If Space-Time Is Discrete, We May Be Able to Solve NP-Hard Problems in Polynomial Time

Traditional physics assumes that space and time are continuous. However, this reasonable model leads to some serious problems. One the approaches that physicists follow to solve these problems is to assume that the space-time is actually discrete. In this paper, we analyze possible computational consequences of this discreteness. It turns out that in a discrete space-time, we may be able to solve NP-hard problems in polynomial time. 1 Why Discrete Space-Time Why discrete space. Traditional physics assumes that space and time are continuous. In most situations, this assumption works well, but a detailed analysis shows that in some cases, this continuity assumption leads to serious problems. One of such cases is the attempt to compute the overall energy of an electron – or of any other electrically charged elementary particle; see, e.g., [1, 11]. The overall energy of an electron can be computed as the sum of its “rest energy” – i.e., the energy E0 = m0 · c related to its rest mass m0 – and the