| ISSUE 16/30 · PHYSICS |
~4 MIN |
FOUNDATION / YOUR PHONE · WEEK 03 — NOISY TRUTH
Relativity is running inside GPS
START HERE
Your phone can work out where it is by timing radio signals sent from several satellites. The Global Positioning System, or GPS, is that satellite network. Each satellite carries an extremely precise clock and broadcasts both its position and the time a signal left. If a satellite clock and an Earth clock drift apart by even a tiny amount, the phone converts that timing error into a large distance error.
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/ WHY NOW
Your phone finds its position by comparing time signals from several satellites. Light travels about 30 centimetres in one nanosecond, so a small clock error becomes a large location error. Relative to clocks on Earth’s surface, satellite motion makes the orbiting clocks run slower while weaker gravity makes them run faster. GPS works because engineers account for both effects.
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/ THE IDEA
In an Earth-centred reference frame, special relativity makes the moving satellite clocks accumulate less time. General relativity makes clocks deeper in Earth’s gravity accumulate less time than clocks higher up. GPS satellites move quickly, producing about 7 microseconds per day of slowing, but orbit where Earth’s gravity is weaker, producing about 45 microseconds per day of speeding. The net is about 38 microseconds per day faster than Earth clocks.
THE FORMAL IDEA
distance = speed of light × signal travel time
| the satellite broadcasts when a signal left | | the receiver measures when it arrived | | several distances locate the receiver in three dimensions and correct its clock |
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RUN THE TINY EXAMPLE
Let 38 microseconds accumulate
Clock difference after one day: 38 × 10⁻⁶ s Light distance in that time: 300,000,000 × 38 × 10⁻⁶ Result: about 11,400 m of timing-equivalent distance
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GPS uses corrections rather than accepting that drift. The calculation shows why relativity is not philosophical decoration when position comes from light-travel time.
/ SO WHAT?
Whenever precision timing crosses large differences in speed or gravity, relativity moves from tiny curiosity to engineering requirement. The same issue will matter for future navigation networks around the Moon or Mars.
ONE CAVEAT |
| The 11.4 km figure is a simple distance-equivalent illustration, not the exact daily error of an uncorrected receiver. Real GPS solves for multiple clocks, changing geometry, atmosphere and other relativistic effects. |
KEEP THIS
GPS measures distance with time, so it must correct anything—including relativity—that changes how its clocks tick.
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