I had planned to add this story to my pre-existing gravitational
coupling "constant" thread at the "CosmoCoffee Blog", but the
thread seems to have been censored and removed. Well, it
was a good run. About 75 posts and about 2200 views.
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In 1955 a conference was organized in Italy to celebrate
"Fifty Years Of Relativity". Einstein was invited, but could
not attend because of health reasons. Instead, he wrote up
an essay on his most recent efforts at further generalizing
General Relativity and formulating a unified theory that would
incorporate electromagnetism and atomic phenomena.
In this essay he noted that a general property of the unified
field equations, one that kept appearing and could not be
avoided, was the fact of solutions that were "similar, but not
congruent". In modern terms, it seemed that self-similar
solutions were generic to a more unified relativity.
But, he said, we know the atoms have definite sizes
and masses, and one does not find atoms that are
1.2 or 2.5 times bigger than the familiar ones. This
paradox between the intrinsic self-similarity of a more
unified relativity and the the apparently absoluteness of
scale in nature bothered Einstein greatly. He said it
might mean he was totally on the wrong track.
One thing he had not considered was discrete self-similarity.
There were no atoms that were 2.5 times bigger than "normal",
but might there be atoms that were 5.2 x 10^17 times bigger.
For example a neutron star is 5.2 x 10^17 times bigger than
an atomic nucleus and a galaxy is 5.2 x 10^17 times bigger
than a neutron star. This discrete self-similarity might be
consistent with observation - and solve Einstein's paradox.
If Einstein had lived long enough, I think he would have
come around to developing this idea. Alas, he died not long
after writing the essay. So his last student has taken up the
quest for that unified description of nature based on
discrete self-similarity.
Is that really so radical [unacceptable]?
Seems like sensible, testable science to me.
RLO
www.amherst.edu/~rloldershaw