greypilgrim
- 579
- 44
Hi.
In this video of Looking Glass Universe, the host "proves" the Born rule by breaking down states into "finer" ones and then applying the principle of indifference. In the description, she bases this on papers by Deutsch, Hossenfelder, Zurek and Hardy. I have never heard of this argument so far and it seems way too simple, but those are quite respectable names...
How does this "break down" work in Hilbert spaces where the dimension is too small for the number of states needed? E.g. for a qubit in
$$\left|\Psi\right\rangle=\sqrt{\frac{2}{3}}\left|1\right\rangle+\sqrt{\frac{1}{3}}\left|0\right\rangle$$
how would one break down the first state? Or do I need to assume more "hidden" dimensions?
In this video of Looking Glass Universe, the host "proves" the Born rule by breaking down states into "finer" ones and then applying the principle of indifference. In the description, she bases this on papers by Deutsch, Hossenfelder, Zurek and Hardy. I have never heard of this argument so far and it seems way too simple, but those are quite respectable names...
How does this "break down" work in Hilbert spaces where the dimension is too small for the number of states needed? E.g. for a qubit in
$$\left|\Psi\right\rangle=\sqrt{\frac{2}{3}}\left|1\right\rangle+\sqrt{\frac{1}{3}}\left|0\right\rangle$$
how would one break down the first state? Or do I need to assume more "hidden" dimensions?