Jeff Forshaw and Brian Cox’s guide to the cosmos

To understand cosmos, we first need to get to grips with the nature of space and time. And when we start to do that, some strange ideas emerge...

In Part 1 of our new series, Brian Cox and physicist Jeff Forshaw ponder the baffling idiosyncrasies of the space-time continuum.

About this series

In this exclusive four-part series, physicists Jeff Forshaw and Brian Cox introduce us to the biggest ideas in modern physics and cosmology. What is the nature of time? What is everything made from? What happened before the Big Bang, and how will the Universe end? We’ll delve into the deepest questions concerning the very essence of space, time, matter, and reality itself… Here's a strange idea: it is imposible to catch up with a beam of light. Light travels at 300 million metres every second, but if you chased after it at 299 million m/s, it would still be receding from you at 300 million m/s, not at the 1 million m/s you might expect (strictly speaking, the light should be travelling though empty space). That crazy-sounding idea comes from Albert Einstein and is the bedrock of his Special Theory of Relativity.

“Time does not tick at a steady rate across the Universe – in some places it ticks faster”

The implications of Einstein's idea are enormous. For example, it means .hat time does not tick at a steady rate across the Universe —in some places it ticks faster than in others, and it Becomes possible for people to age at different rates depending on where .hey are and what they are doing. Perhaps the most dramatic example Di this is the 'twin paradox', where an astronaut departs from Earth, leaving her twin brother behind. She zips 3round for a bit in her super-fast spaceship and then lands back on 3arth a year later, only to find that many more years have passed back acme, and her brother is now an old nan. This is exactly the kind of weirdness that must be true if Einstein s right —though we aren't aware of it n nor evervday lives because we can't zip around. as enough,an so are ricked into thinking time is more constant than it actually is. The fact that a moving clock does no ick as fast as a stationary one is actually quite easy to demonstrate. first, imagine a clock made from two a parallel mirrors, between which a article of light or 'photon' bounces back and forth (see 'The key idea', light). Imagine you have one of these little clocks in your hand, and that you can watch the particle as it goes up an own, counting the bounces as a way f measuring time. Now imagine that a friend also has one of these clocks, but hat she's moving horizontally. From your point of view, her photon races out two sides of a triangle as it ounces from one mirror to the other and back again, travelling further during each round trip than the photon in your clock. There's nothing controversial in hat we just said. Here comes the weird bit. Because, according to Einstein, the light bouncing in your friend's clock is travelling at the same peed as the light in your clock, the light in your friend's clock must take longer to bounce between the mirrors. n other words, your friend's clock is running slower than yours. This remarkable conclusion might sound like a special feature of light locks. But it isn't... it is a feature of all locks. To understand why, we need to introduce Einstein's second crucial idea — an idea first introduced by al Galileo Galilei in the early 1600s.

IT’S ALL RELATIVE

Galileo imagined a ship moving at fixed speed over a calm ocean. Inside this ship, below decks, is a host of 'flies, butterflies and other small flying animals". He noted that, from 3bservations of the creatures made only inside the ship, it would be impossible to tell whether the ship was moving or standing still. The idea that experiments and observations made in 3 laboratory 'at rest' give exactly the same results as those made in a laboratory that's moving uniformly is called the 'principle of relativity', and Einstein followed Galileo in assuming it to be true. According to this principle, if a moving light clock is

slowed down, then so must all other moving clocks be, including our wristwatches and our heartbeats. To appreciate this point, let's suppose light clocks are actually special, and that they slow down while other types of clock do not. If this were true, a person could compare their light clock with their wristwatch and, because the light clock would be running slow, they would know that they were moving. Since this contradicts the principle of relativity, logic tells us that light clocks cannot be special. The principle of relativity also means that movement is always relative. It makes no sense to say "I am moving when I cycle down the road" — it only makes sense to say "I am moving relative to the road". This isn't as borinf an observation as it sounds. A moving clock runs slow compared to one at rest, but it would be equally valid to regard the moving clock as being 'at rest' and the other clock as moving. In which case we appear to be saying that each clock runs slow compared to the other, and that sounds like nonsense. But remarkably, there is no logical contradiction here. For example, it is okay for person A to say that person B ageing more slowly and for person B to say that it's person A who is ageing more slowly; these two statements are Soth true so long as A and Bare in uniform motion relative to each other. 3f course, A and B cannot both be younger than each other if they actually meet up for a cup of coffee. 3ut in order to do that, one or both nust accelerate or decelerate, and then .he two of them will no longer be moving relative to each other. We can use this logic to shed a bit nore light on why the astronaut twin -sally dnes age legs than her Earth- bound brother. From the point of view 3f her brother, she is always ageing more slowly than he is because she is always moving relative to him, and because he never accelerates or decelerates (he is 'in a state of uniform motion'). This means his sister must be younger than he is when she returns. Understanding this from her point o view is more tricky. Actually, her brother is ageing more slowly than she is during those parts of her journey where she is moving uniformly. It is 3nly when she is accelerating or decelerating (which she needs to do in )rder to return to Earth) that her brother suddenly ages and this is why, when she finally returns he is older.

FLIGHTS OF FANCY

Andromeda Is our neighbour. It is a spiral galaxy containing one trillion tars, and is situated around 2.5 ill ion light-years from Earth. This means that light arriving in our telescopes today started its journey rom Andromeda before there were any humans on Earth. It also means that a pace expedition travelling at the speed f light would take at least 2.5 million ears to reach the galaxy, as determine sing clocks at rest relative to the Earth. such a long journey seems to imply that o human could ever travel to andromeda. But that is not true, and hose italicised words are the key. Just as with the twin paradox, the astronauts onboard the spaceship will get much more slowly than the folks back on Earth, and the faster the spaceship travels, the more this will be he case. In fact, we can work out that a spaceship travelling at 99.99999999 per cent of the speed of light could travel to Andromeda in just 50 years as measured by those on board the spaceship (and 2.5 million years as measured by people on Earth). This is a lovely result because it implies that humans can conceivably explore the cosmos. We are not forever trapped within the confines of the Milky Way—we just have to invent a spacecraft that will transport us fast enough. Putting dreams aside, the feasibility 3f a 50-year-long journey to Andromeda highlights another intriguing conundrum, which again calls into question the nature of

“This is a lovely result because it implies that humans can conceivably explore the cosmos”