Lorentz Lectures of Sir Roger Penrose, 2011.

New Developments in Physics and Cosmology

In these lectures, various ideas will be described that challenge
the conventional outlooks on physics in different areas, from the very small
to the very large. A modification of standard quantum mechanics will be argued
for, based on general relativistic principles, this having striking
implications for cosmology, in relation to the second law of thermodynamics.
The primacy of massless particles leads to a viewpoint that conformal
(null-cone) space-time geometry is more over-reaching than its metric,
suggesting a radically new cosmological picture. This geometry is also basic
to twistor theory, for which new roles have recently been found, particularly
in high-energy physics. 

Lecture 1: Quantum Foundations: Influences from Gravitational Theory.
I argue that the quantum measurement paradox must find its resolution in inputs 
from foundational principles of Einstein's general relativity.

Lecture 2: Conformal Cyclic Cosmology I: The General Scheme
According to conformal cyclic cosmology (CCC), what we presently regard
as the entire history of the Universe, from its Big-Bang origin (but
without inflation) to its final exponential expansion, is merely one
aeon of a continual succession of such aeons, where the big bang of each
is taken to be a smooth conformal continuation of the remote future of
the previous one. The 2nd Law of thermodynamics, with the curious nature
of its origin, is automatically incorporated. Inflation is replaced by
the exponential expansion of the previous aeon.

Lecture 3: Conformal Cyclic Cosmology II: Detailed Equations at 
Crossover and Observational Implications 
To express CCC mathematically we need a formulation of Einstein's
equations extending over the crossover joining each aeon to the next,
governed by the requirement of ultimately massless material and a
cosmological constant with a fixed positive value. This entails the
introduction of a self-coupled conformally invariant massless scalar
field carrying no physical degrees of freedom prior to crossover, but
which emerges following the subsequent big bang as an actual (“dark”)
initial material, rest-mass reappearing in the early stages. The
evolution is governed by entirely classical equations, in contrast with
the conventional view that quantum fluctuations are responsible for
primordial irregularities in our early universe. Events involving super-
massive black holes in the aeon previous to ours have observational
implications.

Lecture 4: Twistor Theory I: Twistor Geometry and the Wavefunctions 
of Massless Particles
Twistor theory offers a novel picture of basic physical processes where
the very arena of space- time is replaced by twistor space, non-locally
related to it, where space-time points are regarded as secondary, the
elements of twistor space being primary. A single twistor represents the
entire history of a massless entity with intrinsic spin. Space-time
points may be regarded as Riemann spheres in twistor space, the complex
geometry of which directly relates both to relativity and to the
foundational complex numbers of quantum theory. Wavefunctions for
massless particles find a remarkable twistor description in terms of
holomorphic geometry and analysis, expressing some of the curious
non-local aspects of quantum physics.

Lecture 5: Twistor Theory II: More Recent Developments. 
General Relativity, High-Energy Physics, Twistor Strings 
An obstruction to developing twistor theory into a full-blown framework
for physics has been the incorporation of right-handed helicities (the
"googly problem") into the non-linear interactions of Eintstein and
Yang-Mills theory, the left-handed ones being already described in
elegant twistor terms. Some recent progress will be described, as will
developments in simplifying calcuations in high-energy physics which
followed from ideas introduced by E. Witten and others, where concepts
from string theory are united with those of twistor theory.