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Apr
7
revised Composition of Lorentz Transformations
fixed metric signature
Apr
7
answered Composition of Lorentz Transformations
Apr
7
comment In continuum mechanics, why is the stress vector $T=\sigma\cdot n$ not a covector?
I'm not. See user1260696's answer. The musical isomorphism makes the distinction between vectors and covectors irrelevant.
Apr
7
comment In continuum mechanics, why is the stress vector $T=\sigma\cdot n$ not a covector?
Are we not working in the presence of a metric? If we are, there's a canonical isomorphism between such tensors, and the distinction between them is utterly without meaning.
Apr
6
comment Special Relativity - Distance Not Increased?
I suggest perusing some of Thorne's consulting for the movie, then. They specifically remark on how fast the black hole must be spinning to produce the amount of time dilation experienced, in terms of gravitational time dilation on a planet (the water planet) at the innermost stable circular orbit of a kerr black hole. The time dilation experienced in the middle act of the movie is almost entirely from this phenomenon--and incidentally, such a black hole must be spinning at almost maximal spin parameter to produce such a pronounced effect.
Apr
6
comment Special Relativity - Distance Not Increased?
That had far more to do with them going deep inside a black hole's gravity well than anything to do with their speeds.
Apr
6
comment Special Relativity - Distance Not Increased?
This being a reasonable explanation of special relativistic time dilation, Interstellar concerns gravitational time dilation, which is a different phenomenon.
Jan
31
answered Why do the Einstein field equations (EFE) involve the Ricci curvature tensor instead of Riemann curvature tensor?
Jan
20
answered What is the mathematical nature of the stress-momentum-energy tensor?
Jan
16
comment Is a metric tensor field the same thing as $ds² = -dt² + dx²+ dy² + dz²$?
@StanShunpike Multilinear maps are functions. They're just linear in each argument.
Jan
1
awarded  Nice Answer
Dec
10
revised Basic question in electromagnetic duality
fixed some sines and cosines
Dec
6
awarded  Enlightened
Dec
6
awarded  Nice Answer
Nov
27
revised Do there exist functions $\phi$ and $A$ such that $\vec E$ satisfies the Helmholtz Theorem $\vec E = -\nabla \phi + \nabla \times \vec A$?
fixed some math about the symbol for reals
Nov
26
comment What do people actually mean by “rolling without slipping”?
@NeuroFuzzy Interesting. I suspect this comment section isn't the place for this discussion, though. Perhaps you could ask a question about rolling on curved surfaces, present your work, and ask for references that might verify or refute your idea? I'd be happy to follow that question if you link to it here.
Nov
26
comment What do people actually mean by “rolling without slipping”?
@NeuroFuzzy Sure, if you define the overall travel of the wheel with respect to the center of the wheel. If instead you measure the overall distance traveled by whatever point is in contact with the ground, I think the bold statement still holds. Regardless, travel of a wheel along a curved surface is more involved, and I think it's good you point that out.
Nov
7
comment Can Gauss' and Ampere's Laws be written in terms of the divergence of an energy four-vector?
Are you not familiar with the special relativistic form of the EM fields, the faraday bivector $F$? Of how Maxwell's equations in vacuum can be written $\nabla \wedge F = -\mu_0 J$ and $\nabla \cdot F = 0$?
Oct
29
comment Is $E^2=(mc^2)^2+(pc)^2$ correct, or is $E=mc^2$ the correct one?
@user929304 It's a purely geometrical phenomenon. It'd be like rotating a vector and asking it to trace out an ellipse instead of a circle. In Minkowski space, boosting a four-velocity traces out a hyperbola. Hyperbolas have asymptotes--lightlike rays, in this case.
Oct
19
awarded  Yearling