At big bang, the scale factor $a(t)$ of the FLRW metric was zero, meaning that all points were in touch with one another for a moment. The horizon problem occurs, because two sufficiently far apart points A and B are homogenous even though light from A could never reach B even if it starts on big...

I recently installed three pendant lamps in my dining room. They're three large glass spheres, about 40 cm in diameter, arranged in a line on cables of equal length. I live on the 28th floor of an apartment building and I have neighbors above me (although I've never heard any noise from them). Th...

In a spacetime $(M, g)$ the following identity for the divergence of a vector field $X$ holds $$ \nabla_{\mu} X^{\mu} = \frac{1}{\sqrt{-\det g}} \, \partial_{\mu} \big( \sqrt{- \det g} \ X^{\mu} \big)$$ Does this relation hold term-wise, e.g. does the above relation imply $$ \nabla_0 X^0 = \frac...

I've been working on a problem involving the electric field inside a hollow sphere with known inner/outer radii and a volume-charge density $\rho=\frac{k}{r^{2}}$. I start with Gauss' Law as normal: $\oint_{S}^{}(\overrightarrow{E} \circ d\overrightarrow{a}) = \frac{Q}{\varepsilon_{0}}$ I have no...

I was reading the chat-room associated with this answer, and several times the point is made that the CMB being uniform breaks our expectation that it should be heterogeneous. The analogy given is that it would be weird if everyone showed up to a party dressed identically, and you would likely a...

Let us assume a continuous wave function. Suppose we make a measurement of the position of the particle and obtain as a result the interval $(x_0-\delta, x_0+\delta)$. $\delta>0$ stays for the accuracy of the instrument. If I understand correctly, following the measurement, the collapse axiom (L...

From Newtonian mechanics, the precession of Mercury can be calculated by taking into account the gravitational pull of other planets. From that, I assume that in the absence of external planets, Newtonian mechanics predicts that the elliptical orbit does not precess at all. From General Relativit...