*Last updated June 28, 2018 at 9:51 am*

## It’s about time engineers learnt the value of Einstein’s practical mathematics, too.

**General relativity is one of humanity’s greatest intellectual leaps**. Special relativity, arguably, would have been discovered without Einstein. It was ripe for it. The speed of light had been measured to be constant in a vacuum, and the mathematics of the Lorentz transformations had already been developed. But general relativity – and the idea that gravity wasn’t a force but the curvature of the space-time continuum – wow, that was just crazy talk.

In his theory, Einstein describes an effect that we now call time dilation.

Special relativistic time dilation predicts that a clock at the Earth’s equator will run slower than a clock at a pole. In his famous 1905 paper Einstein proposed an experiment to test his new theory, by measuring the time difference between a clock placed at the equator and another at the pole.

Fortunately for him (and for us), clocks in those days were not sufficiently accurate to measure the predicted effect. If suitable clocks had been available, then Einstein’s experiment would have shown that they remain synchronised despite their relative motion!

But this was before Einstein had discovered the General Theory of Relativity.

While the Special Theory tells us that a clock at the equator runs more slowly than one at the pole, the General Theory tells us that the clock at the pole runs more slowly than the one at the equator.

Amazingly these two effects exactly cancel each other out and clocks at the equator and the pole remain synchronised.

### Thank goodness for inaccurate clocks!

So, if the Swiss clocks had been accurate enough to perform the experiment that Einstein proposed, the world would have concluded that Einstein was wrong and the General Theory may never have been developed.

Relativity is often considered one of those esoteric physics subjects that may be fascinating but has no practical value – probably because when we talk about relativity we talk about black holes, the big bang theory, or gravitational waves. But nothing could be further from the truth.

Did you know, for example, that, if that relativistic effects were ignored, your GPS receiver would be out by a kilometre after just two hours of operation. That is because GPS works basically by knowing where the satellites are, and at precisely what time they sent you a message. When you receive the signal, you can work out how far away the satellite is by multiplying the time taken to arrive by the speed of light.

Given enough satellites (four to be precise) you can determine where you are. This is the bare bones of how the system works, but the key point is that, for your GPS receiver to work, timing is everything.

Now left me ask you a question. GPS satellites are about 20,000 km above you head and moving at a speed of about 14,000 km/hr. The fact they are so far above the Earth means that they are in a weaker gravitational field and consequently their clocks run faster – that’s the general relativistic effect. But special relativity says that, because they are moving so fast, their clocks run more slowly. So which of these two effects is greater? The answer is the general relativistic effect – it is seven times greater.

If you doubt that general relativity is crucial to the global satellite navigation then you’re wrong – but you are not alone.

### Engineers hedge their bets on relativity

When the original GPS satellite was launched, some of the engineers on the project were not convinced that relativistic effects would be observable.

They insisted that a frequency synthesiser was included in the design of the original satellites. That way if general relativity wasn’t a thing, they could throw a switch and the GPS satellite would go back to the Earth frequency setting.

The engineers were wrong, bless their pocket protectors, and the satellite’s atomic clocks operated exactly as predicted by the General Theory of Relativity.

As an aside, the organisation I work for, the government’s Defence Science and Technology Group, hosts one of 16 global GPS monitoring stations. For more than 50 years our site north of Adelaide has been tracking GPS satellites passing overhead and feeding data back to the master control station in the US. We’ve been running the station for so long now, and providing data with such accuracy, that the Americans can use the historical data to measure Australian plate tectonic movement (we’re moving closer to the US!).

We are incredibly lucky to have the general theory of relativity. If the experiments Einstein had proposed in 1905 had been conducted, then Einstein would probably have vanished into obscurity.

Would the general theory of relativity still have been developed then? Maybe. One day we would have realised that Newtonian gravity wasn’t working and perhaps somebody would have come up with a theory that described gravity as curvature of space-time, but it’s far from certain.

Whatever the case, we have it now. But it has been trapped in the physics and mathematics departments for too long. It’s high time that it was taught to engineers as well so that its full potential can be realised. They won’t find it fun, because relativity is not that – it’s frustrating, hard work – and absolutely fascinating.