The Measurement Problem: Turtles All the Way Down

October 21, 2021

Quantum mechanics. What is so strange about it? One aspect, which is truly peculiar to most (including me), is the measurement problem.

I recently had this conversation with a good friend and collaborator, Ivan, about quantum mechanics—particularly the measurement-problem as it applies to quantum field theory, but we won't discuss this aspect. 

The measurement-problem is well illustrated with the above image of the famous double-slit experiment: When the monkey, an observer (we're all monkeys really...), looks away from a QM "particle" going through a double-slit, the "particle" acts as a wave and produces an interference pattern. However, when the monkey tries to observe the particle doing wavy-things by looking at which slit the particle goes through, the particle starts doing particle things, like going through one slit or the other (as opposed to "going through both" and interfering, as a wave does). Certainly this is strange, but why is it a "problem"?

The problem with measurement is that it is strikingly odder than any other process in quantum mechanics. That is, every other evolution of the system is dictated by unitary, reversible dynamics. Now, it turns out, that we can extend the measurement process to a unitary process by "Going to the church of the larger Hilbert space" (technically, by purification or unitary extension of the quantum measurement-channel), but in doing so, we introduce another peculiar aspect of quantum mechanics— quantum entanglement of the measurement devices with the things that we are suppose to be measuring. We can then continue to do this for all possible measurement processes—in other words, it's entanglement (turtles 🐢) all the way down. 

This produces a cosmological conundrum. We cannot expand the congregation of the church indefinitely, as eventually all of the constituents of the universe will be entangled. Once we fill the church, the question is then:  Can the universe be measured, or is it some vast ball of entanglement undergoing internal unitary dynamics (what is driving a global unitary, if there is one, may altogether be another issue)—in which case our universe is some globally coherent object, irrespective of anything external? And if it can be measured, then measured by what? A universal measurement would inevitably lead us to the same reasoning as before—turtles all the way down into, e.g., the multi-verse. In a nutshell, this is (to me) the measurement problem 🐢🐢🐢...