2,096 reputation
11031
bio website berkeley.academia.edu/…
location Berkeley, CA
age 24
visits member for 3 years, 5 months
seen Oct 21 at 19:10

Currently a graduate student in mathematics at the University of California - Berkeley.

Previously obtained a MASt. in Applied Mathematics from the University of Cambridge (2013), and a B.S. in Mathematics and a B.A. in Physics from the University of Chicago (2012).


Feb
13
revised Why quantum mechanics?
added 2 characters in body
Feb
12
comment Charge conjugation in Dirac equation
This can be taken as a definition of $C$ if you like, although it does not uniquely specify a $C$. You have to normalize. Let $\gamma ^\mu$ be an irreducible representation of the Clifford algebra $\mathcal{C}\ell (1,3)$. You can check that the matrices $\gamma '^\mu :=-(\gamma ^\mu )^T$ also define a representation of this algebra. There is a theorem about Clifford algebras that says there is essentially only one (faithful) irreducible representation, and hence these two representations must be equivalent, i.e. there is a unitary $C$ such that $C\gamma ^\mu C^{-1}=-(\gamma ^\mu )^T$.
Feb
11
awarded  Nice Question
Jan
26
awarded  Nice Question
Jan
26
comment Is the quantization of gravity necessary for a quantum theory of gravity?
I've since added to my original question, and I would be interested if you have anything additional to say.
Jan
26
comment Is the quantization of gravity necessary for a quantum theory of gravity?
I've since added to my original question, and I would be interested if you have anything additional to say.
Jan
26
comment Is the quantization of gravity necessary for a quantum theory of gravity?
I've since added to my original question, and I would be interested if you have anything additional to say.
Jan
26
revised Is the quantization of gravity necessary for a quantum theory of gravity?
Extended question
Jan
25
asked Is the quantization of gravity necessary for a quantum theory of gravity?
Dec
8
awarded  Nice Question
Dec
7
comment Why quantum mechanics?
@juanrga I completely rewrote one part of my question that I realize was not worded so well. Perhaps it makes more sense now?
Dec
7
revised Why quantum mechanics?
Clarified meaning (hopefully) immensely.
Dec
7
comment Why quantum mechanics?
@juanrga I was trying to demonstrate what I meant when I originally said "Make as little use of experiment as possible.". What I really meant was "When you make use of experiment, use it to justify as fundamental results as possible". In principle, you would reduce kinetic theory to even more fundamental physics, and so on, and eventually you would get to the point where you couldn't reduce things theoretically anymore, the only thing you could do is justify your assumptions on the basis of experiment, as opposed to just more theory.
Dec
7
revised Why quantum mechanics?
added 263 characters in body
Dec
5
awarded  Announcer
Dec
5
comment Why quantum mechanics?
@dmckee No, that wasn't really what I was thinking of. I already have an abstract formulation in mind: the usual Hilbert space formulation in which states are elements of the space and observables operators on it. If all you were aware of is classical mechanics, no one in their right mind would guess that's how things should work. Are there a couple of fundamental physical principles that we can make use of that could convince a student who had never seen any of this before that this formulation is in fact quite natural.
Dec
5
comment Why quantum mechanics?
In the Weinberg example, he takes a couple of assumptions that we feel are relatively fundamental and in principle verifiable by experiment (Loretnz invariance of the $S$-matrix and Cluster Decomposition Principle), and uses them to show that the concept of a field naturally arises as a result of demanding the interaction be of a particular form (which itself is dictated by the assumptions). I would like to see an argument that utilizes just a few physical principles to justify the usual Hilbert space formulation of quantum mechanics.
Dec
5
comment Why quantum mechanics?
@EmilioPisanty Essentially, yes.
Dec
5
revised Why quantum mechanics?
added 136 characters in body
Dec
5
comment Why quantum mechanics?
See edit to question. Obviously, you'e going to have to appeal to experiment somewhere, but I feel as if the less we have to reference experiment, the more eloquent the answer would be.