Recent content by Sagittarius A-Star

Yes. But ##\Phi_B = \int \int_\Sigma {\vec B \cdot d\vec S}## changes over time, because the angle between the magnetic field and the normal to the rotating surface changes over time. ##\Phi_B (t) = SB \cos {(\omega t + \alpha})##, where ##S## is the area of the loop. ##EMF = - {d\Phi_B...

For geometric intuition: In Geometric Algebra, the electromagnetic bivector can be written in the following way as the sum of a projection on the parallel and a rejection on the perpendicural part. The sandwitch product ##uFu^{-1}## is a reflection with respect to the hyperplane with normal...

I think in GR tidal gravity, it just has to be small enough and insensitive enough.

Is it a matter of adoption of a definition, what a true force is? I think a true force can be measured with an accelerometer.

Why? I think a true force creates a deviation from the geodesic.

I don't think so. If for example an asteroid breaks in tidal gravity, the related forces are electrical forces between parts of it.

This video shows, how to use ##\LaTeX## in MS word.

This is not a full solution for problem (3b), but maybe a useful hint. When I substitute the RHS of (3b) into (3a), the two Levi-Civita-symbols share 2 indices, like in the given identity. Problem (3b) with renamed indices: ##F^{\gamma \delta}=(space/time-part)+\epsilon^{\gamma \delta}{...

Additional insight: The 4-vector ##E_{\vec U}^\alpha## from problem (3a), multiplied with charge ##q##, gives the Lorentz 4-force on a test charge with 4-velocity ##U##. ##f^\alpha=qE_{\vec U}^\alpha=qF^{\alpha\beta} U_\beta##.

The following refers to special relativity. It is sufficient to prove the validity of the equation of part (b) in only one basis. This would prove automatically it's validity in any basis. The headline of problem (3) is: “3+1 split of the electromagnetic field". A "3+1" split is...

According to Wikipedia, this is a non-relativistic equation. The relativistic equation is shown below in Wikipedia. https://en.wikipedia.org/wiki/Abraham%E2%80%93Lorentz_force#Definition_and_description The same question regarding the relativistic equation is discussed in the Wikipedia article...

What may help is the following hint in the description of problem #3: ##\vec{e}_{\hat 0} = \vec U## In special relativity, in the restframe of the observer, his 4-velocity has the following components: ##U^\alpha = \begin{pmatrix} 1 \\ 0 \\ 0 \\ 0 \\ \end{pmatrix}## You may right-click ("Show...

As delimiters, you can use double $ or double # on each side. See in below LaTex Guide link under "Delimiting your LaTeX code".

For a rotating disk with only 3 rings (because of Wolfram Alpha calculation limitations): ##\lim_{v \rightarrow 1} {E/M} =## ## \lim_{v \rightarrow 1} {\sum_{i=1}^3 \frac{2i}{12\sqrt{1-v^2i^23^{-2} }}} = \infty## Calculation

I get from Wolfram Alpha 44.676683503771391589009225229630072178116008914652013623324856498 Calculation