/sci/ - Science & Math

>>6538871
dont worry much about ODEs and analysis

hassani is much better than boas

whats important are geometry and topology, group theory and algebra
topology and geometry for physicists by nash and sen is a good intro to those subjects, then nakahara
gr books are good for more differential geometry
for group theory and algebra i kinda picked it up through qft books and a couple books on lie algebras. hassani has some group theory as well. the core ideas are simple enough that you can figure out the gaps pretty easily if the books dont cover it, the rest you can learn as you go.

please everyone, shut the fuck up, you have no idea what youre talking about

first of all, this is not crackpot shit. and its not just speculation. there is actual reasonably well grounded theory behind it. this has nothing to do with the matrix

one of the main guys working on this right now is my advisor, so i know a bit about this.

the basic idea is that the description of physics, most notably in gravity, when including quantum mechanics, is somehow redundant. the idea of a hologram is that it represents an object with a description on one less dimension- the lower dimensional description has fewer degrees of freedom, so you would think it cant contain the same amount of information. HOWEVER, we (most notably pic related) have discovered that a quantum mechanical theory of gravity in some number of dimensions is equivalent to a certain kind of quantum field theory (describing something more like the nuclear forces) on a space that has one less dimension. since the theories are equivalent, this implies that the theory of gravity carries "redundant degrees of freedom"

so heres a bit about what this can mean-
since this suggests that our description of gravity needs rethinking, it brings up the question of "what is spacetime?". a theory of gravity is just a theory of spacetime. it now seems like the way we think about spacetime is a bit outdated. the way we've been doing it is thinking of spacetime as something "fundamental", while now we think it might be "emergent"
what i mean by this is that though spacetime seems like a very basic idea that it is impossible to do without, the structure in physics that we call spacetime might be a result of more fundamental (more basic ingredients of a theory) structures. the thinking right now is that quantum entanglement is what spacetime may arise from. not too well understood at the moment
thats about as much as i feel like i can say at a layperson level

>quantum field theory
>general relativity
>thermodynamics
>electrodynamics
>auditing/possibly taking string theory
>possibly taking group theory
>research in quantum gravity

>>6188709
same here, theoretical physics. want to be a professor
its a very competitive field, im doing really well so far though, so i think i might have a chance. im a third year undergrad but im taking a full set of grad classes in one of the best programs and am dominating almost all the grad students, im already published in nuclear phenomenology from summer research, and by some miracles, im about to start working with one of the best theoretical physicists there is
despite all this shit im still not guaranteed that ill eventually get a job in this though... one of my friends just got his phd last spring and he only was offered one postdoc, which he turned down. hes making 100 grand a year now though so whatever
goddamn it though, i dont know if i could be happy doing anything else than physics

holography is an interesting idea. if you want to find out some more concrete things about it look up black hole entropy and ads/cft correspondence (pic related). i dont know much about it but im hoping to do some research on it soon

>>6176352
no youre a goddamn idiot shut up please and never talk about science again
>>6176358
babby thinks classical physics is formula for universe, lel

ITT people talking out of their fucking asses

please learn math and physics before coming up with "theories"

two of my professors are top researchers in quantum gravity and this is the basics of what they told me

1) naively applying the standard procedures of quantization (QFT) to the classical theory of gravity (GR) gives you a non renormalizeable theory, one that doesnt make sense at high energies. this can be easily seen from the fact that the coupling constant for gravity gets larger with higher energies.

Applying QFT to slightly different theories of gravity, like supergravity, also fucks up

2) Quantum field theory, the framework of the standard model of physics, is based on 3 tenets- unitarity (essential conservation of probability), lorentz invariance(becomes local in gravity, as GR is just the gauge theory of the lorentz group), and locality.

3) Arguments about black holes, with this whole information paradox, implies that one of these three tenets must be wrong. Apparently it is widely believed that locality is the one we must throw away. String theory, for example does away with locality in a way that seems to make everything work out. String theory also gives you "GR" but in a stringy way.

4) According to one of the guys, one of the main problems in quantum gravity is that the notion of applying quantum mechanics to spacetime is not a well defined thing. Apparently one of the best ways of understanding quantum gravity is through the ADS/CFT correspondence, which does away with locality. ADS/CFT correspondence shows that yang mills theory in some sense contains string theory (maybe some circumstantial support for further research there) and that spacetime in some sense is emergent. the Weingberg-Witten theorem says that emergent gravity is forbidden in 4 dimensions, but really we have no strong reasons to reject the possibility of there being more dimensions


So pretty much, GR is an approximation (a good one), but we have yet to find a way to properly apply quantum mechanics to gravity (string theory and ads/cft shit are some good leads though)

ITT
some people talking about the original topic
and
a bunch of faggots who hate on the one valid candidate for quantum gravity just because it appears to be non testable any time soon, and despite the fact that, regardless of its status as a "true" theory, it has enriched the both math and physics, especially with ads/cft

lol'd/10