It From Bit or Bit From It? by Anthony Aguirre Brendan Foster & Zeeya Merali

Author:Anthony Aguirre, Brendan Foster & Zeeya Merali
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(11.3)

where is the one-particle action which can be expanded in powers of via the general expression

(11.4)

Here, is the classical action and are order quantum corrections. We now make the assumption that quantum gravity is self-similar 2 in the following sense: the higher order corrections to the action, , are proportional to , i.e. where are constants. With this assumption, Eq. (11.4) becomes

(11.5)

From Eq. (11.5), one sees that is dimensionless. In the units we are using, i.e. , has units of the Planck length squared, i.e. , thus should have units of an inverse distance squared to the th power. The natural distance scale defined by Eq. (11.1) is the horizon distance , thus

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