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Anyone familiar with the mathematical formalism behind GR?
- Thread starter samoth
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redguru
New member
samoth said:Yeah, I need a topic for a research project. I don't know if I can stretch it out over two semesters, but I was hoping to do something more along the lines of mathematical physics... and I think twistor theory isn't a possibility, lol.
I had a hard enough time working with arrays in diffeq. I'd probably have a much harder time with multi-dimensional ones.
calimuscle
New member
Do you want a theoretical project or a "Matematically explain how this works" project?
calimuscle said:
It will inevitably be the latter. I don't think anyone can jump into anything too theoretic without graduate-level knowledge of mathematical physics.
The main purpose of this is that I want to familiarize myself with the mathematical foundations of GR, e.g. tensor calculus, topology, differential geometry, algebraic structures, 4-manifolds and such. While one of my interests pertains to Penrose's idea of the Weyl curvature hypothesis applied to initial spacetime singularities and consequences of time-assymetric quantized theories of gravity, that's about as out of reach as studying Twistor Theory, lol.
calimuscle
New member
What to do when the math gets too hard:
1) Ignore the hard part
2) Make the quantity that induces hardness zero
3) Consider a similar problem that is easy
4) Make assumptions that are totally unrealistic to simplify the problem
5) Consider only Integers
6) Use a computer to do monte carlo or other approximation techniques
7) Consider a different field that is newer and therefore the fruit is lower hanging.....
Just my two cents....
1) Ignore the hard part
2) Make the quantity that induces hardness zero
3) Consider a similar problem that is easy
4) Make assumptions that are totally unrealistic to simplify the problem
5) Consider only Integers
6) Use a computer to do monte carlo or other approximation techniques
7) Consider a different field that is newer and therefore the fruit is lower hanging.....
Just my two cents....
majutsu
Well-known member
samoth said:
problem is that i can think of a classic book for each of those. Each one, like topology, diff geo, etc is a one semester class usually.
Frankly, I don't know how you physicists do it anymore. The maths are in the stratosphere, and each could require a lifetime of study, then you are supposed to novelly apply it?!?! jeezy creezy, man . . .
that's why i stuck to math in school a lot. you can read some great science papers with understanding, and then apply the same math tool in different fields of study.
anyway, much respect for you guys. short answer is a year minimum i'm guessing, although i'm sure your mentor knows better. Why don't you just do tensors one semester, and all the stuff that uses that. Than do lie algebras and whatever later. You can't really have a manageable project on "mathematical physics". Seems kind of broad. but be sure to ask around near you, and don't take some sweaty meatheads' ideas about it. Maybe you princeton geniuses do this kind of thing in a week or two
majutsu said:problem is that i can think of a classic book for each of those. Each one, like topology, diff geo, etc is a one semester class usually.
Frankly, I don't know how you physicists do it anymore. The maths are in the stratosphere, and each could require a lifetime of study, then you are supposed to novelly apply it?!?! jeezy creezy, man . . .
that's why i stuck to math in school a lot. you can read some great science papers with understanding, and then apply the same math tool in different fields of study.
anyway, much respect for you guys. short answer is a year minimum i'm guessing, although i'm sure your mentor knows better. Why don't you just do tensors one semester, and all the stuff that uses that. Than do lie algebras and whatever later. You can't really have a manageable project on "mathematical physics". Seems kind of broad. but be sure to ask around near you, and don't take some sweaty meatheads' ideas about it. Maybe you princeton geniuses do this kind of thing in a week or two
I was hoping to familiarize myself with the mathematics well enough to be able to analyze, e.g., the Ricci tensor or something to that effect in GR. The problem is the maths, so I would basically concentrate on that for the bulk of the time... hence wondering the time needed to acquaint oneself with such prerequisites.
Unfortunetly, of the three profs I spoke to thus far, two flat out said they didn't have the knowledge, and one was of the "maybe-kinda-but-I-really-don't-wan't-to-because-it's-not-my-area" attitude, lol. All recommended me to pursue an advisor in the math department, but after looking at their respective research areas, none really fit these areas of math, save one who's interests include set-topology... nor do I want to (or would be able to in within the time constraints) concentrate on the mathematics at the rigorous pure-math kind of way that mathematicians do.
Hopefully the next couple profs I talk to tomorrow will be more interested and familiar with such areas. I want to pursue this kind of study rather than experimental research or even something in astro leading to publication because I realize the importance of knowing all these different areas of math, and I think it would yield greater benefit in the long run. Unfortunetly, this isn't a heavy mathematical physics school at all.
Man, I'd love to be at Princeton, lol. Feynman did his graduate work there.
majutsu
Well-known member
is princeton still as respected as the days of einstein, feynman etc?
sounds good, man. I found a guy at my school when i went who was an expert in hamiltonian matrices. The guy was awesome. I used the hamiltonian matrices to formulate a qed theory. I also got him to teach path integrals. I loved that guy. Ended up being way more influential than the physics guy who did the class. I think the math prof was pissed when i went into medicine. I always wonder. Its a fun life so far, but i wonder what a life pursuing knowledge would have been like. medicine is a decent upper middle class life, and you can learn a lot about people and their families, and how they deal with life and illness. But there is something beautiful and pure about the physical sciences or math. Like a reflection of the eternal laws of the universe. history, medicine, politics, stock markets -- anything that involves people -- becomes a cesspool. you have to love the chaos.
anyway, i think your project sounds cool and useful. i will pm you the name of my old mentor. he's teaching still and you can contact him. he'll steer you right. maybe know someone at purdue for you to work with.
sounds good, man. I found a guy at my school when i went who was an expert in hamiltonian matrices. The guy was awesome. I used the hamiltonian matrices to formulate a qed theory. I also got him to teach path integrals. I loved that guy. Ended up being way more influential than the physics guy who did the class. I think the math prof was pissed when i went into medicine. I always wonder. Its a fun life so far, but i wonder what a life pursuing knowledge would have been like. medicine is a decent upper middle class life, and you can learn a lot about people and their families, and how they deal with life and illness. But there is something beautiful and pure about the physical sciences or math. Like a reflection of the eternal laws of the universe. history, medicine, politics, stock markets -- anything that involves people -- becomes a cesspool. you have to love the chaos.
anyway, i think your project sounds cool and useful. i will pm you the name of my old mentor. he's teaching still and you can contact him. he'll steer you right. maybe know someone at purdue for you to work with.
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majutsu said:
Princeton's still a top three university in the U.S., and in science, in my opinion, it surpasses Yale and possibly Harvard as well.
The big problem with physics in today's world is the lack of jobs, especially tenure-track professorships. There's simply far too many degree holders and not nearly enough positions. I've definitely been looking at other options, from industry to computer science related fields (but let's face it, those are boring
). In contrast, the fields of medicine and pharmacology seem to be pretty strong. The time and money put into either are pretty extreme, but job options are plentiful compared to physics and mathematics.Unfortunetly, I'm not at Purdue anymore, either. Transferring at the same time as the original diagnosis and surgery followed by two additional surgeries during subsequent semesters pretty much destroyed the cost/benefit ratio of staying at an out-of-state university, so I'm back at Wisconsin - Oshkosh. I shouldn't have to worry about any more medical problems, so I'm quite happy about that... although it's rather annoying to not be able to hear out of my left ear anymore, lol.
calimuscle
New member
When I was in Industry, there were a series of very bright, young physicists from Lawerence Livermore (Berkley) National Labs that scrambled for jobs in the private sector. They found that LLNL Scientists spent more time on powerpoint presentations fighting over a smaller and smaller piece of physics funding. Essentially, they were fighting for survival to the detriment of their peers.
The ending of the Cold War essentially killed physics and mathematics.
The ending of the Cold War essentially killed physics and mathematics.
calimuscle said:
Yep. Businesses used to conduct research because it was favorable in the public eye, as well as attracting new employees (much in the same way Google hires all-star programmers on their team). Businesses have changed, and science and research fight for the few funding pennies left.
While I would hope to stay away from anything computational or computer-related, I realize that's a big area nowadays, so I've began poking around in that area.
I've always been attracted to the idea of doing research, but I've never had any interest in college-level teaching... and that's pretty much the only physics-related area left to get into, as overcrowded as it may be, lol.
I find it rather funny that a majority of astrophysicists end up on Wall Street.
calimuscle
New member
samoth said:Yep. Businesses used to conduct research because it was favorable in the public eye, as well as attracting new employees (much in the same way Google hires all-star programmers on their team). Businesses have changed, and science and research fight for the few funding pennies left.
While I would hope to stay away from anything computational or computer-related, I realize that's a big area nowadays, so I've began poking around in that area.
I've always been attracted to the idea of doing research, but I've never had any interest in college-level teaching... and that's pretty much the only physics-related area left to get into, as overcrowded as it may be, lol.
I find it rather funny that a majority of astrophysicists end up on Wall Street.
There is always Engineering: the applied physics. Physicists tend to go into areas where no one else understands the Math involved. Of course, some businesses hire PhDs in Math & Physics just because they think these people are smart.
Sheesh, none of the physics faculty were familiar with GR or this area of mathematical physics, so I'll be going through the math department, lol. Luckily, my advisor is close with the physics faculty, and visa-versa, and seems to be well-versed in differential geometry and tensor analysis. I'll be doing something along the lines of, "Selected Mathematical Formalisms of General Relativity: Minkowski Space as a Four-Dimensional Pseudo-Riemannian Manifold Representing Spacetime in Special and General Relativity". I have a strong feeling that applications to physics and GR are going to totally obfuscate everything, since I don't think I'll have a real link between the math and the physics: It'll be either one or the other, and linking them together... well, I suppose that's the whole purpose of doing this kinda thing, lol. I have a several outside people that should be able to help grease the wheels with applying one to the other.
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