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| bio | website | cambridge.academia.edu/… |
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| location | Cambridge, United Kingdom | |
| age | 23 | |
| visits | member for | 2 years |
| seen | May 16 at 1:28 | |
| stats | profile views | 651 |
Currently undertaking Part III of the Mathematical Tripos at the University of Cambridge.
Previously obtained a B.S. in Mathematics and a B.A. in Physics from the University of Chicago (2012).
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Mar 16 |
awarded | Nice Question |
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Mar 15 |
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The interpretation of mass in quantum field theories added 421 characters in body |
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Mar 15 |
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The interpretation of mass in quantum field theories For what it's worth, I mixed up sign conventions in my previous comment. It should be that $p^2=-m^2$, with the convention used in the Lagrangian. |
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Mar 15 |
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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? |
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Mar 15 |
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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? |
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Mar 15 |
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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? |
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Mar 15 |
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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. |
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Mar 15 |
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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? |
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Mar 15 |
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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? |
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Mar 14 |
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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. |
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Mar 14 |
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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. |
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Mar 14 |
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The interpretation of mass in quantum field theories @LubošMotl 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?". |
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Mar 14 |
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The interpretation of mass in quantum field theories @LubošMotl "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. |
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Mar 14 |
asked | The interpretation of mass in quantum field theories |
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Feb 28 |
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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. |
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Feb 28 |
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Why one-dimensional strings, but not higher-dimensional shells/membranes? added 3 characters in body |
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Feb 28 |
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Why one-dimensional strings, but not higher-dimensional shells/membranes? deleted 14 characters in body |
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Feb 28 |
asked | Why one-dimensional strings, but not higher-dimensional shells/membranes? |
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Feb 28 |
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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. |
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Feb 27 |
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Is the quantization of gravity necessary for a quantum theory of gravity? added 256 characters in body |
