The Space-Time Continuum and Your GPS

Did you know that every time you use your GPS to guide you to your destination you are applying one of the most profound ideas put forth in the twentieth century—the idea of the space-time continuum?

Albert Einstein proffered the idea in 1915 with his new theory of general relativity. He theorized that space and time are not independent, isolated entities, but merge into one element or “fabric” called space-time. The general theory addresses gravity and acceleration and shows in part that one can not distinguish between being in a gravitational field or under constant acceleration. But, it goes much deeper, as we shall see.

One can see how space and time are intimately related when you consider how the Global Positioning System works. Your location is determined by your GPS device when it receives a signal from at least 4 GPS satellites in orbit. By comparing these satellite signals to a reference signal in your GPS it can calculate the time-lag between them and thereby your distance from the satellites. By using multiple satellites your location can be accurately determined. Precision clocks on board the satellites are required to generate the satellite’s signal. These clocks will drift because of two relativistic effects that affect them: the speed they are traveling at—14,000 km/hr (8,424 mph)—and the distance from the Earth—about 26,600 km (15,960 miles).

Note that if we used only Newtonian mechanics to design the GPS system it would not work. We need to incorporate both of Einstein’s theories—special and general relativity if we are to eliminate these errors. (Newtonian mechanics are still very important and useful in determining orbital parameters of spacecraft and the planets—except for Mercury, but that’s another blog topic!)

First, let’s look at the Special Theory of Relativity, since most people are familiar with its basic premise that the closer you travel to the speed of light, the slower time passes. (Remember the twins paradox?) For the satellite in orbit moving at a high rate of speed, its clock will run slower than a corresponding clock on the surface of the Earth.

Now let’s consider the General Theory of Relativity. If a clock is in a gravitational field it will run slower the closer it is to the source of the gravity field—i.e.: closer to the surface of the Earth. The further the clock is from the source of the field, the weaker the field is—i.e.: the higher your altitude above Earth’s surface, the faster the clock will run. (The field falls off as one over the distance-squared.)

The effect on the satellite’s clock due to the gravitational field is almost six times that of the effect due to its speed. The combination of these two relativistic effects would cause your GPS to accumulate an error, which is on the order of 6 miles or 10 km per day!

This application of Einstein’s two theories shows how time and space are tied together in a way that our day-to-day life experiences would never reveal. Our internal biological clocks are being affected by the speed at which we travel and when we move through a gravitational field. So it’s not just covering a distance when you travel from point A to B, but moving through time as your biological clock changes as your speed changes and you move through a gravitational gradient. These effects are very small at the speeds we travel and the typical change in altitude we might experience. They are on the order of nano-seconds (billionths of a second)—small but real.

For more details on the topic of GPS and relativity, check out my article at Bright Hub.

Till next time,
RC Davison

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