Quantum Gravity, the Arrow of Time and Free Will

Linas Vepstas, December 1999. Draft. Work in Progress.

Abstract

This webpage examines some (meta-)physical suppositions that seem to lead in a natural way to an arrow of time, and to an unpredicatble future. These suppositions also seem to avoid some of the discomfiture caused by Quantum Measurement and the theories (such as the Many-Worlds Hypothesis) that attempt to deal with it. The hypothesis presented is 'meta-physical' only in the sense that this paper contains no equations, and makes no testable predictions.

In breif, the argument goes as follows: gravity, at planck scales (10e-40), is a foam of wormholes of four spatial dimensions, rife with 'grandfather-paradox' type connections. These paradoxes can be resolved only by splitting spacetime into three spatial dimensions, where consistency is absolute, and one time dimension, where consitency is indeterminate. The sense of an arrow of time and a 'here-and-now' that moves forward in time is really just the result of resolving paradoxial situations between space-like separated regions. Furthermore, it is argued that this resolution is fundamentally unpredicatable, which is why there is a 'now', as well as why quantum measurements seem to be indeterminate until macroscopic scales are reached. Whether this has anything to do with free will, or not, is not clear, but some points are touched on there as well.

If all this sounds like crack-pot science to you, well, then, you are not being charitable: we prefer the term 'pseudo-science'. You can excercise your free-will and not read any further. If you are in the mood for dense entertainment, then do read on. To help you balance incredulity with credibility, take note: I've got a PhD in Physics, I don't like to look foolish in public, I enjoy thinking about this stuff, and I operate from the envious position of not having a career to damage by expousing what may be to you a 'lunatic' theory.

Introduction

Physics of the last few centuries has been beset by a variety of paradoxes that lead to meta-physically unpleasenet situations. These tend to get debated in a very hot-headed, emotional fashion, thus giving them the great credence and importance that they deserve. Minor issues don't get argued over for centuries. The earliest of these that concerns us is the reconcilliation free-will and self-determination with Newtonian mechanics. If the Universe just obeys some physical laws, some mathematical equations, then wouldn't it run just like clockwork? And we know that the gears and levers of a clock have no free will. Predestination seems inevitable. With the advent of Quantum Mechanics and more recently, Chaos Theory, one might think that notions of predestination have fallen by the wayside. But no: there have been articles in the popular press espousing just such an idea (reference that recent article in nature? science?)

This is a peculiar situation, since both Quantum Mechanics and Chaors Theory both seem to provide (in very very different ways) the 'wiggle-room' needed to argue for an unpredicatable future. Yet they seem to introduce only more troubling questions. On the quantum side, we have everything from the Schroedinger Cat paradox, to the Many-Worlds Hypothesis. It is my beleif that the only people who brush these things off are those who either haven't bothered to think about thier implications, or who refuse to acknowledge thier own inability to find a better answer. On the Chaos side, things are only a little bit better. Here, the very strangest concoctions, from Cantor dusts to Devil's Staircase's, are true mathematical marvels, but fail to rescue us from our Quantum Predicaments. To make matters worse, it seems that current thinking has mounted further questions, such as 'why is time one-dimensional and not two or three-dimensional?', or 'why does time flow forward and not backward'?

Enough of this introduction. Lets just dive in. Recent work in gravity has explored the use of wormholes for time-travel, and, in particular, has lead to discussions of the grandfather paradox. In one school of thought, the grandfather paradox is rescued by the Many-Worlds hypothesis. Bzzt. This is just replacing one meta-physically unappetizing notion by another. Another other school of thought states that the universe only allows self-consitent physical histories: viz. a billiard ball sent back in time cannot knock itself out of the path of the time machine which is sending it back in time. (Or alternately, we might imagine a ball traveling back in time, apearing just so in order to knock itself into the machine to send it back into time.)

hypothetical jump: At planck lengths, spacetime is a foam of wormholes, and this sort of stuff happens all over the place.

hypothetical jump: Such histories of paths as they travel through planck-scale wormholes can be made self-consistent only in the backwards light-cone. Unresolved paths have to be merged into consistent states with other paths arriving from space-like separated regions. The merging these paths into a self-consistent whole results in a one-dimensional cusp, which we call 'time'. These patch are fully self-consistent only in the past (this is why the past is untouchble). The active resolution of these paths is occuring in a region we call 'right now'. (which is why we are aware of three dimensions, not four) Paths in the future are only partly indeterminate: macroscopic events are proscribed by macroscopic laws, and microscopic uncertainties are adressed by quantum mechanics.

What this implies: (listed in no particular order):

  1. Quantum uncertainty has its origins in planck-scale phenomenon. When studying the paths that contribute to the Feynman Path Integral (during second quantization), there is a beginer question that is frequently posed: 'why do all those non-physical paths contribute to the integral?" The answer is usually 'because they do', which is simply not appealing, or 'because one must sum over all quantum states', which is not appealing if you like to think of the paths as actual trajectories through 3 or 4 dimensional space.

    But if we imagine spacetime to look like a sponge, then we can have geodesics take all sorts of crazy paths from point A to point B. Thus, the Feynman Integral might in fact be nothing more than a sum over geodesics through this foam. Thus, the seeming accidental resembleance between various diffusion & stat mech equations and quantum equations might not be so accidental: Similar statistical rules apply.

    Unfortunately, the nature of this claim is what renders all this pseudo-science. I personally do not have the mathematical tools at hand to explore the nature of geodesics in a highly distorted spacetime, much less to take statistical averages over these to derive any sort of meaningful conclusions. I doubt anyone else can make any simple progress.

  2. time is one dimensional because that's all that is needed to make room for uncertainty.