Have you ever wondered how your phone determines your exact location when you launch Google Maps or another GPS app? It appears to be magic, but behind this everyday convenience lies one of the most groundbreaking scientific theories ever developed: Einstein’s theory of relativity. What fascinates me is how a complex, century-old theory can help us navigate our modern world so precisely.
To understand GPS, we must first discuss Einstein’s theory of relativity, specifically his theories of special relativity (1905) and general relativity (1915). These ideas fundamentally altered our understanding of the universe. Simply put, Einstein demonstrated that time and space are not absolute—they are flexible and depend on your speed and the strength of gravity around you. These effects, known as time dilation and gravitational time dilation, are minor but noticeable when dealing with satellites in orbit.
Now, let’s get into the mechanics of GPS. The Global Positioning System (GPS) is a network of 24 satellites orbiting the Earth at an altitude of approximately 20,200 kilometres. Each satellite transmits a signal that includes the current time and its precise location. The GPS receiver in your phone or car listens for signals from multiple satellites and calculates the time it takes for each signal to arrive. It uses this information to determine your location using a process known as triangulation. But here’s where Einstein’s theory comes into play: GPS time and distance calculations must account for relativity in order to be accurate.
Einstein predicted that moving clocks would run slower. This is known as time dilation in special relativity. Satellites orbiting the Earth move at approximately 14,000 kilometres per hour, so their clocks would tick slower than clocks on the ground if we did not account for this effect. But there’s another factor: satellites are much farther away from the Earth’s surface, where gravity is weaker. General relativity states that clocks farther away from a gravitational source (such as the Earth) run faster than those on the surface. So we have two competing effects: the special relativity effect, which slows the satellite clocks, and the general relativity effect, which accelerates them.
The net result? Satellite clocks run approximately 38 microseconds faster per day than clocks on Earth. Without correcting for this, your GPS will be off by kilometres within a few hours! Thanks to Einstein, we know how to account for these time differences, allowing GPS to be astonishingly precise—down to a few meters.
Time dilation effects can be calculated using Einstein’s equations. The time dilation factor in special relativity is calculated as γ = 1 / √(1 – v²/c²), where v is the satellite’s velocity and c is the speed of light. For GPS satellites, this causes a time dilation of approximately -7 microseconds per day. The general relativity effect is represented by the equation Δt = (gh/c²) × t, where g is the gravitational acceleration on Earth’s surface, h is the satellite’s height, and t is the time interval. This effect causes time dilation of approximately +45 microseconds per day. The difference between these two values adds up to +38 microseconds per day.
GPS precision has a significant impact in the real world. For example, in agriculture, GPS-guided tractors can plant crops with a 2.5 cm accuracy, reducing overlap and saving up to 10% on fuel, seed, and fertiliser costs. GPS-based systems have improved aviation safety and efficiency, with one study indicating a 50% reduction in controlled flight into terrain accidents following their implementation. The economic impact is also significant, with the GPS industry estimated to generate more than $300 billion in the United States alone, according to RTI International’s 2019 report.
GPS technology originated during the Cold War. The US Department of Defence initially developed it for military use. By the 1980s, the system was ready for civilian use, but the accuracy was initially reduced for non-military applications until the year 2000, when full precision became available to the public. But, even before that, scientists knew that relativity would have to be incorporated into the system’s design. The brilliant minds who developed the first GPS system in the 1970s and 1980s relied on Einstein’s equations to ensure its accuracy.
Each GPS satellite has four atomic clocks, two caesium and two rubidium. Our clocks are accurate to within one second every 100,000 years. The satellites orbit at an altitude of approximately 20,200 kilometres, completing two full orbits in a single Earth day. They are organised into six orbital planes, each inclined 55 degrees to the equator, so that at least four satellites are visible from any point on Earth at any time. These satellites transmit very weak signals, about 20 watts, equivalent to a refrigerator light bulb, but they can be detected by Earth receivers thanks to sophisticated signal processing techniques.
Interestingly, the engineers who developed GPS were aware of Einstein’s predictions but conducted tests to validate them. The results confirmed that relativity had a measurable impact on the timing of satellite signals, necessitating the incorporation of those corrections into the system’s algorithms. This was one of the first practical confirmations that Einstein’s theory is applicable not only in the distant universe, but also in our daily lives.
Moving forward, the next generation of GPS technology, known as GPS III, promises even greater accuracy and resilience. These new satellites will be three times more accurate than current ones, as well as eight times more jam-resistant. Furthermore, the combination of GPS with other global navigation satellite systems such as Europe’s Galileo and Russia’s GLONASS could result in sub-centimeter accuracy. This level of precision could lead to new applications such as self-driving cars, more efficient air traffic control, and even early warning systems for natural disasters like earthquakes and tsunamis.
In conclusion, every time you use GPS to navigate your way through traffic, find a new restaurant, or track your run, you’re relying on one of the most brilliant ideas in the history of physics—Einstein’s relativity. It’s amazing to think that a theory developed over a century ago is at the heart of such a modern, everyday technology. The beauty of science is how these ideas evolve and find their way into our lives, often in ways we never imagined. GPS is a perfect example of how deep scientific principles can become part of something as routine as navigating to your destination.
