Heisenberg’s Uncertainty Principle

This is an excerpt from the book series Philosophy for Heroes: Continuum.

Ask me if an ordinary person could ever get to be able to imagine these things like I imagine them. Of course! I was an ordinary person who studied hard. There are no miracle people. It happens they get interested in this thing and they learn all this stuff, but they’re just people. There’s no talent, no special ability to understand quantum mechanics, or to imagine electromagnetic fields, that comes without practice and reading and learning and study. I was not born understanding quantum mechanics—I still don’t understand quantum mechanics! I was born not knowing things were made out of atoms, and not being able to visualize, therefore, when I saw the bottle of milk that I was sucking, that it was a dynamic bunch of balls bouncing around. I had to learn that just like anybody else. So if you take an ordinary person who is willing to devote a great deal of time and work and thinking and mathematics, then he’s become a scientist! —Richard Feynman, Fun to Imagine [Feynman, 1983]

Please note: this and the following sections are but an introduction into quantum mechanics—the current field of research in physics explaining the world at the particle level. In later chapters, we will return to the theory to get a deeper understanding, just like this book goes back to Philosophy for Heroes: Knowledge. My own attempt to understand quantum mechanics took me more than two years, so please be patient—it is by its very definition a non-intuitive topic! I also recommend reading the referenced secondary literature to really wrap your mind around it.

How can we actually measure the position of a particle?

Heisenberg’s Uncertainty Principle was formulated in 1927 by Werner Heisenberg. It states that you cannot determine the location as well as the impulse (the energy of the movement) of an entity with infinite precision. An interpretation of this principle is that there cannot be objective measurements insofar as measurements always influence the entity that one is measuring. This is especially an issue for smaller particles like electrons.

To understand this principle, it is important to understand how we perceive the world. A measurement is nothing but a form of perception or observation. In contrast to the ancient view that our eyes send out “seeing rays,” we do not perceive our environment directly but rely on light reflected from objects. In order for an object to reflect light, light has to be beamed at the object. When examining very small particles, we encounter the problem that the smaller the particle, the smaller the wavelength of light has to be in order to be reflected at all. But the smaller the wavelength of light, the more energy is required and the more the beam of light influences the particle.

We can determine the position of a particle with precision limited only by the technology currently available to us. But this determination could cause the particle to be slowed down or redirected in its course, destroying the information about the impulse of the particle. Likewise, one could measure the impulse of a particle by simply having it hit a screen; however, this destroys the information about the position of the particle (replacing it with the known position of the screen).

Example Sound waves are the directed vibration of air molecules caused by a sound source. There is no way to determine the frequency or other properties of a sound wave by a single “snapshot” of the air. Even if you knew all the positions of the air molecules at a certain point in time, you would know nothing about how they vibrate. If you instead used a microphone and let the air molecules hit a membrane, you could get information about the whole sound wave and its frequency.

Revisiting Objective Perception

With this new knowledge about the inner workings of the physical world, it is time to reflect on our existing concepts. This reflection is not a violation of our philosophic principles established in the first place, quite the opposite: we refine our epistemology and ontology constantly in order to get a better view of reality.

So, what follows from our inability to measure location and impulse of entities with arbitrary precision? For the creation of concepts, this does not bother us because we omit the measurement anyways. We have to take a step back, though, from the idea that by building better measurement tools we could measure anything. The underlying issue simply is that we are part of the universe, so any action we take—including observing it by measurements—influences the universe. The consequence is that we cannot be omniscient. But as we have established in the first book, omniscience is not required in order to have an objective perception of reality (and vice versa, objective perception does not mean potential omniscience).

Something seems wrong, though. Can we really say that we know the properties of a particle if we cannot determine their position and impulse at the same time? Are entities like electrons or atoms really entities in the classical sense, similar to tiny billiard balls? Taking a look at atoms, we really cannot take a “photo” of an atom with its electrons, yet a very popular depiction is the core being surrounded by electrons (see Figure 3.5):

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But this depiction does not reflect reality. Classical mechanics, with an entity-based philosophy, with a single particle (a negatively charged electron) orbiting the atom core (neutrons and positively charged protons), provides no explanation of why the electron does not fall into the core.

In classical physics, there are no fixed quanta. In quantum mechanics, there are no distinct electron particles but electron clouds with certain energy states around the nucleus based on the probability of where the electron could be.

In that regard, Heisenberg’s Uncertainty Principle correctly identifies that position and momentum cannot be measured together. But by talking about measuring position and measuring momentum, it could falsely imply that particles are in fact particles in the classical sense with a position and momentum and that only by some weird circumstance, we are unable to measure both together.

How would we approach this issue with philosophy? The problem the uncertainty principle poses for our definitions is that concept creation involves making observations of reality, and omitting measurements in order to focus on the actual properties of an entity. But if we cannot make those measurements in the first place, they cannot be omitted either! Logically, it would follow that we cannot create concepts of particles in the (small) quantum world that do not have both a position and momentum. But if we cannot create a concept based on entities for those small particles, what would that mean for our ontology?