A Note on R and the 2nd Law of Thermodynamics

Photo taken from NASA video, Solar Dynamics Observatory

What is really cool is that Penrose challenges the time-symmetry of quantum mechanics from two directions, the non-reversibility of the reduction of the Schrodinger wave and the irreversibility of entropy according to the second law of thermodynamics. He shows that while the linear superposition exists going forward in time for a particle in the classic, simple half-silvered mirror scenario, when one attempts to reverse the process it becomes obvious that once R has occurred, absurdities, such as emission of a photon from a non-light source which absorbed it, will occur. R seems, therefore, to be related to entropy, another irreversible process.

Penrose discusses how entropy is related to gravity using the idea of light cones. On the theory of general relativity, he proposes that the gravitational field is a kind of all-pervasive refracting medium, tilting light cones in space, thereby influencing the direction of light (by curving it), and thus, influencing the relations of cause and effect. He reminds us that cause and effect are only relevant under general relativity and not under Newtonian physics, because in relativity theory, light has a speed limit beyond which paradoxes occur in time-space. This is crucial when one is considering quantum superpositions, as there are also time-space paradoxes involved in their current mathematical description.

In The Emperor’s New Mind, Penrose states:

“…there was a huge gain in entropy due to gravitational contraction…all the remarkable lowness of entropy that we find about us – and which provides this most puzzling aspect of the second law – must be attributed to the fact that vast amounts of entropy can be gained through the gravitational contraction of diffuse gas into stars.” (417)

In fact, what is really bizarre is the assertion that such a low entropy state as the original singularity could have existed spontaneously, as the “natural” state of matter is a high-entropy state of thermal equilibrium. In discussing why entropy is not time-symmetric, Penrose notes that, on the basis of the phase-space model of entropy:

“Our phase-space argument gave us completely the wrong answer when we tried to apply it in the reverse direction of time!…What that argument actually showed was that for a given low-entropy state (say for a gas tucked in a corner of a box), then, in the absence of any other factors constraining the system, the entropy would be expected to increase in both directions in time away from the given state…The argument has not worked in the past direction in time precisely because there were such factors. There was indeed something constraining the system in the past. The tendency towards high entropy in the future is no surprise. The high-entropy states are, in a sense, the ‘natural’ states which do not need further explanation. But the low-entropy states in the past are a puzzle. What constrained the entropy of our world to be so low in the past? The common presence of states in which the entropy is absurdly low is an amazing fact of the actual universe that we inhabit – though such states are so commonplace and familiar to us that we do not normally tend to regard them as amazing. We ourselves are configurations of ridiculously low entropy!” (410)

So, entropy and gravity are related.

Penrose notes that in the space-time of general relativity there is an ‘obstruction,’ called the WEYL tensor, which is the conformal part of the relativistic equations. This obstruction prevents uniformity of space-time in terms of his illustration using light cones; that is, the light cones cannot be aligned perfectly with one another because of WEYL:

“The tensor WEYL describes just half of the information – the ‘conformal’ half – that is contained in the full Reimann curvature tensor of space-time…Only if WEYL is zero can we rotate all the light cones into the Minkowskian arrangement [i.e. perfectly aligned with one another]. The tensor WEYL measures the gravitational field – in the sense of the gravitational tidal distortion – so it is precisely the gravitational field, in this sense, that provides the obstruction…”(Shadows of the Mind, 224)

The point about light cone tilting is that this action, this character of gravity had gone unnoticed in classical physics and was only identified in Einstein’s theory. Recent observations of gravitational lensing have provided good evidence for this hitherto “invisible” aspect of gravity. Analogously, perhaps there is some unseen, non-computational aspect of physical matter that is organized in biological design for the purpose of producing consciousness.

Penrose argues that instances of quantum superposition in nature are rare and unstable. The occurrence of coherent, prolonged quantum superposition in a biological organism must be the result of design and constitutes a novel use, in nature, of such special properties of matter that are not well understood. Stuart Hameroff alludes to this when he mentions that the objective reduction time of an individual particle in space, which avoided decoherence, would be in the order of 10 million years, and that it would be of low frequency, low intensity. The implication is that for consciousness to occur on the basis of the objective reduction of coherent quantum superpositions, a special design which organizes this phenomenon is necessary.


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