From Osher Doctorow
I pointed out in the previous subsection that Dirac believed in
simplifying equations in terms of their length and contents, even if
it meant using new types of mathematics or "models'.
But how can we, everybody in physics, do something similar in Quantum
Gravity? At the risk of making a pun on E.T. (the movie about an
alien from outer space), the answers appear to be in equations like:
1) y = k exp(t) (k e^t in other words, k > 0)
2) y(t) = 0 (all real t > = 0)
3) y = k exp(-t) (k > 0)
We can build "models" for various domains of t, say t_i < = t < = t_f
where t_i is an initial time and t_f is a final time, using one or
another of the above equations - models of inflation, models of rapid
collapse or decay, models of conservation or constancy.
In arXiv, such "restricted" solutions would probably be categorized
under the "Phenomenological" branch of Higher Energy Physics, which is
quite substantial, rather than the Theoretical branch. But what's in
a name?
Now look at this:
4) y = exp(t)
5) Dt(y) = dy/dt = exp(t)
6) Dtt(y) = exp(t)
7) Dt...t(y) = exp(t), nth partial derivative of y = exp(t) wrt t
Together with Dt(0) = 0, (4) is the "Loudest" (Simplest) Equation in
the Universe in the sense of all derivatives being the same and hence
(in the Birkhoff sense) all Causations.
What about:
8) y = exp(-t)
Then we have:
9) Dt(y) = -exp(-t) = -y
10) Dtt(y) = +exp(-t) = y
etc. So the absolute values of Dt(y), Dtt(y), etc., in (9), (10),
and so on and y. In this sense, y = exp(-t) is also the "Loudest"
Equation in the Universe.
I am saying that arguably, when equations get too difficult, too long,
have too much content especially of multiplicative and divisive and
matrix/tensor form on top of additive and subtractive, then the Grand
Computer of the Universe (to take a leaf out of Adams' "Hitchhiker's
Guide to the Galaxy" should prune the equations back to
"Simplification Loudness" even if it means using different types of
mathematics.
To deal with black holes, with the early Universe, with Inflation,
with the onset and continuation of late Acceleration, and Quantum
Gravity in general, we need equations of the Simplicity of (1)-(10)
above, not equations of wheels within wheels that tell us that space-
time-matter is a bunch of discrete pieces and not much else or which
tell us that space-time-matter is a bunch of tensors-upon-matrices
that even Heisenberg and Einstein wouldn't recognize.
As for the name "Quantum Gravity", it relates the small and the
large. That should be enough to retain the name, not the "blessings"
of Founding Fathers or Mothers.
Osher Doctorow
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