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  1. Living inside a simulation - several conditions have to meet in order to prove that we are actually living inside one.
  2. Chance of our computing/processing power to become unlimited is becoming a reality year by year.

PS: The question focuses on the conditions that have to be met in order for us to perceive/understand that we are actually in a simulation.

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    $\begingroup$ The answer to the second question is easy: it's not possible. Computing power cannot be "unlimited". There are limits on computing power arising from first principles: the quantization of action implies that a computer cannot count infinitely fast. $\endgroup$
    – AlexP
    Commented Jan 20, 2018 at 16:01

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This would be the place to start: https://arxiv.org/abs/1210.1847 An obvious constraint, then, is the quantization of spacetime and of all states. (You can't store an infinitely precise number. You are, however, allowed constants that you can evaluate to an arbitrary precision as needed. There will still be a rounding error.)

The number of interactions possible is likely too high for a simulation, so a simulation would take shortcuts, hierarchical simplifications so that you model objects as black boxes in black boxes rather than every quantum particle to every quantum particle.

This is speculative and harder to prove, but quantum foam is vast and there are something like a googol of each particle in the visible universe, which is just a segment of the full universe. Every pair of particles in all of this would need to be calculated for. Combinatorial explosion time, so simplification, so possible to break things.

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