Not according to quantum mechanics.
So ...
Are you saying an omniscient being is impossible, because something about quantum mechanics implies that it is impossible to possess all possible knowledge?
Or are you saying that even if an omniscient being possesses all possible knowledge, they would nevertheless be unable to accurately predict all sequences because of some knowledge we have about quantum mechanics?
That is, a "truly omniscient being that would not have to rely on measurement" would apparently violate the laws of physics, is one thing quantum mechanics maybe seems to say.
https://en.wikipedia.org/wiki/Uncertainty_principle
"Thus, the uncertainty principle actually states a fundamental property of quantum systems and is not a statement about the observational success of current technology"
> Or are you saying that even if an omniscient being possesses all possible knowledge, they would nevertheless be unable to accurately predict all sequences because of some knowledge we have about quantum mechanics?
That's an extremely astute question. I'm impressed that you managed to realize that that's an important distinction and that you don't know which it is.
It's actually the latter, and incredibly we can prove it. And the proof of this is surprisingly accessible:
Maybe I'm thinking about a form of omniscience that exists outside of time, in which case, of course an omniscient being would know what happens next, because they would know the future just as well as the past. (Example: Any omniscient being will know which photons will pass through a polarizing lens not based on prediction but based on already knowing the outcome.)
As a less powerful entity, if you know all the result in the lab until now, you can consider an experiment made 1 hour ago and "predict" the outcome without breaking the laws of quantum mechanics.
Can you tell me more about why you think it can't?
Of course that still leaves room for an omniscient being that never collapses the wave function and just deals in probabilities. But then your predicitions sound like "there's a 99.978% probability you will be hit by a car on tuesday at 10:04 am." with the remaining 0.022% accounting for quantum flactuations adding up to produce a different result. Whether you call that "all knowing" and whether that proves that nothing is random sounds like an interesting philosophical question.
Randomness implies unpredictability, which implies a lack of knowledge; if you can accurately predict what is going to happen next in some sequence, temporal or otherwise, by observing what has come before, then it isn't a random sequence.
But to someone who possesses all possible knowledge, nothing is random, because everything is predictable. A sequence might still retain certain properties that we associate with randomness (e.g. an unbiased distribution), but no sequence is random if you can always accurately predict the next item.
Obviously, none of us mere mortals is omniscient, but it is possible, for instance, to develop new predictive techniques and to turn once-thought-random sequences into non-random sequences.