On Saturday, March 10, 2018 at 10:08:15 PM UTC-6, Bruce wrote:
>
> From: Russell Standish <[email protected] <javascript:>>
>
>
> On Sun, Mar 11, 2018 at 01:24:19PM +1100, Bruce Kellett wrote:
> > From: *Russell Standish* <[email protected] <javascript:>
> > <mailto:[email protected] <javascript:>>>
> > >
> > > 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 - I never claimed that. Just that the symmetries observed
> tell us more about what we've evolved to see in our environment
> rather than an intrinsic property of the environment.
>
>
> If we have evolved to see it in our environment then it follows that it
> was actually in the environment to be seen, and not merely a product of
> evolution. Our eyes evolved to be sensitive to particular wavelengths of
> light because they corresponded to wavelengths to which the atmosphere was
> largely transparent so that there was a lot of radiation of these
> wavelengths around. Evolution is an adaptation to the conditions of the
> environment, not something that creates that environment. Or are you saying
> that we see in the visible range rather than the IR (to which some animals
> are sensitive) merely by chance? So that the symmetries we observe are a
> chance selection from a much wider range of symmetries that actually exist.
>
> A lot of the symmetries that Lawrence is referring to when he talks about
> wider symmetries are essentially abstract -- we do not immediately see the
> SU(2) symmetry of isotopic spin, that is a construct of our theories, as
> are most abstract gauge symmetries. Evolution did not equip us with senses
> that intuitively see that protons and neutrons are related by a symmetry
> transformation.
>
> Bruce
>
It is hard to know to what extent we are evolved to see symmetries. We do
exist in a world that has some measure of symmetry, say easily seen
visually with crystals etc, and chaos. We in fairly recent history found
various patterns such as Kepler;s law that the cube of the radius or
semimajor axis of an orbit is proportional to the square of the period. The
large scale world has a lot of complexity, but a bit of symmetrical
simplicity that permits us to identify and use them. The structure of rocks
probably provided one of the earliest type of structure that lead to making
stone tools.
Isospin has a curious history. It started out as a type of charge for
nucleons in MeV scale nuclear physics. Nuclear physics did not start out as
a theory of symmetry. It started with Rutherford's observation of
transitions between different nucleons and reached a critical level when
Han and Meitner discovered nuclear fission by chemical means. The atomic
bomb was developed without much of a symmetry system of the nuclear force.
That emerged after WWII with Mills and Yang theory of the SU(2) gauge
bundle.
The two weights of SU(3) in QCD decompose to two SU(2)s, but where one is a
conserved symmetry and the other is not. The isospin symmetry is conserved
in it modular action and the chiral symmetry is violated. Given a group G
and a subgroup of it K to which it is spontaneously broken, the broken
generators ("axials" in the chiral symmetry breaking paradigm of low energy
QCD, SU(2)×SU(2)/SU(2)_{isospin}) is the coset space H = G/K. The
generators of G than break up into the unbroken ones, k, (isospin), and the
broken ones, h, parameterized by the goldstone/pions serving as projective
coordinates of that manifold (In QCD this is just S^3). The low energy
nuclear force is then SU(2) ~ SU(2)×SU(2)/SU(2)_{isospin} that is invariant
under isospin and this then serves as a form of nuclear charge.
This then has been carried to weak interactions as weak isospin. The old
nucleon theory is still used, in fact a lot of perturbation work with it is
done to compute nuclear physics, but is limited in its contact with
foundations. With GUTs we have some concept of weak isospin symmetry
becoming embedded in a larger symmetry.
Nature is then arranged with certain patterns and we humans are clever
enough to look at nature at greater detail. What we call symmetries are
manifestations of our mental ability to construct abstract systems we call
mathematics. This ability may have some connection with our neural
evolution and having a large brain.
LC
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