the Michelson-Morley experiment set out to measure the presence of the hypothetical luminous aether by measuring the difference in the speed of light of two paths of a split beam of light that are at right angles to each other. assuming the Earth must be traveling through the aether at some time during the year as it revolves around the Sun, this difference of speed should be measurable with their apparatus.
the performed the experiment many times, at different times of day and different seasons of the year and never got a positive result (that is a measurable difference of the speed of light in those two directions).
Einstein simply said "hell, yes. why not? there was no measured difference in the speed of light because there was no difference in the speed of light to measure." that the speed of light (which is really the speed of any instantaneous interaction, E&M, gravity, strong force, whatever) in a vacuum is constant and the same for any (inertial) observer anywhere in any direction is a postulate of SR. from that postulate Einstein notices that all sorts of strange things happen regarding time, length, apparent mass, especially if one observer is whizzing by another at a speed approaching c.
1. The Big Idea:
According to Einstein’s relativity, all motion is relative. You can’t tell if you’re moving at a constant velocity without looking outside. But what if there is a universal “rest frame” (like the old idea of the “ether”)? This experiment tries to find out by looking for tiny, directional differences in how objects move inside a sealed box.
2. How It Works: The Two-Stage Process
Imagine a perfectly isolated spacecraft (our lab) moving through space at some unknown speed V...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.
The Relativator was sold by (as printed) Atomic Laboratories, Inc. 3086 Claremont Ave, Berkeley 5, California , which seems to be a division of Cenco Instruments (Central Scientific Company)...
Source: https://www.physicsforums.com/insights/relativator-circular-slide-rule-simulated-with-desmos/
by @robphy
In Philippe G. Ciarlet's book 'An introduction to differential geometry', He gives the integrability conditions of the differential equations like this:
$$
\partial_{i} F_{lj}=L^p_{ij} F_{lp},\,\,\,F_{ij}(x_0)=F^0_{ij}.
$$
The integrability conditions for the existence of a global solution ##F_{lj}## is:
$$
R^i_{jkl}\equiv\partial_k L^i_{jl}-\partial_l L^i_{jk}+L^h_{jl} L^i_{hk}-L^h_{jk} L^i_{hl}=0
$$
Then from the equation:
$$\nabla_b e_a= \Gamma^c_{ab} e_c$$
Using cartesian basis ## e_I...