Boltzmann Brains: Why Your Life Might Be An Illusion

We should celebrate the infinite richness of reality… as long as it actually exists.

What if I told you that nothing is real? The rich, complex world you see around you is just a dream. Everyone you think you know is a figment of your imagination. Even you do not really exist. Your memories are false. Your body is an illusion. Your life is a fantasy.

Philosophers have worried about this possibility for centuries. It led Rene Descartes to his famous first principle: “I think, therefore I am.” By this, he meant that even while doubting all else, one thing remains beyond question – the existence of oneself as a being capable of having these doubts. Even if all else is a deception, my existence is assured. Yet, this is not as comforting as it may seem. It does not necessarily mean that I am a human being – I could simply be a brain in a vat. Indeed, it does not even guarantee that I exist through time; my mind may exist for only this fraction of a second in which I am thinking and will return to the void in the next instant. I may be nothing more than a momentary flash of delusion in a universe of nothing.

To a pragmatic scientist, such fears may seem like idle speculations. Virtually anything could theoretically be true. The practical act of doing science necessitates only countenancing those possibilities that are likely according to legitimate scientific theories. Unless there is a scientifically motivated reason to believe I am merely a momentary mind in a void, then we need not dwell overlong on the idea. Unfortunately, it turns out that there is such a reason. In fact, it is exactly what is predicted by our best understanding of physics!

The Big Freeze

To understand how science calls our reality into question, we must consider the ultimate fate of the universe. Cosmic eschatology has occupied great minds of history no less than questions of reality but, from a scientific viewpoint, the phenomenon that will ultimately bring about the end is actually quite straightforward.

If you leave a hot cup of coffee in a cool room it will lose its heat to its surroundings until it is no warmer than the rest of the room. A lit candle in the same room will stay hot for longer than the coffee because the energy stored in the candle’s wax is used to constantly replenish the heat the candle releases. But, eventually, the candle’s stored energy will run out and then it too will cool to the same temperature as its surroundings. At an astronomical level, the same thing eventually happens even to stars. Like a candle, a star has stored energy (in this case, nuclear energy) that allows it to stay hot even as it constantly loses heat to outer space. But, after billions of years, this energy is exhausted. At this point, what was once a shining star will become just as cold and dark as the void of space.

An illustration of a white dwarf star. Like the dying glow of a candle that has run out of wax, a white dwarf is a star that has exhausted all of its usable nuclear energy and is slowly fading to darkness. The Sun will become a white dwarf in six billion years, before eventually going dark. Image Source: NOIRLab/NSF/AURA/J. da Silva (processed by M. Zamani and M. Kosari (NSF's NOIRLab)), CC BY 4.0, via NOIRLab.

Ultimately, this is the fate of all things. Given enough trillions of years, all the stars will go out and all the heat and energy that once made life and complexity possible will dissipate across outer space. Eventually, it is predicted that even matter itself will decay into energy (in accordance with the equivalence of matter and energy encapsulated by Einstein’s famous formula E=mc²), and this energy too will dissipate. Nothing will remain in the universe but a cold, dark and featureless void. This eventuality is called The Big Freeze and, according to our current understanding of cosmology,¹ an eternity in this state is the inevitable future of our universe.

Boltzmann Brains

However, curiously, The Big Freeze will not truly be the end of all things. This is because what happens in the physical world is not ultimately governed by certainties, but by statistical tendencies. In The Surprising Physics of the Star Wars Force, I explained how there is a chance at any moment that, through the random motion of particles, the energy contained in the air could spontaneously arrange itself in just the right way to allow a heavy object to suddenly rise into the air. In fact, even more remarkable things could occur. There is a chance that the energy of the air could become arranged, through random chance, in just the right way that it produces all of the atoms, in exactly the right configuration, necessary to make an exact replica of your mind. The reason we never observe such peculiarities is that, while they are technically possible, they are incredibly unlikely.

However, given infinite time, even incredibly unlikely things eventually occur. Even in The Big Freeze, trace quantities of energy will remain across all of space, and this energy will continue to randomly rearrange itself just as the heat in the air does now. So, even in The Big Freeze, there is some extremely tiny chance that the random motion of energy will give rise to an exact copy of your mind. Because the chance is so incredibly small, it will take an unthinkably long time for this to occur — long enough to make the fourteen-billion-year history of the universe up to now seem like less than the blink of an eye. But since The Big Freeze persists for eternity, even if it takes an incredibly long time (say, a googolplex years) before a copy of you comes into being, it will eventually happen. Indeed, if we then wait another googolplex years, it will happen again. In fact, since there is infinite time in which it can keep occurring, it will ultimately happen infinitely many times. So, while The Big Freeze is nearly always a featureless void, across the unfathomably long sweep of its existence, one could find infinitely many brief moments in which there will exist an exact replica of your mind!

This is where the worries begin. Since each of these replicas will share every aspect of your thoughts, they will believe themselves to really be you. They will believe they exist inside a body that was born on Earth to your parents and that they are living a rich full life identical to yours. But they will be wrong. They will actually be nothing but the chance product of random motion of energy in a lifeless universe long after the Earth ceased to exist. Indeed, the vast majority of beings that emerge from the void of the Big Freeze believing themselves to be you will be disembodied minds equipped with false memories and illusions of reality, since this is far simpler to create than the entire Earth or universe as we perceive it. In nearly all cases, these minds will survive only long enough to perceive their existence, before immediately evaporating back into nothingness. These minds are called Boltzmann brains.

This brings us to the crux of the argument – how can you be sure you are not a Boltzmann brain? According to the above reasoning, the vast majority of beings that will ever exist believing themselves to be you will be Boltzmann brains. So, statistically, although you believe yourself to be the real you, it is overwhelmingly more likely that you are a Boltzmann brain. Rather than being a real person, you are probably a disembodied mind that spontaneously formed a fraction of a second ago from the eternal void left at the universe’s end, and you will probably return to the void in a moment’s time. Oh well, at least you can take consolation in the fact that your brief existence is spent reading Quantemplation!

Photograph of Ludwig Boltzmann. Boltzmann pioneered the field of statistical mechanics which implies the possibility of objects like Boltzmann brains. The odd implications notwithstanding, statistical mechanics is an extremely important field of physics that is indispensable to modern science.

Irrational Truths

Should you really believe that you are a Boltzmann brain? You may well reject one or more of the premises of the above argument (called the Boltzmann brain hypothesis), in which case you will confidently answer no. Indeed, future discoveries in physics may well vindicate your conclusion. But, paradoxically, even if you accept the validity of the above argument, the answer is arguably still no. This is because a Boltzmann brain cannot rationally conclude anything. While Boltzmann brains may believe their thoughts, knowledge and beliefs to be coherent, rational tools developed through experience and education, in truth they are nothing more than random products of chance configurations of energy. There is no reason for a Boltzmann brain to come to correct conclusions about reality, since the entire reality in which they believe is only an illusion. So, if you really are a Boltzmann brain, then you should not to trust your own reasoning, and so cannot use that reasoning to validly determine that you are a Boltzmann brain. On the other hand, if you are not a Boltzmann brain, then you can trust your rationality and may be right to accept the above argument and conclude that you probably are a Boltzmann brain. But in that case, the conclusion would be incorrect! Belief in the Boltzmann brain hypothesis is therefore either true but unjustified, or justified but false. In either case, it is not rational to believe in it.²

In summary, there are two possibilities: either the Boltzmann brain hypothesis is false, or it is true. If it is false, then we may hope to find a compelling refutation of it that resolves the issue. However, if it is true, then we can have no hope of ever showing this, since believing it is true is inherently irrational. Therefore, if this latter alternative is correct, then the problem of Boltzmann brains is doomed to remain forever unsolved.

This possibility should teach us humility. Many physicists believe that physics is ultimately leading to a theory of everything – a single theory that encapsulates the absolute and complete truth underpinning all of reality. A century ago, mathematicians had a similar belief about their discipline. They assumed that a complete system of mathematics, which could allow any mathematical question to be answered, would soon be achieved using mathematical logic. However, unresolvable paradoxes, such as the Liar Paradox, stood in the way of this goal (as described in How Mathematical Logic Uncovered the Power of Human Intuition). Ultimately, Gödel’s incompleteness theorems showed that there are facts in mathematics that are true but can never be proven mathematically to be true. The paradox of the Boltzmann brain hypothesis points to the possibility that the same may be true in science – there may exist scientific facts that are true but are logically impossible to demonstrate scientifically. If so, a complete theory of everything will always remain out of reach.

An illustration of the Liar Paradox. Since Pinocchio’s nose grows when he lies, declaring that his nose grows creates a paradox; either he is telling the truth (in which case his nose should not grow) or he is lying (in which case his nose should grow). While this may seem like a triviality, it was ultimately the basis for undermining the quest to construct a complete system of mathematics. This is why it is worth contemplating peculiarities like Boltzmann brains — they may lead to surprisingly deep insights.

However, this should not discourage us. Mathematics remains useful even in light of Gödel’s incompleteness theorems. Indeed, arguably the incompleteness of mathematics makes it even richer since the lack of an absolutely true foundation opens up an infinity of different variations to explore. If the Boltzmann brain hypothesis suggests the same may be true of physics, we should not lament. The potential of a limitless future of new discovery and scientific progress without bounds should excite us far more than a world where we stand on the threshold of knowing all there is to know. We should celebrate the infinite richness of reality… as long as it actually exists.

1. This understanding dates back to the discovery in 1998 that the universe is expanding at an accelerating rate, rather than its expansion slowing as was previously assumed. In 2002, Dyson, Kleban and Susskind identified the disturbing implications of this new understanding that are discussed in this post (see https://doi.org/10.48550/arXiv.hep-th/0208013).

2. This effect was identified by Sean Carroll in https://arxiv.org/pdf/1702.00850.pdf, who referred to it as cognitive instability. This paper explored the paradoxical implications of Boltzmann brains discussed here, but with different interpretations of what this means for physics.