All science ( hard and soft, including evolution and λ-CDM )
is based on the notion that nature is innately ( and fully ) causal.
Semi-randomness is always due to semi-ignorance, nothing more.

4-D gravitational fields are useful when one is fully informed,
while Planck's constant is useful when one is semi-informed.

For example, from Brownian ( semi-random ) motion
it's possible to derive Planck's law and Planck's constant.

Consider this Inverse Gaussian Probability density function,
which is useful for describing
“ the time a Brownian Motion with positive drift takes
to reach a fixed positive level ”:
http://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/PDF_invGauss.png/993px-PDF_invGauss...

compared to this blackbody spectrum:
http://upload.wikimedia.org/wikipedia/commons/thumb/a/a2/Wiens_law.svg/744px-Wiens_law...

Quoting “ http://prola.aps.org/abstract/PRD/v4/i6/p1597_1 ”:
“ Derivation of the Blackbody Radiation Spectrum by Classical Statistical Mechanics
O. Theimer
New Mexico State University, Research Center, Las Cruces, New Mexico 88001
Received 15 March 1971

It is assumed that
the fluctuating radiation energy density in a blackbody cavity
is the sum of two stochastically independent terms:

a zero-point energy density ρ0 with Lorentz-invariant spectrum
which persists at the absolute zero of temperature, and

a temperature-dependent energy density ρT
which satisfies the laws of statistical mechanics.

The mean-square fluctuation 〈 ( δρT ) 2 〉of ρT is calculated
from classical electromagnetic theory and is shown to
depend explicitly on 〈 ρ0 〉.

Classical statistical mechanics leads then uniquely from
〈 ( δρT ) 2 〉 to 〈 ρT 〉,
which turns out to satisfy Planck's formula. ”.

Quoting WikiPedia:
“ Brownian motion is among the simplest
continuous-time stochastic processes, and it is a limit of
both simpler and more complicated stochastic processes
( see random walk and Donsker's theorem ).

This universality is closely related to
the universality of the normal distribution.

In both cases, it is often mathematical convenience
rather than the accuracy of the models that motivates their use. ”.

Quoting “ www.SpringerLink.COM/content/j52856u3164314r4/ ”:
“ Radiation model for nanoparticle:
extension of classical Brownian motion concepts

Niti Nipun Sharma1 [ Contact Information ]
(1) Mechanical Engineering Group,
Birla Institute of Technology & Science,
Vidya Vihar, Pilani, Rajasthan, 333031, India

Received: 2 December 2006 Accepted: 16 May 2007
Published online: 3 July 2007
Abstract

Emissive power per unit area of a blackbody
has been modeled as a function of frequency
using quantum electrodynamics, semi-classical
and classical approaches in the available literature.

Present work extends
the classical lumped-parameter systems model of Brownian motion
of nanoparticle to abstract
an emissive power per unit area model for nanoparticle
radiating at temperature greater than absolute zero.

The analytical model developed in present work has been based on
synergism of local deformation leading to
local motion of nanoparticle due to photon impacts.

The work suggests the hypothesis of
a free parameter f' characterizing
the damping coefficient of resistive forces to local motion of
nanoparticle and the manipulation of which is possible to realize
desired emissivity from nanoparticles.

The model is validated with
the well established Planck’s radiation law. ”.