# Time dilation is easy to measure now

Physics Explained: Deriving Einstein’s most famous equation: Why does energy = mass x speed of light squared?

At 19:56 the ? is the time derivative of the gravitational time dilation which has terms for gravitational potential, velocity potential, and electric and magnetic potential. For satellites (GPS/GNSS) velocity and gravitational potential are used. And it changes constantly. Now there are gravimeters, gravity gradiometers and various sensors that can measure it. Lots of groups using many methods. Usually it is more intuitive if you multiple by the speed of light top and bottom. That gives c/sqrt(c^2 + 2*GM/R – V^2 + magnetic and electric terms) All the terms in the square root have units of potential (Joules/kg) But these simple equations are never used. You go to the groups doing the measurements and see what models and data they use for real. Look for time dilation, combined effect of velocity and gravitational time dilation. These are big effects with today’s sensor networks. The magnetic fields needed are hundreds of Tesla, but that too is routine now with high harmonic gain lasers and accelerator beams. G and mu0 are simply related in energy density terms to convert from acceleration to magnetic units.

LIGO ought to measure these things and share in geophysics research and solar system efforts. But they ignore it and call it “Newtonian noise”. A few people still keep trying there. But it is taking them decades to do things they could do in a short time, because they ignore the earth’s really large signals and groups.

You miss a big opportunity for teaching by only talking about things, and not giving tools, data and community. Talking does very little.

Richard Collins, The Internet Foundation