Quantum Gravity 146.0: y = 0, y = k exp(t), y = k exp(-t) As Infinitely Stable Causation Equations of the Universe

From Osher Doctorow

From Section 145, the equations:

1) y = 0 (all t > = 0)
2) y = k exp(t)
3) y = k exp(-t)

are the Infinitely Stable Causal Equations of the Universe in the
sense that they have derivatives of all integer order and those
derivatives or their absolute values are equal to y. Birkhoff
Causation, which is an approximation to Probable Causation/Influence
(PI), regards Causation as contained in the derivative with respect to
time or in corresponding differential equations.

The implications for Quantum Gravity are as follows. Since Quantum
Gravity relates the microscopic to the macroscopic and Quantum Theory
to GR, it is arguably desirable for it to be based on Infinitely
Stable Causation. The above 3 equations fit these requirements.

Notice that (2) is Expansion, (3) is Contraction, and (1) is
constancy.

But (1) is not merely "any" constancy. Remember that in PI, the
Fundamental scale is the interval [0, 1], whose minimum value is 0.
The value 0 for probability maximizes PI and thereby optimizes
(Probable) Causation/Influence. There is simply no probability below
0, just as there is no temperature below 0 Kelvin. Moreover, 0
distance (of any type) is maximum proximity, and PI is a proximity
measure.

In this thread and previous ones, I have given examples where the
exponential function which is a solution of the Ricatti Differential
Equation (exp(t) and exp(-t)) plays a key role in physics. For a key
role in Quantum Gravity, see "Genral asymptotic solutions of Einstein
equations and phase transitions in quantum gravity," Dmitri Podolsky,
U. Helsinki Finland (on leave from Landau Inst Moscow Russia), arXiv:
0704.0354 v2 [hep-th] 24 Apr 2007, 8 pages. The scalar field
potential is exponential in that paper, which Podolsky mentions is the
case in ekpyrotic scenarios and gauge supergravity models and quite
often in string theory landscapes.

Osher Doctorow

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