Recent content by PAllen

The sectional curvature as described can be directly related to the Riemann tensor as written in terms of the metric. BUT, for connection different from the Levi-Civita connection, this would not be the 'right' curvature tensor. So the reliance is there, but rather hidden. If you consider the...

Note, there are other ways to define intrinsic curvature constants. For example, consider the area of a small circle on the surface of a sphere. Measure its area and take the difference with the plane area formula for the same radius as measured on the sphere. Divide by the plane area to get a...

I would think of that more like the case of lightlike coordinates. That a time coordinate is the same along a null path in some direction doesn't make it a possible set of simultaneous events. I would still require that a path be spacelike to make such claim.

Ok, yes, I don't see a reason you couldn't apply the definition in a Riemannian manifold - books just assume a timelike curve. For the Riemannian context, the elements allowing the definition of FW transport are sometimes called Frenet-Serret formulas, but authors don't seem to define FW...

Yes, not the best choice of words.

I've generally seen FW transport only defined along timelike curves, so that definition would simply not apply to Riemannian manifolds. For Lorentzian manifolds, for a vector tangent at some point to a timelike curve, the FW transport of the vector remains tangent to the curve, while the...

I disagree. The definition of a geodesics as a curve that parallel transports its tangent vector makes no sense without parallel transport also being defined for other curves. I have never seen a definition of parallel transport that assumes geodesics. The connection is what defines which...

I would say no change to the status of any inflation aimed at ‘explaining’ the standard model initial state, since the conclusion is to increase confidence in the standard model of cosmology.

A little off topic, but since I alluded to Faraday's long apprenticeship with Sir Humphrey Davy that acted as bridge from self teaching to actual research, an amusing quote from Davy is that when asked, late in life, what he thought his greatest discovery was, he said Michael Faraday.

Wrong. He did a long apprenticeship with Sir Humphrey Davy (president of the Royal Society, world famous chemist) before his work on EM. Also, the field was young and undeveloped compared to physics fields today. Wrong again. He graduated from a top physics school, and was working in a patent...

The problem is (mostly?) fixed now. Just tested it.

I’d never seen that one. At first glance, I like it. Now, I have dig in to determine whether I can believe it …

You, could, of course. I was trying to realize the notion of potential in contrast to surface gravity, as a function of position.

Thanks!

I gave you a single diagram showing that, including where there is 20 kg force.