetrical to its environment.
Vor TagBELLA- 🔥𝐆𝐨 𝐓𝐨 𝐌𝐲 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 [𝐋!𝐯𝐞]
I'm so excited to see the channel starting to slowly dip into the world of Quantum Chromodynamics. It's always seemed fascinating to me that there is a whole other level of particles and interactions going on inside the atomic nucleus, but trying to read about it on my own has always been daunting.
Vor 13 TageOjus Singhal
Matt: "Let's make sure we understand *exactly* what we are trying to do here." Matt's next line: "We want the probability that some wiggly quantum field wiggles between one state and another." Matt is god.
Vor 8 TageEnter My Horizons
That half life 3 comment got me cackling out loud in my steel factory job. Thank you for all your fine work, detailed laymen explanations and humorous add-ons.
Vor 14 Tagedixia xie
You managed to get me interested in Lattice QCD, I hope to learn more in the future. Anyway, doesn't the fact that the correct particle mass is found only for a strictly continuou
Vor 10 Tage7th Quark
Easily one of the most fascinating episode, well done!
Vor 10 Tagegyu
Just wanted to say thanks for the effort/content, it's really appreciated. Learned a lot from this channel, most of which I didn't even know anything about to begin with. Pretty insane there's all this content for free, and still coming.
Vor 15 TageÁlvaro Rodríguez
Awesome to have virtual particles clarified. I heard they obeyed no conservation law and always had me greatly confused. It would be very nice if you further delved into particles, because It seems everything can be regarded as a particle, which is a bit confusing. I'm thinking of phonons and excitons, for example. Or of gravitons, which is at the same time "not a force" and mediated through particles.
Vor 15 Tagecobb m
@JD its true wether or not u believe in it,feynman won noble prize for this
Vor 13 TageJD
@cobb m I don't believe in 'feilds'
Vor 13 Tagecobb m
@JD https://youtu.be/1qJ0o4U63aw @1:40 Is that blue colour what can be called as a gluon field?(AKA one of quantum field ) and red colour a gluon particle?? Or the lowest energy density which is not shown/render in this image (prf.derek said tht in this video) is what we can call as GLUON-FIELD? Or is that RED COLOR RECTANGLE @1:21 is what can be called as gluon-field(AKA one of quantum field)
Vor 13 TageDr Gamma D
@nagualdesign not exactly. The problem is you are describing are Feynman's Lorentz covariant virtual particles, while many a science-tuber will switch from them to Old Fashion Perturbation Theory virtual particles which are not covariant and don't conserve energy (with the confusing "borrow energy for hbar/E"). That then leads to time-ordered emission and absorption, which is not how Feynman diagrams work (t channel has negative momentum squared, e.g. space like particles)...it's not something a laymen needs to worry about. It confuses experts enough.
Vor 13 TageX. Sanctus
Okay, great video, very interesting subject! When will we get the follow up that addresses everything that couldn't be covered in this video? Let's talk more about QCD :D Also, what would the mass difference for the neutron be, if the lattice spacing would be in the order of magnitude of the Planck length?
Vor 14 TageWeFunk World News by Tomachi NZ
This inspires me to run simulations of crystals at atomic resolution, I wonder if that has been done. I heard researchers discovered the speed of temperature is highly random using this.
Vor 11 Tagethat_interloper
I haven't touched anywhere near this subject in years, but you do a fantastic job making modern ideas accessible to us all. Love it!
Vor 14 TageFlockOfWingedDoors
"If I tried to explain that too, we would be here all day" That sounds great to me, no problem, please go on
Vor 15 TageDhruv Patel
Dear PBS team, Please, keep the more of QED/QCD/QFD/Neutrino/Higgs Physics coming. Thanks!
Vor 12 TageDr. Frozenranger
Would a time crystal be perfect for simulating the inside of a proton on a quantum computer?
Vor 12 TageThe Science Asylum
The graph at 13:10 was really interesting! The linear relationship between pixel size and mass is surprising.
Vor 9 TageRME76048
Kind of like the limit in calculus.
Vor 8 TageJeremiah Young
I had a question for you. If temperature is the measure of the particles speed, does relativistic time dilation happen to objects that are hotter or colder?
Vor 9 TageDavid Rosenfelder
Gosh, I love this channel. Thank you for the amazing content! The dig at Half-life 3 at the end was over-the-top amazing 😂
Vor 14 TageSpace
That is a great explanation for being a Physicist "think of how the universe works, describe the theory with math, test the model with reality."
Vor 15 TageHyperduality
@Space There is a 4th law of thermodynamics:- Syntropy (prediction) is dual to increasing entropy -- the 4th law. Teleological physics (syntropy) is dual to non-teleological physics (entropy). From a converging, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality. The observed is dual to the observer -- David Bohm. The Big Bang is a Janus hole/point (two faces = duality) -- Julian Barbour, physicist. Topological holes cannot be shrunk down to zero -- non null homotopic. Gaussian negative curvature is non null homotopic by definition so the big bang becomes an infinite negative curvature singularity, a duality! Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Black holes are dual to white holes. "Always two there are" -- Yoda.
Vor 13 TageJason Clouse
@Katie Barber There are a lot of questions people have about reality. What you call science has become strictly focused on a small subset of them, and primarily on the question “how do things move?” Meaning how do they move the way they do, at the velocity they do, in all the different circumstances that we see things moving? What parts make up the things we see moving and what relationships do they have to each other? But there are plenty of other questions about reality. Why do things move? What caused the first motion? Why do things exist? Is there a reason? Is there a goal? What part do we play in it, if any? What is consciousness? Why does it exist? Are there other consciousnesses beyond our own? These questions are every bit as much about reality and its character as the first set of questions. In fact, they all used to be asked and answered together as part of a unified model: religion. Until very recently, the greatest minds throughout history considered all of these questions together. For reasons I don’t have time to go into, we decided to split these questions apart categorically. But there’s no question the ancients saw religion as a model of reality, even to answer questions like “why does the sun set and rise?” Helios hooked his horses up to his chariot and dragged it across the sky each day. 😏
Vor 14 TageSpace
@Hyperduality Boi, whatchu goin on about?
Vor 14 TageKatie Barber
@Jason Clouse in what way is religion a model of reality?
Vor 14 TageJason Clouse
@Katie Barber Not really. Religion is a model of reality too. It just deals with different aspects of reality. It’s complicated by the fact that religion is also often used incorrectly or used to control people. But science is often used that way too.
Vor 14 Tagezijuiy wttuy
I had a question for you. If temperature is the measure of the particles speed, does relativistic time dilation happen to objects that are hotter or colder?
Vor 7 TageFalk Lumo
Great video on a topic I actually contributed to with my research, thanks! I would have thought though that you briefly touch on a big complication in lattice gauge theory: that you have to deal with anticommuting numbers in a computer …
Vor 12 TageSharon-🔞𝔽**СК МЕ - СНЕℂ𝕂 𝕄𝕐 Рℝ𝟘𝔽𝕀𝕃Е💛
I retired a few years ago from a career in experimental particle and nuclear physics... and now I'm watching these videos and getting insights that had eluded me all those years. Thanks!
Vor 13 TageM i Α vℓσg gσ тσ му ¢haηηєℓ!
I retired a few years ago from a career in experimental particle and nuclear physics... and now I'm watching these videos and getting insights that had eluded me all those years. Thanks!
Vor 13 TageAgent Vault
I'm grateful for always referencing the relevant past video, it is very helpful. "real particles are sustained oscillations in a quantum field" I interpret to be like quantum cavitation structures shaped by the different forces that vary as waves. They interact or don't based on how they can be nullified or overtaken by their structure density in the same space like bubbles filled with smaller bubbles consuming each other while also needing to be constantly cycled/stimulated by the fundamental forces. Time crystal are a case of this nullified balance to one or more of the forces to create an internal structure of perpetual motion. You should be able to have the classification of different time crystal structures as weak, strong, electromagnetic, or gravity time crystals. Perhaps the combined effect of all four across great distances can account for the discrepancy of the dark matter theory. Edited: Expanded the mentioned required sustaining force to be from only electromagnetic to the 4 fundamentals.
Vor 14 TageElene
The explanation of the difference between real and virtual particles was eye-opening and extremely helpful. I've read so much about these concepts over the years, but this is the first time anyone described the concept of virtual particles this way. Thank you.
Vor 10 TageHadron90
Can you do a video on energy conservation in General Relativity? Like when a high energy violet photon gets gravitationally redshifted to a low energy red photon...my understanding based is that simply doesn't conserve energy in any traditional sense. Is that correct? Does GR replace energy conservation with something more general, and what are the implications to time-translation symmetry in GR if there is no energy conservation?
Vor 7 Tagescientistpac
So cool that you go in harder and harder topic! I can't wait to learn more!
Vor 14 Tagemat hazle
If we can do this, could we simulate hydrogen / helium atoms "normally" and how they function when they fuse in stars as a potential means of learning how to create / finesse terrestrial viable fusion?
Vor 15 TageDFPercush
@mat hazle To put the pressure required for stellar fusion in perspective - On Earth, a column of air from sea level to the edge of space is about 100 km tall. When compressed by the gravity of one earth mass, it results in a pressure of 1 atm. The sun's radius is 695,700 km of mostly gas, with 332,950 times more mass compressing it. The temperature is also higher, and if you have hotter gas in a given volume, according to the ideal gas law, you get higher pressure. Add it all up, and it's about 68,000,000,000 atmospheres at 15,000,000 degrees C/K. Pretty sure there's no material that could withstand either of those extremes, but if you find one, you could do a lot more than fusion with it.
Vor 11 TageHand hdhd
@Halfnattyboomer pressure and temperature are proportional. The pressure is so large at the core which heats up the atoms causing fusion. If you wanna say tunneling which I don’t think is true, the atoms have very high kinetic energy overcoming the electromagnetic potential barrier which technically isn’t tunneling. Tunneling refers to when the energy of the particle is lower than the barrier. So for fusion to occur, it’s a strong function of pressure, temperature, and volume. So a temperature “threshold” only exists at that volume and pressure. Water can be liquid under freezing point (at 1 atm). Furthermore from Maxwell Boltzmann distribution, we know that temperature is AVERAGE kinetic energy of particles meaning that there are percentage with higher energy enough to sustain fusion. It’s not cold fusion - there’s no such thing.
Vor 13 TageDr Gamma D
@Pfhorrest the sun doesn't have insane density, it's 150 g/cm^3....that's a lot (6x gold), but it is not insane. A neutron star is insane, like 1000000000000000000000 g/cm^3.
Vor 13 TageDr Gamma D
@Halfnattyboomer the sun has fuel for 10,000,000,000 years, so the half life of a proton in the sun is 5B years. Meanwhile, in a thermonuclear weapon, it is under 10 nanoseconds. That is a difference of 25 orders of magnitude. Sun is cold compared to a nuke.
Vor 14 TageDr Gamma D
atoms in stars? No. They are fully ionized. It's protons and alpha particles.
Vor 14 TageRalph Dratman
Wow, this is so helpful! Thank you, PBS Spacetime.
Vor 12 TageDean DeanN
The best episodes of PBS Spacetime are those episodes that give me an unexpected insight. It does not happen often. This episode gave me an insight re the fine structure constant and what was really meant when it is described as a coupling constant of the electron with the em field. I had never considered what that meant in a Feinman diagram.
Vor 12 TageRoo sh
Doing a video with a Half-Life 3 joke was the last hurrah needed for this channel to reach geek-out perfection, and I’m happy to report we have reached that threshold. Bravo. 👏
Vor 12 TageLydianLights
Very good video, I love this computational physics stuff! I always wondered why we never did computations with fields as the fundamental elements instead of particles -- turns out it's just because it's wayyyyyy harder.
Vor 14 Tageinbox me now on telegram @PBS22
thanks for watching And congrats you have been selected among our shortlisted winner's 🎉 contact us on telegram now to claim your prize 🎁🎁🎁🎁...........☑️☑️☑️☑️☑️
Vor 14 TageBilly Te
Very cool techniques to delve deeper into QM! I'd love to see a deep dive on how entanglement is treated in deBroglie Bohm Theory.
Vor 14 Tagemichael gleason
The diagrams ,drawings and explanations are great , I like the math too. I don't think there's any way you'd be able to show me any of this over here in the real world ?
Vor 8 TageXKloosyv
Thank you for such amazing content. It's fascinating to learn about and I'm going to make sure to try to pass along my own curiosities to my little boys.
Vor 15 Tagedixia xie
tricks as he called them. Lattice QCD... Unreal. It's amazing he's explained this in an understandable way for those of us who have no background in physics at all.
Vor 12 TageRichards Richards
this is good work...would you do a part 2 on colour superconductivity and other colour quantum phases of matter as we vary pressure and temperature
Vor 15 Tageecneafmaretotndei_
Great video. Also thoroughly enjoyed the prospect of a PhD astrophysicist saying the word "Booba" because another PhD holder with that name asked a good question.
Vor 14 TageAnthony Polonkay
So I'm no PHD physicist or anything, but I do more than my fair share of digging into all this kind of stuff. And the more I read, and learn, the more confident I grow in the idea that we have next to zero idea on how any of this works. Even everything you described in this video simply amounts to trying different simulation methods until we arrive at something that has an output that matches close to observable reality. And despite claims to the contrary after 10 years we learn almost nothing about these types of things even after these so called "breakthroughs" All we get are more theories, and more hypothetical numerical descriptions of said theorys. No actual answers to how anything works.
Vor Tagealindart
It's been shown that when we watch someone doing something, our brains simulate an experience similar to the doing process. If our experience of existence is the amalgamation of our awareness and understanding, could we say that each person constantly, individually, mentally "simulates" some "small" "local" portion of spacetime using the "algorithms" that person's quantum "location" in spacetime has made available? As you say, we learn a lot by doing these simulations; Everything learned is just a "relevant simulation" that's been saved for later. In conclusion: Everyone lives in their own, relativistic, self simulated, perspective of reality. The "combined agreement" of how "the time crystal of reality" seems in each moment is where "the world" operates. Spacetime "spins" on, yet grander, in so many dimension, than we have witnessed or calculated for thus far. The "Feynman Lattice Trendshape" as I might call it, (of the quark-gluon field) describes comparatively well how I visualize the "wavelike" interactions between pseudo and real particles at the "human-simulated" "boundary" between "empty space" and the "tensile" "fabric of reality". Upon this lattice, the strain of relativity pulls, and like a chromophore contorted into different refraction shapes, the baseline energy of the lattice is twisted and untwisted through currents of intercorrelation, these would spin off points of the pseudo-mass into "particle" state by "waves", standing or sudden, change in what I call the "RelativityInteractiveQuantumDensityField" or RIQDField; and Marty, no matter what you say, never gonna give you up. Triple Play, three strikes, I'm out.
Vor 5 TageVladyslav Danilov
Thank you very much for the video on the CQD topic. Do you have plans to make a separate video about Yang-Mills equation? It's important for QCD, and it's important as a math problem. Here is the question - don't you think that we can't have analytical version of QCD due to a "wrong" or inappropriate math approach? Maybe we need to develop a special math like Einstein proposed with GTR?
Vor 14 TageJan Kowalski
In lattice you calculate the inside of that "crystal". The question is, what makes the border of said "crystal"? Maybe it is sufficient to just calculate the states on the "edge" of that "crystal"? At least we assume, that calculating inside that lattice, there are rules for bouncing (from that mysterius "edge") or "propagating" (inside of the space enclosed by that "edge").
Vor Tagstephanie parker
Excellent video, loved the info and graphics! Well done!
Vor 12 TageRobert
I asked this question in your feedback form a while back! Not sure how much those forms direct your content, but it’s great to see you making stuff in the direction my mind goes
Vor 14 TageGray Mars
As a layman, my mind went 🤯 for the way you changed the calculation from particles to the fields themselves! It’s just genius. Thanks for the upload.
Vor 14 TageKrikey Dial
I'm still trying to figure out what's inside Tontons.
Vor 10 TageAndré KZ
Phenomenal explanation of a complex topic. Space Time's years of scientific communication are showing. I'm very glad to be on this trip to explain the roots of our reality, as best we know.
Vor 14 TagescrewyouGoogle
Love this show! I’m very excited to see QCD here.
Vor 14 TageBetsy Jimenez
I’ve been watching your content for over a year now. My background is in pure mathematics and you are seriously convincing me to start studying physics .
Vor 15 TageHyperduality
@Dr Gamma D Energy is dual to mass -- Einstein. Dark energy is dual to dark matter. Dark energy is negative curvature or hyperbolic space -- a repulsive force (inflation)! All forces are dual, attraction is dual to repulsion, push is dual to pull. Action is dual to reaction -- Sir Isaac Newton (the duality of force).
Vor 13 TageHyperduality
@Dr Gamma D I care. There is a 4th law of thermodynamics:- Syntropy (prediction) is dual to increasing entropy -- the 4th law. Teleological physics (syntropy) is dual to non-teleological physics (entropy). From a converging, convex (lens) or syntropic perspective everything looks divergent, concave or entropic -- the 2nd law of thermodynamics. According to the 2nd law all observers have a syntropic perspective. My syntropy is your entropy and your syntropy is my entropy -- duality. The observed is dual to the observer -- David Bohm. The Big Bang is a Janus hole/point (two faces = duality) -- Julian Barbour, physicist. Topological holes cannot be shrunk down to zero -- non null homotopic. Gaussian negative curvature is non null homotopic by definition so the big bang becomes an infinite negative curvature singularity, a duality! Positive curvature is dual to negative curvature -- Gauss, Riemann geometry. Black holes are dual to white holes. "Always two there are" -- Yoda. Mind (the internal soul, syntropy) is dual to matter (the external soul, entropy) -- Descartes or Plato's divided line. According to Descartes, Plato et al the mind/soul is dual. An infinite negative curvature singularity is identical or dual to an infinite positive curvature singularity -- topology. With a bit of luck and lots of hard work the penny will drop.
Vor 13 TageDr Gamma D
@Hyperduality no one cares
Vor 13 TageHyperduality
The W+ boson is dual to the W- boson -- there are 6 force carriers not 5, the W boson is dual. Neutrons decay into protons & electrons -- the electro-weak force. Electro is dual to weak -- the electro-weak force. Mesons are dual:- quarks are dual to anti-quarks. Action is dual to reaction -- Sir Isaac Newton (the duality of force). Attraction is dual to repulsion, push is dual to pull -- forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Thesis (up quark) is dual to anti-thesis (down quark) synthesizes another up quark (proton) -- the time independent Hegelian dialectic. The 3rd quark in a proton is synthesized by conserving the duality or correlation of the first two quarks (up & dowm). The quark triality of a proton is actually duality -- the synthesis of the 3rd quark is a by-product of conserving duality. Energy is duality, duality is energy. Quarks are made out of energy hence duality! Duality creates reality. "Always two there are" -- Yoda. Atomic forces are dual -- attraction, repulsion, convergent is dual to divergent. Integration (syntropy) is dual to differentiation (entropy).
Vor 14 TageWilliam S
Love the particle physics episodes
Vor 15 Tageevilotis01
@Hyperduality ooooooooookkkkaaaaayyyyy
Vor 14 TageHyperduality
Mesons are dual:- quarks are dual to anti-quarks. Action is dual to reaction -- Sir Isaac Newton (the duality of force). Attraction is dual to repulsion, push is dual to pull -- forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Thesis (up quark) is dual to anti-thesis (down quark) synthesizes another up quark (proton) -- the time independent Hegelian dialectic. The 3rd quark in a proton is synthesized by conserving the duality or correlation of the first two quarks (up & dowm). The quark triality of a proton is actually duality -- the synthesis of the 3rd quark is a by-product of conserving duality. Energy is duality, duality is energy. Quarks are made out of energy hence duality! Duality creates reality. "Always two there are" -- Yoda. Atomic forces are dual -- attraction, repulsion, convergent is dual to divergent.
Vor 14 Tageevilotis01
yesssss me too
Vor 15 TageHenrik
I would love to know how exactly physicists figured out this complex model
Vor 14 TageDFPercush
It looks remarkably similar to volumetric fog and cloud calculations in video games, except instead of random noise it's an actual wave function. I wonder if they used GPU shaders to run the simulation.
Vor 11 TageJean-Francois Belanger
Training my brain with this kind of stuff is truly the best kind of exercise. Thanks for the amazing job guys 😉
Vor 14 TageDani01
Perhaps at some point in the near future, we'll be able to train a neural network to these kind of complex particle interaction simulations, just like what happened with protein folding.
Vor 12 Tageaditya srivastav
Great Video, You have started videos on QCD. It is always pleasure to see how you explain things. It will be great if you can make some comments about Effective Field Theory frameworks... I am currently a Grad student
Vor 9 TageJohn Bragg
"We dont do these things because they are easy we do them because they are hard." What we need are quantum computers.
Vor TagBernard Skibinski
Awesome video, I wonder would quantum computing help with simulating QCD lattices? I know quantum computing is not some silver bullet for any problem, but I remember it should be good for these kind of very complex and chaotic simulations. And again thx for not dumbing things down, even though I understand 10%, just watching these videos over the years has made a lot of topics a lot less scary! Edit: on second thought, from your point of wisdom this is probably dumbed down 😅
Vor 15 TageDr Gamma D
it's not a matter of dumb v smart. It's beautifully symmetric vs ugly non-linear and intractable.
Vor 13 TageMatt White
Great video!!! I’m super excited to learn more about QCD!
Vor 14 TageEmmett O'Brian
I've always been told that virtual particles were real actual particles that only exist for a tiny amount of time. I actually got shouted down when I suggested that they could be perturbations in the field and not actually particles. Glad to hear i wasn't far off
Vor 14 TageHyperduality
The W+ boson is dual to the W- boson -- there are 6 force carriers not 5, the W boson is dual. Neutrons decay into protons & electrons -- the electro-weak force. Electro is dual to weak -- the electro-weak force. Mesons are dual:- quarks are dual to anti-quarks. Action is dual to reaction -- Sir Isaac Newton (the duality of force). Attraction is dual to repulsion, push is dual to pull -- forces are dual. If forces are dual then energy must be dual:- Energy = force * distance -- simple physics. Thesis (up quark) is dual to anti-thesis (down quark) synthesizes another up quark (proton) -- the time independent Hegelian dialectic. The 3rd quark in a proton is synthesized by conserving the duality or correlation of the first two quarks (up & dowm). The quark triality of a proton is actually duality -- the synthesis of the 3rd quark is a by-product of conserving duality. Energy is duality, duality is energy. Quarks are made out of energy hence duality! Duality creates reality. "Always two there are" -- Yoda. Atomic forces are dual -- attraction, repulsion, convergent is dual to divergent.
Vor 14 TageJack O'Donnell
This was so well written and explained that I walked away understanding way more on this topic than I should have
Vor 9 Tageeuisa cous
I appreciate the information in this excellent video by this great presenter... not very far. Too complex for my inferior brain. (Not that I'm stupid, just too much of a struggle).
Vor 9 TageMeme hi
I'm so excited about what this channel is diving into.
Vor 5 TageOne Two
What would happen if you measured spin of 2 coupled electrons at the exact same time, essentially not giving the universe the time for the two electrons to "communicate" to each other what the spin of second electron should be? Also, lets imagine that we have a mechanism that can report if the spins of 2 electrons are the same without determining what it actually is. Now take 2 pairs of tangled electrons A and A' and B and B'. Now measure if A and B are the same or not, without measuring the actual direction. Then measure if A' and B' are the same or not. if spins are predetermined the 2 measurements should have the same result.
Vor 14 TageKayODave
Haven’t watched yet but FINALLY! I’ve been looking forward to Space Time covering QCD for years!
Vor 15 TageFerarn McÆternitum
Does this prove that virtual particles are essentially just another type of quasi-particle, but in a different setting?
Vor 15 TageScipio Africanus
Making predictions is very difficult, especially when it concerns the future. Nils Bohr. Nobel laureate, philosopher, noted wit and father of Quantum physics.
Vor 7 TageJakub Mintal
Monte Carlo always seems like magic. I mean, they always say "learn the theory first" but that method is more like "just give it a try" (or few tries). And it works!
Vor 15 TageCees Timmerman
Suppose a big black box you can grab items from. To be certain about its contents, you'd need to inspect every single item. If you don't have time for that, you can just pick 10 or so at random (to avoid bias and hence the casino name) and make an educated guess.
Vor 12 Tagebodoti qwiu
Dear PBS team, Please, keep the more of QED/QCD/QFD/Neutrino/Higgs Physics coming. Thanks!
Vor 7 TageStephanie Herman
If this model works with 4 dimensions, could that be prove that there are no tiny small dimensions needed for string theory?
Vor 4 Tageevilotis01
yayyyy i've always found QCD fascinating and i'm super glad you're looking at it
Vor 15 TageINGIE32
Wow, I finally understand "what" virtual particles really are.
Vor 15 TageTonyface
Love that we've finally got a decent vid on QCD! Another way to think about the Shrodinger's Glove from the comment replies: You put two gloves in the box, but instead of opening a box and seeing left or right handed, you measure to see whether the glove is left/right handed, or up/down handed, or front/back handed, and whichever you measure, the other will be the opposite if measured along the same axis.
Vor 14 TageGabriel Fair
I would love all these videos organized into a playlist ordered by increasing complicity so new ppl can get started
Vor 14 TageToughen Up, Fluffy
“It was just a colour out of space—a frightful messenger from unformed realms of infinity beyond all Nature as we know it; from realms whose mere existence stuns the brain and numbs us with the black extra-cosmic gulfs it throws open before our frenzied eyes.”—HP Loveraft, _The Colour Out of Space_
Vor 15 TageThalia Nero
Oh gosh, Lovecraft would have definitely wrote a horror story about QCD
Vor 15 TageCorbin Simpson
I know that your description of lattice QCD is introductory, but I wonder whether we could study observable properties which don't cleanly converge as we increase the density of the lattice. I would imagine using cohomology and sheaf-driven sensor analysis, but I'm sure that there are non-category-theoretic approaches being used already today.
Vor 13 TageFriedel Majoor
Hi, I'm a long time viewer of PBS space time and it is an amazing show. How is Gabe doing these days. It's been a long time since we've seen him. Understandably recovering from a jedi lightsaber dual takes a while. But It would be an awesome episode seeing Gabe pop up like a virtual particle in spacetime
Vor 15 TageJason Clouse
This episode made me think of him for some reason. Yes, it would be good to see him again.
Vor 15 TageSantee Black
Great job!!. I was thinking if spacetime could cover just how exactly we are made of stars! Could be a cool video!
Vor 15 TageMichael Sommers
It's simply that every atom heavier than helium is formed in stars, or in supernovas, or neutron star collisions.
Vor 15 TageAdam Wulf
I’m very curious what happens with the lattice spacing is the plank length, do we get exact results for measurements, or does it break down at that scale? Matt mentioned that space is filled with infinite points, but the plank length would give us a lower bound for the lattice spacing I think, though maybe that’s small enough to still be effectively infinite
Vor 14 TageDave Goldthorpe
From looking at this video presentation, I'm assuming that the lattice spacing is just a mathematatical modelling tool and does not represent anything real. For example, we can estimate the area of a circle by diving a circle into n sectors, use a triangle to approximate the area of each sector, then add the areas of these triangles together. As n increases to infinity, the error of the estimate tends to zero, so we take this estimate to be accurate. As n increases to infinity the size of these sectors will go below the Plank length but it doesn't change our calculation. The sectors and triangles don't actually exist.
Vor 14 TageLoren H
Shout out to protons, the most under rated particles in the universe!
Vor 15 Tage