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 an 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.
A paradox is an apparently true statement that seems to lead to a logical self-contradiction, or to a situation that contradicts common intuition.
Thus, the paradox of Frederic's birthday in The Pirates of Penzance establishes the surprising fact that a person may be more than N years old on his Nth birthday.
Elevator paradox: Elevators can seem to be mostly going in one direction, as if they were being manufactured on the roof, and disassembled in the basement.
For example, the Birthday paradox is more of a surprise than a paradox, while the resolution of Curry's paradox is still a matter of contention.
Paradox of hedonism: When one pursues happiness itself, one is miserable; but, when one pursues something else, one achieves happiness.
Low birth weight paradox: low birth weight babies have a higher mortality rate, babies of smoking mothers have lower average birth weight, babies of smoking mothers have a higher mortality rate, but low birth weight babies of smoking mothers have a lower mortality rate than other low birth weight babies.
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