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A Plague of Infinities
2011.03.15 / Krzysztof Jastrzembski
TAGI: English page
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Summary of the critical review

Stephen Hawking and Leonard Mlodinov are brave souls, venturing into unchartered territory. In particular, Steven Hawking is brave enough to co-publish a book which undermines the Standard Model (the big bang theory and its associated technology) of which he is considered the founder together with Roger Penrose, through their early work on black holes.

This controversial book is essentially philosophical. It begins with the statement that “philosophy is dead” – effectively replacing it by science – and features Stephen Hawking’s talent in presenting difficult ideas with clarity, humour and lavish illustrations. After a review of Greek and modern philosophers, the authors explore quantum theory, the wave/particle duality, the Uncertainty Principle, the Feynman sum-over histories method, with a brilliant exposition of the unification theories of Maxwell, Einstein’s Relativity and quantum electrodynamics and chromodynamics, prior to the new ideas such as M-theory, the focus of their work.

The central thesis of this book is that” there is no theory-independent concept of reality”. The authors propose “model-dependent realism” and assert that it short-circuits the age-old discussion between the realist and the anti-realist: “it is pointless to ask whether a model is real, only whether it agrees with observation”. In this view, the Ptolemaic and the Copernican systems are equivalent (although the latter is evidently simpler).The authors define a good model by 4 criteria, of which the first is “elegance”, thus bridging the gap between science and art by introducing aesthetics as a first requirement. They also assert the existence of scientific laws, such as the law of gravity.

In their tour-de-force the authors do not refer to any world religions apart from Catholicism, which seems unbalanced, particularly as Buddhist philosophy (of the radiant void) is a natural candidate for a linguistic description of quantum theory. They assert the impossibility of miracles as exceptions to scientific laws, yet state elsewhere that the deterministic description (based on the laws of nature) is incomplete. Further they state, with reference to M-theory, that “because there is a law like gravity, the universe can and will create itself from nothing”.

It is with reference to the criteria of testability and elegance that logical contradictions arise in the conclusions of this otherwise magnificent work. The authors argue from M-theory for the existence of many parallel universes. This is pure metaphysics and not philosophy as, by definition, the existence of another universe apart from ours is not testable in principle. Further, they posit universes in which different physical laws may exist, for instance where there is no law of gravity, thus contradicting their own argument based on the laws of nature. It should be noted that M-theory, although exciting, is speculative.

It is the requirement of elegance that is most problematic. With reference to a process called renormalisation, the authors admit that attempts to unify current theories lead to infinities in the equations, which are then got rid of (renormalized) by using fuzzy mathematics. Further they admit that certain theories such as quantum gravity cannot be renormalized at all. From a mathematical standpoint, equations plagued by infinities are certainly not elegant! As for M-theory, the criterion of elegance cannot be applied as the equations are yet to be written down; elsewhere the authors refer to it as a “candidate” for a final theory.

Spontaneous creation is limited by the anthropic principle because, looking back, the initial conditions must be unique, unless we argue for an infinity of universes, which would not be elegant. It should be mentioned that there is a little-known calculation by Roger Penrose (The Emperor’s New Mind, OUP, ’89) where an attempt is made to calculate the odds for a universe to arise by itself, based on Hawking’s formula for the black hole. Penrose ends up with supra-astronomical odds against, and an extension of the calculation can show a zero probability for such an event. The Grand Design is a landmark, pointing to the future, yet should be read critically, together with Lisa Randall’s published work such as “Warped Passages” (2005) and the current research in the field.

The Grand Design by Stephen Hawking and Leonard Mlodinow, Bantam Press 2010


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