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I know there are theories (or postulates) that hold that our Universe could be a simulation. I was wondering, if Special Relativity states that two events which are not causally linked can be judged to have happened simultaneously or not, depending on the reference frame of the observer, can someone (or something) simulating the Universe reproduce this effect (if one observer says that two events were simultaneous, and the other disagrees, and they are both equally justified in their claims, what would the simulator conclude regarding their simultaneity)?

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    $\begingroup$ If our Universe were a simulation, then all bets are off regarding what happens in 'the real Universe'. This is purely metaphysics. $\endgroup$ – Danu Feb 25 '14 at 19:56
  • $\begingroup$ I think there is a problem that you won't want to speak of computational complexity. Computational science doesn't often give answers in terms of you "can" simulate it or you can't. Instead, they formalize the amount of computations needed to solve a problem that is so-large. For instance, that the problem is n^2, or n!, but even this would be very difficult to answer. $\endgroup$ – Alan Rominger Feb 25 '14 at 20:28
  • $\begingroup$ Also, the whole framework of scientific knowledge doesn't make sense if we're postulating that our Universe isn't 'the real one'; you might as well give up on all knowledge we have of our 'fake Universe'. $\endgroup$ – Danu Feb 25 '14 at 20:34
  • $\begingroup$ This may be better suited for Philosophy.SE. $\endgroup$ – Shivam Sarodia Feb 25 '14 at 22:34
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The actual question in this question, is a good physics question. Freely interpreted, it basically asks if SR effects, in particular time-ordering of spacelike separated events, make it difficult or impossible to simulate physics.

The answer to that is no. An "external" Simulator (be it a particle physicist or the hypothetical people simulating our universe) can set up a simulated spacetime so it reproduces the SR effects which are internal to the simulation.

In particular, the spacelike timeordering of events is ambiguous because of the Lorentz transformations applicable on the Minkowski space (that is, the normal 4-D space we live in) that "custom transform" all coordinates in the spacetime for a certain observer at a certain point and speed, which can mix up time-ordering for spacelike separated coordinates.

This is true for the Simulator as well - she will not necessarily agree about the time-ordering with the observers inside the simulation - but this contributes no paradox or problem, because it's the definition of time and time-ordering inside the simulation which is the real ambiguity in that case. The simulator can just pick one particular transformation frame to program the simulation with (or similar).

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