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Jul
16
comment Why does wet skin sunburn faster?
water drops can focus light; a quick google search yielded eurekalert.org/pub_releases/2010-01/w-cad010810.php and onlinelibrary.wiley.com/doi/10.1111/j.1469-8137.2009.03150.x/…
Jul
12
comment Maxwell's Equations in curved spacetime
Maxwell's equations characterize the critical points of the Yang-Mills functional of a $U(1)$ principal connection; arguing from a subjective point of view of mathematical 'beauty', any generalization that doesn't come with an equally nice geometric story would smell iffy to me...
Jul
2
awarded  Fanatic
Jun
19
answered Is the Green function a prescription for a connection?
Jun
15
comment Can the photoelectric effect be explained without photons?
note that a semi-classical treatment of Compton scattering (which Schrödinger derived in 1927) does get parts of the physics right - but not all of it (as with the photoelectric effect, you need QED for that); also note that a semi-classical approach that attributes clicks of a detector in optical experiments to the quantum nature of the detector (instead of the field) can be closer to reality than the naive picture of photon particles hitting the detector - a QED photon is inherently delocalized and shouldn't be confused with localized wave packets (which we sometimes call photons as well)
Jun
15
comment Examples of “pseudo quantum effects” in history of physics
classical and semi-classical descriptions can give descriptions that are indistinguishable from quantum results at a given experimental accuracy; eg violations of Bell's inequality can be created classically via sampling bias due to threshold detectors; this loophole has (afaik) been closed experimentally, but only fairly recently (which makes this a counter example and thus not an answer to your question); in a similar vein, Khrennikov is developing a classical formalism that approximates quantum mechanics, but leads to a modified Born's rule;
Jun
12
comment How is a Hamiltonian constructed from a Lagrangian with a Legendre transform
The action is a functional, but it's perfectly fine to call the Lagrangian a function; actually, in case of first-order mechanics it should be a 1-form $L=\mathcal L\mathrm dt$ on the jet bundle $J^1Q$ of some configuration bundle $Q\to\mathbb R$, but if we don't care about generalizations, we can get away with considering the Lagrangian a function $\mathrm TM\times\mathbb R\to\mathbb R$ for $Q=M\times\mathbb R$
Jun
9
comment Small unclarity in proof of Noether's Theorem
it's the chain rule - regardless if you're looking at $L$, $L\circ q$ or $L\circ\phi^\lambda\circ q$, the leftmost term will always be $\partial L/\partial x$
Jun
9
comment Small unclarity in proof of Noether's Theorem
in both cases, it's the partial derivative of $L$ with respect to its first variable; it might be less confusing if you'd given the variable and the trajectory a different name, eg $L=L(x,v,t)$ and use $\partial L/\partial x$, regardless if you evaluate the function at $(q(t),\dot q(t), t)$ or $(\phi^\lambda(q(t)),\partial_t\phi^\lambda(q(t)),t)$
Jun
3
comment If particles can find themselves spontaneously arranged, isn't entropy actually decreasing?
(continued) some people claim a single point of view works for everything, and that is - with respect - bullshit; in particular, the physics of equilibrium systems make a lot more sense if you take the point of view I described in my answer
Jun
3
comment If particles can find themselves spontaneously arranged, isn't entropy actually decreasing?
@josephf.johnson: basically, there are 2 points of view - the bayesian/information-theroretic one, which is important in statistical mechanics to explain where thermodynamics comes from and why it works at all; however, once we've arrived at equilibrium thermodynamics, a frequentist/dynamical point of view becomes important so we can relate abstract statistical quantities to physical ones (temperature as average energy in case of equipartition, pressure as number and strength of collisions if the particle approximation holds, the characterization of entropy given above for ergodic systems)
Jun
1
comment How does the boiling time depend on the number of eggs
@userØØ7: but wouldn't the energy used to cook the eggs dissipate into the environment anyway if they weren't present?
Jun
1
comment How does the boiling time depend on the number of eggs
even in a text book on proportionality, it could be a 'trick question' to establish limits of applicability, so I'd be careful with such meta-reasoning; as a side note, when I'm boiling eggs, the more eggs, the less water I'll use...
May
28
awarded  Talkative
May
27
comment Can one of Newton's Laws of motion be derived from other Newton's Laws of motion?
I disagree - from a geometric point of view, the important part of the first law is the existence of a notion of being at rest or of moving uniformly straight forward; I'm actually reading through Giachetta, G.; Mangiarotti, L.; Sardanashvily, G., Geometric Formulation of Classical and Quantum Mechanics right now, where this translates to the choice of a holonomic connection on the jet bundle $J^1Q\to\mathbb R$, whereas external forces are given by sections of the vertical cotangent bundle of $J^1Q\to Q$
May
25
revised Group Theory in General Relativity
added 14 characters in body
May
25
answered Group Theory in General Relativity
May
22
comment How do moving charges produce magnetic fields?
@ChrisWhite: thanks for the clarification, I failed to understand the premise of your setup; a non-vanishing magnetic field will generally have a effect on the test charge, though (alignment of intrinsic magnetic moment); can that be modelled sensibly as well, eg by making the rest frame of the test charge rotate?
May
22
comment How do moving charges produce magnetic fields?
I don't think that's the whole story. The electromagnetic field can only be reduced to an electric one in case of $P<0$. In case of $P>0$, your description breaks down and you'd be forced to consider magnetostatics the fundamental interaction that gets boosted to different frames...
May
21
revised How do moving charges produce magnetic fields?
added 38 characters in body