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seen Mar 14 at 14:18

Oct
19
revised Reconciling Units in Classical System Analogies: Why Does Torque Have Units of Energy?
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Oct
19
revised Reconciling Units in Classical System Analogies: Why Does Torque Have Units of Energy?
added 148 characters in body
Oct
19
answered Reconciling Units in Classical System Analogies: Why Does Torque Have Units of Energy?
Oct
16
comment Are Lockheed Martin nuclear fusion claims realistic?
see also en.wikipedia.org/wiki/Magnetic_mirror
Oct
16
revised What is divergence?
make answer easier to digest
Oct
16
revised What is divergence?
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Oct
16
answered What is divergence?
Oct
16
comment What is divergence?
The divergence of a vector field is the infinitesimal relative change in volume when transporting a volume element along its flow. The abstract definition in terms of Lie derivative and volume form is quite intuitive here.
Sep
30
awarded  Explainer
Aug
21
awarded  Announcer
Aug
20
awarded  Nice Answer
Aug
10
comment QM without complex numbers
@Problemania: $U(n)=Sp(2n,\mathbb R)\cap O(2n)\cap GL(n,\mathbb C)$; however, the intersection of any 2 of the groups on the RHS is sufficient, and in particular $U(n)=Sp(2n,\mathbb R)\cap O(2n)$; complexity arises naturally when we deal with compatible symplectic and orthogonal structures; of course it's equally valid to say that symplectic structures arise naturally from compatible orthogonal and complex structures or orthogonal ones from compatible symplectic and complex ones; but complex structures are arguably less well motivated from a physical (or perhaps 'philosophical') point of view
Aug
3
comment Why can't we do some basic algebra in tensor calculus?
assuming a background in basic linear algebra, think in terms of matrices (which are rank-2 tensors): not all matrices are invertible, and those that are generally aren't orthogonal (ie $A^t\not=A^{-1}$)
Jul
31
comment Which function denotes the energy of thermal motion within a system?
$\frac32 NkT$ for translational motion as well as appropriately weighted multiples of $NkT$ for vibrational and rotational motion as long as quantum effects can be neglegted (ie the spacing of the discrete energy levels is much smaller than $kT$)
Jul
27
comment Can statistical mechanics explain the second law completely?
Let us continue this discussion in chat.
Jul
27
comment Can statistical mechanics explain the second law completely?
I also never understood how your 'logical arrow of time' isn't killed by Loschmidt's paradox; in case of Markov processes, it apparently is, but I have yet to read the cited paper in detail
Jul
27
comment Can statistical mechanics explain the second law completely?
@LubošMotl: note that Botzmann's position on entropy evolved over the years in reaction to cricism by others like Poincaré and Zermelo; in Zu Hrn. Zermelo’s Abhandlung "Ueber die mechaniche Erklärung irreversibler Vorgänge", he mentions the idea that the universe started from an improbable low-entropy state and that there might be regions of the universe with opposite directions of the thermodynamic arrows of time (to which the subjective arrow of time would assumably align); Schrödinger (and probably others) argued that this latter case is impossible under certain (mild) assumptions
Jul
26
comment Can statistical mechanics explain the second law completely?
@BenCrowell: arXiv:0809.1304 cites Uffink, "Compendium of the foundations of statistical physics" (sections 7.6, 7.7) and Bacciagaluppi, "Probability and time symmetry in classical Markov processe", which both essentially conclude that there is no such T-breaking without further assumptions (which was also Boltzmann's position)
Jul
23
answered Why is Entropy's Definition Useful?
Jul
21
comment What is “Energy” of a vacuum in the context of quantum theory?
The problem with 'true nothing' is that it is unphysical: Take a volume of space and remove 'everything', and you won't end up with 'nothing', but with the vacuum, which, philosophically speaking, is a 'something'. Krauss goes a step beyond the vacuum and assumes that spacetime as well as the laws of physics as we know them emerge dynamically (eg via symmetry breaking) from the true groundstate of a theory of quantum gravity. This groundstate is what he calls 'nothing'.