Statistical mechanics helps relate the quantum world to objects that seem solid and not governed by the whims of observation, but there are still questions to be answered, says Chanda Prescod-Weinstein.

I RECENTLY walked by a physics department office that had a sticker on it saying something like “Heisenberg may or may not have been here”. This is in part a nod to the quantum cat, which, while it is inside a box with no observer, may be dead or alive. We aren’t sure until we look at it.

Y. Wang/Shanghai Jiao Tong University |

This feline thought experiment is intended to help us visualise a deep conceptual difficulty in quantum mechanics: the fact that the act of observing seems to determine what state matter is in. This is due to the probabilistic nature of quantum mechanics, and also the wave-particle duality I described in last month’s column.

credit: Daria Kulkova/Alamy |

The mathematical structure that we use to describe quantum states of matter is an equation that describes waves. The wave equation, as it is known, requires a different way of thinking than what we are used to in classical, Newtonian mechanics. In the old picture, if we know the position, speed and direction of an object, we can use established laws of physics to calculate for certain what those properties will be in future.

Quantum mechanics, however, has a rule called Heisenberg’s uncertainty principle: suddenly, we can’t know the exact position and speed of an object simultaneously. We have to pick which one we want to be certain about. In addition to this uncertainty, the law that describes them in time is statistical in nature: we describe quantum objects using something called the wave function, which can be used to calculate probable values of position and speed, but we can never guarantee that those are the values we will measure.

So, there is a chance the cat is dead. There is a chance it is alive. But not all probabilities are created equal. Obviously, assuming the cat hasn’t been in the box for an unreasonable period without air or sustenance, we can generally expect it to be alive. We know this from everyday life, and it is a certainty that we feel about many of the objects that we deal with routinely. This is because we live life on the scale of the macroscopic, not the microscopic, which is where the features of quantum mechanics are most evident.

This raises an obvious question: if quantum mechanics describes microscopic reality, why doesn’t it also visibly govern macroscopic reality? And actually, we would still have a similar question even without the presence of quantum mechanics: even in the scenario where the objects behave classically, how do we describe their behaviour when they are all added together?

The good news for both you and me is that I can – partially – answer this question with confidence. Here is the part that I do know: macroscopic objects are made up of lots of little microscopic objects. There is a whole subject that helps us calculate the properties of macroscopic objects based on their microscopic qualities, which is called statistical mechanics.

When I was a graduate student, one of my PhD advisers impressed upon me that statistical mechanics is one of the most important, if not the most important, subjects in all of physics. Roughly speaking, statistical mechanics is the mathematical framework that underpins thermodynamics and explains the relationship between measurable properties of matter, such as temperature, heat and pressure.

Stat mech, as we physicists call it, is a subject students learn both as undergraduates and as graduate students. But my early impression of it was that it is derivative and isn’t fundamental, so I wasn’t particularly impressed and didn’t think it had earned its reputation as the “most important topic in all of physics”. If it were so important, I would have heard about it before I went to college, right?

Now that I am older and much greyer, I am the professor walking around telling students that statistical mechanics is a central subject in physics. Not only does stat mech act as a connector between the very small and larger phenomena, but it also acts as an important bridge between quantum mechanics and the world of everyday life.

I did say I could only partially answer the question of how the quantum world relates to objects that seem solid and not governed by the whims of observation. Though quantum statistical mechanics helps us bring these wildly different scales of existence together, questions remain. For example, we experience space-time as smooth and continuous. But we now know that other phenomena that appear smooth and continuous on large scales are actually discrete – quantised – on small scales. Does space-time similarly have this property?

I don’t know the answer, but I always assume there is a chance that the students I teach may be the ones to work it out.

Chanda Prescod-Weinstein is an assistant professor of physics and astronomy, and a core faculty member in women’s studies at the University of New Hampshire. Her research in theoretical physics focuses on cosmology, neutron stars and particles beyond the standard model.