The long answer is as follows: Cosmic radiation consists of energetic particles that may interact with your computer hardware. One possibility is to hit a RAM chip, and flip a bit of information. If it hits in the right place and changes an "important" bit, it may cause a crash.
This concern is of greater importance in airplanes, especially ones that fly at high altitudes without the shielding of the atmosphere from cosmic rays. The intensity of cosmic rays decreases exponentially as you approach sea level, but even there cosmic radiation exists. However, I must add, your reason for crashes is much more likely to be from faulty equipment or bad software rather than cosmic rays, because they are known to produce measurable effects only in high-flying aircraft.
I also recall an experiment being performed at the Los Alamos National Laboratory, where the neutron beam was used as a much more intense replacement for cosmic rays at high altitudes, essentially with the same spectrum. Unfortunately, I was unable to find the reference now; the experiment was done in the late nineties.
Answered by: Yasar Safkan, Ph.D., Instructor, Yeditepe Universiry, Istanbul, Turkey
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