What is space? What is time? We deal with these entities all our lives but we rarely stop and think about them.

Is space a thing itself or just the absence of things? Could empty space exist if there were no things? And could time exist without space? Why can we remember the past but not the future? What happens to all those moments of time that no longer exist?

Notes From a Small Universe is a book that brings together modern theories of cosmology and quantum mechanics to show what we truly know about space and time.

From Aristotle to Newton

In renaissance Italy, Galileo would revolutionise ideas in physics and astronomy that had been in place since Aristotle. But far more than simply describing the motions that objects have, Galileo's ideas would change the way we saw ourselves within the universe. It was the start of seeing ourselves as part of the universe rather than separate from it, and suddenly humankind needed to find its role in a universe that wasn't centred around it. Newton, who built upon Galileo's new physics, would write laws of physics that would stand unchallenged for hundreds of years.

These laws give us insights into the fundamental structure of the universe, giving us an idea of its size and age. Even more deeply, they put our understanding of the universe on a material footing and show how we can dismiss the idea of souls.

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The Space and Time of Albert Einstein

This chapter introduces Einstein's theory of Special Relativity. Einstein's insight was to promote light to being a fundamental part of the universe. One consequence of this was that light would have the same speed to all observers, that is to say that everyone would measure light to travel at the same speed.

This might sound like a small step but actually leads to incredibly deep and counterintuitive results that challenge our ideas of space and time. For example, an event that appears to take a second from one person's perspective could take a thousand years from another person's perspective. Similarly with the size of objects, one person could measure a building to be five foot high, and another person would measure the same building to be the height of a skyscraper. How we reconcile this with our understanding of the universe is covered further in the next chapter.

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A Warp in Time

In this chapter, General Relativity is introduced. This was Einstein's masterpiece, it incorporated gravity into his earlier theory of Special Relativity. What Einstein showed is that gravity will warp space and time, and can stretch them out, concepts beautifully displayed by space-time diagrams. For the first time it was shown that space and time are malleable entities that can be affected by matter.

The main result that we see from this chapter is that space and time can be understood as an entity with its own existence. The idea that time is fleeting, with a past present and future, only makes sense from our own viewpoint embedded in time.

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Quantum Mechanics and Causality

This chapter begins with a historical overview of how quantum mechanics was born. Experiments performed in the early part of the 20th century showed that under the correct conditions matter would behave in ways that were difficult to explain on a fundamental level. For example, results implied that particles could exist in two places at once. Such behaviour made many physicists uncomfortable and led to much discussion about how the universe was structured. This soul searching was encapsulated by the famous thought experiment of Shroedinger's cat.

After going over the problems, the many worlds interpretation of quantum mechanics is introduced as a way of resolving them. All of the experimental results can be understood if we can expect the existence of other universes existing parallel to our own. Finally, Richard Feynman's path integral method of quantum mechanics is explained. In this technique, particles can split up to explore many different paths through space. By applying the interpretations of relativity and Mach's principle we learnt in earlier chapters, we can see why we remember the past but not the future.

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