Recent content by Orodruin

The Levi-Civita connection is the unique metric compatible and torsion free connection on a Riemannian manifold (or pseudo-Riemannian). In general a connection has nothing to do with any basis, although its connection coefficients can be expressed in it. The Levi-Civita connection is...

Parallel transport is perfectly well defined along non-geodesic curves. The manifold described in the video is a Riemannian manifold so there is no need to define (or use for) a Fermi-Walker transport.

No, definitely not. There should be no outside reference. If he walks straight forward, he keeps the arrow in the same direction relative to himself. If he walks in a curved path, he needs to adjust the arrow accordingly when he turns. No, see above. No.

This is only correct if you view ##\Delta L## and ##\Delta B## as fixed numbers. In a setting where you have estimated errors, it is more appropriate to view them as statistical distributions, normally Gaussian distributions. If these are uncorrelated then you would obtain the result with the...

They are the same to the ordered considered in the ##\simeq## relation.

The problem statement also states different masses with the same velocity. So we have to go with that? But those two are incompatible. As stated, something in the problem statement needs to be corrected. The simplest change is striking out the y in ”any”, but we simply cannot know what was the...

Of course they can, but not at all times.

I think I found my issue. I was trying ##\sin^2(\theta)##, but when mapping from SU(2) to SO(3), the ##t## here is actually ##\theta/2##? Using ##\sin^2(\theta)## I obtained that the fundamental representation should contain the trivial one once, which would be absurd. Using...

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g)...

For things moving free or at rest, Observe what the first law does best. It defines a key frame, Inertial by name, Where the second law then is expressed. Source: https://www.physics.harvard.edu/undergrad/limericks

You’ve gotten things wrong. The basis is a choice. The typical coordinate basis depends only on the coordinates chosen - the manifold does not even need to have a metric.

Your post seemed to indicate otherwise …

This dependence is present also far away from the dipole.

There is no need to split into cases as you do. The third index is just an additional copy of the 2-index system for every possible value of the index as compared to the basic 2-index systems you mentioned. It follows directly that the symmetric case is 3x6 = 18 and the anti-symmetric 3x3 = 9.

Hint: You don’t need to compute the flux integral. Edit: with the dimensions of A, the cylinder does not completely enclose the sphere. The cylinder radius is too small.