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This article says that 'mathematically' it could have happened before but leaves it at that. Does anyone know what kind of math? And the prerequisite knowledge

This article says that 'mathematically' it could have happened before but leaves it at that. Does anyone know what kind of math? And the prerequisite knowledge I might need to know (subjects, bonus points for good textbooks). I myself have a pretty firm knowledge of undergrad and some grad level physics. But I find myself recently interested in (big time/spacial scale) cosmology and also quantum phys, but I don't really know where to begin.

krastanov 7y ago
A typical suggestion is to check "The Theoretical Minimum" series (books and lectures). That would also inform you on what to read if you want to delve deeper in a particular subfield.
parsimo2010 7y ago
This pretty much all falls under the umbrella of mathematical physics- any mathematician will tell you it's not "real" math. Don't let that stop you from studying it if you're interested, but it's not for the faint of heart and most people require a mentor (aka an advisor and PhD program)- many self proclaimed "autodidacts" stall out once there are no longer online tutorials and they have to slog through textbooks written by physicists and mathematicians who seem to enjoy making a subject hard to understand. Starting with analysis, measure theory, and I suppose the obligatory linear algebra should first if you don't already have those. Spectral theory and maybe group theory are probably next steps to having enough background to do the quantum and relativistic stuff. I glanced at the abstract for the source material for the HN post (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.061302 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.12...), and it almost certainly requires spectral theory. I'm not an expert in this area, so a mathematical (or theoretical) astrophysicist might chime in and fill in the gaps.

krastanov 7y ago

A typical suggestion is to check "The Theoretical Minimum" series (books and lectures). That would also inform you on what to read if you want to delve deeper in a particular subfield.

parsimo2010 7y ago

This pretty much all falls under the umbrella of mathematical physics- any mathematician will tell you it's not "real" math. Don't let that stop you from studying it if you're interested, but it's not for the faint of heart and most people require a mentor (aka an advisor and PhD program)- many self proclaimed "autodidacts" stall out once there are no longer online tutorials and they have to slog through textbooks written by physicists and mathematicians who seem to enjoy making a subject hard to understand. Starting with analysis, measure theory, and I suppose the obligatory linear algebra should first if you don't already have those. Spectral theory and maybe group theory are probably next steps to having enough background to do the quantum and relativistic stuff. I glanced at the abstract for the source material for the HN post (https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.123.061302 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.12...), and it almost certainly requires spectral theory. I'm not an expert in this area, so a mathematical (or theoretical) astrophysicist might chime in and fill in the gaps.