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is why scientific theories are different from matters of opinion. This scientific meaning of the word ‘theory’, by the way, is different from its ordinary usage, where it often suggests a degree of speculation. Scientific theories may be speculative if they have not yet been confronted with the evidence, but an established theory is something that is supported by a large body of evidence. Scientists strive to develop theories that encompass as wide a range of phenomena as possible, and physicists in particular tend to get very excited about the prospect of describing everything that can happen in the material world in terms of a small number of rules.

One example of a good theory that has a wide range of applicability is Isaac Newton’s theory of gravity, published on 5 July 1687 in his Philosophiæ Naturalis Principia Mathematica. It was the first modern scientific theory, and although it has subsequently been shown to be inaccurate in some circumstances, it was so good that it is still used today. Einstein developed a more precise theory of gravity, General Relativity, in 1915.

Newton’s description of gravity can be captured in a single mathematical equation:

This may look simple or complicated, depending on your mathematical background. We do occasionally make use of mathematics as this book unfolds. For those readers who find the maths difficult, our advice is to skip over the equations without worrying too much. We will always try to emphasize the key ideas in a way that does not rely on the maths. The maths is included mainly because it allows us to really explain why things are the way they are. Without it, we should have to resort to the physicist-guru mentality whereby we pluck profundities out of thin air, and neither author would be comfortable with guru status.

Now let us return to Newton’s equation. Imagine there is an apple hanging precariously from a branch. The consideration of the force of gravity triggered by a particularly ripe apple bouncing off his head one summer’s afternoon was, according to folklore, Newton’s route to his theory. Newton said that the apple is subject to the force of gravity, which pulls it towards the ground, and that force is represented in the equation by the symbol F. So, first of all, the equation allows you to calculate the force on the apple if you know what the symbols on the right-hand side of the equals sign mean. The symbol r stands for the distance between the centre of the apple and the centre of the Earth. It’s r2 because Newton discovered that the force depends on the square of the distance between the objects. In non-mathematical language, this means that if you double the distance between the apple and the centre of the Earth, the gravitational force drops by a factor of 4. If you triple the distance, it drops by a factor of 9. And so on. Physicists call this behaviour an inverse square law. The symbols m1 and m2 stand for the mass of the apple and the mass of the Earth, and their appearance encodes Newton’s recognition that the gravitational force of attraction between two objects depends on the product of their masses. That then begs the question: what is mass? This is an interesting question in itself, and for the deepest answer available today we’ll need to wait until we talk about a quantum particle known as the Higgs boson. Roughly speaking, mass is a measure of the amount of ‘stuff’ in something; the Earth is more massive than the apple. This kind of statement isn’t really good enough, though. Fortunately Newton also provided a way of measuring the mass of an object independently of his law of gravitation, and it is encapsulated in the second of his three laws of motion, the ones so beloved of every high school student of physics:

Every object remains in a state of rest or uniform motion in a straight line unless it is acted upon by a force;

An object of mass m undergoes an acceleration a when acted upon by a force F. In the form of an equation, this reads F = ma;

To every action there is an equal and opposite reaction.

Newton’s three laws provide