A fluctuating energy–momentum may produce an unstable world

Quantum gravitational effects may induce stochastic fluctuations in the structure of space–time, to produce a characteristic foamy structure. It has been known for some time now that these fluctuations may have observable consequencies for the propagation of cosmic ray particles over cosmological distances. We note here that the same fluctuations, if they exist, imply that some decay reactions normally forbidden by elementary conservation laws, become kinematically allowed, inducing the decay of particles that are seen to be stable in our universe. Due to the strength of the prediction, we are led to consider this finding as the most severe constraint on the classes of models that may describe the effects of gravity on the structure of space–time. We also propose and discuss several potential loopholes of our approach, that may affect our conclusions. In particular, we try to identify the situations in which despite a fluctuating energy–momentum of the particles, the reactions mentioned above may not take place.