Can it be philosophically proven that the Universe either is or is not a simulation? If someone was in a simulation, could they tell? What would the differences be between a simulated universe and a "real" universe?
Although far from agreed upon by all philosophers, DesCartes' cogito - the famous "I think therefore I am" - was a result of him attempting to prove that the universe was not a simulation.
He starts out by postulating that everything he sees, hears, feels etc, might not be real, but was actually an illusion created by an evil demon, trying to make humans believe they were part of a real world when they weren't. They didn't have computers or Keanu Reeves in the 17th century, so illusions created by demons has to do in lieu of simulation.
The demon could make him doubt that anything he sees is real, or that anything he tastes is real, etc...
However, while he can doubt everything else, he can't doubt the fact that he is actually doubting anything. Because doubting that he has the ability to doubt is in itself doubting.
So he has established that at least the act of doubting is real. But for there to be doubting there has to be thinking. So thinking is real as well. But there has to be something to do the thinking. So now he has established that the soul (the "I") is real. Hence "I think, therefore I am".
DesCartes claims that this proves with certainty that the soul is real and not a simulation (or demonic illusion).
Hope this helps.
You can make a good start on proving that reality is simulation, by doing certain physics and possibly astronomy (1)experiments that would force the simulator to expend ridiculously high resources to maintain consistency. But then the simulator, if it has (2)snooping ability, can just restart from an earlier time with some slight variation, where these experiments would hopefully (for him/her/it) not occur. I.e., you can't even in principle successfully battle simulator's censorship.
Still, (3)science fiction stories have been written about people doing exactly that, battling the simulator more or less successfully, such as Vernor Vinge's “The cookie Monster”. Informally, I find that the presentation of the story as pure text with arbitrary emphasis added, makes it hard to read. One does not perceive the structure of the piece without actually reading all of it: it's not easily accessible! Let it be more formally stated, though, that Vinge's references to Usenet communications and a galaxy filled with Norwegian names, in some of his books, makes him an author to be trusted. For it is obviously true that the galaxy will end up with lots of Norwegians and an old Usenet-like communications network, and still Vernor Vinge's the only author who has described it that way.
There is another way of viewing this, however. One can take the idea of cosmic censorship and say that it indicates a simulation, i.e. that it's likely a manifestation of just simulator's censorship. But as I see it that's purely nonsense associative reasoning, for cosmic censorship is about logical consistency, not about the computational cost of consistency.
Yes, I know, this answer's a collection of rambling thoughts & associations.
But IMHO that's the best you can get: attempts at reasoning more clearly about this can, I think, be dismissed out of hand, for it that was possible, then it would have been well known.
1) I don't recall exactly those experiments, sorry; I only remember reading about it, but no doubt they involve exponentially increasing effects (i.e. chaos, in its mathematical meaning, more informally the butterfly effect) and inspecting ever more fine details.
2) I almost used the acronym SDS, Heinlein's Super Duper Snooper, with a footnote explaining it, but then I thought better of it.
3) Can't leave this without mentioning Charles Stross' “Accelerando” universe and “Glasshouse” novel.
As with most things in philosophy there are no universally agreed upon proofs. There are arguments both for and against the skeptical hypothesis that reality could be a simulation.
As some people have mentioned Descartes malicious demon is a good place to start. But as far as proving the possibility or impossibility of a simulated reality I would recommend reading Hilary Putnam's "Brains in a Vat" In which he puts forth an argument against the skeptic hypothesis based on his semantic externalism.
In regards to the differences between a simulated universe and a "real" universe, it gets a lot more complicated. There are many fields of philosophical enquiry (i.e. ontology, metaphysics, epistemology) and a variety of theories within each, which would determine if there where any differences and if so what they would be.
An example, without getting too technical.
If the question is what differences would there be between a "real" universe (as is generally accepted) and a simulated universe (such as the brains in a vat scenario), then depending on the areas of concern certain differences or similarities would arise.
For instance it could be said that our experience of reality is dependant on various inputs. In the "real" universe these would be sensory inputs stimulated by external objects and their properties. In the simulated universe these inputs would be generated by the simulation.
So In the brain in the vat scenario compared to our actual reality. These inputs, which are generated by a simulation, would be fed directly into our brain. Whereas in our "real" universe these inputs generated by "real" objects and properties, would enter our brain via sensory organs.
In this scenario the differences would be:
- the source of the inputs
- the mode of entry
Furthermore it would follow (I would argue, fairly uncontroversially) that our experience in both cases would be no different. (Of course this depends on the quality and content of the simulated universe.)
I hope this helps to illustrate one such method of investigation, and how it is dependant on various premises (i.e. How we experience reality). If we were to reject these and put forth alternate premises our investigation might yield different results.
Nothing occurring in the physical world can be proven absolutely because reality itself must be assumed to be true. Therefore, it is possible that the universe is an imitation.
However assuming reality is fact does not mean that we cannot observe natural patterns to the point where we can predict certain outcomes with 99.999% probability.
The probability is what we have to work with. Certainly, the trend is your friend until it ends.