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Re: mirrors: two or more?



At 08:07 AM 8/7/00 -0500, Glenn A. Carlson wrote:

Of "other" what? Mirrors? Perhaps, I still don't understand what
some people are talking about when they use the terms "mirror" and
"reflection." If we are not referring to the transformation x -> -x,
then *what* are we talking about?

Some of us, at least, are talking about possible *generalizations* of the
reflection operator. Being able to generalize is an important part of a
scientist's job description.

Enantiomorphs are *defined* by their behavior under the reflection
transformation, i.e, an enantiomorph is an object which cannot be
superimposed on its mirror image.

All of us know the properties of the un-generalized reflection
operator. That is the starting point, not the roadblock, to a discussion
of possible generalizations.

Anyone who assumes that generalizations are not possible is going to miss a
lot of fun, and miss a lot of physics. Consider the following
examples; the first half of each statement is true, and the second half
follows if you closed-mindedly assume that no generalization is possible:

* Every time I count something, I get a positive number
... therefore negative numbers don't exist.

* Multiplication is *defined* to be commutative
... therefore quaternions and matrices don't exist.

* Probabilities are *defined* to be positive
... therefore probability amplitudes (i.e. QM) cannot exist.

* The un-generalized reflection operator is *obviously* the only
non-continuous distance-preserving symmetry of Euclidean space
... therefore antimatter does not exist.

The list goes on and on....