The next math department colloquium at Stanford will feature Lenny Susskind lecturing on p-adic numbers and cosmology, here’s the abstract:http://www.math.columbia.edu/~woit/wordpress/?p=4011
The biggest conceptual problem of cosmology is called the measure problem. It has to do with the assignment of probabilities in an exponentially inflating universe, which falls apart into separate causally-disconnected regions. Neither I nor my friends had ever intended to learn about p-adic numbers until we realized how similar such a universe is to an endlessly growing tree-graph. The result has been some new insights from p-adic number theory into the measure problem and other puzzles of eternal inflation. Within the constraints of a one-hour lecture, I will explain as much of this as I can
A comment from above:
"But since the infinite tower of bubbles in the past of “our” infinite branching tree contains bubbles whose coordinate radii presumably get ever larger without limit as we go to earlier times, there is no “room” in the usual infinite flat extended spatial dimensions to put those other infinite branching trees of bubbles. So perhaps Lenny is trying to use the compactness property of p-adic numbers to get around this. I would guess that the resulting “enlarged” spatial dimensions might look something like infinite numbers from Non-standard analysis."http://en.wikipedia.org/wiki/P-adic_quantum_mechanics
As early as 1965, Feynman had stated that path integrals have fractal-like properties.[14] And, as there does not exist a suitable p-adic Schrodinger equation,[15][16] path integrals are employed instead.
