/sci/ - Science & Math

[Anonymous No.3808565]

What do I need to study in order to be able to understand Einstein's general relativity and quantum mechanics? Of course, I know the non-mathematical outline of these theories, but I believe these are too oversimplified.

What I already know:
Algebra 1
Algebra 2
Integration
Derivation

I haven't worked with more than 2-dimensional functions, though.

What else do I need to know?

[Anonymous No.3808585]

HELP!

[Anonymous No.3808595]

>find his papers online (for free)
>look at his proofs and read his theory
>get off of fucking /sci/ and learn

Fuck off now.

[Anonymous No.3808601]

nothing, all derivations of the theory can be done with simple integration.

[Anonymous No.3808669]

>>3808565
You are way out of your league son. You will need alot of pre-rec physics as well. There are a ton of physics concepts you need to understand very well, before you can do GR or QM. This is becuase GR and QM will use, or build upon those concepts.

For the mathematics basics you will need:

Calculus (all of it 1,2,3,4)
Linear Algebra (not just matrix algebra)
Tensor Calculus
Real Analysis
Complex Analysis
Fourier Analysis

There are probably more, but I can't recall right now. Calculus 4 = differentail equations

[Anonymous No.3808680]

>>3808669
>You are way out of your league son.

What do you mean by 'out of YOUR league'? The fact that I want to be able to understand QM and GR properly, and yet don't have the level of mathematics required for this?

[Anonymous No.3808684]

>>3808565
>I know the non-mathematical outline of these theories

If you can't do the math, then you don't know the theories at all. Most of the shit you think you know is probably wrong. Most of pop-science is complete bullshit.

[Anonymous No.3808689]

>>3808684
>If you can't do the math, then you don't know the theories at all. Most of the shit you think you know is probably wrong. Most of pop-science is complete bullshit.

I know, that's why I want to learn the proper mathematical versions of these theories.

[Anonymous No.3808727]

Do you have any knowledge of classical mechanics, classical field theory, and special relativity (using 4-vectors, not just the shit they teach in high school)?

If not, go learn them. You'll also have to pick up some math along the way.

[Anonymous No.3808728]

>>3808680
The fact that you listed "algebra 1" and "algebra 2".....really? REALLY? You probably just don't know what I mean. Let me clarify:

It is like you saying, "Hey, guize, I know how to add, is it enough to understand the mathematical structure of the standard model of partciel physics?"

Make sense now?
It is laughable that you will even mention such extremely low level mathematican concepts. "Algebra 1" and "Algebra 2" are basically shit, they aren't really that much more complicated the basic arithmetic. They are such low level mathematics, that they are taken as a "given", just like basic "arithmetic" is. It is given, that anyone doing any kind of physics or mathematics is an expert is such low level concepts.

[Anonymous No.3808736]

Your goal shouldn't be to understand Einstein's general relativity or quantum mechanics, your goal should be to understand math and physics.
Anyway, if you want to learn somethin 4chan not the best medium to be honest.

[Anonymous No.3808739]

>>3808727
I should add: To learn classical field theory, you should be looking for textbooks about "electrodynamics" / "electricity and magnetism." That might not be clear to a beginner.

[Anonymous No.3808745]

>>3808728
this.

Seems like you just learned derivation the next logical step is NOT quantum physics.

[Anonymous No.3808751]

A lot more than what you already know.

[Anonymous No.3808757]

Don't underestimate the power of:

1. Get a textbook on what you want to learn.
2. See the stuff it's referencing that you have no clue about? That's what you needed to study first.

[Anonymous No.3808758]

>>3808728
Aren't algebra 1 and 2 group and ring theory?

[Anonymous No.3808761]

>>3808728
But I need to mention things I know starting from the most basic level.

[Anonymous No.3808762]

>>3808758
There's no such thing as algebra "1" or "2". There's only algebra

[Anonymous No.3808775]

You're all set, actually. Just down Einstein's papers and start reading

[Anonymous No.3808776]

>>3808565
It is great that you want to learn these concepts, but it takes time. You can't just directly jump into junior/senior level physics. There will be alot of fundemental concepts you lack. You need to start small, just pick up a basic intro university physics book, STUDY THAT! It may be boring as shit, but you need those concepts!

You cannot understand General Relativity and Quantum mechanics, without knowing basic+intermediate college physics.

There are at least 6 physics course loads you need, before you can even understand Quantum Mechanics or General Relativity. There are at least 6 math course as well.

If you start with Physics 101 (basic intro university physics), you will be on your way!

[Anonymous No.3808777]

Let me list it properly this time. What I know:
>Algebra
>Integral calculus
>Differential calculus

What else do I need to learn to be able to learn GR and QM?

[Anonymous No.3808783]

>>3808776
>There will be alot of fundemental concepts you lack.

Don't listen to this shit, OP - most general relativity and quantum physics is unrelated to most of the other stuff taught. You just need to learn what's related to it, and not learn everything that's taught before it, because then you'll just waste time.

[Anonymous No.3808786]

You would need to go to school and get a phd if you want to contribute to research. Honestly, the prereqs are damn fucking hard and tedious, and in the end, the only way to make it worthwhile is to actually solve problems- math and physics were made to solve problems. Also, being amongst teachers is better than learning from grad students on the internet because professors actually know what they're talking about most of the time.

If you want to learn by yourself, you would need to know a bunch of math concepts. Now, understanding a mathematical concept WELL (which you will need or else you will have to stop every 2 pages in an advanced physics book) is not much different than understanding literary criticism, historical analysis, etc. They all require you to not only see a glimpse of the concept, but to see it from every fucking angle, and apply it to everything to surrounds it- the smartest people can apply it to not so obvious connections. Math is different because while other concepts (including those in physics, which is why we need math) are vague and very open, math is incredibly rigorous, so you not only have to see a 'glimpse' of it, but you have to actually see the entire construction. You can do this by going through problems, and digging/slashing away at the dark cavern until you reach gold. In other words, the reason why proofs are a great way to learn math is because you must use the concept correctly, or it cannot be used in the proof at all.

1. Read the concept and theorems, then their proofs. 2. Even if you don't understand, follow the advice of Ian Stewart "Skip it." Go to another one or go to the problems (ASAP).
3. As you're doing a problem, don't be isolated. Look through your notes, connect the concepts, look for transformations and relations of concepts and try to prove it.

[Anonymous No.3808788]

>>3808565
Go for it, OP. Sounds like you have a high level of interest for such a young one. You will be surprised at what even a novice can learn and do if he/she puts his/her mind to it. Never let anyone tell you that you couldnt possibly understand something.
Most of sci is jealous of young intellectuals-in-training, don't let it get to you.
That being said, you say you know algebra. You also know integration/derivation. integration/derivation will be what calculus is all about. My advice to you is to begin to learn more calculus while you learn some physics. Some physics concepts will be easily available to you with just an education in algebra. Some physics concepts will require knowledge of calculus too, though. You must learn calculus and physics, and eventually you will stumble on the same problems and questions Einstein dealt with. Then you will be ready to learn his theories for yourself.
Good luck

[Anonymous No.3808789]

>>3808758
>>3808762
Algebra 1 and 2, are the names of shit math courses American highschoolers take.

Bascially, they learn wtf a "varible is", very very very basic univarite equations.

It is basically shit, just an extension of simple arithemetic.

[Anonymous No.3808795]

>>3808786
>which you will need or else you will have to stop every 2 pages in an advanced physics book

Why not?
This way, he would look up all the stuff that's related to it, and by the end of the textbook, learn all the mathematical concepts needed for understanding QM and GR.

[Anonymous No.3808804]

>>3808795
Oh, and not to mention, it would take shorter.

[Anonymous No.3808806]

>>3808786
books:
art and craft of problem solving
calculus, spivak
strang's linear algebra + any diff eq
calculus on manifolds, spivak

again, the way to learn is by making mistakes while solving problems. you will not appreciate knowing GR or QM if you don't acquire a love for problem solving and imagination. the beauty of it comes from how expansive and limitless the world is- the world is your sandbox, and it allows you to play its games.

[Anonymous No.3808818]

>>3808777
>GR
Linear Algebra
Real Analysis
Differential Equations
Tensor Analysis
Differential Geometry


>QM
Linear Algebra
Real Analysis
Complex Analysis
Measure Theory
Functional Analysis
Differential Equations
Partial Differential Equations
Spectral Theory
Operator algebras

[Anonymous No.3808825]

>>3808783
0/10

[Anonymous No.3808853]

>>3808795
>>3808804
It won't work that way. It will actually take much much much longer.

Do you know anyone who was able to learn calculus, before they knew how to count?

Why do we still teach kids how to count then?

[Anonymous No.3808874]

>>3808565
The algebra you learn in highschool is not what mathematicans mean when they say "algebra".

You actually don't know what algebra is yet. Algebra is a very very very broad field. All you know is some basic varible manipluations, not actual algebra.

[Anonymous No.3808916]

>>3808874

Left and Right Nullspaces.

[Anonymous No.3808940]

>>3808874
Yes, but other than knowing what a group is, what mathematicians mean by algebra largely isn't necessary for quantum mechanics.

[Anonymous No.3808945]

>>3808940
Note: Linear algebra is a different subject and is very useful for QM.

[Anonymous No.3808996]

>>3808853
Nobody's suggesting that. To use your analogy, the guy would look at a calculus textbook, see that there were strange symbols called numbers in them, and be motivated to find out what they were. Approaching things in a nice neat order is great if you're taking classes, but if you're doing it on your own time you need motivation.

Of course, OP would be wise to enroll in some classes if he wants to do research in the field at some point, as he'll need that degree.

If he is enrolled in classes, he should just look at the prerequisite lists and maybe talk to the professors.

OP can download these from bib.tiera.ru and start reading NOW:

pop sci level: Feynman, QED: The Strange Theory of Light and Matter
early undergrad level: Feynman, Leighton, Sands, Feynman Lectures on Physics, Vol. 3
late undergrad level: Griffiths, Introduction to Quantum Mechanics
grad level: Sakurai, Modern Quantum Mechanics

And when he gets stuck, which he will, he'll have some idea why he's learning the prerequisites. Once he's gotten into those, presumably he'll find them interesting enough to read everything about them rather than skipping back to the QM every time he figures out what "momentum" or whatever he had to learn about is. If someone finds classical mechanics boring, somehow I doubt they'll do well with the quantum stuff.

[Anonymous No.3809023]

>>3808996
>Once he's gotten into those, presumably he'll find them interesting enough to read everything about them rather than skipping back to the QM every time he figures out what "momentum" or whatever he had to learn about is. If someone finds classical mechanics boring, somehow I doubt they'll do well with the quantum stuff.

Already know classical mechanics.