Reference: Essays on Substance
Testing a Theory
A theory is as sound as the postulates it stands on. The postulates underlying the theory of relativity are:
- The laws of physics are the same in all inertial frames of reference.
- The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source or the observer.
The soundness of the theory of relativity depends on the soundness of these two postulates.
Similarly, the postulates underlying quantum mechanics (its key principles) are:
- Wave Function Postulate: The state of a quantum system is completely described by a wave function Ψ(r,t), which contains all accessible physical information about the system.
- Observables and Operators: Every observable quantity in quantum mechanics is represented by a linear, Hermitian operator.
- Measurement Postulate: When measuring an observable associated with operator A, only the eigenvalues that satisfy the eigenvalue equation will be observed.
- Expectation Values: The average value of an observable for a system in a normalized state Ψ is given by the expectation value of the corresponding operator.
- Time Evolution: The wave function of a system evolves in time according to the time-dependent Schrödinger equation.
- Pauli Exclusion Principle: The total wave function of a system with N spin-1/2 particles (fermions) must be antisymmetric with respect to the interchange of all coordinates of one particle with those of another.
- Superposition Principle: Quantum systems can exist in a superposition of states, exhibiting wave-particle duality.
The soundness of quantum mechanics depends on the soundness of these postulates.
I have examined the soundness of the above postulates to some degree in layman terms. We can evaluate their soundness in mathematical terms too.
I have no quarrel with mathematics. The mathematics is a system of very specialized self-consistent logic. The trouble comes when mathematics is interfaced with reality. The mathematics should be applied to physics in a way that it is consistent with reality. That is the principle of the Scientific Method. The scientific method views reality as continuous, consistent and harmonious.
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