Quantum Information and General Relativity

[leo.]

Last year I've finished the undergraduate course in Mathematical-Physics and Mathematics and this year I've started on graduate school on Physics in order to obtain a master's degree. What I'm really interested are two main topics: general relativity and quantum field theory. I also like mathematicaly rigorous approaches to physics, which I agree are available in GR but unavailable in QFT.

My initial guess for research topic on the graduate research was to deal with QFT in curved spacetimes, since I'd be working on both things I like.

It happens that when I was searching for an advisor, unfortunately I wasn't able to find anyone working on this topic on the university I study. After talking to some professors there were two main topics that are available at first, and they are: (i) quantum information theory applied to the study of black holes and (ii) extended bodies in general relativity following Dixon's approach.

Considering (ii) I found it a nice thing, but I don't know if it would be worthwhile to dedicate a whole master thesis for it. I mean, there is quite a bunch of interesting mathematics that goes into it. I just took a look on Dixon's papers, and one deals with the theory of vector bundles and connections and a lot of results from differential geometry. So it can be cast into a rigorous and rich differential geometry form and is GR after all. It also seems to have interesting applications such as describing the dynamics of planets, and perhaps even bigger objects like galaxies. It is fully classical though and I don't know if something nice in astrophysics and cosmology, for example, could be derived from it.

As for (i), a professor whose main interest is quantum information said he was interested in the results quantum information could provide in the context of black holes (something about correlation, if I understood well) and suggested a research together with professor which works in general relativity, since he doesn't know much about it.

I have considered working on this topic, but since I'm more inclined to mathematical-physics, I'm unsure if that would be a good topic to work with. My main concerns are:

1. I don't know if there's much of interesting mathematics to deal with in this topic. Take General Relativity for instance. I find Differential Geometry a quite rich and interesting mathematics topic. Now, I have no idea if the mathematics used in this research would be interesting as well. This concerns me because as someone with an undergraduate course in mathematics I really want to deal with more advanced and rigorous mathematics, in particular differential geometry.
2. My main interest is GR. My impression (which might be totally wrong, being one of the main reasons for this thread) is that studying quantum information on black holes doesn't involve GR at all, apart from defining what a black hole is. My impression is that it is much more of information theory than GR.

In summary, I'm quite confused on what to choose - to pick either of these topics, or look for other options.

Regarding quantum information and black holes, is there something I could do, on which I would be able to deal with a little more of General Relativity and more interesting mathematics? Or it will certainly fall into just information theory (which seemed to me as a pretty boring thing from the mathematical point of view)?

 

[mpresic]

Your problem with ii is that the treatment is entirely classical, and consequently, you can't see if anything interesting can come from it.

Many papers by S Chandrasekhar involve beautiful mathematics and results, (e.g see Stochastic Problems in Physics and Astronomy, It is one of the most cited papers in the field over about 7 decades). I think it runs about 100 pages and I don't think there is a single h-bar in all that. Many aspects of astrophysics are entirely classical.

Many interesting results are entirely classical. In contrast, many results that are irrelevant may come from quantum mechanical treatments. I think sometimes physics programs are in such a hurry to produce researchers in quantum fields they skimp on the possibilities of classical treatments to their problems.

In addition, you are considering a Master's thesis. The first page in most theses state. "a thesis given in partial fulfillment for the degree: Masters of Science", or something like that. A Master's program is usually about 2 years. Given this: You do not know if (ii) is worth dedicating a whole master's thesis on it? You are not committing a 30 year career on it. It is a Master's thesis. (By the way, your thesis advisor, (I presume this is your funding source) will be most concerned with your results and progress, than whether you find the project interesting. You can do a good job on something you consider dull, especially when it is a year, maybe 2 year effort and commitment.)

 

[leo.]

Your problem with ii is that the treatment is entirely classical, and consequently, you can't see if anything interesting can come from it.

Not only that. As I said, my main interest is both GR and QFT. It is not that someone has told that things must be quantum (nor do I think like that by the way), is just what I'm interested in.

It is a Master's thesis. (By the way, your thesis advisor, (I presume this is your funding source) will be most concerned with your results and progress, than whether you find the project interesting. You can do a good job on something you consider dull, especially when it is a year, maybe 2 year effort and commitment.)

I still think that if one has decided to produce such a thesis, it must be something they actually find interesting, by the way.

But still this isn't really my point. I'm trying to decide wheter or not I'd find (i) interesting considering the points I made in the OP, and finaly decide which of the two subjects I would prefer. The issue is that even though I have idea on what (ii) is about because I have prior experience with DG, I have no idea on what to expect of (i) as detailed in the two points I made in the OP.

So my question remains about the first topic. I want to know more about it, so that I can take a decision with knowledge of what I am deciding. If in the end I find (i) boring and uninteresting, I would certainly pick (ii) even though it is classical.