4 ms·

I finished up my PhD in scattering amplitudes recently. I checked out the abstract of this paper, and it certainly looks like an interesting result and will lik

by joe__f 4y ago

I finished up my PhD in scattering amplitudes recently. I checked out the abstract of this paper, and it certainly looks like an interesting result and will likely be the basis for new results in the field. For perspective, I estimate that there are a few such results in the field per year which could have roughly the same quanta magazine article written about them.

mmazing 4y ago
Any guesses what this could stem from?
- joe__f 4y ago
  I think it's a bit of a feature of quanta magazine's approach to science journalism (and probably the current zeitgeist in science journalism in general). If you want to make work like this accessible then it's necessary for a large portion of the (pop science) article to be covering topics that are common to most of the recent work in the field, with a lot of the same analogies and motivations. I think it's nice that quanta magazine are trying to make this kind of work accessible and interesting for people, but I feel that their approach sacrifices perspective on how relevant that work is, which is why I tried to add some here.
  - ravi-delia 4y ago
    I agree with everything here, but suspect the person you replied to was asking what caused the strange correspondence :P (or, even if they weren't, I'd like to ask for myself)
    - joe__f 4y ago
      I'm happy to answer your question, but I'm not sure what you're asking
  - mmazing 4y ago
    Thanks for the response, but I was mostly asking about your experience as someone working in this particular field. Do you have any guesses for what might be the connection between these two different scattering amplitudes in seemingly disconnected physical phenomenon?
    - joe__f 4y ago
      I read the paper more carefully and had a think about this, and here are my thoughts; Dixon et al. find a duality linking form factors and scattering amplitudes. Scattering amplitudes are written as a 'loop expansion', which you could think of as a bit like a Taylor expansion, and I think a remarkable feature of their result is that it appears to hold for all orders of this expansion. I've seen some results relating form factors and scattering amplitudes at only the first order of this expansion before. Their result is based on a mathematical observation that the functions that the scattering amplitudes are built from at each loop order (called polylogarithms) have a natural operation on them called the 'antipodal map', and in applying this operation to every polylogarithm in the amplitude they recover the form factor. It's intuitive to me that if the mathematical building blocks of your amplitude behave nicely under some operation, you might expect the amplitude to have nice properties under that operation also. So it's clear mathematically why this new relationship exists, and I guess the question is, 'what does it mean physically?'. Dixon et al. comment that they don't know, and I don't really have any thoughts on this either. What I can say is that, over the last 20 or 30 years there have been many different discoveries of duality between seemingly disparate areas of mathematical physics. The first and most famous was the AdS-CFT relationship which relates gravity to gauge theory, and there is lots of work in amplitudes currently on a different relationship which writes gravitational physics as the square of physics in gauge theory. There are many others. So, my experience working in the field has taught me that there are many unexpected dualities and relationships between different physical theories, and that nature is more deeply connected at a fundamental level than is indicated by the initial (apparently disparate) mathematical formulations of those theories.
      - mmazing 4y ago
        Thanks a bunch for the detailed reply! I would like to learn more about stuff like this.
Rebirth-0822 4y ago
Hey, I know that this is probably too broad a question, but I'm curious: what kind of mathematics did you require to do your doctorate? I'm curious as to what I'd need to (re)-learn to truly understand this.
- analog31 4y ago
  You didn't ask me, but I can shed some light, having earned a physics PhD in the early 90s, after doing an undergrad double major in math and physics. The undergrad physics curriculum includes the standard college sequence of calculus and differential equations. Many physics students take more math than this, or today, probably some computer science. We took a "physics" course called "theoretical physics" that filled some gaps in the math sequence, most notably multivariate calculus in cylindrical and spherical coordinates, path integrals, and some stuff like that. Specific upper level physics courses also introduced math topics as needed. Graduate coursework re-iterated the same "theoretical physics" course, but it was called "mathematical methods." We used a textbook by Arfken, that covered the same multivariate calculus plus vector and tensor math. Finding out what the current textbook du jour is for this course, and perusing the table of contents, would give you a pretty good idea of what to expect. I didn't go into scattering theory as a specialty, but we covered it in some of the other courses, and I remember doing difficult integrals and differential equations in spherical polar coordinates. The coursework quickly runs you out of problems that can be solved in closed form. I'd be shocked if the real work isn't done today with mostly numerical techniques.
- MengerSponge 4y ago
  https://webspace.science.uu.nl/~gadda001/goodtheorist/index.html https://webspace.science.uu.nl/~gadda001/goodtheorist/index.... You need to work up to (and through) Quantum Field Theory to understand this. Thankfully, you don't need to be as good or as thorough as Gerard 't Hooft as you learn all those things!
- joe__f 4y ago
  Scattering Amplitudes in Gauge Theory and Gravity by Elvang and Huang is a standard introduction to the field, if you wanted to take a look and see what you might need to learn to get up to scratch. There are a lot of prerequisites.

by joe__f 4y ago

mmazing 4y ago

Any guesses what this could stem from?

joe__f 4y ago
I think it's a bit of a feature of quanta magazine's approach to science journalism (and probably the current zeitgeist in science journalism in general). If you want to make work like this accessible then it's necessary for a large portion of the (pop science) article to be covering topics that are common to most of the recent work in the field, with a lot of the same analogies and motivations. I think it's nice that quanta magazine are trying to make this kind of work accessible and interesting for people, but I feel that their approach sacrifices perspective on how relevant that work is, which is why I tried to add some here.
- ravi-delia 4y ago
  I agree with everything here, but suspect the person you replied to was asking what caused the strange correspondence :P (or, even if they weren't, I'd like to ask for myself)
  - joe__f 4y ago
    I'm happy to answer your question, but I'm not sure what you're asking
- mmazing 4y ago
  Thanks for the response, but I was mostly asking about your experience as someone working in this particular field. Do you have any guesses for what might be the connection between these two different scattering amplitudes in seemingly disconnected physical phenomenon?
  - joe__f 4y ago
    I read the paper more carefully and had a think about this, and here are my thoughts; Dixon et al. find a duality linking form factors and scattering amplitudes. Scattering amplitudes are written as a 'loop expansion', which you could think of as a bit like a Taylor expansion, and I think a remarkable feature of their result is that it appears to hold for all orders of this expansion. I've seen some results relating form factors and scattering amplitudes at only the first order of this expansion before. Their result is based on a mathematical observation that the functions that the scattering amplitudes are built from at each loop order (called polylogarithms) have a natural operation on them called the 'antipodal map', and in applying this operation to every polylogarithm in the amplitude they recover the form factor. It's intuitive to me that if the mathematical building blocks of your amplitude behave nicely under some operation, you might expect the amplitude to have nice properties under that operation also. So it's clear mathematically why this new relationship exists, and I guess the question is, 'what does it mean physically?'. Dixon et al. comment that they don't know, and I don't really have any thoughts on this either. What I can say is that, over the last 20 or 30 years there have been many different discoveries of duality between seemingly disparate areas of mathematical physics. The first and most famous was the AdS-CFT relationship which relates gravity to gauge theory, and there is lots of work in amplitudes currently on a different relationship which writes gravitational physics as the square of physics in gauge theory. There are many others. So, my experience working in the field has taught me that there are many unexpected dualities and relationships between different physical theories, and that nature is more deeply connected at a fundamental level than is indicated by the initial (apparently disparate) mathematical formulations of those theories.
    - mmazing 4y ago
      Thanks a bunch for the detailed reply! I would like to learn more about stuff like this.

Rebirth-0822 4y ago

Hey, I know that this is probably too broad a question, but I'm curious: what kind of mathematics did you require to do your doctorate? I'm curious as to what I'd need to (re)-learn to truly understand this.

analog31 4y ago
You didn't ask me, but I can shed some light, having earned a physics PhD in the early 90s, after doing an undergrad double major in math and physics. The undergrad physics curriculum includes the standard college sequence of calculus and differential equations. Many physics students take more math than this, or today, probably some computer science. We took a "physics" course called "theoretical physics" that filled some gaps in the math sequence, most notably multivariate calculus in cylindrical and spherical coordinates, path integrals, and some stuff like that. Specific upper level physics courses also introduced math topics as needed. Graduate coursework re-iterated the same "theoretical physics" course, but it was called "mathematical methods." We used a textbook by Arfken, that covered the same multivariate calculus plus vector and tensor math. Finding out what the current textbook du jour is for this course, and perusing the table of contents, would give you a pretty good idea of what to expect. I didn't go into scattering theory as a specialty, but we covered it in some of the other courses, and I remember doing difficult integrals and differential equations in spherical polar coordinates. The coursework quickly runs you out of problems that can be solved in closed form. I'd be shocked if the real work isn't done today with mostly numerical techniques.
MengerSponge 4y ago
https://webspace.science.uu.nl/~gadda001/goodtheorist/index.html https://webspace.science.uu.nl/~gadda001/goodtheorist/index.... You need to work up to (and through) Quantum Field Theory to understand this. Thankfully, you don't need to be as good or as thorough as Gerard 't Hooft as you learn all those things!
joe__f 4y ago
Scattering Amplitudes in Gauge Theory and Gravity by Elvang and Huang is a standard introduction to the field, if you wanted to take a look and see what you might need to learn to get up to scratch. There are a lot of prerequisites.