Whilst being trapped in a prison you can not see, taste or feel is considered a paranoid fantasy is might be a possible solution to a problem 100 trillion years in the making, the end of the universe. Why the sudden interest in the Matrix? It has been 10 years since its release at cinemas worldwide, a film that stimulated a great deal of speculation not only in philosophy, particularly existentialism but religion, cyberpunk culture and digital story telling effects.
With enough processing power it would be possible to create artificial environments similar to that in the films, the limit being the amount of processing power available. One high powered solution is a Matrioshka brain, by surrounding a star in a sphere (similar to a Dyson Sphere) you can harness it as a stellar engine to power a computer on its internal surface. Whilst the processing power and size of the simulation would be vast it would have a limit to the number of people able to use it.
So the idea of the Matrix is a scary one, instead of a star we are the power plant and the virtual reality a method to control our rejection to the slavery. If you take away the slavery part, ie being a battery, then housing people’s consciousness in a virtual reality isn’t all that bad. You could think and experience extraordinarily longer than a decaying biological body would permit, the limitation would be the life of a star, which isn’t particularly long in comparison to the universe.
At rough guestimations the Universe should end in around 100 trillion years in 1 of 3 ways, either its flat, open or closed. If our universe is a geometrically flat one it will slow its expansion and eventually reach an equilibrium. An open universe expands forever and fundamentally due to thermodynamics the ever increasing volume decreases the temperature (and pressure) of the universe resulting in heat death called a big freeze. In a closed universe all the total mass in it has sufficient gravity to retard and reverse expansion leading to a super black hole colloquially called a Big Crunch (opposite of the Big Bang).
In an open universe the cooling increases exponentially over the heat that a current processor produces, to truly take advantage you would need a Technological Singularity. A TS is technology capable of perpetual improvement, for instance a processor running an artificial intelligence can make a better processor which runs a better AI, its a positive reinforcement. Since the universe is cooling quicker than the heat a processor produces the computational power and the time perceived in the simulation could increase faster than time to the end of the universe. You could live in a perceived infinity inside a finite universe!
A scenario I’m not as confident explaining, in a closed universe the final singularity (black hole) dilates the perception of time. Therefore a technological singularity would be exponentially increasing computational power as time exponentially dilates but this would from a outside perspective be slowing down whereby producing the same affect as above.
From an external viewpoint in both cases the universe would continue doing its thing and either construct would be destroyed by freezing into inactivity or crushed into plasma, of course this is so ridiculously far in the future that no-one, or no-thing created before the Technological revolution would stand a chance at experiencing it. Certainly a nice idea though…