From: *Russell Standish* <[email protected]
<mailto:[email protected]>>
On Sun, Mar 11, 2018 at 10:17:01AM +1100, Bruce Kellett wrote:
>
> My feeling is that we observe that the world has certain symmetries,
then we
> design our theories to reflect these symmetries, because theories that
> incorporate the observed symmetries work better. Since the starting
point is
> observation, we have some prospect of learning something other than the
> nature of our thought processes.
>
> Bruce
My claim is that there are always symmetric theories. Assuming some
horrible
non-symmetric world, we can make a symmetric theory by a suitable
transformation of variables - in rather the same way we can see a
computation in a rock by a suitable transformation of variables.
I think that in general it requires a little more than just a
transformation of variables. If we fail to see rotational symmetry in
the world around us (same laws in all directions), then we would have to
postulate some oriented field, or some interaction that depended on
position and/or direction. To do it by a transformation of variables you
would require the variables themselves to reflect this non-symmetric field.
What do you say to the proposition that evolution might have equipped
us with the facility to see those symmetries "intuitively", since it
makes computing things about the world easier?
I don't think that actually changes anything -- what that means is that
those symmetries existed in the world, and evolution took place in the
context of those symmetries. So it is anything but an arbitrary
imposition by our minds on a non-symmetric world.
Of course it's not
quite so simple, as naive physics had things coming to a stop if you
remove the force, and heavier things falling faster than light things,
but still it probably came close enough that science could refine
observations into the symmetries we see today.
Symmetries such as translational and rotational invariance are
sufficiently non-obvious in our friction-dominated world that it took
millennia for it to become clear that the laws of physics actually
respected those symmetries. And even longer for Emmy Noether to
recognize the connection between symmetries and conservation laws.
Bruce
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