What is quantum field theory and why is it incomplete?

https://www.quantamagazine.org/what-is-quantum-field-theory-and-why-is-it-incomplete-20220810/

by digital55 • 4 years ago

106 117 4 years ago

andrew_eu2• 4 years ago

Probably the highest point in my physics "career" was when my advisor recommended Quantum Field Theory for the Gifted Amateur [0] to me. It was after I had basically decided to abandon hope at academia and become an engineer, but I was just barely past the threshold of being able to understand the contents. I worked through the book solo and really greatly enjoyed it; highly visual and well paced. I'd recommend it to any undergrad+ who has made it past bra-kets and wants to see how far the rabbit hole goes.

[0] https://www.goodreads.com/book/show/18781406-quantum-field-t...

m_a_g• 4 years ago

My undergrad is in Computer Science and Engineering, but I would love to read and understand this book. Any recommendations for what to know beforehand? Some prerequisite books or subjects, maybe?

andrew_eu2• 4 years ago

It's been a while now since I've picked it up, but I think the main content it assumes your comfortable with is on the order of a semester of Quantum Mechanics. Otherwise, it definitely uses quite a few tricks in calculus (e.g. integrating probability amplitudes, variational calculus, and likely some higher dimensional stuff). The later chapters probably get even more exotic, but the book prepares the reader pretty well I think.

For book recommendations, the ones that come to the top of my mind are:

- Griffiths' Quantum Mechanics [0]. It's become a pretty standard undergrad QM text, and in my experience was very approachable.

- Div, Grad, Curl, and all that by Schehey [1]. I don't remember how much into vector calculus the QFT book got, but this one turned the tide of my undergrad personally. For ~120 pages it gave me a better intuition with 3D calculus than any other resource.

- Something that covers calculus of variations, Euler-Legrange equation, etc. I first covered this in Classical Mechanics but don't remember the textbook. The Feynman Lectures of Physics [2] probably covers it, but I don't know for certain. Incidentally, Feynman is all over QFT, so his undergrad materials are probably excellent prep materials.

I don't remember whether the book introduces bra-kets (Dirac notation) or assumes them, and I don't remember if Griffiths uses it at all. I first saw this notation in General Relativity, with Spacetime and Geometry [3], but I think there are definitely better materials that can explain the notation better.

I'm pretty sure all of these books, and plenty more on these topics, should be widely (or freely) available. Good luck :)

[0] https://www.goodreads.com/book/show/153908.Introduction_to_Q...

[1] https://www.goodreads.com/book/show/703104.Div_Grad_Curl_and...

[2] https://www.goodreads.com/book/show/5546.The_Feynman_Lecture...

[3] https://www.goodreads.com/book/show/259680.Spacetime_and_Geo...

Edit: newlines always get me

mhh__• 4 years ago

If you have a talent for manipulating symbols before really understanding them, only a little bit of quantum mechanics.

Realistically an undergraduate physics education

sigmoid10• 4 years ago

Another great book at that level is Student friendly Quantum Field Theory by Klauber. Especially if you struggle with the incomplete math treatments in standard books like Peskin & Schroeder, where the first chapter basically assumes you already know all the weird complex contour integrals that you usually only encounter in QFT. If Klauber says "from this easily follows ..." then you can expect to understand it even if you're not yet an expert. Ofc that comes with less depth in total, but there's no point in talking about renormalization if you haven't understood field quantization.

daniel-cussen2• 4 years ago

I second the sentiment, that working through a book is the absolute best education. I worked through many.

I copied down all the code in ANSI Common Lisp and answered all the questions in the book explicitly, wrote down my answers and everything. Except for the object-oriented part which the author says not to read. Says it was a requirement for the book in the 90s, he didn't want to include it. I didn't read it on his advice. That book also includes cryptic objections to political correctness, in a simulation you're supposed to run about a contest in an alien race that always ends in a tie or near-tie. The simulations the book proposes reveal equality of outcome in these contests is due to manipulation. You don't get even representation from fair contests. Whereas university admissions in general do end up with a lot of "underrepresented minorities"--and this Daniel Cussen saying that, my torturer said that I'm a "minority of one"--but the ties and near-ties are because of fixing. The game is rigged.

But a book! That is an education! Then I attended Stanford and it was like, what is this shit? I gotta cheat to pass, the fuck? If you say I can't cheat and then you say I can cheat in a specific manner, eg asking a TA for all the answers, what do I do? My Chilean logic says, if they say you can't and say you can, you can't. Same rules as Magic: the Gathering, negative prevails over positive--and it's a matter of integrity, there's reasoning for this, both in Chile and in Magic, it makes perfect sense to me. Basically it's conservative. Not "negative" in the pejorative sense.

Hell, weight loss is negative, is it bad to lose fat? Fatness is positive, bigger number on the scale. Why is negativity worse? Further I'm in the Southern Hemisphere, the negative hemisphere, there's a physical definition for its negativity. Is this wrong? Does negative magnetism translate to negative morality, which I truly do recognize as wrong? Manicheanism, yes, right is positive wrong is negative. I basically buy that. But with all physics? And of course technically positive current is incorrectly defined, it should be the other way around, electrons are what moves so they should be positive.

Stanford I guess thinks can prevails over can't, should go over that in orientation. There shouldn't be contradictions like this in the first place, though. Admitted students have to be able to pass all courses without any cheating. I guess that's where I fucked up. Getting myself lobotomized, guess I'm no longer Stanford material despite having already been admitted.

No longer have the brains. Literally no longer having the brains. That's literally it.

But Stanford refused to protect me from lobotomy, I kept telling them how much harm I would go through, crying in my lynching meeting on February 6 2009, begging for a trial and always getting denied, going to every office I could, writing emails nobody gave any replies in writing to, telling my whole dorm I was getting lynched (apparently nobody does this). Stadmin only pushed me further into that system, jammed me further into the meat grinder. Meat grinder. Think of it like a blender, what happens to meat that goes in? Does it retain its shape? No it gets diced right?

Just watched gloatingly as I got put through the system. Watched with relish. Young white man getting lynched. That is the consummation of the Civil Rights Movement, young white man getting lynched. It's not as platonic, abstract and noble as it pretends to be. White is negative. Young white man getting lynched? Justice.

But back to my point: the book. It used to be, before universities monopolized annointing the intelligent as such, that it wasn't about going to the right schools. It was about being well-read. Universities didn't exist before AD 1000, University of Bologna. And even then it started slow.

Books are better.

garbanz0• 4 years ago

Any book recommendations for someone who almost failed physics in college but wants to understand QM at a high level?

dQw4w9WgXcQ• 4 years ago

https://www.amazon.com/dp/1492656224

https://www.youtube.com/c/pbsspacetime

eurasiantiger6• 4 years ago

To paraphrase Tesla, fundamental answers will elude us until we decide to abandon the particle model.

peteradio• 4 years ago

Was this said prior to the formulation of modern QFT? I imagine Tesla would agree that QFT is the thing to be done to add waviness to the particular questions we humans like to ask, although he didn't exactly believe in the concept of electron, maybe he would see its formulation in QFT and say yes?

eurasiantiger6• 4 years ago

I think Tesla would still object to seeing quantum phenomena through such a classical lens. It is very much ”not seeing the forest for the trees”.

In fact, Tesla might even object to the usage of the word ”quantum”, since it implies that same top-down view. Tesla would start from the field(s) and let whatever phenomena emerge from that, quantized or not.

fsh2• 4 years ago

Tesla may have been a capable engineer in his early years (before turning into a crackpot and/or fraud). However, his understanding of modern physics appears to have been extremely poor. He certainly has not contributed anything significant to the field.

kloch2• 4 years ago

I suspect it's an approximation of much lower level deterministic processes that we don't understand yet.

One serious issue is renormalization, a crude mathematical hack that nobody likes but has turned out to be a very useful workaround to our limited knowledge.

tines2• 4 years ago

Pretty sure it's been proven that no deterministic theory can reproduce all the predictions of quantum mechanics. That's the essence of Bell's theorem isn't it?

drunkpotato• 4 years ago

The two explanations or interpretations I’ve come across that recover determinism are many worlds interpretation and superdeterminism. I don’t think either are testable with current technology so it’s not a very satisfying or experimentally useful explanation. At least not yet.

kloch2• 4 years ago

From wikipedia:

Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles were able to interact instantaneously no matter how widely the two particles are separated.

It's true that with our current theories, instantaneous action at a distance does not seem possible. Yet quantum experiments (wave function collapse over large distances) consistently suggest this might be possible at macro (non-quantum) scales. I think our knowledge is incomplete on this topic.

Gravity is another area where I don't think non-local effects have been fully ruled out. Gravitational waves (energy emitted/thrown off by certain mass/momentum configurations) have been proven to travel at or near the speed of light, but the propagation speed of the first order gravitational effects an open question. This is an area I would love to see more experimentation done. To simultaneously measure the gravitational and optical positions of the Moon or Sun for example.

https://en.wikipedia.org/wiki/Speed_of_gravity

immmmmm3• 4 years ago

Gerard 't Hooft would disagree

https://arxiv.org/abs/quant-ph/0212095

effie9• 4 years ago

No. Bell's theorem states that local hidden variable theory obeys Bell's inequalities. Quantum theory models and some experiments with light violate those inequalities. At best, we can conclude that any deterministic theory supplanting quantum theory can't be Bell-local, or that it violates some other assumption of Bell's theorem (e.g. independence of actions at two separated experimental sites).

auntienomen• 4 years ago

Renormalization hasn't been a conceptual problem since Ken Wilson's work in the 1970s. Before that, it looked like a mathematical hack (rather like linear algebra without the geometric interpretation) and a lot of physicists who came of age in the postwar period never got over this.

bowsamic15• 4 years ago

I suspect it's an approximation of much lower level deterministic processes that we don't understand yet.

All current evidence heavily leans towards this not being the case

zmgsabst5• 4 years ago

What evidence do you believe shows that?

immmmmm3• 4 years ago

Still the basis of the most precise prediction by a Physics theory:

https://physicstoday.scitation.org/doi/10.1063/PT.3.2223

I'm always amazed by quantum field theories, with a particular taste for the two dimensional ones (as string theorist :))

formerly_proven• 4 years ago

Also the basis of the least precise prediction made by a physics theory: https://en.wikipedia.org/wiki/Cosmological_constant_problem

Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude

immmmmm3• 4 years ago

yes and no. physical theories always have a domain of validity where their prediction make sense and QFT and QM do not give an absolute value of energy (density). sure you can do QFT on curved spacetime (Hawking had some success w/ it) but comparing the QFT vacuum energy with the cosmological constant is sloppy at best.

but yeah, sure, it doesn't work for that :)

Eupraxias6• 4 years ago

I would love to hear any critical take on David Tong's excellent video here: https://www.youtube.com/watch?v=zNVQfWC_evg "Quantum Fields: The Real Building Blocks of the Universe"

I'm interested to talk to others who want to think about QFT past the maths. I had my own stab at making sense of related ontological implications here: http://www.katabane.com/mt/ontology.html#back8

effie9• 4 years ago

I really detest this kind of peppy proselytizing lecture. It is about mainstream science, but the poor form and lack of respect for the listener is horrible.

He is wooing the public a lot with a priest-like confidence on what the world is made of, look how amazing our 12 digit results are, everything is fields, even particles are really fields, even your bodies are fields, we can't really calculate this, it's so hard, but trust us. Matter, universe, big-bang, black holes, Faraday, Maxwell, Einstein, big scary equation, the single greatest equation, bombard and overwhelm the listeners with lots of astonishing statements and make them believe that we are really smart.

No experimental rationale for the reality of quantum fields; no mention of the opposing viewpoints of experts such as Schwinger (his source theory), also of large part of particle physics experimenters who tend to think that particles like electrons are real and quantum fields are really just tools that exist in our brains and on paper to predict what happens to these particles.

I am afraid this is not teaching people anything of value about physics. It's more about what this group of physicists (high energy theorists) are occupying themselves with.

bowsamic15• 4 years ago

I do hate this stuff, same with Sabine and Carlos, the latter giving me a huge number of lay people that religiously believe in MWI.

However, I would say that most physicists do believe that quantum fields are the most basic building block of our world, so this isn’t some kind of pop science mess or even a mischaracterisation. Could it be the religion of physicists? Maybe. But it is a widespread one among experts.

Physicists generally consider their models to be real rather than just a mental idea that produces the correct results. This kind of thing was controversial in quantum theory until Bells theorem proved that quantum mechanics says things about reality itself (that it is either non local or non deterministic) and PBR theorem proved that the wavefunction is in some sense ontologically real. Now it is less controversial to say that quantum fields are real and the building block of reality

kbr-4• 4 years ago

There is a mathematical theorem that forbids you from writing down a discrete version of certain quantum field theories.
(...)
You know, if you take this theorem at face value, it’s telling us we’re not living in the Matrix. The way you simulate anything on a computer is by first discretizing it and then simulating. And yet there’s a fundamental obstacle seemingly to discretizing the laws of physics as we know it. So we can’t simulate the laws of physics, but it means no one else can either. So if you really buy this theorem, then we’re not living in the Matrix.

I don't buy this reasoning.

I can encode the continuous function f(x) = x^2 on a computer. Then I can calculate this function for any number up to any digit, if I allocate enough memory.

I don't need to allocate a discrete domain up-front and then stick to it at all times. I can increase and decrease the accuracy as needed.

In a similar fashion I could simulate a continuous universe encoded with continuous operators. I could simulate it on a discrete lattice with certain precision as long as nobody inside the simulation builds equipment that can measure things "in-between" the lattice points. And when somebody does, at that moment, I can simply pause the simulation, calculate the values of my operators using a locally-denser lattice, then unpause. The observer with their equipment wouldn't notice anything because the simulation was paused, they would just get the correct measurement.

blueprint2• 4 years ago

What theorem is he talking about though?

kbr-4• 4 years ago

The theorem is called the Nielsen-Ninomiya theorem. Among the class of quantum field theories that you cannot discretize is the one that describes our universe, the Standard Model.

mxkopy2• 4 years ago

I don't think continuous and discrete-with-arbitrary-precision are the same thing, maybe even to the degree where we can't use the latter as a universal approximation for the former. I think there are some cases where approximating a continuous function on a lattice produces an error that isn't a function of precision (I think the Weierstrass function is one).

yarg• 4 years ago

It really comes down not to the question of equivalency, but distinguishability.

If the universe is lazy evaluating things discretely down to scales well below that of observation, there's probably no damned way to tell the difference.

blablabla123• 4 years ago

It's the current state of the art anyway. But also it's worth mentioning it's more complex than just a function x^2. When looking at a Feynman Path Integral you integrate an Operator (mapping a function to a function) over a an uncountable domain of functions. The other approach which is used to calculate probabilities goes with an approximation that cannot be used for simulations though. All this is not mathematically bullet-proof as Mechanics also speaking about Wightman axioms. (And even in Mechanics it's possible to construct infinities)

atty3• 4 years ago

The point is that it can’t be simulated on any lattice of any density. It doesn’t matter how fine the lattice is compared to the sensitivity of the measurement. For your case you showed, it would be like if x^2 simply didn’t exist on a lattice, and couldn’t be calculated by a computer no matter how much memory you threw at the problem.

Certain parts of QFT work fine in lattice based calculations (lattice-QCD, for instance, where it’s simulated on a certain lattice scale, and then extrapolated to the continuous limit), and some seemingly don’t work at all.

kbr-4• 4 years ago

The point is that it can’t be simulated on any lattice of any density. It doesn’t matter how fine the lattice is compared to the sensitivity of the measurement.

It feels like you want to do sth like: first discretize (choose a lattice), then simulate (do calculations on this lattice).

I want to do the opposite: first simulate (do calculations on a continuous domain), then discretize (restrict my results to a lattice).

For your case you showed, it would be like if x^2 simply didn’t exist on a lattice, and couldn’t be calculated by a computer no matter how much memory you threw at the problem.

So the functions we're talking about do exist on continuous domains - but they don't have a corresponding definition on a lattice?

Couldn't we embed a lattice in the continuous domain, then restrict the function along the embedding, thus getting a definition on a lattice?

Unless it's not possible to embed the lattice in a continuous domain - then my reasoning breaks.

(note: I know nothing about physics, I'm a programmer with math education, talk to me like I'm an idiot)

criddell• 4 years ago

Do analog computers have the same fundamental limitations?

machina_ex_deus• 4 years ago

The theorem mentioned is Nielsen-Ninomiya. A good analogy is aliasing in signal processing. It's not that you can't define a theory and compute it. It's that under certain conditions, you get more than one electron, you will get electrons that behave like electron does but they are different, and they are an artifact of the discretization.

This is similar to aliasing in signal processing. A high frequency signal behaving like low frequency. And there are solutions to this problem, but it's hard to reason which one is the "right" solution.

hyuijk• 4 years ago

But who says the computer running the simulation must be exact?

We are using a lot of low precision computations in graphics, neural networks, ....

Pi also can't be calculated exactly to infinite precision, yet that doesn't stop us to compute circles and so on.

x86x87• 4 years ago

You cannot have arbitrary small precision past a certain point no matter how much memory you allocate.

You will run into this limit and it's a physical hard limit. Lookup why it's called quantum (mechanics, physics, field theory, etc).

Before you simulate an entire universe try accurately simulating one atom. Let me know how it goes (spoiler alert: the computing power needed to do this is beyond the computing power we have today)

jmyeet• 4 years ago

This transcript doesn't mention it specifically but the most accurate prediction they're referring to is likely the anonalous magnetic dipole moment of an electron [1] where theory matches experimental value to at least 10 significant digits. The article talks about 12 decimal places so maybe they're referring to somethign else?

At the other end of the spectrum is the s-called vacuum catastrophe [2] where the predicted and actual values for the energy density of a vacuum diverge by as many as 120 orders of magnitude.

As for the incompleteness of QFT, this is well beyond my knowledge. I really wish this were an article instead of a transcript though. Transcripts are such poor means of conveying information.

[1] https://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_mome...

[2] https://en.wikipedia.org/wiki/Cosmological_constant_problem

analog31• 4 years ago

One sleight of hand is to write down g instead of g-2, in which case you pick up a couple more digits but haven't added any useful information because the value of 2 is already known.

photochemsyn• 4 years ago

There's a very good book on quantum physics, published in 1978, by PCW Davies, called 'The Forces of Nature', which discusses most of this in nice detail. One gets the sense that not a whole lot of new physical theories have been confirmed since this book was published.

For example, the renormalization problem:

'Fortunately the problem of infinite self-energy can be overcome... Manipulating infinte quantities requires some mathematical care, but it can be proved that all <observable> quantities are finite. The technique, developed in the 1930s and 1940s, of absorbing infinities into unobservable 'bare' quantities to get a finite answer, is called renormalization. It may appear like a trick, and nobody pretends that it is completely satisfactory, but without renormalization the predictive power of quantum electrodynamics would disintegrate. With it, the answers obtained have the legendary accuracy already described.'

According to this book, the problems with renormalization are much more severe with weak interactions:

'The renormalizability of QED can be traced directly to the masslessness of the photon. Like all massless particles that spin, it can direct its spin either parallel or antiparallel to its direction of motion, but not in between as well. In contrast the massive W can align its spin in three different directions, for example, parallel, antiparallel and perpendicular to its motion. This seemingly innocuous property is the cause of all the difficulty, because it turns out it is the W particles with the perpendicular spin directions that prevent the infinities from being renormalized away."
"These observations suggest that if the W particle were massless, it might be possible to construct a unified renormalizable theory of weak and electromagnetic interactions in which the photon and W are combined, like the hadrons, into a single family."

Notably there's no mention of the Higgs boson in this book, which is nevertheless remarkable in how it covers the background of almost every physics story I've come across for years. However, is this basically the entry point to why the Higgs boson is important? For example:

https://en.wikipedia.org/wiki/Electroweak_interaction

"In the Standard Model, the W± and Z0 bosons, and the photon, are produced through the spontaneous symmetry breaking of the electroweak symmetry SU(2) × U(1)Y to U(1)em, effected by the Higgs mechanism (see also Higgs boson), an elaborate quantum field theoretic phenomenon that "spontaneously" alters the realization of the symmetry and rearranges degrees of freedom."

nobodyandproud• 4 years ago

This Q&A was extremely understandable.

I really enjoyed how he broke down why the Standard Model—as far as we can tell—cannot be made mathematically rigorous.

nyc111• 4 years ago

"And cells, in turn, are made of molecules and molecules are made of atoms. Dig even deeper and pretty soon you’ll find yourself at the level of electrons and quarks. These are the particles that have traditionally been considered to be the end of the line, the fundamental building blocks of matter."

To me, the so-called "the end of the line" is a philosophical question not a physics question. For the simple reason that, we can never know, if something is really indivisible, or if we are unable to divide it because of our insufficient technology. We can never know this. The story of physics makes this clear. Each generation of physicists with new techology available to them take pride in showing that the previous generetion was lying, and that it is their atoms which are the real "end of the road". Then comes the next generation with a better technology...

quandumbspiels• 4 years ago

There are two main reasons why the theory is “incomplete”

1> human perception is not often considered; in many ways humans are like dogs trying to see in full color depth. Humans are “colorblind” to types of information.

2> structure of the flow is not often considered: the assumption is a flow through some X-dimensional space: what if this flow is defined according to a chaotic map: not just a fractal but a subset of other rules which create chaotic flows across multiple dimensions in time which collapse /retroactively/ along a chaotic Riemann geometry

Quantum more like quant dumb

bowsamic15• 4 years ago

Then, propose a theory that reproduces QFT as well as the missing parts

syspec• 4 years ago

Accompanying podcast: https://pca.st/episode/af3ea556-c30b-4784-a901-404f7b8c03e5

What is quantum field theory and why is it incomplete?

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