How Einstein's Relativity Theory Help GPS Become More Accurate

"What do you want to be when you grow up?"

My funny uncle who was a professor of engineering asked with a twinkle in his eye; his brow wrinkled mischievously.

I hesitated. I wanted to be a lot of things. But at that moment I shouted, "A magician!"

"Here is magic for a fellow magician," he appeared solemn for a second.

True to the comical nature he reached behind my ear and pulled out one candy.

Well, my five-year-old self had never wanted to be a magician so bad like I did that day. Imagine the never-ending supply of candies by merely reaching behind people's ears.

But knowing what I know now, I think I would have wanted to be an Einstein. The man is more than a genius. Today we can find our way to that event courtesy of GPS or track our stolen car, bicycle or truck to an accuracy of up to 5m courtesy of the incredible technology of the GPS.

And who do we owe the accuracy and precision of the technology? You guessed it. Einstein!

In 1905, a young Albert Einstein, at the age of 26, proposed the special theory of relativity. It was a theory that reconciled the ideas of Newton Laws of electromagnetic induction and physics of a body in motion as set by Galileo Galilei.

The theory is of the view that the speed of light remains unchanged irrespective of the position of the person that measures it.

So, a person on a broken-down truck and the pilot flying at twice the speed of sound will measure the same speed of light. There is no change in the speed of light to both observers.

It examined the relationship between space and time; they are intertwined more than previously thought possible.

Later in 1915, Einstein published another paper known as the theory of general relativity. The gravity in the universe gets involved while considering its relativistic behaviour.

The concept of equivalence principle is important at this juncture. It equates the pull of gravity in one direction to that of acceleration in the other.

The equivalence principle explains the feeling of decreased gravity in an elevator that is descending and an increased gravity in one that is ascending.

In other words, we equate the inertial forces due to gravity to that as a result of acceleration; it implies gravity and acceleration affects the measurement of time and space.

So a massive object like a star warps its time and space via its gravity.

Here we have gravity as a warp of space-time and not a force. And we have Einstein to thank for that. Thank you, Einstein.

Scientists observe that clocks on Earth are slower than those in orbital satellites that is far (approximately 20,200 km (12,550 miles) from the earth. Time as we know it passes faster in that orbit that is far away from the earth's mass than clocks on earth. This phenomenon is known as the gravitational time dilation.

The Global Positioning System (GPS) at the cost of over $10 billion built mainly for the military navigation is an industry that has found a lot of application in our daily, often, civilian living.

It is a system that is based on the use of 24 arrays of satellites, each orbiting the earth. Onboard each satellite is a precise atomic clock.

A low-end android phone armed with a GPS receiver can receive the radio transmission from any three or four of the GPS satellites at any given place on earth.

It can decode the received message to determine the latitude, longitude or altitude of a particular location. The accuracy of such is correct to up to 4.9 m or 16 feet in the open sky, and determine the time to an accuracy of within 100 nanoseconds or 100 billioths of a second.

At the launch of the first navigation satellite, the Navigation Technology Satellite 2 (NTS-2) in 1977, some were sceptical of the relativistic effect on the accuracy of the GPS signal.

So they deployed the satellite with the switch that can counter relativity switched off

^{At the time of launch of the first NTS-2 satellite (June 1977), which contained the first Cesium clock to be placed in orbit, there were some who doubted that relativistic effects were real. A frequency synthesizer was built into the satellite clock system so that after launch, if in fact, the rate of the clock in its final orbit was that predicted by GR, then the synthesizer could be turned on bringing the clock to the coordinate rate necessary for operation. The atomic clock was first operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was 442.5 parts in 1012 faster than clocks on the ground; if left uncorrected this would have resulted in timing errors of about 38,000 nanoseconds per day. The difference between predicted and measured values of the frequency shift was only 3.97 parts in 1012 parts in, well, within the accuracy capabilities of the orbiting clock. This then gave about a validation of the combined motional and gravitational shifts for a clock at 4.2 earth radii. Neil Ashby Professor Emeritus - Theoretical Math and Physics at University of Colorado}

GR= General Relativity

The Einstein's general relativity theory has that the gravity curves the space and time which makes clock tick that is in orbit tick faster by about 45 microseconds per day. From above we have already seen that the GPS clock is faster than the one on the ground clock by 38,000 microseconds per day.

That change may appear not to be much until you factor that it changes the accuracy of a GPS by a distance of about 11km or 11,000 meters as against the current accuracy of 5m. This inaccuracy renders the GPS unusable entirely.

^{To achieve a navigation accuracy of 15 meters, time throughout the GPS system must be known to an accuracy of 50 nanoseconds, which simply corresponds to the time required for light to travel 15 meters. But at 38 microseconds per day, the relativistic offset in the rates of the satellite clocks is so large that, if left uncompensated, it would cause navigational errors that accumulate faster than 10 km per day!Clifford M. Will is James S. McDonnell Professor of Physics at Washington University in St. Louis}

That is 38 x 10^-6 x speed of light

(38 x 10^-6 )x (3 x 10⁸) = 11,400 m, approximately 11km

Due to its precise nature of GPS timing, it is employed by the telecommunication operators to synchronise their base stations, businesses timestamp transactions with it, tracking of other transactions where precise timing is essential.

Other applications include aeroplane navigation, oil exploration, movie business as Hollywood studios now incorporate GPS timing in movie making to sequence multiple cameras, time movie slates, etc.

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^{This post was inspired by this sentence from @lemouth from this post}

^{General relativity is today in agreement with all experimental data, all its predictions have been verified experimentally, and it is at the basis of applications like the GPS.}

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^References

• ^{General Relativity Insight}
• ^{General Relativity}
• ^Relativity
• ^{GPS Timing}
• ^{General relativity in the global positioning system}
• ^{Real-World Relativity: The GPS Navigation System}

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