Date: June 5, 2025
A necessary condition for a physical theory to be called complete is that “every element of the physical reality must have a counterpart in the physical theory”.
We have the following “EPR Criterion of Reality”:
If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity.
The “EPR Argument” is an argument that quantum mechanics cannot be a complete physical theory:
- If quantum mechanics were a complete theory, this would imply that particles could not have their positions and momenta be “simultaneously real”, by Heisenberg’s uncertainty principle.
- Assume that two entangled quantum systems X and Y that are sufficiently far apart spatially cannot causally interact with one another (i.e., assume locality).
- Measuring the position and then momentum of a particle x in X determines the corresponding position and momentum of a particle y in Y, since X and Y are entangled quantum systems.
- However, since measuring particle x can have no effect on particle y (by locality), the EPR Criterion of Reality implies that the position and momentum of y were simultaneously real before we did any measurement.
- Hence, quantum mechanics is an incomplete theory.
References
- Albert Einstein, Boris Podolsky, and Nathan Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? https://cds.cern.ch/record/405662/files/PhysRev.47.777.pdf
Albert Einstein Quantum Mechanics Quantum Entanglement Heisenberg Uncertainty Principle