The Paradox of Plato’s Quantum Ball
Imagine you have a ball at the macro-level. The macro-level ball has a clear identity and a clear set of properties. It also has a definite position (P) and momentum (M) that are identifiable and independent. Now, imagine that you go down to the quantum-level of the ball. It still exists, but at the quantum-level, we don’t see a ‘ball’ anymore; we just interact with P, M, or ‘particles’ that have to do with the ball.
But P and M are not fundamentals — they are observables. That is, P and M don’t tell us about any of the properties or the identity of the ball. Furthermore, they are no longer independent. But the ball must still be there at the macro-level. Its wavefunction still exists. We have, however, begun focusing on another subsidiary wavefunction. This subsidiary wavefunction is of the quantum ball as it exists in Plato’s Cave.
The Allegory of the Cave appears in Plato’s Republic. It describes reality as experienced by a group of prisoners who have lived their entire lives chained inside a cave. Behind the prisoners is a fire, and between the fire and the prisoners is a walkway. On the walkway, people pass by carrying objects, which cast shadows on the cave wall in front of the prisoners. The prisoners mistake these shadows for reality.
Let us refer to this wave function as Plato’s Quantum Ball Wavefunction.
It keeps collapsing when we observe it per the Born rule and as filtered by the dominantly accepted Copenhagen Interpretation of quantum mechanics. Incidentally, that is also why Schrodinger is reported to have said he wished he had nothing to do with it.
We then have to use statistical analysis to make sense of it. But we can’t understand it because the P and M are just observables. Heisenberg’s insightful idea captured in his uncertainty principle tells us that the nature of observing observables is that there is always uncertainty in their observed values. We aren’t seeing the quantum ball's properties, identity, or nature.
No matter what our basis states (spin-up/spin-down, horizontal polarization/vertical polarization, ground state of an atom or ion/excited state of an atom or ion, one electron occupancy state/another electron occupancy state, lower energy state of circuit/higher energy state of circuit) this will always remain true. We must leave the cave to see that we are dealing with a quantum ball.
Then, we will also see that, instead of using aggregation based on P and M to infer other properties of the ball (assuming that is possible), we will be better served by using disaggregation to try to make sense of P and M, knowing the nature of what we are looking at is a ball. The former seems formidable, given decoherence, lack of scalability, etc. Further, superposition, so long as it concerns superposed values of P and M, is not telling us anything useful unless we begin to deal with the ball's superposed properties.
That is why Einstein suggested that quantum theory was incomplete.
But we have been approaching it as though it is complete. We have built quantum mechanics using classical mechanics as a basis. We have built the math of Quantum Field Theory (QFT) in terms of the math of single quantum particles. Everything becomes a nail with a hammer in the hand.
We have not elevated to “function,” so we can’t leverage the possibilities of disaggregation. Classical physics is focused on precise physical law. When we deal with the quantum level, which separates the visible from the invisible, we are dealing with the physics of the situation and other possibilities that are being parsed out. Yet, we are fundamentally only leveraging a view based on classical mechanics. If we do that, then we will miss out on other richness. But is not Schrodinger’s wave function also about something else?
“Function” has to express itself variably, perhaps even as patterns of particles, say. But if we don’t see it, we miss the possibility. Digital computation has integrated “function” in one way. Quantum computation needs to integrate it in another way.
That is why we need a different approach.
In such a systems theory view of the quantum level, the latter is integrated with physics, chemistry, biology, philosophy, etc. For the very adventurous, here is a reflection on the nature of the quantum seed that may result from such integration. For the reasonably adventurous, here is a recent and brief Forbes article on different developmental trajectories for quantum computation. Alternatively, here is a representation of a potential architecture focused on “function.”
