The Greisen-Zatsepin-Kuzmin limit (GZK limit) is a theoretical upper limit on the energy of cosmic rays from distant sources.

This limit was computed in 1966 by Kenneth Greisen, Vadem Kuzmin and Georgi Zatsepin, based on interactions between the cosmic ray and the cosmic microwave background radiation predicted by special relativity. They predicted that cosmic rays with energies over 5×1019 eV will be absorbed as they travel through space from their distant sources, and so should never be observed on Earth.

A number of observations have been made by the AGASA experiment that appear to show cosmic rays from distant sources with energies above this limit: this is the so-called GZK paradox or cosmic ray paradox.

These observations appear to contradict the predictions of the theory of special relativity. However, there are a number of possible explanations for these observations that are consistent with special relativity. Firstly, the observations could be due to on instrument error or an incorrect interpretation of the experiment. Secondly, the cosmic rays could have local sources (although it is unclear what these sources could be). Another suggestion involves ultra-high energy weakly interacting particles (for instance neutrinos) which might be created at great distances and later react locally to give rise to the particles observed.

A number of exotic theories have been advanced to explain these observations, of which the most notable is the theory of doubly-special relativity.

As of 2003, a number of cosmic ray experiments such as GLAST and the Pierre Auger Observatory are now planned which are intended to confirm or deny the correctness of the earlier observations.

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