Reality Beyond Imagining: Probability and the Quantum Multiverse
Quantum mechanics brings probability into physical reality.
Author’s Note: This post is Part 1 of a two-part exploration of interpretations of probability and their implications for quantum mechanics. Part 2 is available here.
Children easily understand probability. Scientists find it more difficult. Philosophers have argued for centuries about how to interpret probability without any satisfactory conclusion. While numerous ideas have been proposed, each appears either to be fundamentally limited or to lead to absurd implications. Of course, inconclusive argument is endemic in philosophy, and physicists may be tempted to dismiss such debates as academic navel-gazing divorced from the real world. Probability does not seem to be a part of the physical world like an atom or a star. It seems natural therefore for the physicist to treat probability simply as a useful mathematical tool. We know how to calculate probabilities, so why must we worry about what they mean?
Quantum mechanics undermines this complacency. Classical physics offered theoretical certainty, making the appearance of probability an artefact of human imperfection. By contrast, quantum mechanics assigns probabilities to the most fundamental processes of nature. This extends the issues and absurdities of interpreting probability to challenges in understanding the nature of physical reality itself. Quantum mechanics has a reputation for incomprehensibility. Richard Feynman famously claimed that “nobody understands quantum mechanics”. This quip is a striking echo of Bertrand Russell’s remark that “probability is the most important concept in modern science, especially as nobody has the slightest notion what it means.” This is no coincidence. Much of the apparent strangeness of quantum mechanics traces directly back to the strangeness of probability.
Yet while quantum mechanics is esoteric, probability is familiar. Exploring probability can therefore provide an accessible pathway into understanding how to interpret quantum mechanics. In modern science, there are two dominant interpretations of probability: frequentism and Bayesianism. Across this post and the next, we will explore the incredible implications of each, and the interpretations of quantum mechanics they inspire. Here, we examine frequentism. We will see that it leads us to a reality of countless parallel universes in which somewhere everything that could possibly happen is happening, and myriad copies of you are living out every possible version of your life. In frequentist probability, we will discover the multiverse.
The Probabilistic Multiverse
Frequentism is the standard objective way of understanding probability. It defines probability of an event in terms of its relative frequency or experimental probability – the proportion of the time it occurs. For example, the probability of a rolled die showing six is 1/6 because if you roll it many times you will find that almost exactly one sixth of the rolls show six. For such a simple example, we could also argue that the probability is 1/6 because the die has six faces and only one shows six; this is called the theoretical probability. However, the theoretical probability does not work more generally. For example, it is possible to make loaded dice that show six more often than other numbers. Using frequentist probability allows for the probability of rolling a six on a loaded die to be more than 1/6, while theoretical probability does not. Indeed, frequentist probability is extremely useful as it can be applied to real-world situations that are far too complicated to approach theoretically. For example, we can say that the probability that it will rain on a random Sydney day is 26%, because that is the percentage of observed past days in Sydney on which it has rained.
However, this understanding implies that we can only apply probability to events that occur many times. For example, we can talk of the probability of a typical Sydney day being rainy because it there are many Sydney days which we can use to determine the relative frequency with which Sydney days are rainy. If I instead want to know the probability that tomorrow will be rainy, I have a problem. Tomorrow is not just a random day with a 26% chance of rain; it is a specific day where the Australian Bureau of Meteorology instead puts the probability at 60%. The probability of rain tomorrow is determined by the specific atmospheric factors over and around Sydney today – the history of rain over previous days, the low- and high-pressure systems present and, ultimately, the exact configuration and behaviour of all the water molecules in the air that could coalesce into raindrops. Therein lies the rub; these precise atmospheric conditions are unique. The exact same conditions will never be repeated in exactly the same way on any other day. This means that we can only assign a probability of rain to tomorrow if tomorrow somehow occurs many times, starting from essentially the same initial atmospheric conditions but then evolving in different ways to produce different weather.
In fact, weather forecasters make this happen by creating many mini simulated parallel worlds, simplified so that they include only the information most relevant to the weather in Sydney, and then run them through tomorrow. They then find the proportion of these worlds that experience rain in Sydney and call this the probability of rain tomorrow. However, this is only an approximation. Indeed, it is said that the flap of a butterfly’s wings in Brazil can cause a tornado in Texas. This encapsulates the fact that weather is chaotic, meaning that it can be substantially affected by even very minor events. Therefore, to exactly calculate the probability of rain in Sydney tomorrow, the parallel worlds would need to include everything in the world, right down to butterflies – yourself very much included. Moreover, if we believe that there is a probability of rain tomorrow even when weather forecasters are not calculating it, these parallel worlds cannot only be simulated in computers. They must exist naturally, independently of human creation.
This leads to a stunning conclusion. Believing that there is truly a 60% probability of it raining tomorrow implies the existence of innumerable parallel worlds. These worlds are necessary for there to be a meaningful relative frequency of rain tomorrow, and hence for there to be a meaningful probability in accordance with frequentism. Across these worlds, countless copies of you are about to experience tomorrow in all physically possible different ways. This is the probabilistic multiverse.
From Classical Abstraction to Quantum Reality
There is a way to escape from the probabilistic multiverse; we can assert that probability is not real. If probability is just a human tool, then the multiverse need not physically exist – it can be just an academic abstraction. This is consistent with classical physics – the best understanding of nature we had until a century ago. Classical physics is deterministic, meaning that it says that what will happen in the future is not random but is instead predetermined by the current state of the universe. According to classical physics, if you were a supernatural being who could know the exact position and motion of every atom in the world you could use the laws of physics to calculate the future exactly. You would not believe that there was a probability of rain tomorrow; you would simply know for sure that either it was going to rain tomorrow, or it wasn’t. Even the roll of a die is not truly probabilistic in classical physics; it is predetermined by the exact details of how it is thrown which in turn is predetermined by the exact details of the atoms that make up the thrower. According to classical physics, we need no multiverse because everything is predetermined. In this understanding, probability is not a physical reality; it is an approximation we humans use because we have incomplete knowledge about the world. With no probability, there is no need for a true multiverse.
However, quantum mechanics changes everything. Quantum mechanics is our current best understanding of nature, to which classical physics is an imperfect approximation. It has provided solutions to the biggest mysteries of science, from how the sun shines to what gives things colour. However, unlike classical physics, the laws of quantum mechanics do not dictate with certainty what we will see happen in the future. Instead, quantum mechanics assigns probabilities to seeing different possible outcomes. Everything that happens in the universe and our lives can ultimately be traced back to probabilistic quantum effects and, therefore, is itself probabilistic. This means that, far from being just a useful tool, probability is foundational to our most fundamental understanding of the universe. Quantum physics requires that probabilities are a physical reality.
The Quantum Multiverse: God’s Game of Dice
This leads us to the many-worlds interpretation of quantum mechanics. Since quantum mechanics implies that probabilities are physically real, it implies that the probabilistic multiverse is not just an abstraction but a physical reality – the quantum multiverse. The quantum multiverse consists of countless parallel universes across which all of the possible outcomes that can occur as a result of all of the quantum processes that run nature at the atomic level are manifested. This means that all physically possible realities happen somewhere, in all possible variations. In most worlds of the multiverse you were never born, but across the minority in which you were versions of you exist that are experiencing every possible version of your life. Everything that could ever have happened to you, or that you could ever have done, happened somewhere, and an alternative version of you is living with the consequences.
The quantum multiverse may sound absurd, but it does give a logical framework to the ostensibly mysterious nature of quantum mechanics. Indeed, Albert Einstein was famously repulsed by the probabilistic structure of quantum mechanics, famously declaring that God “does not play dice” with the universe. Einstein rejected probability in physics because it seemed to introduce a fundamental inexplicability and arbitrariness to the universe. His God was that described by Baruch Spinoza – the totality of nature as an internally logical and complete whole – while probability in quantum mechanics seemed to suggest a randomness that was beyond any explanation or reason. Yet, the quantum multiverse resolves Einstein’s concern. While the events of individual universes appear random, the totality of the multiverse is not. It follows a simple, predictable rule: everything that can happen does happen. Nature as a whole is not capricious, but it can appear so to us because we can only see a fragment of its logical whole.
Probability Made Physical
Quantum mechanics has a reputation for weirdness and incomprehensibility. Yet, understood from the perspective we have taken here, it is just the physical manifestation of the strangeness that is inherent in the concept of probability itself. Indeed, it is possible to construct quantum mechanics as a mathematical extension of probability theory, with the additional allowance of negative probabilities. These negative probabilities give rise to quantum interference. This is a process, only observable at the atomic level or in exquisitely designed devices such as quantum computers, by which different universes in the multiverse can interact and affect each other. So, quantum mechanics takes the abstraction of the probabilistic multiverse and realises it as a real, interacting physical entity.
The concept of probability is part of our intuitive understanding of the world. If quantum mechanics seems beyond our understanding then, perhaps it is because we do not appreciate the profound implications of probability. Whether we have studied physics or not, we are all equipped with the intuition and knowledge to contemplate what probability means. The insights of such contemplations can offer invaluable clarity in interpreting the more arcane phenomena of quantum mechanics. Quantum mechanics is a deep theory which, as with all deep ideas, only reveals full understanding with detailed study. Yet in general terms we can grasp why it can seem so counterintuitive and attract such confusion by internalising a basic idea with deep ramifications. Quantum mechanics brings probability into physical reality.