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1d
comment What is $\omega \times v$?
@Neyamul Better yet, why not learn what cylindrical coordinates are? mathworld.wolfram.com/CylindricalCoordinates.html They're just like plane polar coordinates except with the $z$-direction added.
2d
answered What is $\omega \times v$?
Apr
15
comment Are Newton's “laws” of motion laws or definitions of force and mass?
@CuriousOne Come on dude, I appreciate your substantive criticisms, and I'm happy you read the post carefully because your input helped correct bad errors. Just try to come off as less of a prick; there are more than enough of those to go around.
Apr
15
comment Are Newton's “laws” of motion laws or definitions of force and mass?
@CuriousOne I agree with almost everything you've said -- I'm not sure I read my own post carefully enough in this instance, and both laws have been modified. On one point I'm not sure I agree: I do think isolation makes the situation better (as you indicated at first with "That's better" but backed away from with "which doesn't really make the situation any better"). I'm also not sure (ironically) how exactly comments like "That's kind of sad for the quality of this forum" help improve the quality of this forum and make the situation less "sad," which presumably is the aim of the comment?
Apr
15
revised Are Newton's “laws” of motion laws or definitions of force and mass?
deleted 1674 characters in body
Apr
15
comment Are Newton's “laws” of motion laws or definitions of force and mass?
@CuriousOne You're right that's a glaring (unintended) error. The intention was to include the qualifier "isolated," but I somehow didn't include that and missed it upon further reads. I'll make the appropriate edit in a moment. Let me know if you have anything else to add before I do.
Apr
10
comment Statistical Physics: How do we derive this equation?
@whatwhatwhat Expand the second term in brackets using the product rule for differentiation. I think I'm gonna let you grapple with the rest. It's good for character-building :)
Apr
10
comment Statistical Physics: How do we derive this equation?
@whatwhatwhat Note that $\sum_i \frac{\partial p_i}{\partial V} = \frac{\partial}{\partial V}\sum_i p_i = \frac{\partial}{\partial V} 1 = 0$, but with the $E_i$ in the sum, you cannot do this sort of thing to get zero. As for the entropy expression, you're very close. The log and exponential undo one another, so you get $-k\sum_ip_i(-\beta E_i) = k\beta \sum_ip_iE_i = k\beta U$.
Apr
10
comment Statistical Physics: How do we derive this equation?
@whatwhatwhat Yes. See the addendum. Note that whatever method you use, the trick is deciding what you're willing to accept as the mathematical expression for pressure as your starting point.
Apr
10
revised Statistical Physics: How do we derive this equation?
added 1452 characters in body
Apr
10
comment Why is renormalization necessary in finite theories?
@innisfree I think we're getting unnecessarily pedantic / concerned with semantics. RG is so useful in analyzing certain systems (e.g. studying critical phenomena), that it would be difficult to make do without it. I am not a condensed matter expert, but I would also wager that there are certain results that cannot currently be derived without RG, so in that sense, one could legitimately say that it's necessary. Perhaps something along these lines is what the authors are trying to say in the original quote.
Apr
10
answered Statistical Physics: How do we derive this equation?
Apr
9
comment Statistical Physics: How do we derive this equation?
So you're looking for a justification of the result 4.10? Would you be willing to accept a thermodynamical expression for pressure as a starting point?
Apr
9
comment Why is renormalization necessary in finite theories?
The partition function $Z(\mathbf u, \Lambda)$ is for a finite theory (one that perhaps happened to arise from regularization of an ill-defined one), and the ensuing renormalization analysis (which has nothing to do with infinities and everything to do with scaling) is illuminating. Another example would be some theory on a lattice in condensed matter. The theory may be finite, but a renormalization analysis is useful to understand how it behaves at different scales. en.wikipedia.org/wiki/Renormalization_group
Apr
6
awarded  Good Answer
Apr
3
comment Statistical Mechanics: Computing a system's microstate multiplicity
@SkyTalentz See the addendum.
Apr
3
revised Statistical Mechanics: Computing a system's microstate multiplicity
Added intuition addendum
Apr
3
comment Statistical Mechanics: Computing a system's microstate multiplicity
@SkyTalentz I'm not sure it's productive to try to identify a "main" difference. If you want intuition about why they're different, I think a great way to obtain it would be to try imagine those two scenarios for small numbers $N$ and $Q$, and see what happens.
Apr
3
answered Statistical Mechanics: Computing a system's microstate multiplicity
Mar
30
comment Physical meaning of $Tr(\rho ^2)$
It's not clear to me how this constitutes an interpretation of the quantity $\mathrm{tr}(\rho^2)$.