/sci/ - Science & Math

Bacon number 4
Erdos number 5
reporting in

Also
>"I could never..."

Given that you start from an elementary theory (say standard model) then electrons being "elementary" really just means that these are the particles, which are represented in it's Lagrangian density. Quasiparticles is the name for emergent degrees of freedom, e.g. not being a represenation in that sense. From a good quantum mechanical positivist point of view, what matters are the observables, that is the matrix elements of the theory. Then that debate becomes a argument about language.
>why does this happen in materials and not in free space?
Again, if you start with the fundamental Lagrangian, what does "material" really mean, but a spatial area with alot of particles in (otherwise empty) space? Think about that - what means material to you?
Then with a material, because you have a large system, there are emergent phenomena like the ones you ask about. That's not a surprise, because more is different.

http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf

>>4343773
functional analysis and linear algebra for basic QM books. String theory is to be learned about two years later and can be approached from many angles

the current standard model (TM) is using this:

http://en.wikipedia.org/wiki/Lagrangian#Quantum_electrodynamic_Lagrangian

dF=0 & d*F=-*j

is good too

>>3721684
>the statment x is a closed system is not vague, it defines specific properties of the system
But since you don't know if the universe is bounded or not, if the unobservable universe should be counted in etc. that all not really helpful.
It's a difficult task to define the energy of the whole universe in the first place.

>Why does cold air sink?
comes from
http://en.wikipedia.org/wiki/Clausius-Clapeyron_relation#Applications

temperature T up
--> preassure P up
--> density rho up
--> mass m per unit volume up
--> specific weight up

>Why does cold air float?
comes from
http://en.wikipedia.org/wiki/Properties_of_water#Density_of_water_and_ice

given a block of ice, the lower part will melt - unlike other usual substances: If you have a block of dirt, then the bottom dirt will not melt.

>>3300979
http://en.wikipedia.org/wiki/Penrose_diagram

>>3262885

var = a;
Block[{a = b}, a - var]
Module[{a = b}, a - var]

Block computes and then makes the replacements {} and Module does it the other way around. I think if you're not writing a package where you need local vars like in objects, then you'll always mean to use Block.

>>3168105

Let M be a manifold. Then the fol lowing are equivalent:

1. M is metrisable;
2. M is paracompact;
3. M is strongly paracompact;
4. M is screenable;
5. M is metacompact;
6. M is σ-metacompact;
7. M is paraLindel¨of;
8. M is σ-paraLindel¨of;
9. M is metaLindel¨of;
10. M is nearly metaLindel¨of;
11. M is Lindel¨of;
12. M is linearly Lindel¨of;
13. M is ω1 -Lindel¨of;
14. M is ω1 -metaLindel¨of;
15. M is nearly linearly ω1 -metaLindel¨of;

>>3138252
is that an argument against his statement?

I kinda see a problem there.
Namely that the order of things you learn matters.

I'm doing physics and I often get the feel that I can't into chemistry because if see that it's "just a bunch of rules" (not trying to be mean here) and I just can't learn it if I know that it's "just derived".

Also, I don't think that there are too many people who are simultaneously interested in theory for theory sake and application.

like I know nobody who would do p-adic number theory and at the same time wants to do biomechanical engeneering.