The Quantum Universe

Brian Cox & Jeff Forshaw

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First annotation on Nov 19th, 2025.

Chapter 2

In 1900, Rutherford noted the problem: 'all atoms formed at the same time should last for a definite interval. This, however, is contrary to the observed law of transformation, in which the atoms have a life embracing all values from zero to infinity.' This randomness in the behaviour of the microworld came as a shock because, until this point, science was resolutely deterministic. If, at some instant in time, you knew everything it is possible to know about something, then it was believed you could predict with absolute certainty what would happen to it in the future. The breakdown of this kind of predictability is a key feature of quantum theory: it deals with probabilities rather than certainties, not because we lack absolute knowledge, but because some aspects of Nature are, at their very heart, governed by the laws of chance. And so we now understand that it is simply impossible to predict when a particular atom will decay. Radioactive decay was science's first encounter with Nature's dice, and it confused many physicists for a long time.
The first step towards a consistent, unified answer is widely credited to the German physicist Werner Heisenberg, and what he did represented nothing less than a completely new approach to the theory of matter and forces. In July of 1925, Heisenberg published a paper throwing out the old hotchpotch of ideas and half-theories, including Bohr's model of the atom, and ushered in an entirely new approach to physics. He began: 'In this paper it will be attempted to secure the foundations for a quantum theoretical mechanics which is exclusively based on relations between quantities which in principle are observable.' This is an important step, because Heisenberg is saying that the underlying mathematics of quantum theory need not correspond to anything with which we are familiar. The job of quantum theory should be to predict directly observable things, such as the colour of the light emitted from hydrogen atoms. It should not be expected to provide some kind of satisfying mental picture for the internal workings of the atom, because this is not necessary and it may not even be possible. In one fell swoop, Heisenberg removed the conceit that the workings of Nature should necessarily accord with common sense. This is not to say that a theory of the subatomic world shouldn't be expected to accord with our everyday experience when it comes to describing the motion of large objects, like tennis balls and aircraft. But we should be prepared to abandon the prejudice that small things behave like smaller versions of big things, if this is what our experimental observations dictate.
Heisenberg's philosophy, though, is not pure magic. It is simple and it lies at the heart of our approach in this book: the job of a theory of Nature is to make predictions for quantities that can be compared to experimental results. We are not mandated to produce a theory that bears any relation to the way we perceive the world at large. Fortunately, although we are adopting Heisenberg's philosophy, we shall be following Richard Feynman's more transparent approach to the quantum world.
A good scientific theory specifies a set of rules that determine what can and cannot happen to some portion of the world. They must allow predictions to be made that can be tested by observation. If the predictions are shown to be false, the theory is wrong and must be replaced. If the predictions are in accord with observation, the theory survives. No theory is 'true' in the sense that it must always be possible to falsify it. As the biologist Thomas Huxley wrote: 'Science is organized common sense where many a beautiful theory was killed by an ugly fact.' Any theory that is not amenable to falsification is not a scientific theory – indeed one might go as far as to say that it has no reliable information content at all. The reliance on falsification 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.
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 r 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 m and m 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.

Chapter 3

The interpretation of the squared length of the clock hand as the probability to find a particle at a particular place is not particularly difficult to grasp, but it does seem as if we (or to be more precise, Max Born) plucked it out of the blue. And indeed, from a historical perspective, it proved very difficult for some great scientists, Einstein and Schrödinger among them, to accept. Looking back on the summer of 1926, fifty years later, Dirac wrote: 'This problem of getting the interpretation proved to be rather more difficult than just working out the equations.' Despite this difficulty, it is noteworthy that by the end of 1926 the spectrum of light emitted from the hydrogen atom, one of the great puzzles of nineteenth-century physics, had already been computed using both Heisenberg's and Schrödinger's equations (Dirac eventually proved that their two approaches were in all cases entirely equivalent).
Einstein famously expressed his objection to the probabilistic nature of quantum mechanics in a letter to Born in December 1926. 'The theory says a lot but does not really bring us any closer to the secret of the "old one". I, at any rate, am convinced that He is not playing at dice.' The issue was that, until then, it had been assumed that physics was completely deterministic. Of course, the idea of probability is not exclusive to quantum theory. It is regularly used in a variety of situations, from gambling on horse races to the science of thermodynamics, upon which whole swathes of Victorian engineering rested. But the reason for this is a lack of knowledge about the part of the world in question, rather than something fundamental. Think about tossing a coin – the archetypal game of chance. We are all familiar with probability in this context. If we toss the coin 100 times, we expect, on average, that fifty times it will land heads and fifty times tails. Pre-quantum theory, we were obliged to say that, if we knew everything there is to know about the coin – the precise way we tossed it into the air, the pull of gravity, the details of little air currents that swish through the room, the temperature of the air, etc. – then we could, in principle, work out whether the coin would land heads or tails. The emergence of probabilities in this context is therefore a reflection of our lack of knowledge about the system, rather than something intrinsic to the system itself.
The probabilities in quantum theory are not like this at all; they are fundamental. It is not the case that we can only predict the probability of a particle being in one place or another because we are ignorant. We can't, even in principle, predict what the position of a particle will be. What we can predict, with absolute precision, is the probability that a particle will be found in a particular place if we look for it. More than that, we can predict with absolute precision how this probability changes with time. Born expressed this beautifully in 1926: 'The motion of particles follows probability laws but the probability itself propagates according to the law of causality.' This is exactly what Schrödinger's equation does: it is an equation that allows us to calculate exactly what the wavefunction will look like in the future, given what it looks like in the past. In that sense, it is analogous to Newton's laws. The difference is that, whilst Newton's laws allow us to calculate the position and speed of particles at any particular time in the future, quantum mechanics allows us to calculate only the probability that they will be found at a particular place.