Things I’d Like to Know More About

This is an accountability post, of sorts.

As a kid, I wanted to know everything. Eventually, I realized this was a little unrealistic. Doomed to know some things and not others, I picked physics as a kind of triage. Other fields I could learn as an outsider: not well enough to compete with the experts, but enough to at least appreciate what they were doing. After watching a few string theory documentaries, I realized this wasn’t the case for physics: if I was going to ever understand what those string theorists were up to, I would have to go to grad school in string theory.

Over time, this goal lost focus. I’ve become a very specialized creature, an “amplitudeologist”. I didn’t have time or energy for my old questions. In an irony that will surprise no-one, a career as a physicist doesn’t leave much time for curiosity about physics.

One of the great things about this blog is how you guys remind me of those old questions, bringing me out of my overspecialized comfort zone. In that spirit, in this post I’m going to list a few things in physics that I really want to understand better. The idea is to make a public commitment: within a year, I want to understand one of these topics at least well enough to write a decent blog post on it.

Wilsonian Quantum Field Theory:

When you first learn quantum field theory as a physicist, you learn how unsightly infinite results get covered up via an ad-hoc-looking process called renormalization. Eventually you learn a more modern perspective, that these infinite results show up because we’re ignorant of the complete theory at high energies. You learn that you can think of theories at a particular scale, and characterize them by what happens when you “zoom” in and out, in an approach codified by the physicist Kenneth Wilson.

While I understand the basics of Wilson’s approach, the courses I took in grad school skipped the deeper implications. This includes the idea of theories that are defined at all energies, “flowing” from an otherwise scale-invariant theory perturbed with extra pieces. Other physicists are much more comfortable thinking in these terms, and the topic is important for quite a few deep questions, including what it means to properly define a theory and where laws of nature “live”. If I’m going to have an informed opinion on any of those topics, I’ll need to go back and learn the Wilsonian approach properly.

Wormholes:

If you’re a fan of science fiction, you probably know that wormholes are the most realistic option for faster-than-light travel, something that is at least allowed by the equations of general relativity. “Most realistic” isn’t the same as “realistic”, though. Opening a wormhole and keeping it stable requires some kind of “exotic matter”, and that matter needs to violate a set of restrictions, called “energy conditions”, that normal matter obeys. Some of these energy conditions are just conjectures, some we even know how to violate, while others are proven to hold for certain types of theories. Some energy conditions don’t rule out wormholes, but instead restrict their usefulness: you can have non-traversable wormholes (basically, two inescapable black holes that happen to meet in the middle), or traversable wormholes where the distance through the wormhole is always longer than the distance outside.

I’ve seen a few talks on this topic, but I’m still confused about the big picture: which conditions have been proven, what assumptions were needed, and what do they all imply? I haven’t found a publicly-accessible account that covers everything. I owe it to myself as a kid, not to mention everyone who’s a kid now, to get a satisfactory answer.

Quantum Foundations:

Quantum Foundations is a field that many physicists think is a waste of time. It deals with the questions that troubled Einstein and Bohr, questions about what quantum mechanics really means, or why the rules of quantum mechanics are the way they are. These tend to be quite philosophical questions, where it’s hard to tell if people are making progress or just arguing in circles.

I’m more optimistic about philosophy than most physicists, at least when it’s pursued with enough analytic rigor. I’d like to at least understand the leading arguments for different interpretations, what the constraints on interpretations are and the main loopholes. That way, if I end up concluding the field is a waste of time at least I’d be making an informed decision.

4 thoughts on “Things I’d Like to Know More About

  1. Rami Rom

    I enjoy very much reading your blog and your analysis of the status of different topics in physics. I will be glad to follow up and learn more about the progress in these fields and I am probably most interested in the third topic the fundumental quantum theory questions. I am also interested in the question if massive black holes may be seen as Carnot engines that operate between cold and hot reservoirs transforming heat to matter.
    BR,
    Rami.

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  2. Jan Reimers

    I don’t know much about worm holes, but if you have any aspirations of being a sci-fi writer, then I think some technical knowledge of worm holes would make your writings much more interesting. Since you’re an N=4 SYM guy I guess you live and work at a critical point and there is no RG flow. Does this mean you don’t need any Wilsonian QFT ides in your current work?
    Regarding Quantum Foundations, I would be very interested to hear your opinion on this blog entry and discussion http://www.math.columbia.edu/~woit/wordpress/?p=10533 . The idea is that probability only enters QM when you don’t know the initial state of the environment/measurement-apparatus.

    Cheers
    Jan

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    1. 4gravitons Post author

      Indeed for N=4 because it’s a CFT I don’t need to think about renormalization at all. More generally, even in theories with RG flows amplitudes people usually calculate unrenormalized amplitudes (typically though not always in dim reg) with the expectation that someone else will use it to do renormalization “further down the pipeline”. In the few cases where something vaguely Wilsonian is being investigated, it’s in terms of higher-dimension operators being added to an IR Lagrangian. So the perspective of defining a theory with UV CFT perturbed by additional operators is maximally distant from what I run into day-to-day!

      I remember seeing that blog post, and it’s part of why Quantum Foundations is on this list. I keep running into Quantum Foundations arguments like that one and thinking “oh, that sounds reasonable” and then running into an incompatible argument somewhere else and thinking “oh, that sounds reasonable”. There’s an aphorism that the most important role of philosophy is to inoculate you against other philosophers, and it’s pretty clear to me that I need more of the right kind of philosophy here before I can have any useful opinions.

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  3. Nabil Atlam

    I would like to learn algebraic topology, algebraic geometry, string theory, Supersymmetric Yang-mills theories, S-matrix bootstrap, conformal bootstrap, number theory,….. 😀

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