This series was meant to be a few, fun archives about lava lamps and rolling dice. Instead, I sit here, hours before my Monday deadline, surrounded by articles on quantum mechanics, formal logic, and God. I still don’t know if quantum measurement is random. Honestly, at this point, I don’t even know if I want it to be random.

My problem begins with cats, specifically the cat that Schrödinger put in a box. Schrödinger’s cat is in a superposition of alive and dead, and this superposition constitutes the state of the cat. The state is just our interpretation of the cat, which in this case is an evenly split probability distribution of alive and dead. When we measure the cat by opening the box, the cat collapses to either alive or dead, not both. My question hinges on one key problem: can you peek inside the box beforehand?

The analogy is coarse and imperfect, but the problem hinges strongly on that concept. Just replace the word “cat” with “system” and “alive/dead” with actual eigenstates. Obviously, for real cats, you can peek inside the box, but the answer is not so clear for quantum systems. Quantum systems are best understood through representations of their probability distributions. The distribution constitutes the state of the system. A measurement of the system selects from this distribution and destroys the state. If quantum systems and their measurements cannot be explained by some hidden mechanism, then, for my purposes, they are truly random. They are the final frontier in this quest for pure, statistically independent randomness.

Scientists have been exploring the issue of hidden variables in quantum mechanics for decades. Any deterministic theory of quantum mechanics must comply with the no-go theorems. The no-go theorems are strong limitations on what must be true for deterministic explanations of quantum mechanics. One particularly famous no-go theorem is the Kochen-Specker Theorem. Kochen and Specker (and Bell) showed that measurement cannot simply reveal values that already exist. In other words, measurement also depends on what other objects in the system can be measured. The full argument includes a construction of the partial algebra on comeasurable observables. I don’t understand half the words I just said, but I do know this: creating a hidden-variable explanation for quantum mechanics would be very, very difficult.

The hidden-variable approach may be difficult, but it may not be impossible. Superdeterminism is a deterministic, hidden-variable approach to certain parts of quantum mechanics. It’s not a replacement for quantum mechanics, just an augmentation. In particular, it is a deterministic approach to local phenomena. Some of you may think, “Wouldn’t that violate Bell’s theorem?” Apparently, it doesn’t, so long as you believe that preparing a quantum state and its future detector cannot be done independently. If this were true, superdeterminism would violate statistical independence, ultimately killing the randomness of quantum measurements.

At this point, we don’t know which parts of quantum measurement are deterministic, if any. As I tried to understand this problem further, I stumbled into another philosophical issue: determinism. Let’s say we discover a deterministic model for quantum mechanics. Let’s also say this extends to a Unified Field Theory. Then, every event could be fully modeled as a result of everything before it. Dice rolls, lava bubbles, quantum measurements, everything would be determined. Does this mean the human will is determined? Does the Universe roll dice? I fell down a rabbit hole, trying to understand how developments in quantum mechanics would impact broader philosophical issues. After some digging, I realized that any physical model of the universe has a lot more questions to answer before we discuss free will. We would need to understand if physical phenomena can explain human will and what it means to make a decision. The answer to the question of free will is not currently in quantum mechanics, for better or worse.

Returning to the matter at hand, I still need to figure out whether quantum measurement is truly random. I’ve spent far too long reading physics, math, and philosophy papers, and none of them have any answers, so I’m going straight to the source. Using my limited knowledge of quantum computing, I wrote a program for a quantum coin flip. Heads, it’s random; tails, it’s deterministic. With this program, quantum measurement will reveal the truth of quantum measurement. It is currently running on IBM Quantum, and I will update you with the results shortly.

Update: the program crashed.

References

  1. Schrödinger, Erwin. Cat Paradox. Translated by John D. Trimmer. 1935. Proc. of the American Philosophical Society.
  2. Hossenfelder, Sabine. Superdeterminism: A Guide for the Perplexed. 2020. arXiv.
  3. Landsman, Klaas. Randomness? What randomness?. 2019. arXiv.
  4. Specker, E. P. and Kochen, Simon. The Problem of Hidden Variables in Quantum Mechanics. 1967. Journal of Mathematics and Mechanics.
  5. Paterek, Tomasz et al. Logical independence and quantum randomness. 2010. arXiv.
  6. Causal Determinism. Stanford Encyclopedia of Philosophy
  7. Hossenfelder, Sabine and Palmer, T. N. Rethinking Superdeterminism. 2019. arXiv.
  8. Bell’s Theorem. Stanford Encyclopedia of Philosophy