Re: mirror world vs. real world

[John Denker <jsd@MONMOUTH.COM>]

I wrote:

> > a) Under "normal" conditions, for an object of dimensionality d in a space
> > of dimensionality D, the object can't be chiral if d is less than D -- you
> > can always pick it up and flip it over.
> >
> > b) This implies that for any object it is the last dimension (the
> > step from d=D-1 to d=D) that breaks the symmetry.
> >
> > But this begs the question of how you prove statement (a).  Under what
> > conditions does statement (a) hold?  Before you assert that statement (a)
> > is obvious, be warned that it is not always true!  It's bad luck to prove
> > things that aren't true.


At 02:05 PM 8/5/00 +0530, Abhishek Roy wrote:
>         Why is a) not always true? If d < D then all the instances of a
> object look the same - n'est ce pas? Proving it, is of course  another
> matter, and I'm hoping someone can help me there.


In this thread we have been discussing two general topics:
  1) What does a mirror do?
  2) What happens when a space alien builds something for you?

My point is that although these questions are related, they are different
in important ways.

To say it another way, there is a huge difference between looking at mirror
images in the mirror (where you can't actually touch them), and building
pairs of tangible mirror-image objects.



=========
Details:

1) We know what mirrors do.  A standard mirror creates an image in which
        X(object) = -X(image)
        Y(object) =  Y(image)
        Z(object) =  Z(image)
All other mirrors differ from the standard mirror by a rotation and/or a
translation.

2) If you send a space alien a list of measurements (i.e. distances) and he
builds something for you, he might build the right thing, but it is also
conceivable that he will build the mirror image.  Ooops.

Abhishek Roy started this thread by asking, in effect, whether
mirror-imaging was the only possible ooops.   My answer is that it is NOT
the only possible ooops.   Proof: It is equally conceivable that the space
alien will build the antimatter version of what you wanted.

In fact, these two possibilities are related:  If the space alien can tell
the difference between matter and antimatter, then he can tell the
difference between left and right (i.e. between clockwise and
counterclockwise) by doing a beta-decay experiment.  You can send him the
measurements describing the apparatus, and he can build the left- and
right-handed versions and see which works.

So really we've uncovered only one possible ooops so far.  If you ask for a
regular right-handed glove the space alien might build what you want or
might build an antimatter left-handed glove.  There are no other
possibilities we know of.

Reference:  _The Feynman Lectures on Physics_ volume 1 section 52-8.

This answers today's question:  It is not true that a hypercreature can
come into our world and turn a right-handed artifact into a left-handed
artifact by flipping it through the Nth dimension, unless he also exchanges
matter <--> antimatter.

This also underscores my answer to Abhishek's original question:  we have
not proved there are no other possibilities.  Somebody could discover a new
quantum number tomorrow -- perhaps one that distinguishes regular matter
from uncle-matter (generalizing the notion of anti-matter).

Not knowing about X is not the same as knowing that X does not exist!

Things might go the other way.  It might be possible for the space alien to
go into the lab and tell the difference between matter and antimatter (on
an absolute, universal basis), and therefore to have an absolute universal
definition of left-handed and right-handed.  This depends on what you
believe about CPT.  I'm not convinced, but I'm not an expert on CPT so I
won't go into it.