This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
From: Jobst Brandt <email@example.com>
> Mirrors are mandatory on virtually every other type of vehicle on
> the road. Competent drivers/riders learn the limitations of the
> information available from their mirrors and act accordingly.
I suppose the question is appropriate because no one seems to have
a good explanation for this. In such an event, when there is much
evidence that what would seem obvious is not what is practiced, I
assume there are other things at work. I for one don't wear glasses
to which to attach a mirror and putting it on a helmet seems a
fragile location when the helmet is placed anywhere but on the head.
These are not the real reasons though, because I have found that when
looking in a head mounted mirror, I cannot accurately tell anything
about the following vehicle's position except that it is behind me.
That is because I am looking into a mirror whose angular position
with respect to the road is unknown. The rear view mirror in a car
is fixed with respect to the direction of travel and objects seen in
it are seen with reference to ones own vehicle, be that the rear
window frame or side of the car. I find the image in a head mounted
mirror on a bicycle to be distracting and a source of paranoia if
I watch it enough. It does not tell me whether the upcoming car is,
or is not, going to slice me.
I additionally I find it difficult to focus on objects when my
eyeballs are distorted by turning them as much as 45 degrees to the
side of straight ahead. You can try this by reading these words with
your head turned 45 degrees from the text.
I believe these two effects are the prime reasons for the unpopularity
of such mirrors. They don't provide the function adequately and still
require the rider to look back. I do not doubt that it is possible to
rely on the mirror but it does not disprove my contention that the
information seen is by no means equivalent to motor vehicle rear view
mirrors to which these mirrors have been compared. It is not a valid