Objective reality is a disturbingly difficult thing to prove.
This is a very simple and even tautological conclusion, that a lot of smart people I know seem to have a hard time accepting. I think that this is because people assume that science assumes materialism, which it doesn't, of course. Science requires no metaphysical commitment.
https://iep.utm.edu/met-scie/ or
https://philosophy.stackexchange.com/questions/48844/axioms-...
You can’t really do science without having certain metaphysical beliefs about the uniform nature of causality across time and space, for example.
Nothing can exist without causality as we know it, i.e. a thing happens which is the cause of another thing that happens.
That does not mean the order of events is as perceived, or that there is even an order of events. The order of events is the way observers perceive the events, and is independent of the cause and effect.
For example, everything that happens in the universe may already have happened, at the instance the universe was born. But we, as members of the universe, perceive it as happening one thing at a time, like watching a movie already created.
David Hume spoke a lot about this: https://iep.utm.edu/hume-causation/
Not only is this not true of all conceivable worlds, it's not even true for the most commonly accepted explanation of physics. In the Copenhagen Interpretation of quantum mechanics, the value that will be observed in an experiment has no cause - it is random in some range. For example, if we detect an electron passing through the left slit of a double slit apparatus, there is no cause for why it passed through the left slit and not the right one (in the CI of QM).
Of course, this is ultimately a model and can be wrong. But my point is that we can definitely conceive of models of the world in which causality is not a strict requirement - and not just fantasy ones, but very concrete models with workable predictions.
You can do science without holding any beliefs just like birds can fly without a theory of aviation. Metaphysics just provide interpretations of scientific results beyond what's observable.
In fact outside of physics we don't really posit uniformity in any science, because what you study changes all the time anyway, in fact the scientific method itself changes. Science itself is a dynamic, evolving process. Certainly looking back 500 years science was pretty different, and it probably will be in another 500.
In which case your metaphysical assumptions will simply be implicit rather than explicit. For example, in doing science, you'll be "explaining" things, which assumes a certain position of the nature of explanation and causality. You'll be choosing a theory out of a number of competing ones, a choice which will rely on some assumptions (e.g. simpler is better?). You'll be trying to uncover "laws of nature", which would assume their existence in the first place, etc.
Are our perceptions and experiences of reality not also a part of reality? If not, then what are they a part of?
> This is a very simple and even tautological conclusion...
This itself is an experience of reality, an objectively incorrect one if you ask me.
> I think that this is because people assume that science assumes materialism, which it doesn't, of course.
Science, having no volition, does not assume anything. Scientists on the other hand, whom I've spoken to hundreds of, very often do assume materialism. I personally believe that humans are unable to not assume most things, and as evidence I would present the content of all internet forums.