/sci/ - Science & Math

[Anonymous No.10361410]

I'm sick of every explanation of quantum physics being either so simple it provides no information or so technical it's unreadable to someone who doesn't already understand it!

can someone please just spin to me in a way that's simple enough for someone with almost no higher education to understand, but still tells me most of what I need to know about how it works?

>why is spin described with a complex number?
>does the spin vector refer to an actual direction in space
>why is the spin vector complex
>what exactly is parity when we're talking about spin?
>why does wikipedia say particles have even parity while antiparticles have odd parity
>why do particles and antiparticles share the same spin vector?
>do you really have to turn a fermion around 720º to get it to go back to its starting position?
>if angular momentum is supposed to be a matrix rather than a vector, how would you convert a spin vector to a matrix
>what's the deal with the pauli matrices?

[Anonymous No.10361415]

>>10361410
there is no golden road to QM. you gotta go through the math to appreciate the why

[Anonymous No.10361416]

>>10361410
>why is spin described with a complex number?
Because everything in QM is probability, absolutely everything.
QM is different to any other science in the way probability is defined - no other branch does it thru amplitudes:
https://youtu.be/gCAxGTt7nLg?t=8m

[Anonymous No.10361423]

>>10361416
this explains some of the math shortcuts used in the video
[math] \displaystyle
\\ z_1 = x_1+y_1i \; \; \; \; \; z_2 = x_2+y_2i
\\ z_1^* = x_1-y_1i \; \; \; \; \; z_2^* = x_2-y_2i
\\ | z_1 | = \sqrt{x_1^2+y_1^2} \; \; \; \; \; | z_2 | = \sqrt{x_2^2+y_2^2}
\\ z_1+z_2 = x_1+x_2 + (y_1+y_2)i
\\ \left | z_1+z_2 \right |^2 = \left ( \sqrt{(x_1+x_2)^2+(y_1+y_2)^2} \right ) ^2 = (x_1+x_2)^2 +(y_1+y_2)^2
\\ z_1z_2^* = x_1x_2 -x_1y_2i +y_1ix_2 -y_1iy_2i = x_1x_2+y_1y_2 +(x_2y_1-x_1y_2)i
\\ z_1^*z_2 = x_1x_2 +x_1y_2i -y_1ix_2 -y_1iy_2i = x_1x_2+y_1y_2 +(x_1y_2-x_2y_1)i
\\ z_1z_2^* + z_1^*z_2 = 2(x_1x_2+y_1y_2) = \text{2Re}(z_1z_2^*) = \text{2Re}(z_1^*z_2)
\\ |z_1|^2+|z_2|^2 + z_1z_2^* + z_1^*z_2 = x_1^2+y_1^2 + x_2^2 + y_2^2 + 2(x_1x_2+y_1y_2)
\\ = (x_1^2 + 2x_1x_2 + x_2^2) + (y_1^2 + 2y_1y_2 + y_2^2) = (x_1+x_2)^2 +(y_1+y_2)^2
\\
[/math]

[Anonymous No.10361426]

>>10361415
but does everything have to be explained in the most difficult way possible? Maybe it's my fault because I'm looking on wikipedia for most of my information, but I don't know where else to look to get my information

[Anonymous No.10361431]

>>10361426
learn it through god-tier cs

scott aaronson's lectures

[Anonymous No.10361462]

>>10361426
i have been using wikipedia extensively for 15 years now, and now that i have become an expert on several topics, i realize wikipedia is a mixed bag. When it comes to things i do not know, it often seems like a terrific resource, however when it comes to things i do know, i see large gaps in knowledge. this is not to bash wiki, it is fucking awesome, but it is no substitute for quality textbooks when it comes to learning a subject.

for QM, Sakurai is a terrific graduate text. for undergrads Griffiths is polarizing (i liked it, but i also now realize it didn't prepare me well for the math in big-boy QM) but i don't know of a better book.

the concepts aren't any harder than they have to be. physicists don't like fluff. the notation, ideas, and applications may be challenging to learn about, but once you get on that horse you realize you can go far. then again, you'll also come across things like e raised to matrix powers inside infinitely nested path integrals which are fascinating but nearly useless, but keep in mind QM is very practical; our mastery of semiconductor electronics is largely due to our understanding of the subject

[Anonymous No.10361484]

>>10361410
wtf is dirac notation:
http://www.mathpages.com/home/kmath638/kmath638.htm

[Anonymous No.10361508]

>>10361484
a fancy way to write inner products. the key is to realize an inner product consists of two things: an operator and a vector

Usually we write something like (u dot v), bu tin QM you really need to write it as (u dot) (v), because the (u dot) is a vectorspace all unto it's own (called a dual space). With finite dimension spaces, this isn't important, but when you go to both countable and uncountable infinite dimensional vectorspaces, it's critical. For instance, the typical way to describe the free particle is as a linear combination of sinusoids, however these aren't normalizable, but linear combinations of them are (see Rigged Hilbert Space and Gelfand Triples)

dirac notation just writes shit as <u| and |v>, called a bra and a ket, respectively.

[Anonymous No.10361513]

>>10361462
very good post. also i think Shankar is a good QM book

[Anonymous No.10361568]

>>10361410
>turn a fermion around 720º to get it to go back
https://youtu.be/JDJKfs3HqRg?t=25s

[Anonymous No.10361603]

>>10361410
Try "Picturing Quantum Processes, a First Course in Quantum Theory and Diagrammatic Reasoning." It's simple enough to be taught to high schoolers. There's even some experimental work to teach it to 1st graders and lower.

[Anonymous No.10361614]

>>10361410
its only math because the whole thing is an artificial way to model things we came up with that we memed into being real by believing in it