I propose what I call the physical reality hypothesis. It says that all physical systems, from a single electron up to the entire universe, have an objective physical reality, but no faithful mathematical model.
By "objective", I mean independent of any observer. Different observers might still see different things, if the act of observation interferes with the system. By "faithful", I mean an error-free representation of the physics.
This hypothesis is contrary to the Weak mathematical universe hypothesis.
Since 1926, Heisenberg and Bohr have based quantum mechanics on the idea that observations can be accurately modeled mathematically, but not the underlying physical reality. Von Neumann showed in 1930 that straightforward attempts to mathematize the physical reality with hidden variables fail. Bohm found an exception to von Neumann's proof, but only by abandoning causality. His work has been a dead-end.
The Bell test experiments showed that electron and photon spin cannot be mathematized (with local hidden variables) independent of observation.
So this physical reality hypothesis is squarely within mainstream physics. It is very hard to make sense out of 20th century physics otherwise.
But nevertheless many people seem to implicitly assume that the hypothesis is false. For example, a quantum computer is characterized by:
In general, a quantum computer with n qubits can be in an arbitrary superposition of up to 2n different states simultaneously (this compares to a normal computer that can only be in one of these 2n states at any one time). A quantum computer operates by manipulating those qubits with a fixed sequence of quantum logic gates.So believers in quantum computing seem to think that they can create arbitrary superpositions, that these mathematical superpositions will perfectly reflect reality, and that these states can be perfectly manipulated by the transformations corresponding to quantum gates. These superpositions and transformations must be accurate to many decimal places because of the way quantum algorithms work.
The quantum computer scientists are always saying that their theory is a consequence of what we know about quantum mechanics. It seems to me that it is the opposite. The lesson of 20C quantum mechanics is that we do not have faithful representations of n-qubit states or any other complex state.
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