Built on Facts

Ever wondered why nobody thought up relativity until Einstein in 1905? Like quantum mechanics, its effects are pretty hard to notice in the everyday world. Here’s a tiny example. According to the theory of relativity, time will pass more slowly for a moving object as measured by someone standing still. Why haven’t you noticed this? After all, when you spend 1 hour in a moving car, it’s not like you arrive at your destination only to find that 2 hours have gone by on the rest of the earth. Physicists will correctly tell you that the difference is real, but is too small to measure. Just how small is it?

Well, tomorrow I’m making about a 6 hour car trip. Let’s say I drive 75 miles per hour. Doing the math, it turns out that I will have experienced less time than the rest of the stationary world… by about 0.1 nanoseconds. See? Hard to measure!

As you go faster, the effect increases. For 6 hours on a jet travlling at 500 miles per hour, the effect increases to about 7 nanoseconds. Still hard to measure, but in fact it has been done and confirmed with sensitive atomic clocks. At space shuttle speeds the effect can be as much as a few hundred microseconds. I don’t know of any experiments done in the shuttle with atomic clocks to measure the effect, but it principle it could be done. But we don’t have to; we can see those exact same effects in GPS satellites which orbit at similar speeds. They accumulate about a 30 microsecond difference per day compared to clocks on the ground, and it has to be corrected for.

By the way, why doesn’t the opposite effect occur? That is, how does a sattelite “know” that it’s moving and that the earth is standing still? And isn’t the earth not actually still, since it’s moving through space?

The answer is of course that there isn’t any preferred “real” reference frame that’s standing still in any real sense. We’ll discuss it more later - but for those who can’t wait, the answer lies in length contraction. From my perspective in the car, the earth’s clocks seem slow by that 0.1 nanoseconds. But I have also covered a smaller distance due to length contraction. The two effects cancel perfectly. But that’s a story for another day.

Slightly more technical note: Curious to plug in some numbers figure out these time dilation factors yourself? Here’s the equation.

Just plug in your velocity v and the speed of light c (make sure the units are the same!) and you’ll get the factor which time has slowed down for you. Multiply that by your time of travel and you’ll find the difference in trip times between your moving clock and clocks on the rest of the earth. This is actually just the first term in the Taylor series of the real equation, so it’s only accurate to around a tenth the speed of light. After that it’s increasingly inaccurate.