The Bridge Between Math and Quantum Field Theory
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- čas přidán 23. 06. 2021
- Even in an incomplete state, quantum field theory is the most successful physical theory ever discovered. Nathan Seiberg, one of its leading architects, reveals where math and QFT converge. Read more at Quanta: www.quantamagazine.org/nathan...
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I like how the producer told him to play with Euler's disk even though it has nothing to do with the topic at hand.
Haha was laughing at this too. Plus all the other cuts to him "doing maths" 🤣
Can someone tell me what it means to be a 'sweeping scientific theory'? It is included in the beginning text alongside the out of tune violin.
@@JM-ty6uq It probably means most widely adopted, in this context
@@JM-ty6uq That means it’s news not related to current silly political news. So sweeping
They be like: it's pretty. Let's film.
Quanta Magazine is such a pleasure. I don't think anyone does a better job of bringing vanguard scientific issues to regular people, so we can share in the thrill of the hunt for new discoveries.
finally some truth
Quanta!
Quanta!
Read all about it!!
World science festival is a gem
Even in incomplete stage even if we are like chimpanzees trying to find how laptop works
I have a background in pure mathematics, and I was surprised to learn how strangely QFT is taught in universities (in physics departments). The fundamental setup would often be to start with creation/annihilation operators and delta functions fly around everywhere, but what the underlying Hilbert space is was never mentioned in such a first course. It was a.. refreshing departure from the expository style in mathematics.
I did learn however that physicists' approaches have a distinct advantage of adeptly disregarding formalities for conceptual innovations. Not sure if entirely appropriate but the discovery of the Dirac equation as the "squareroot of d'Alambertian" was quite refreshing for me, because Dirac invented an algebraic structure to force a previously nonsensical property to work.
Now the half nonsensical calculus of Feynman amplitude also turned out to be physically very accurate (cf. anomalous electronic dipole) and it's linking to some interesting bits of geometry and number theory (motives and multiple zeta values). The connection would only flourish onward.
I don’t know what you said. But here’s a like for the effort.
@@somanshbudhwar Lmao I was thinking the same thing
@@somanshbudhwar i just liked it so other stupidly smart people can see this
Don't be hoodwinked by the anomalous dipole momenta - Dirac's criticism of the regularization schemes is still as relevant today as it was back in the day, and _that's_ what makes both the physics and the math nonrigorous. RQFT is riddled with conceptual problems that, mysteryously enough, one doesn't find in the second-quantization formulation of nonrelativistic many-body systems - yet nobody is willing to backtrack and do something about them
Theoretical physics is like playing with math we don't have, yet.
What he says at the end reminds me of a Dara O'Briain quote: "Of course science doesn't understand everything. If it did, it would stop."
Science understanding is a wrong use of words
Animals understand, Scientists understand
Science is a PROCESS not a sentient being
@@goyonman9655 Exactly, but a lot of time you'll hear people talking about "what science doesn't know" as if they think it makes them smarter than science.
@@sasukesarutobi3862
When in fact they're dumb because science can't know anything
Humans do
This is my favourite channel. I especially like it when you explain everything so nicely. I wish you a lot of success with the channel. Professionalism is the best quality of Quanta magazine!
Plus No Ads
No doubt , I always recommend this magazine to my friends.
When Newton and Leibniz invented Infinitesimal calculus, it wasn't very rigorous. It took nearly two centuries for the modern form of analysis to be developed.
Rigour is necessary for mature theories, but as an introduction these technicalities bog down intuition building. Real analysis, and by extension, calculus, is so formal that you would have never imagined many of the basic techniques it teaches grew out of a desire measure plane curves.
Fascinating short clip I thoroughly enjoyed this discussion
AS ALWAYS EXPECTED, THIS CHANNEL BRINGS THE INTERESTING TOPICS BEFORE US ❤❤
CANNOT AGREE MORE
I actually read the article before the video.
It came up on my google feeds.
It's much deeper than the video
Basically this video contains nothing.
Reading Graham Farmelo's _The Universe Speaks In Numbers_ about this sort of math-physics junction. Great insights for the curious layman.
I am in my 30s and I am going to dust off the precalculus book and work my way back up. I think I can contribute to this bridge. I know some humans want to feel better than, smarter than, or look down on others. Competition. The problem is that only gets one so far before failing. The truth is I think everyone can do math. The problem is they haven't learned the universal language of math to express themselves due to the bad/non-existent ways they were taught. There are also other reasons outside the school as to why they did not build the connection to it. Unfortunately, instead of asking for help, they don't because they don't want to be laughed at for asking questions that everyone around them knows. They don't want to feel stupid or feel like they are burden wasting other's time asking the question. It is those flaw in the human that is stopping something amazing happening. The moment one thinks everybody can't do what they do, it is the moment they've lost the ability to make miracles happen in any field.
I've learned that when people tell me things contrary to what I feel is correct, I ask them to walk me through it like a software program. Then I can learn their point of view and see exactly why they disagree with me. I stopped making assumptions. When the source is right in front of me, I might as well ask for clarification.
I have one goal in life. Making a way to teach people how to learn anything. It's strange because on my quest, even though it's been ages since I've opened a math book after my lack luster college career, I am really understanding all of the math, computer science, physics, painting, drawing, etc. in a different way. I don't know what it is. I realize I didn't have a grasp of life when I was in college. I was just trying to follow the flow. Now that I've gotten out of the flow and went down a path nobody/few went, things are starting to look far different now.
What is this intro song?? SO good
That's why I want a math major girlfriend.
Damn, wrong gender. Sorry, I'm not going to switch mine.
That's probably a good Idea.
@kwokshsee no, lying is inefficient
@kwokshsee just tell her that it is undefined undefined at that point (of time)
Awesome video. Does anyone have the name of the intro song?
Want to know as well
Also want to know
Me too
I think that the fields are the key to understand both the the quantum theory, relativity and particles' behavior.
Hey Quanta Team ,it would be great if you make some videos of recent advancememt in langlands program, Representation theory, Non commutative Algebra ,Number theory etc.
We have one of the above in the works!
Hilbert: "We must know, we will know".
Gödel: "Not necessarily".
Wow, getting Nathan Seiberg on this channel. This is the finest internet entity to get math & physics to the general public at a sophisticated level.
What’s that opening piece of music?
What's the music at the beginning?
What is the math behind the “field “?
If he were living, Shaekesper would say :
to search and or not to search, that is just matter....
Inspiring !! 😀
The way physics relates to other matters to describe reality is beautiful. It's what makes physics the king of all knowledge.
Amazing. To be honest Physics is the right mix of math, reality, deduction, inference, fun and torture. It's formidable yet awe inspiring. And I am excited to spend my life exploring it.
@@existenceisillusion6528 I've read his Book Mathematical Universe. Tbh I cannot comprehend what it means for reality to be mathematical. But I am open to ideas.
@@existenceisillusion6528 oh thanks. I hope to comprehend. I am taking QM course rn. It's fun learning.
@@existenceisillusion6528 Well it's the second one. There will be one more but it's optional. And thanks for your wishes. I will keep what you said in my mind.
I disagree... Pure mathematics is the fundamental framework for humans who wish to appeal to "truth." Without it, nothing makes sense.
Woah very interesting topics I love math 🧮
Genuine question (though I can't promise I'd be clever enough to understand the answer). Can questions like "why is there something as opposed to nothing" be addressed in meaningful way by mathematics (as applied to physics by the theorists). I mean, can concepts like 'something' and 'nothing' be expressed mathematically, and then a path charted leading from one to the other? Or are such questions entirely the realm of philosophy?
I’m also curious
Wouldn’t nothing be 0 and something be >0
Short answer: yes, it's in the realm of metaphysics. Don't be hornswoggled by Krauss and Co., when they claim that a quantum vacuum is "nothing"
I would agree that that is a question of metaphysics (which is in philosophy), and can’t really be answered by math by itself,
but I would add that one can do math to philosophy and use math in philosophy.
Most attempts to use surprising math results in philosophy go wrong and don’t use the math result as the result it actually is, but, that doesn’t mean none of it is applicable.
One can interpret the argument for there being an uncaused cause as being an application of the fact that a directed graph which has at least one vertex, either has a vertex with indegree 0, has a cycle, or has an infinite-in-the-backwards-direction path, combined with taking “is a/the cause of” to define the edges of a digraph, and then arguing that this graph is acyclic, and has no backwards-infinite path.
The math involved in this argument is not particularly sophisticated, but it is math. I think there should be ways to apply some more sophisticated math to philosophical questions, though, these must always rely on some bit of philosophical argument to make the connection between the philosophical question and the mathematical theorem.
But, I suspect this connective tissue can sometimes be fairly small.
And, when one has a rigorous philosophical argument, one can (generally) describe mathematically the structure of the premises and inference rules used in the argument,
and then one can abstract that, taking only the form of the argument, stripped of at least part of the semantics of the premises, and see if arguments of the same form apply to other things.
Here’s an idea: the mathematical concept of a relation is well understood, but perhaps one might argue that it originated as more a philosophical concept? (Well, I guess before that it was an ordinary concept? Or maybe it went from ordinary to math. Idk the history. Pretending it was via philosophy.)
There is a concept of “insofar as”.
Perhaps it could be fruitful for someone to come up with a variety of potential formalizations of the idea of “x insofar as y”, and analyze these mathematically?
Maybe some interesting logics could come out of it?
@@drdca8263 :D I think that's a no, but yes, but only possibly. ;). But (and this may be a completely different thing or only mildly connected) take a statement like "the shortest distance between two points is a straight line." Can it be proven, or is it just one of the founding assumptions of Euclidean geometry that like it or not we have to accept purely on the basis of, well, by definition of the words we can see that it is 'true'?
I couldn't find evidence for the assertion that Nathan Seiberg was a leading architect of quantum field theory in the Wikipedia article about him. It mentions some things about string theory and supersymmetry.
You couldn't find it because it's false.
@@janouglaeser8049 what do you mean?
@@Zero-ok9ze I mean that the claim that Seiberg was a leading architect of QFT is bs.
So what's the bridge?
I love maths 🙂 thank you sir 🙏
I must say i'm glad to see that even a genius like him bites his pen cover during thought process
What does more "rigorous" mean?
People always say that word, but they don't explain it means in the context for physics
Rigorous means structurally built using axioms which are more like definitions and using those definitions to create lemmas which in turn are used to prove theorems
From my understanding (and don't take me on my word since I'm not really qualified to answer this properly): If you have a result, you can backtrack how you got there with theorems and "rules" that we take as fundamentally true. This typically relies on formal mathematics and on physics ideas/laws/etc in the past that have also been rigorously proven.
So a rigorous proof is to basically prove something without a shadow of a doubt. But to be fair, in order to prove something as true, you need things that are "given", or "fundamental truths" that can't be disproven. For example, all of Euclidean geometry is founded on some axioms (given, fundamental truths). But once you get past that, and figure out what is "fundamentally true", then building on from there with rigor allows you to create mathematical proofs.
Again, don't take me on my word for it. This is just what I think I understand, and I'm not studying high levels of math or physics or anything.
The _more_ is the interesting aspect since it makes something that is either true or false somehow have values in-between. _More rigorous_ is like _more positive_ or _less pregnant_.
Why is that fundamental structure(in sense of particle physics) mathematically intelligible? Is matter made out of matter ?
I believe causality is not completely understood.
It's all fun and interesting till you research and learn,
It's a nightmare when you're examined on it,💀
Hoping I pass this dreaded semester
"Seiberg sees the fact that no one has written a standard textbook explaining quantum field theory (despite attempts by Seiberg himself) as a sign that the discipline is not yet fully understood."
Then why are like 85% of my QFT books following the same pattern? Ever heard of Peskin and Schroeder? :)
P&S is good, but they use a _lot_ of heuristics that put me off; Greiner's is slightly better, but still...
Math is limited in that area,,,what is that bridge by the way?
Has anyone noticed that nothing is actually said here?
The bridge between math and qft is rhythm
nice !
He just spun a nobel prize medal
Nice catch!
'***' WRONG TITLE (should be): "MATH = THE BRIDGE BETWEEN REALITY AND QFT"
QFT is Universal Truth according to DMT.
"Math and physics [are] this one intellectual structure that all of us would like to understand. And one day we'll understand that intellectual structure."
Fascinating thought right there, flirting with philosophy.
I love mathematics and physics
I really appreciate Quanta's articles which are in depth but frankly the videos are a bit disappointing. I mean it's great to listen to such smart people talking about what interests them, but I think the video could go in a bit depth to explain the subject matter too.
At the end of the video, I just remember a scientist talking without learning anything about Quantum Field theory.
I appreciate anything that is outside our regular 3 space dimensions with respect to time. I am truly sorry.
Please make a video on dr kumar eswaran as he proved the 161 year old mathematical mystery of reinmann hypothesis
Quantum field theory - can explain every phenomenon of the universe, but can't explain what a field is, if it's just a math trick, or it has physical existence and if it has physical existence then what does that means for the real and physical world.
The same is true for energy.
@@danieltrump9110 Nah. Noether's theorem rigorously defines energy.
Nah, everything in science explains away energy in terms of other things but it never explains WHAT energy is in itself. If you can enlighten me that would be great.
@@danieltrump9110 This is my 2nd try. I hope you'll like it, if you're interested.
By Noether's thoerem, Energy is an outcome of Time Translation Invariance. What does this means? Very roughly, time translation invariance means that things will look the same with respect to time. Now right here you'll say that things don't look the same, change is the ultimate truth etc. That's right, and this is the essence of energy. Things as a whole have to remain the same with respect to time. Because of this, the total amount of change will always add up to a constant quantity.
So roughly speaking, change of energy is basically a measure of "net change" of any system in a process. Energy isn't anything fundamental. It's just an accounting like term we use, to quantify "net change" of any system.
@@aniksamiurrahman6365 you're referring to "things" and "system" in your explanation. What are they if not energy? If they are energy then your explanation doesn't seem to make sense.
And if so, I have to say you're trying to explain away energy in terms of change as if change is some sort of substance the universe is made of.
Please do enlighten me where I'm wrong.
Seiberg-Witten Equation
For people with dyscalcula
who have no chance of
getting better at math,
you can aquire scientific
information by going
into trances like gurus
in ancient India. Of
course you'll never
get a degree in science
but you can become an
artist and just have
science as a hobby.
💗
I love maths and physics ❤. I would love to get into big university to study mathematics rather than becoming no brain millionaire .
The language of the Universe is mathematics. If we ever get a chance to talk with aliens, I think will be through mathematics.
But for me physics is universe 😂
@@ikrishna06 language of physics is maths
Mathematics is the language of science ... we use that language in Physics , Chemsitry and even to sone extent in Biological Sciences to explain the various aspects and events happening around us..and that is what excites me most
It's more accurate to say that *our* language of the Universe is mathematics. And it may be too for any similarly-brained aliens.
We cannot talk to aliens through mathematics but we can talk to universe through it!
Theory of inflation, string theory? You sure you're going to really want to lay claim to that in the long run?
@Imjust Observing Geocentricism with multiples of epicycles has piles of evidence and accurate measurements. You can prove almost anything you like with math when you're allowed to pick and choose from an unlimited amount of parameters. Hmmm, 11 dimensions works beautifully! Why 11 dimensions? Because we need them to make the math work.
@Imjust Observing Inflation is an ad hoc bandage to the big bang model. It is the model equivalent of an epicycle. Epicycles always solve problems. That's the point.
1:06 _"QFT is not mathematically rigorous"_
what does that mean? umh, rigorous in what sense? some examples or analogies?
👁
4 out of 3 people do not understand basic math. Very sad.
Violin music does not make a theory correct. String theory has the same status as astrology. The theory is beautiful but is both contradictory and unprovable. Force caring particles are quantum particles but space isn't quantized. Space can't be quantized. Moreover, gravity isn't a force and it isn't a particle so it can't be quantized either. The video has nothing to do with physics. The video is nothing by physics double talk.
The only reason I agreed with you is because you left exactly 33 comments on this channel; 33 is the magic ancient number. The angelic signs ironically guided me to stop believing in angelic signs altogether. Actual magic... 😢🎉
Kind of a non-video. QFT is not rigorous. This means some statements are not rigorously proved from a set of axioms and logical system. That is all
The problem isn't really axiomatics - is justifying the perturbation theory, the adding up of Feynman diagrams to a convergent series, and stuff like that
@@thstroyur Right but rigorous justification = formal axiomatic proof
@@OMGanger Not really; you seem to be mistaking general mathematical rigor with the specific research area of AQFT
I think Einstein understood better the relationship between mathematics and physics, when he said,… “As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.”
In mathematics, we see patterns and try to explain it using numbers.
As of now science is at an end point. The main problem is the universe is not mathematically consistent.
Why are people chasing quantum anything when the point of the subject is everything is anything. How can you turn everything that can be anything at anytime time into a rigorous application for use or observation?
So true
But when Euler established the continuous creation cause-effect of e-Pi-i Logarithmic Time, superimposed AM-FM Communication in this landscape Perspective containment, these states in Polar-Cartesian self-defining coordination with the zero-infinity field.., roots 1-0 probability of numberness density-intensity, ..the search for ultimate meaning ended.., now the interesting thing is bio-logical re-evolution existence of pure-math combinations and permutations, ..it's Quantum Chemistry wave-packaging configuration and formation in logarithmic spin-spiral condensation of real-time modulation probability. Ie infinite possibilities in a precisely known Mechanism. (Mythologies not welcome)
what "bridge"! Quantum Field *Theory* IS math *Theory* based on math theoretical assumptions erroneously called facts that just happen to give the answer you want
??? QFT has been developed by thousands of physicists since the 1930s. How is this man "one of its architects"? That's a ridiculous label.
Physics and Mathematics are so dependent on each other, they should not be considered separate.
Physics is a bit more practical
So...You're Evil and I'm dumb, where's the good one?
@@lailandadumbmathematician7747 LMAOOOO am i about to witness a legendary mathematical battle?
@@dedopest3305 Maybe 🤫
I don't see how math is dependent on physics at all. Physics is what an omnipotent deity could alter at will. Math is what it couldn't.
Quantum field theory is full of mathematical nonsense. Multiplication of various Schwartz-like distributions and unbounded operators treated as matrices in every possible equation are to much for me.
The miniature iran postsynaptically haunt because city consequently yell times a gorgeous motorboat. actually, kind conga
"Language" do not and cannot explain anything! "Mathematics" is just a description tool for physics ... ! ... just describing, but NOT (!) explaining ... ! ...
Disagree with his last statement. What makes research exiciting is the utility we can derive from research. People dont' really care about information that isn't useful.
String Theory? What's that? Isn't that an old failed theory people wasted time on for 40 years?
no, you must be thinking of something else
That is above my pay grade, but according to Eric Weinstein, yes.
@@lafudge2929 Eric Weinstein is a blatant crank, you can take anything he says with a pinch of salt.
@@twistedsector Yeah, he's such a blatant crank that neither the mathematics nor the physics community can dispute what he's saying.
@@lafudge2929 ...because he refuses to publish anything in a peer-reviewed journal! His "theory" is pandering to media and laymen. Tim Nguyen and others have already shown how his "theory" is full of holes mathematically, it's doomed.
It's all fake. In reality it's just ether.
Math can only describe Nature it can never explain it. That is the real problem with modern-day physics. Its addiction to math is why it is stalled by this dogma. Feynman said it best: Math can create 'scientism', which is the religion of physics today when he said, "if there is something very slightly wrong in our definitions of our theories, then full mathematical rigor may convert these errors into ridiculous conclusions."
What is the alternative? I mean, if you want quantitative predictions.
@@Jehannum2000 Yes, it's the best we have really