Machines for context-free languages which gain no extra power from nondeterminism
As far as I know, we do not know whether Non- deterministic context-sensitive languages are more powerful than deterministic context-sensitive languages. And the simplest reason behind this is: Till now no-one has been able to give a language that is accepted by the non-deterministic LBA and not accepted by the deterministic LBA. So if someone can come up with one such language that is accepted by ND LBA and not accepted by deterministic LBA then only this will be proven. As we know this method of proving is called proof by contradiction.
Because proving something is TRUE is a hard problem but proving something FALSE is easy, just get one instance where it fails and we're done.