0

Some interpretations, like the many-worlds interpretation, treat the wavefunction (modulo an overall phase factor) as objective and fundamental.

But consider the following example for a qubit: a classical probability distribution over wavefunctions with a 1/2 probability of $|0\rangle$ and a 1/2 probability for $|1\rangle$. Then, consider another classical probability distribution with a 1/2 probability for $\frac{1}{\sqrt 2}\left(|0\rangle+|1\rangle\right)$ and a 1/2 probability for $\frac{1}{\sqrt 2}\left(|0\rangle-|1\rangle\right)$.

Both examples are described by the same density matrix $\left(\begin{array}{cc} \frac{1}{2} &0\\0&\frac{1}{2}\end{array}\right)$ and can't be distinguished empirically by any experiment. If wavefunctions are objective and fundamental, why can't we distinguish between both examples?

Qmechanic
  • 220,844
QGR
  • 2,377

1 Answers1

1

If by "objective" you mean "real", a wave function, $Ψ$ is only mathematically fundamental because it is a postulate of quantum mechanics, a function of complex numbers, it cannot be measured independently.

Only $Ψ^*Ψ$ is a measurable prediction as the probability distribution. This allows different formats for $Ψ$, that can give the same real valued $Ψ^*Ψ$ .

The density matrix is another way of organizing the wavefunctions, each $ρ_{ij}$ is a part of the total $Ψ^*Ψ$.

anna v
  • 236,935