—Hume's Problem of Induction—
How do we know the past will reliably predict the future?
This question is the heart of empiricism. When we do scientific experiments we rely on the assumption that experiments giving consistent results imply that in the real world similar conditions will create those same results.
How do we know if this is true? Can we justify empiricism? Can we justify the idea that we can rightfully infer what will probably happen in the future based on past observations?

Hume's answer was no. His argument was that if you look at past observations and see that empiricism works, that past observations can indeed be used to successfully predict future states, and then use that past success to infer empiricism will continue to work, your proof is only valid if you assume past states predict future ones.

This is because if that assumption is wrong, then no matter how many cases of empiricism succeeding at predicting future states you have, that won't allow you to infer future states from right now.

Therefore, to argue that the past predicts the future based on the success of the scientific method, the method of using repeated observations to predict outcomes, presupposes the very thing you try to justify.
This is circular reasoning, you can't use empiricism to justify empiricism, therefore empiricism is left unjustified.


—Why the Future is similar by Causality—
There is a way around this, however. Imagine a world A and world B. They evolve through time. Now imagine B evolves in a way different from A. The moment we look at the divergence from A and ask “why”, and we get a reason that explains the divergence, that reason implies a difference between A and B to begin with, as that reason must apply to B and not to A.

If in contrast, A and B were identical to begin with, then they are either simply the same state, or they will at least evolve in ways that are as similar as the states are similar. For if they do not, if B diverges from A again, we can again ask “why”, and if we get an answer, that reason implies a difference between them that contradicts our assumption they were identical.

When it comes to science, we can infer the future will be relevantly similar to the past because we have no reason to postulate a fundamental difference between them.
The moment some big change does happen over time, we can ask “why” and identify the cause.
The only way this can fail is if B diverges form A for literally no reason at all, or if it diverges for a reason we fail to identify.


—The Consistency of Reality—
This would imply reality acting inconsistently, or physical laws we don't fully understand. We already have good reason to think physical laws are not entirely understood, since we already see some behavior that diverges from our predictions.
Yet suspiciously, such behavior diverges in a consistent way, implying a deeper theory of physics that is consistent it is acting according to.

Is it possible reality could turn inconsistent? Yes, but this is not useful information. To engage in argumentation surrounding physics at all is to presuppose that asking “why” and evaluating claims about physical states is a reasonable endeavor. That requires some sense of logical inference.
And further, we have reduced the problem of induction to nothing more than the principle that physics is consistent, thus divergence from expectation implies greater physics that is probably observable.

There is no good reason to think reality is inconsistent, it is unclear what that would even mean and again makes reasoning about physics itself impossible.
Quantum Mechanics implies certain future states can occur not based purely on past states but instead based partly on past states and based on either true randomness or hidden variables.

For true randomness especially, the explanation is simple. Randomness does not ultimately imply inconsistency, the distribution of probabilities is itself consistent.
To claim reality is inconsistent and that the physical laws we know of could suddenly invert with no cause whatsoever is an entirely arbitrary proposition that is not substantiated.

It is in the same epistemological ground of the idea that empiricism is false or invalid because we could all be insects eating alien mushrooms without knowing it.
There isn't any proof for or against that idea, you can't prove a negative in that way, it would be like arguing there is an invisible teapot floating between Jupiter and Saturn.
Also, to postulate anything that implies our own observations and reasoning is invalid, causes the objection itself to lose its own justification, since it relies on the ability to make consistent inferences on how reality works, to say anything about reality at all.

This is the same issue as saying you’re actually a hallucinating insect. If you are, there is no reason for the physics or logic that led you to that conclusion to be trustworthy in the first place, so the proposition is self-defeating.
Occam’s Razor implies we should accept the argument that requires the least assumptions, least arbitrary stipulations, that does not also result in contradiction.
Therefore, our proposition that the past can reliably predict the future is on the solid ground of consistency itself, something we already presuppose by arguing about reality to begin with.