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| visits | member for | 1 year, 6 months |
| seen | 14 mins ago | |
| stats | profile views | 252 |
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May 18 |
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Why distinguish between row and column vectors? Why not define vectors to be things that act on covectors to product numbers instead? Because infinite-dimensional spaces need not be reflexive |
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May 13 |
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Physical interpretation of Poisson bracket properties @dmckee: notation is domain-specific, and it's quite common to use curlies for Poisson brackets, both in introductory and advanced literature |
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May 13 |
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Physical interpretation of Poisson bracket properties added 13 characters in body |
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May 13 |
answered | Physical interpretation of Poisson bracket properties |
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May 10 |
revised |
If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? add rational |
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May 10 |
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? @LubošMotl: care to comment on the revision to my answer? |
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May 10 |
revised |
If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? add rational |
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May 10 |
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Are there problems solvable with Newtonian physics, GR and QM? two historically relevant examples would be the perihelion precession of mercury (GR vs Newton) and black body radiation (classical Rayleigh–Jeans law vs quantum Planck's law) |
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May 8 |
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? I'd also like to throw in some nice quotes from this paper: As the thermodynamic entropy is not measurable except when the process is reversible, the second law remains useless as a computational tool. and It is (has?) not been possible to show that the statistical entropy is identical to the thermodynamic entropy in general. |
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May 8 |
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? @LubošMotl: Entropy is well-defined for time-dependent processes. Indeed, it has to be well-defined because the second law of thermodynamics says how it changes during such processes - I don't think that necessarily follows: In particular, there are formulations of the 2nd law that explicitly state There exists for every system in equilibrium a property called entropy, and for irreversible processes the 2nd law only makes a statement about initial and final equilibrium states |
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May 8 |
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If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? @Arnaud: it is indeed hard to define entropy if you don't at least assume local equilibrium; take the dual to your experiment: confine the gas to one side of the box, remove the wall and let it expand; because the rate of expansion is fixed, at each point in time you could re-introduce the wall (freeze the instantaneous system parameter volume) and define the entropy of the expanding gas as the entropy of that equilibrium system |
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May 8 |
answered | If particles can find themselves spontaneously arranged, isn't entropy actually decreasing? |
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Apr 30 |
revised |
First and second fundamental forms embed formula |
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Apr 30 |
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First and second fundamental forms deleted 8 characters in body |
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Apr 30 |
answered | First and second fundamental forms |
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Apr 29 |
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English translation of Helmholtz' paper: “On the Physical Significance of the Principle of Least Action” I just took a quick look at the paper, and the notation is funny - the same letters are used, but with different meanings: the coordinates are $p$ instead of $q$, which in turn is used for the velocities $\dot q$; momenta are $c$ instead of $p$, potentials are $F$ instead of $V$, the Lagrangian is called $H$ and has the opposite sign, ie corresponds to $-L$; kinetic energy is called $L$ instead of $T$; the Hamiltonian is called $H'$ instead of $H$ |
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Apr 28 |
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Rate of spontaneous tachyon emission clarifications |
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Apr 28 |
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Rate of spontaneous tachyon emission @BenCrowell: the point is that there is no local environment of available tachyons: the interaction is non-local and the environment is basically the whole spacetime (or rather the subset at space-like distance); I should probably edit my answer to make this more explicit; I've yet to think about how general relativity (where there's not necessarily a single critical frame) changes the picture |
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Apr 28 |
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Forces as One-Forms and Magnetism velocity-dependent forces cannot be represented as 1-forms on $M$, but rather as 1-forms on $TM$ (the differential of the Lagrangian) or, factoring out a force of inertia, as sections of the pullback of $T^*M$ over $TM\to M$ |
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Apr 27 |
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Is this statement about quantum mechanics valid? see also plato.stanford.edu/entries/qt-quantlog |
