Einstein’s Birthday and Pi Day

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It is 3.14, after all.

First, Einstein’s birthday: March 14, 1879. Do you ever use a GPS? Then you are indebtted to Einstein for the Relativistic Time Dilation equation.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

I won’t include the equation, since it won’t add anything. You can find it in many places on the web.

And it is Pi day. π = 3.1415926535… (That is 10 digits, and enough for most applications.)

The video is “A Brief History of Pi.” It is a bit long at just over 16 minutes, but the videos either are just short and entertaining but don’t really explain anything, or they jump into some fairly stiff mathematics and would lose everyone. Go get some pie, and coffee, and enjoy learning a bit of history, and maybe even a bit of math. It won’t hurt, I promise. (Well, maybe for a minute.)

3 thoughts on “Einstein’s Birthday and Pi Day”

  1. There are a couple things going on with GPS satellites. I looked it up a while back.

    First, their orbits take them further out of Earth’s gravity well. Time in a gravitational field runs slower, so in orbit time runs faster relative to the surface of the planet.

    Second, as you observed, time runs slower at higher velocities. So the clocks on the satellites room slower relative to the surface of the planet.

    The time difference due to velocity is greater than that due to gravity, but both have to be taken into account. The frequency of the hardware on the satellites is adjusted to account for the relativistic effects (though I can’t remember which way it’s adjusted). The receivers have to do a bit of math as well, but the satellites send the data they need to calculate an accurate location.

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    • People don’t like to think about time-dilation. Time is supposed to be this universal thing. That it is a function of THIS universe, is confusing to them, because they can’t handle thinking that the math is more real than their everyday experience. (When the truth is, their everyday experience is wrong in a lot of ways.)

      That and math is hard. (or so I’ve been told.)

      When you get to what happens to time around a black hole, their heads really explode.

      But then I love to watch people’s heads explode over stuff like this.

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