Are Boltzmann Brains Real?

Consider the following: a lone brain, suspended in an interminable stretch of the cosmos. It contains memories of what seems like a lifetime, hopes, and dreams, only to disintegrate into chaos a split second later. According to thermodynamics, you are more likely to be such a brain than not.

How can that possibly be?

Entropy may offer an answer. First conceived by Rudolf Clausius in his 1850 paper "On the Moving Force of Heat," entropy describes how spread out or unavailable energy is within a physical system1. Clausius and other scientists in the then-nascent field of thermodynamics postulated that the overall entropy of an isolated system will increase and tend towards a maximum—what would become known as the second law of thermodynamics.

Initially, physicists believed that the increase in entropy in an isolated system was absolute. Imagine a hot metal bar pressed against a cold one. Wait long enough, and the system transitions towards thermal equilibrium, evolving from a low-entropy state with a steep temperature gradient to a high-entropy configuration where heat is evenly distributed. This makes intuitive sense. Everything tends towards a state of equilibrium. Heat only flows from hot to cold, never the other way around. Or does it?

In reality, this could happen—it’s just unlikely. In the 1870s, physicist Ludwig Boltzmann proposed a statistical interpretation of entropy:

where S represents the total entropy of a system, k_B is Boltzmann’s constant (1.38 × 10⁻²³ m2 kg/(s2 K)), and W is the total number of possible microscopic arrangements (microstates) of the system1. This equation reformulates entropy in terms of probability. Imagine the two metal bars again. If heat is regarded as discrete energy packets randomly exchanging between particles, an exchange that temporarily decreases the cold bar’s energy is possible, however unlikely. This is the core of Boltzmann’s great insight: the universe is ruled not by certainty, but by overwhelming probability.

This new interpretation of entropy gives rise to interesting results, especially when applied to the universe, the only true closed system in existence. Back in 1862, Lord Kelvin first envisioned a future where all energy would be spread so thin that nothing could stir. Provided that the laws of thermodynamics remained constant in the future, he reasoned, everything would inevitably enter “a state of universal rest and death”5. This picture, known as the heat death of the universe, is a widely accepted theory of the fate of our universe. However, though the universe may seem “dead” on a global scale, the statistical interpretation of the second law of thermodynamics suggests that it is possible for a local reversal of entropy to occur.

One such possibility is the Boltzmann brain: a self-aware entity born from spontaneous fluctuations after the heat death of the universe. It is difficult for these structures to form. After reaching heat death, the most common particles in the universe will be photons and gravitons, which typically possess extremely low energy. However, it is rare but still possible for high-energy photons and gravitons to appear and collide with each other, leading to the creation of fermion particle-antiparticle pairs. While nearly all such pairs almost instantly annihilate each other, some of these particles can, in theory, travel far enough from each other to encounter other matter. In the extremely unlikely case that enough matter was produced and retained this way, more complex macrostructures like brains could form.3

Despite their unlikelihood, Boltzmann brains are expected to vastly outnumber ordinary observers. In fact, it is more likely for a single mind to arise by accident than for a vast, orderly universe to painstakingly evolve over billions of years. First, assembling a brain complete with illusory memories requires exponentially less entropy reduction than assembling an entire universe containing billions of galaxies, planets, and evolving biospheres. Furthermore, given an infinite amount of time after heat death, however unlike they are, Boltzmann brains are guaranteed to form an infinite number of times. So, by the decrees of modern scientific theory, our treasured reality could be nothing more than a hallucination afloat on a statistical sea of infinite brains.

That’s absurd, you may think. You have a physical body and memories. You can’t be a Boltzmann brain, can you? Unfortunately, there’s no way to definitively rule out the possibility that you are such a brain. After all, the sensory evidence of the world around you could just be arbitrary illusions. Yet there’s a twist: by the same logic, it is impossible to reasonably show that you are a Boltzmann brain. This is what physicist Sean Carroll calls “cognitively unstable”: if you accept that you are a Boltzmann brain, you would have to reject the validity of your own cognitive faculties, observations, and memory—the fundamental assumption upon which all scientific theories, including the Boltzmann brain argument itself, are founded3. The Boltzmann brain is therefore considered a theory that, if shown to be true or overwhelmingly likely, signifies a latent error in our current understanding of the universe—known as a reductio ad absurdum. What could we have gotten wrong?

In 2013, Carroll and fellow physicist Kimberly Boddy came up with the idea that the universe simply may not exist long enough to reach heat death. The properties and interactions of all matter in the universe are determined by quantum fields. Most fields are in the lowest energy level possible—a state known as the vacuum state2. However, measurements of the Higgs boson showed that the Higgs field, which gives mass to matter, may not be in its vacuum state. That is, a lower energy “true vacuum” may exist for the Higgs field. In the case of a random event like quantum tunneling, the Higgs field could bypass the potential energy barrier between its current metastable state and its true vacuum state. This would trigger the formation of a spatial bubble of the true vacuum state that expands at the speed of light and, for all we know, could completely change the laws of particle physics as we know them—and with them, the possibility of the random fluctuations that lead to Boltzmann brains. If this event, known as false vacuum decay, is more likely to occur before heat death, the expected number of Boltzmann brains would be drastically reduced. Yet, later studies show that this may not be the case. The amount of time before false vacuum decay occurs depends on more specific measurements of elementary particle masses, which reflect the stability of the Higgs field. Boddy and Carroll calculated that a top quark pole mass of around 178 GeV is indicative of a decay rate that could prevent the universe from reaching heat death2. However, more recent measurements place the quark’s mass at around 172.93 ± 1.36 GeV, suggesting a far stabler Higgs field and a lower decay rate4.

At any rate, we are a long way off from establishing a cosmological model that steers clear from the implication that our perception of reality is a mere low-entropy, near-instantaneous fluctuation in a dead universe. However, because the Boltzmann brain scenario is cognitively self-undermining, scientists are rationally entitled to reject it. Though the theory cannot be empirically disproven, cognitive stability demands that we trust our observations before a new model of the universe eliminates the statistical dominance of Boltzmann brains for good.