"In physics, determinism means that the state of the Universe at any given time and the basic laws of physics fully determine the Universe’s backward history and forward evolution. This idea reached its peak with the strict, precise laws about how the Universe behaves introduced by classical physics. Take Isaac Newton’s laws of motion. If someone knew the present positions and momenta of all particles, they could in theory use Newton’s laws to deduce all facts about the Universe, past and future. It’s only a lack of knowledge (or computational power) that prevents scientists from doing so.
Along with this distinctive predictive power, determinism underwrites scientific explanations that come close to the ‘principle of sufficient reason’ most famously articulated by German polymath Gottfried Leibniz: that everything has an explanation. Every state of the Universe (with one obvious exception, which we’ll come to) can be completely explained by an earlier one. If the Universe is a train, determinism says that it’s running on a track, with no option to switch to any other path because different tracks never cross.
US physicist James Hartle, who died earlier this year aged 83, made seminal contributions to this continuing debate. Early in the twentieth century, the advent of quantum theory seemed to have blown out of the water ideas from classical physics that the evolution of the Universe is ‘deterministic’. Hartle contributed to a remarkable proposal that, if correct, completely reverses a conventional story about determinism’s rise with classical physics, and its subsequent fall with quantum theory. A quantum Universe might, in fact, be more deterministic than a classical one — and for all its apparent uncertainties, quantum theory might better explain why the Universe is the one it is, and not some other version.
In physics, determinism means that the state of the Universe at any given time and the basic laws of physics fully determine the Universe’s backward history and forward evolution. This idea reached its peak with the strict, precise laws about how the Universe behaves introduced by classical physics. Take Isaac Newton’s laws of motion. If someone knew the present positions and momenta of all particles, they could in theory use Newton’s laws to deduce all facts about the Universe, past and future. It’s only a lack of knowledge (or computational power) that prevents scientists from doing so.
Along with this distinctive predictive power, determinism underwrites scientific explanations that come close to the ‘principle of sufficient reason’ most famously articulated by German polymath Gottfried Leibniz: that everything has an explanation. Every state of the Universe (with one obvious exception, which we’ll come to) can be completely explained by an earlier one. If the Universe is a train, determinism says that it’s running on a track, with no option to switch to any other path because different tracks never cross.
Physicists have conventionally liked determinism’s predictive and explanatory power. Others, including some philosophers, have generally been more divided, not least because of how determinism might seem to preclude human free will: if the laws of physics are deterministic, and our actions are just the summation of particle interactions, there seems to be no room for us to freely choose A instead of B, because the earlier states of the Universe will already have determined the outcome of our choice. And if we are not free, how can we be praised or blamed for our actions? Neuroendocrinologist Robert Sapolsky’s 2023 book Determined touches on this fascinating and controversial issue.
Space invaders
The strange behaviours of quantum particles that began to emerge in the twentieth century fundamentally shifted the debate surrounding determinism in physics. The laws of quantum mechanics give only the probabilities of outcomes, which can be illustrated with the thought experiment devised by Austrian physicist Erwin Schrödinger in 1935 (although when he devised it, he was concerned mainly with how the wavefunction represents reality). A cat is trapped in a box with a vial of poison that might or might not have been broken by a random event — because of radioactive decay, for example. If quantum mechanics applied to the cat, it would be described by a ‘wavefunction’ in a superposition of ‘alive’ and ‘dead’. The wavefunction, when measured, randomly jumps to one of the two states, and quantum mechanics specifies only the probability of either possibility occurring. One consequence of the arrival of quantum mechanics was that it seemed to throw determinism out of the window.
How Stephen Hawking flip-flopped on whether the Universe has a beginning
But this accepted idea might not be the whole story, as developments in the second half of the twentieth century suggested. The quantum Universe could actually be more deterministic than a classical one, for two reasons. The first is technical. Newton’s laws allow situations in which the past does not determine how things will move in the future. For example, the laws do not provide an upper bound on how much an object can be accelerated, so in theory a classical object can reach spatial infinity in finite time. Reverse this process, and you get what have been called ‘space invaders’ — objects that come from spatial infinity with no causal connection to anything else in the Universe, and which can’t be predicted from any of the Universe’s past states.
In practice, this problem is solved by the universal speed limit, the speed of light, introduced by Einstein’s special theory of relativity. But unruly infinities also plague Einsteinian relativity, which is a classical theory. The equations of general relativity lead to ‘singularities’ of infinite curvature, most notoriously in black holes and at the Big Bang at the beginning of the Universe. Singularities are like gaps in space-time where the theory no longer applies; in some cases, anything can come out of them (or disappear into them), threatening determinism.
Many physicists think that quantum theory can come to the rescue by removing such singularities — for example, by converting the Big Bang into a ‘Big Bounce’, with a Universe that continues to evolve smoothly on the other side of the singularity. If they are right, a theory of ‘quantum gravity’ that fully unifies quantum theory, which predicts the behaviour of matter on the smallest scales, and Einstein’s relativity, which encapsulates the large-scale evolution of the Universe, will smooth out the gaps in space-time and restore determinism.
Into the quantum cosmos
With Stephen Hawking, Hartle went on to become one of the founders of quantum cosmology, which applies quantum theory to the entire Universe. In a classical Universe, there is freedom in choosing how it all started. Even setting aside the extreme situations mentioned earlier, classical mechanics is deterministic merely in that it lays down many possible evolutionary histories for the Universe, and offers conditional statements about them: if this happens, then that must happen next. To return to the train analogy, a deterministic theory does not, by itself, say why the train is on any one given track out of many: why it is going from A to B via C, rather than from X to Y via Z. We can go back to earlier states to explain the current state, and do that all the way back to the initial state — but this initial state is not explained by anything that precedes it. Ultimately, standard determinism fails to fully satisfy Leibniz’s principle of sufficient reason: when it comes to the initial state, something remains without an explanation.
This failure is not just philosophical. A complete theory of the Universe should predict the phenomena we observe in it, including its large-scale structure and the existence of galaxies and stars. The dynamic equations we have, whether from Newtonian physics or Einsteinian relativity, cannot do this by themselves. Which phenomena show up in our observations depend sensitively on the initial conditions. We must look at what we see in the Universe around us, and use this information to determine the initial condition that might have given rise to such observations.
A theory that specifies deterministic laws of both the Universe’s temporal evolution and its exact initial condition satisfies what English physicist Roger Penrose called ‘strong determinism’ in his 1989 book The Emperor’s New Mind. This is, according to Penrose, “not just a matter of the future being determined by the past; the entire history of the universe is fixed, according to some precise mathematical scheme, for all time”. Let us say that a Universe is strongly deterministic if its basic laws of physics fix a unique cosmic history. If determinism provides a set of non-crossing train tracks, without specifying which one is being used, then strong determinism lays down a single track that has no choice even about where it starts.
A universal wavefunction
Strong determinism is hard to implement in classical physics. You might consider doing it by specifying the initial condition of the Universe as a law. But although the dynamical laws of classical physics are simple, the Universe itself is complex — and so its initial condition must have been, too. Describing the precise positions and momenta of all the particles involved requires so much information that any statement of the initial condition is too complex to be a law."