TIME, INFORMATION AND THE QUANTUM
The quick way to explain this work is backwards, starting from a conclusion, albeit one which with the benefit of hindsight seems both stunningly obvious and clearly important. It is also unclaimed, so Andrews Principle of Epistemology will state that the amount any intelligent species can learn about reality must be constrained by the power of their brains. Notice that while this idea does not appear anywhere in our science, apparently having slipped through the gaps between physics, neuroscience and philosophy, it is taken for granted in science fiction. Those large-brained aliens always have better physics than us because they are smarter. But it would be better in what way exactly?
The implication that our physics is a specifically human activity limited by our very finite brains recalls the recent finding that it can explain only 4% of the matter in the universe, but the idea is sufficiently disconcerting to demand deeper analysis. Given only the computational theory of mind, the notion that what the brain does is to process information, its power can be quantified by the speed at which it does so, 1/τ bits/s, where τ is the neurological time constant, the average time it takes to process a single bit. A personal parameter like τ can certainly not appear explicitly in the objective logic of physics, but might it be lurking unseen somewhere? Imagine yourself as an observer in the four-dimensional reality of the general theory of relativity. Information about events going on around you floods through your senses into your brain where it gets processed into the picture that appears in your consciousness. This information comes in discrete bits and the smallest increment of space-time from which you can acquire a complete bit is τ, which as a time is of the order of 10-19 to 10-18 seconds or as a length 0.3 to 3 Angstroms, the size of atoms. It follows that any human brain studying reality at the sub-atomic level will find their knowledge to be uncertain because they are looking at a fraction of a bit, which is exactly what happened at the birth of quantum mechanics. We must therefore suspect that the probabilities that characterize the quantum were a harbinger of the inherent limitation on our knowledge arising from the Principle of Epistemology, and that τ is the long-sought connection between reality and the “consciousness” of the observer required by the Copenhagen interpretation.
Proving this suspicion involves an excursion into the other great philosophical difficulty of physics, the nature of time. That “t” in the fundamental equations is reversible and shows no trace of the arrow, the flow in a particular direction that is the essential feature of our experience of the concept. Some theorists have even suggested that time does not exist, apparently forgetting that the criterion for existence in science is not theory but experiment and that time flows along in its usual irreversible way in all experiments. It can be shown that if physics is considered as a system of logic then time is the last, irreducible, operationally-defined axiom on which it is based, and the confusion about its nature follows from this unique status. Most physicists, like everyone else, simply take it for granted that time hums along automatically out there somewhere at a rate that is somehow the same as that shown on our earthly clocks. Physics is what we get by studying reality using physical clocks. Unfortunately, while these clocks give very precise answers to the practical question “What is the time?” they are no help with the deeper question “What is time?”. Indeed this cannot be a physics question: an axiom cannot be explained from within its logic system.
The time scale created by these physical clocks has no inherent sense of direction because every tick is the same as every other tick. There are however many other types of clock (biological, astronomical etc) that can be thought of (somewhat unconventionally) as each creating their own time scale, that may come closer to the source of the concept. The logical procedure is to find one that encapsulates the essential differences between the past, present and future, and this difference is neurological. If definite information about the outcome of an event is to be found in anyone’s brain then that event must be in the past. The appearance of this bit in the observer’s brain in the present (which must last one increment of τ) is the irreversible fact that moves time along, as the observed event moves from the uncertain future into the knowable past. We therefore need a conceptual time scale called Wtime that ticks along by one τ whenever the brain processes a bit of information. This scale proves to quantify the individual perception of the flow of time, the kind that flies when we are having fun.
Replacing physics’ axiom that time flows automatically, objectively, (perhaps) continuously, everywhere, with the hypothesis that Wtime (what Hawking calls the “psychological” arrow of time) is the source of the flow, makes no difference to the substance of physics, instead creating a parallel system of logic that provides a new perspective on its philosophical difficulties. This new system (essentially physics plus the one subjective parameter τ) sits on its boundary with neuroscience, its goal being to find out not so much how reality is as how much a species of brain speed 1/τ can be expected to learn about it. The final proof of the argument is that in this new system all the familiar puzzles and paradoxes of quantum mechanics simply vanish. Time proves to be so central to our thinking that a small change in its nature can reduce everything from the state of Schrodinger’s cat to the results of the two-slit experiment to common sense.
The need for this original approach can be seen in the words of Hermann Weyl (quoted in Wilczek F., A Beautiful Question, Penguin 2015):
The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling along the lifeline of my body, does a section of the world come to life as a fleeting image in space which continuously changes in time.
To explain why time passes in experiments its passage must be added as an axiom to the logic of objective physics. Only the explicit inclusion of the observer (something that physicists struggle mightily to avoid in their interpretation of quantum mechanics) can make “a section of the world come to life”. The resulting “fleeting image in space which changes . . in time” is what our new logic system describes.
This outline can be criticized at several points. A three-part paper giving a longer and more rigorous argument is available on request.