Introduction

The work of a curious fellow
   

The article that follows is on a topic that I am thinking about. I would appreciate any feedback that you might be able to provide. Especially errors in concept or calculation. Please check the speculation archive for previous articles. The archive might provide some context for the present speculation.

Please send an email jdj@mcanv.com if you would care to comment.


I am preparing this document to share some of my thoughts on the nature of the boundary between past and future with interested folks not necessarily in the math or physics business.† To facilitate that objective I provide sort of an inflated glossary on my website with links in this document.† Please do follow the links at least once to ensure common understanding of the terms used if there is any doubt. When you come to a colored bar on the page, you might want to review the material above the bar before moving on. There are four main pages here. A continue button at the bottom of each page to follow the string of pages. From the last page you can jump to any of the previous pages.

James D. Jones

In this essay on the nature of now (Notice the use of the boldface now to indicate now the noun as opposed to now the adverb or adjective.)†I will say every thing I know about now and some things that I donít know. Like most ideas about how Nature works, my view of now is certainly incomplete and probably wrong. That does not necessarily mean that it is useless. At the very least writing it down will force me to really think about my perception of the passage of time and to improve my understanding of some things previously taken for granted. I hope that for some readers it will provide a way to think comfortably about past, present and future.

The way we experience the universe includes an evolution of events characterized by an irreversible time order.† This order naturally leads us to separate the stream of events into future events that might happen, present events that are happening and past events that have happened, where future, present and past identify the segment of time that contains each class of events.† What we experience as the present is actually a slice of the recent past because when we have received sensory input and processed it, time has marched on.† The now whose nature we are considering here is the leading edge of that slice of the past we think of as the present, that boundary between past and future.†

The conjecture is that the boundary between past and future we call now, has a physically significant role to play in the workings of the universe.† I am going to try to address the following question.

What happens at that boundary called now between an unknowable future where systems, including the universe as a whole, have an enormous number of possible states and an unchangeable past characterized by the single state in which the universe was† caught as now swept by?

You should know that my speculations in this matter are based on the notion that time exists as one of the fundamental properties of nature, a component of spacetime (More about spacetime later).† I am aware that there are other points of view but the physical as opposed to philosophical treatment of time has the advantage that it allows verifiable predictions to be made about events that have not yet transpired.

I will be using results from the special and general principles of relativity due to Einstein and from quantum mechanics, two areas of physics that have been well verified experimentally and are thoroughly documented elsewhere.† I present the results as statements of fact without making any attempt to derive them from theory.† That approach saves us a huge amount of time.† The best plan is to suspend disbelief and just forge ahead regardless of our inability to visualize the situations I am going to describe, regardless of the strangeness of spacetime and regardless of other effects of relativity and quantum mechanics that are outside our everyday experience.


Foundation

Space includes three mutually perpendicular dimensions that we might think of as forward-back, left-right and up-down.† For the sake of brevity I will call forward-back the x dimension, left-right the y dimension and up-down the z dimension.† To locate an object in space we need to choose a reference point along each dimension from which to start our measurements.† We will call that reference point zero.† We get to choose the reference point because space is symmetrical with regard to location and orientation.† If I move my apparatus to another lab table and turn it around to face a different way to repeat an experiment, I get the same results.

Next picture three real number lines, one along each spatial dimension, placed such that their zero points coincide.† We will call the common intersection the origin.† This arrangement allows us to identify any point in space by a set of three numbers, each representing the distance from the origin along a dimension.† The three lines are called the x-axis, y-axis and z-axis each named according to the dimension it spans.† The three numbers, written as (x, y, z), called coordinates, specify a point in space.† The arrangement of three lines is called a reference frame.† Each observer of events in spacetime may have her own reference frame.† These frames may overlap, coincide or be in motion relative to one another without interference.† If a frame is not rotating and not accelerated, it is called inertial.† In inertial frames particles not subject to external forces, called free particles, move with constant velocity (speed and direction).

Points in space may be identified by (x, y, z) but events require additional specification.† We must say not only where (location) but also when (time) in referring to events.† Prior to the advent of Einsteinian Relativity people thought of space and time as two independent aspects of nature.† In ordinary human experience the unity of space and time is not obvious.† In fact events, which are the things that really matter in understanding the universe and predicting the future, take place in a unified spacetime framework.†

So, we need to include the t-axis in the discussion.† The t-axis intersects the space axes with the chosen time zero at the origin.†Since we move along the t-axis at a speed dictated by Nature, without necessarily moving along any of the spatial axes, the t-axis must be perpendicular to all three spatial axes.† We cannot visualize a fourth line perpendicular to three others but it surely is there.†

With this unification, space and time are on an equal footing.† That does not mean there is no difference between space and time but they may be treated in the same way and combined in mathematical expressions.†One distinction between time and space is that time seems to have had a definite beginning (more on this later) whereas space has no natural limit in any direction.† The second significant difference is that to use time in meaningful mathematical expressions in exactly the way that space is used; one must replace the time coordinate with the time coordinate multiplied by the square root of -1.† No amount of mathematical finagling will get rid of the pesky minus sign that appears on squaring the time coordinate.

The location of an event is specified by (x, y, z, t) where t is the time coordinate of the event.† Distances along the spatial axes are commonly reckoned in length (meters for example) while distances along the t-axis are commonly reckoned in units of time (seconds for example).† In spacetime calculations it is often convenient to have common units on all axes.† Fortunately Nature has provided us with the conversion factor between seconds and meters.† One second is approximately 300,000,000 meters.† We know this universal and constant conversion factor as the speed of light, 300,000,000 meters per second.

It may help to forget about two of the space dimensions for the moment and focus on the x-axis and the t-axis.† It turns out that limiting our displacements to forward and back does not hide any of the essential features of spacetime and does avoid a lot of complicated mathematical expressions.† Also we can show the axes on a two dimensional surface like a computer screen or a sheet of paper.

Figure 1

Spacetime Diagram

Above is a spacetime diagram showing two events, one of which marks a commonly used zero point of the t-axis, the other of possibly lesser significance.† Any event, idealized as a point in spacetime, may be plotted on such a diagram.

Two points in space are separated by a distance which may be calculated from the six coordinates of the two points.† In accordance with the Pythagorean Theorem, distance

D=√(x2+y2+z2)
where √ represents the square root of the parenthetical quantity that follows and x, y, and z are the differences in the corresponding coordinates of the two points.† Distance is always positive since the squares of negative real numbers are positive.

Two events in spacetime are separated by an interval which may be calculated from the eight coordinates of the two events.† In accordance with Einsteinís Relativity, interval

I=√(t2-D2)
where t is the separation in time between the two events.†An interval may be positive, negative or zero, depending on the relation between the distance and time contributions to the interval.

As predicted by special relativity, different observers whose reference frames are in motion relative to one another will disagree on the time and distance between events and they will both be equally correct.† It is the interval between events, which is fixed for all observers in inertial reference frames.† How much of the interval is distance and how much time is a matter of perspective.† Different observers may not agree if two events are simultaneous or if they happen at the same place. This is bad news for a person wondering about the nature of now but we will fearlessly plunge onward.

Continue