From Osher Doctorow
I have generally attacked algebraic physics when it unifies with
geometry or topology (algebraic topology, algebraic geometry) for over-
complicating and leading away from simplicity.
There are, however, two indications that algebra can be exceptionally
intuitive and physically applicable when in the hands of people who
openly admit their own errors and who in fact are oriented toward
resolving past errors.
The first indication is by Bert Schroer, perhaps the most well known
advocate of Local Quantum Physics (LQP) which was popularized by
Rudolf Haag's volume Local Quantum Physics, Springer-Verlag: Berlin
1989 or 1990.
Schroer's new paper, "Localization and the interface between Quantum
Mechanics, Quantum Field Theory, and Quantum Gravity," Free University
Berlin Germany and CBPF Brazil, arXiv: 0711.4699 v1 [hep-th] 29 Nov
2007, 51 pages, is an algebraic attack on Quantum Gravity as it is
usually thought of in the Superstring/String/Brane/M Theory and Loop
Quantum Gravity (LQG) schools. The paper is extremely error-
correction-oriented, and it is almost impossible in my opinion to read
the paper without giving up on those schools of Quantum Gravity. It
is also Simplicity-oriented because it reveals a deeper nature of
Quantum Field Theory that doesn't seem to require an elaborate
external machinery of Quantum Gravity to yield many results that we
would ordinarily attribute to Quantum Gravity. Schroer also shows the
disadvantages of the usual Lagrangian and Lagrangian density
approaches.
The second indication is my latest comparison of Quantum Mechanics and
GR using Probable Causation/Influence (PI). I have noticed that both
the Einstein Field Equation and the Schrodinger Equation have the
form:
1) f = g
for two functions f, g, and that from the viewpoint of Karl Popper's
"disconfirmation" theory this has the disadvantage that ANY
hypothetical equation like (1) satisfies maximal PI in normalized
form, namely:
2) f - g = 0 iff f - g + 1 = 1 iff P(g -->f) = 1.
This is in contrast to equations with an additional constant like k
(or possibly other equations):
3) f = g + k
because this yields:
4) f - g - k = 0 iff f - g - k + 1 = 1
which is not automatically of the form P(g-->f) = 1 but rather can be
converted to:
5) 1 + g - f = 1 - k
which says:
6) P(g-->f) = 1 - k
and the onus is on the researcher to show that k is between 0 and 1
and why.
As with the Lagrangian or Lagrangian density form, the forms f = g
versus f = g + k algebraically appear to make considerable difference
in the physical picture.
Osher Doctorow
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