Tag Archives: math

In general relativity…

Energy Is Not Conserved

Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.

Don’t look for a free lunch. There are still rules:

….energy and momentum evolve in a precisely specified way in response to the behavior of spacetime around them. If that spacetime is standing completely still, the total energy is constant; if it’s evolving, the energy changes in a completely unambiguous way.

This has been known since the 1920’s, and I learned about it when I first seriously studied GR at Stanford in 1973. However, scientists now need to pay more attention to it. In recent decades astronomical observations have have revealed many more situations where the effects of general relativity are significant.

Mathematical details at Is Energy Conserved in General Relativity?

Subtleties of the Solstice

From The winter of our solsticular discontent

The winter solstice marks the longest night and shortest day of the year. However, it’s not when the Sun rises latest and sets earliest! The Earth has the unfortunate habit of orbiting the Sun in an ellipse, which screws things up a bit when it comes to timing.

Plugging Minneapolis into the Sun or Moon Rise/Set Table for One Year: U.S. Cities and Towns shows that sunrise is going to continue getting later for another couple weeks, while we are well past the earliest sunset. Hence I have been seeing a little more daylight when I get off my bus home in the evening.