In this section of the essay I will share some of the threads of thought I picked up along the way that did not strictly speaking illuminate the nature of now. I must confess that some of these musing drift into the philosophical or even religious.

In my glossary entry for objects I left out a lot of information not necessarily pertinent to the nature of now. By three minutes after the Big Bang the basic constituents of ordinary matter, some relatively heavy particles called baryons and some relatively light particles called leptons, had settled out at their final number.  In the entire universe there are about 10⁸⁰ of each.  The protons and neutrons that make up atomic nuclei are baryons.  The electrons that fill the atom’s shells following the laws of quantum mechanics are leptons.  The total mass of all the atoms in existence is carried by these primordial articles.

Now consider a massive object, a rock for instance.  The baryons and leptons from which it is made have been around since near the beginning of time and will be around forever barring some cataclysmic end of the universe.  Those baryons and leptons have been organized into the atoms of the rock in the process of stars being assembled by gravity and destroyed in explosions called supernovae.  Rocks are literally made of stardust.

There is nothing special about the baryons and leptons from which the rock is built.  It is their arrangement into atoms and the incorporation of those atoms into the structure of the rock that gives the rock its character.  Mass in the form of baryons and leptons is permanent.  The specific arrangement of the baryons and leptons is temporary.  Eventually the rock will be ground to dust by its environment, and dispersed into space when the Sun explodes.  A bit later the dust will be gathered up by gravity into a star.  The star will explode at the end of its life cycle and the dust may be grabbed up by gravity and used in constructing a new planet, to become rock again.

Objects, including living creatures are made of matter that is essentially immortal but it is the arrangement of that matter that characterizes the objects it forms. It seems that living objects are fundamentally different from inert objects. Everything I said about the rock applies to living creatures as well. All are a particular arrangement of stardust. In the case of living beings though there is something there in addition to an arrangement of raw materials. The arrangement has been infused with an animating principle the origins and nature of which we do not know. Living creatures have something extra that inert matter does not. They respond to stimuli by influencing the future state of the universe. Human beings seem to take this an additional step and make willful changes in the future of the universe based on a better sense of the future than other animals. 

The issue is how does revising the spatial location of now from a continuous spatial volume to a collections of points solve the problem of the relativity of simultaneity. Remember that three-dimensional spatial volumes are represented by one-dimensional lines in a spacetime diagram.

Figure 8

Now and Simultaneity Diagram

In Figure 8 we find the world lines of three objects. In the reference frame of this diagram the green object has a positive velocity, the red object has zero velocity and the blue object has negative velocity. A short segment of the line of simultaneity for each object is shown.

When in the parable of the two clocks we tried to claim that the now time coordinate should be at each clock’s proper time we got into a paradox when the clocks were reunited. If the past-future boundary is not at each object’s proper time, where in time is it. One possibility is that now is off the clock altogether. This thought invokes visions of additional dimensions and possible other complications. There is one particular time that appears to be the same time throughout the universe. That is the time recorded by the cosmic microwave background (CMB) radiation as observed from the commoving reference frame, which we take to be the age of the universe.

There is some logic in claiming that the boundary between past and future for every object lies at the age of the universe. This only requires that we terminate all world lines at the age of the universe, regardless of the elapsed proper time along that world line. Object ages may vary but the age of the universe is… well its universal. This time coordinate for now is an unsubstantiated claim on my part. It is just hard to imagine the universe marching into the future and leaving those objects that are in the universe behind to straggle into the future at various later times. That is why in Figure 8, as well as Figures 2, 5 and 7, I placed all objects at the age of the universe.

To deal with those pesky lines of simultaneity we need to look into the spatial extent of now. Lines of simultaneity are lines of constant time in the diagram reference frame as seen by observers that may be or not be at rest in the reference frame of the spacetime diagram. We got into trouble in Figure 2 because we had two conflicting versions of the past-future boundary shown on the diagram, one a now line and one a line of simultaneity.

If we stop thinking about a past-future boundary that exists over all of space, or even a significant chunk of space and define now as the past-future boundary on the world line of each particle in the universe, then now for each particle occupies a point, not a line, surface or volume. The concept of spatially separated objects sharing the same now disappears and all the events in which a particle is involved must happen at that particle’s location in space (no action at a distance).

Each particle then is free to drift up the t-axis at the speed of light, always at the age of the universe, dragging its own relativistic version of the line of simultaneity with it. Its own age simply reflects the number of stretched time units since its birth, having no necessary connections to the time coordinate of its now. Its line of simultaneity may slope this way or that as the particle zigzags through space without conflict with its own now since the now point is always on the line, and without conflict with the now of another particle because that now does not exist for the original particle. A line of simultaneity is in fact a line of constant time for a particular observer but that observer is not free to assume that his now extends to distant events lying on that line.

Let me go back to the coffee sipping event from the section on how now works.  In this sip event, the state changes include the active kind, involving departures from Nature’s preferred state as expressed by maximal aging or the psi-function. My hand moved.  The cup was raised.  Liquid flowed.  Let’s try to isolate the first state change in the sipping event.  Was it the first perceptible change, in the hand’s approach to the cup?  Probably a chain of state changes preceded any perceptible motion, including the state changes in my brain that made up my decision to take the sip.

Perhaps the decision to sip was precipitated by the state changes in the olfactory sensors in my nose, which resulted from the state change in the liquid in the cup to a vapor.  And so on and so forth until the idea of an isolated event, like the sip of coffee, slips from our grasp.

From the time of the Big Bang, my sip of coffee at this particular spacetime location has been included in a possible future of the universe.  Its probability just lay there close to zero for somewhere around 13.7 thousand million years.  During all that time, as now rolled up the t-axis trimming away possible events, it never broke the chain of events that enabled the possibility of that sip of coffee.

Does that mean that the coffee sipping event was preordained from the time of the Big Bang, what with one thing leading to another over the last 13.7 thousand million years or so.  I seriously doubt it.  The possibility of the event has existed since the Big Bang but there are an infinite variety of ways that the probability might have remained vanishingly low. 

In recent history events conspired to raise the sip event probability.  I was born, I was exposed to coffee, and so on.  Also events may have reduced the probability.  The price of coffee went up, I learned to like tea as well, and so on.  Even as late as a few minutes ago the phone might have rung, causing that particular sip of coffee to land on now’s scrap heap of events that never happened. 

Throughout that entire chain of events back to the Big Bang there were very likely instances where the most probable event was not the one realized by quantum state reduction.  The sip of coffee event may even have benefited from that.  It was only with the passage of now that the event became a certainty and immediately passed into history.  The probability of any future possible event is influenced by the realization of current possible events, just as the probability of current events was influenced by the realization of past events.

Those readers inclined to philosophy may ask if I had any choice in taking the sip of coffee.  I think all can agree that after the fact there is no choice, what is done is done, but I have the impression that I could have decided to forego the sip or interrupt it anytime before its completion.  In another context (the role of an attractor in chaotic systems) I have observed that the universe runs on rules, not rails.  In the language of this topic, Nature operates through preferred paths, not rigid regulation.  There seems to me to be enough slack in the working of Nature’s laws, with their element of chance at the quantum level and tolerance for redefining the preferred path at the macroscopic level, taking a realized state as initial conditions for future development, to allow for a considerable degree of free will.

Suppose I had decided to sip the coffee by levitating the cup to my lips by willpower alone.  I just tried it and nothing happened.  Free will has its limits, imposed by an objective reality that governs the workings of the universe.  Still it appears that living organisms have the ability to redirect the stream of events.  The stack of events that leads from the Big Bang to now at this place and time has not been shaped entirely by chance. Animal intent has redirected the flow of history, in ways both trivial and profound.

Those of you familiar with the notion from system dynamics of sensitivity to initial conditions will recognize that it may take only the tiniest nudge to, in a short time, result in a profound change in the state of a system from what would have existed in the absence of that touch. Operating at the most subtle level in the brain might be a principle that makes a bear turn left rather than right and destroy my garbage can rather than that of my neighbor.

I wrote about above about redirecting the stream of events, but how do people actually get a grip on the stream? I think that it begins with forming an intent and proceeds by controlling the body so as to improve the chances of meeting that intent. 

So what is involved in forming an intent?  If seems like that would be something happening in the cranial cavity, which is very nearly empty.  Still there are some baryons and leptons in the brain, each of which at the now instant have their own world line history in spacetime reaching back to about the time of the Big Bang.  Either the intent has been destined throughout all history to appear at a certain spacetime location, in which case we have no choice. Or the intent is an act of free will.  If the former, past, present and future are already determined, as suggested by the block universe theory.  If the latter, some sort of an animating principle must operate in the physical brain at the instant of now to enhance the future probability of that intent being realized.

The irreversibility (see below) of quantum state reduction which is not adequately accounted for in the block universe theory throws me out of that camp.  I have argued above, and experience seems to confirm, that now selects which future state of a system is realized at each instant.  At the quantum level where all state changes take place, this realization collapses the psi function to one of its possible futures.  Because the realized state in unpredictable we assume it happens by chance.  It sort of reminds me of the time a few decades ago when we thought that chaotic data was random.  Lack of predictability does not necessarily mean random. 

I suspect that the same animating principle that makes living beings different from inert matter (see The Nature of Objects above) is capable of tinkering with which quantum state is realized in reduction.  If that were true then free will could reside in the animating principle and from time to time make its entry to the physical world by guiding state changes in the brain that put intent in memory.  Then the brain could retrieve the necessary instructions from memory to control the body in ways that enhance the probability of realizing the intent.  Or perhaps not.  Clearly I know nothing about this but it is fun to guess.

There has been a long history in physics of the apparent dichotomy between the tidy mathematics that is used to model the laws of nature and the messy universe that those models are supposed to reflect. One way this dichotomy is manifest is in the problem of irreversibility.

The mathematical laws used to model very large and very small physical systems, like the Sun’s orbit of the galactic center and the collisions between atoms of gas in a container are reversible. That means if I replace the time parameter, t, with its negative, -t, the models run backward, undoing everything they did when t was positive. On a human scale real physical processes proceed in only one way, from past to future.

It turns out that if you watch a galaxy sized system long enough you see that it does not precisely follow the time-symmetrical laws used to model it. The time-symmetrical laws are only approximations to what is really going on. For the box of gas atoms, we can use thermodynamic principles based on statistical analysis to rationalize the irreversibility. See the glossary entry on system states for this approach.

George Ellis has proposed an even more fundamental reason why time is irreversible. Irreversibility is a property of all quantum mechanical systems. Quantum state reduction, whatever the description of the unitary evolution of the system, is itself irreversible.

Think of quantum state reduction as choosing one of the many states whose time evolution is described by Schrödinger's Equation. If this state reduction were reversible we would have to recover Schrödinger's Equation from the single state that was realized sometime in the past. I can easily choose a single card from a deck but cannot reconstruct a deck from a single card. Since quantum mechanics underlies the evolution of large scale systems including chemical and biological as well as mechanical, we should not be surprised to find that on these scales past, present and future are distinguished from one another. See Professor Ellis’ paper, On the Flow of Time for details.

Introduction

Where Now?

How Now

Glossary