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bio website berkeley.academia.edu/…
location Berkeley, CA
age 24
visits member for 2 years, 11 months
seen 11 hours ago

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).


Mar
15
comment The interpretation of mass in quantum field theories
If it helps to clarify, this is how I think about it. There are two notions of mass involved: the mathematical one that is part of our model, and the physical one which we are trying to model. The physical mass needs to be defined by an idealized experiment, and then, if our model is to be any good, we should be able to come up with a 'proof' that our mathematical definition agrees with the physical one. Does that make sense?
Mar
15
comment The interpretation of mass in quantum field theories
Ironically, the word "precise" here is not meant to be precise; it is open to interpretation. The word that really matters here is "operational": to define mass via some sort of (thought) experiment. In section 2.2 of academia.edu/829613/… , I give a classical definition in the spirit of which I am looking, except now, I want to do this in a relativistic setting. I never thought of this until just now, but maybe the idea behind the classical definition could just be modified?
Mar
15
comment The interpretation of mass in quantum field theories
We can define mass this way, and I already know how to relate this definition to the term appearing in the Lagrangian. The question is, how do we relate this mathematical definition of mass to a precise, physical, operational definition of mass. Does that make sense?
Mar
15
comment The interpretation of mass in quantum field theories
If you go this route, then it's really a question about special relativity, not quantum field theory, but I was thinking there were other, deeper reasons that actually require the framework of QFT to understand.
Mar
15
comment The interpretation of mass in quantum field theories
Perhaps you're referring to the fact that $P|p\rangle =p|p\rangle$ and $p^2=m^2$? ($P$ is the element of the Lorentz algebra in the particle's representation and $p$ is a $4$-vector). That's fine, but this just reduces the question to: if a particle has 4-momentum $p$ such that $p^2=m^2$, why do we interpret $m$ as the mass of the particle?
Mar
15
comment The interpretation of mass in quantum field theories
@MichaelBrown I don't know what you're talking about. I imagine my question is unclear as I've never encountered any "standard presentation" that's answered my question (read P&S and Weinberg). Could you, for example, give a page number in Srednicki so I know the argument you're referring to?
Mar
14
comment Why is mass the quadratic term in a Lagrangian?
As a matter of fact, in what we call "non-inertial frames", the relation between force and acceleration will not be of this form. If anything, Newton's second law provides us with a definition of an inertial frame: "Any frame in which $F=ma$.", and then Newton's second Law could be taken to be the statement "Inertial frames exist.", so that this definition of an inertial frame isn't completely useless.
Mar
14
comment Why is mass the quadratic term in a Lagrangian?
I don't think it's quite right to define mass by $F=ma$. If we take the (admittedly imprecise) definition of a force as "Anything that can change the measured velocity of an object.", then we don't know a priori that the relation between force and acceleration will be $F=ma$. For example, if $F=m\dot{a}$, then this $F$ still changes the velocity of the object, and so would still be considered a force. Newton's Second Law has significant physical significance; it is not simply the definition of mass.
Mar
14
comment The interpretation of mass in quantum field theories
@LuboŇ°Motl Also, the question meant to be in the spirit of "If something is not obvious, let us provide an argument to demonstrate it's truth.", as opposed to, "Why can't everything be obvious?".
Mar
14
comment The interpretation of mass in quantum field theories
@LuboŇ°Motl "What's the problem?" -- The problem is in the details of "...finds that it contains particles whose mass is $m$", namely, that I don't know them and would like to.
Feb
28
comment What made us think that Earth moves around the Sun?
It doesn't; they both happen to rotate (though not necessarily in a circle or constant angular velocity) about their center of the mass (if you ignore the rest of the universe). In practice, however, the rest of the universe is negligible and the sun is so much more massive that the center of mass is actually contained within the sun.
Feb
28
comment Is the quantization of gravity necessary for a quantum theory of gravity?
Perhaps I was unclear about what my professor had said. I don't think he meant that the starting point for string theory is 'promoting' the metric to a quantum field, but rather, at the end of the day, this is how you wind up thinking of the metric. To be quite honest, I'm still in the course, and so quite inexperienced, so I expect my interpretation of his meaning is not so accurate. I would suspect that anything that does not make sense is a result of my ignorance, not his.
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 $C\gamma ^\mu C^{-1}=-(\gamma ^\mu )^T$.
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.
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
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
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.