THE PERPENDICULAR PRESENT

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At first glance, our lives seem to be strings of bead-like events. No sooner have we experienced one sensation, one thought, one feeling, one action then another takes its place. We have a vague, naive sense that we can string these events along a timeline and label it by section: past, present, future.

But on further reflection, it is clear that this is absurd. Events overlap. I am all at once aware of many sensations, thoughts, feelings, and acts; it is hardly ever clear when one stops and another begins.  Events are not points…or beads. Events have duration and different events have different durations.

The human nervous system is attuned to a certain “event wave length”, somewhere between one second and one-tenth of one second. If an event has duration of less than one-tenth of second, we normally don’t notice it; if it has duration of more than a second, we normally try to break it up into multiple, sequential events.

Of course, there are exceptions to this generalization. Mystics report event experiences lasting minutes, even hours. But the more important point is that our naïve sense that events normally last a second or less has everything to do with our perceptual apparatus and nothing to do with the nature of events themselves.

There is absolutely no theoretical reason why event duration should be confined within a single order of magnitude. On the contrary, we know that there are events with durations dozens of orders of magnitude less than a second and there is no good reason to think that there are not other events with durations dozens of orders of magnitude more than a second.

Confining the event wave length within a single order of magnitude reinforces our tendency to categorize events as past, present or future. We need to ask a different question: What are the ways in which the myriad events that constitute our lives relate to one another? Are they always neatly laid out more or less neatly along a timeline like clothes drying in the sun or are more complex species of ordering possible?

It turns out that events may relate to one another in a number of different ways:

(1)   They may be sequential (or “tangent”): this is the paradigm for what we call “causality”. A billiard ball rolls across the felt with a certain momentum; it touches a second ball and imparts momentum to that ball, sending that ball in motion. The momentum of the first ball “causes” the momentum of the second ball.

(2)   They may overlap. While listening to a particular melody, a memory occurs which lingers long after the melody has played out.

(3)   One may be entirely embedded in another. While a thought is composing, I suddenly hear a bird chirp. I am aware of the chirp but the thought process is not interrupted.

(4)   Or they may be entirely disjoint, neither embedded, nor overlapping nor touching one another.

Two events, though disjoint, may nonetheless relate in two different ways:

(5)   There may be a third event (or string of events) that overlaps the two disjoint events. As such, the events may be thought to exhibit seriality. This is the “special case” of relatedness which gives rise to the notion of “past, present, future”: when three events are so connected, one is commonly thought to be in the past and one in the future of the median event.

(6)   Or there may be no sting of events that connects the two disjoint events in which case the events are said to be simultaneous: they inhabit the “same time” (simul-taneous). In the language of physics, they “lie outside each other’s light cone”.

But even simultaneous events may enjoy certain species of connection:

(7)   Two events may lie outside each other’s light cone but both may lie in the light cone of a third event. In this case we can say that that there are strings of events connecting each of our two initial events with a common third event. They are simultaneous with respect to each other but serial with respect to the third event. (This is an expanded case of #1, above.)

(8)   It is also possible that two events which lie outside each other’s light cones may both be embedded in a common event (This is an expanded case of #3, above).

(9)   Finally, two events that lie outside each other’s light cone may nonetheless constitute a third event. This is the case with event pairs that exhibit “quantum entanglement”. The existence of this mode of connectivity was proven by John Bell (“Bell’s Theorem”) and has since been verified by repeated experiments.

Here’s how quantum entanglement works. Two quanta interact strongly with one another, e.g. ‘at birth’. They then move apart from each another. When a certain operation (e.g. measurement) is performed on one quantum, that operation causes the wave function of that quantum to collapse, thereby displaying a certain value. Simultaneously, the wave function of the other quantum collapses, displaying a related value.

We may look at this phenomenon as two events taking place simultaneously on two quanta outside each other’s light cones. Or we can view this phenomenon as a single event that spans a significant distance in space.

Is this list of possible modes of connection exhaustive? Suppose there are two events that do not enjoy any of these modes of connectedness. They are not sequential, they do not overlap, nor is one embedded in the other; they are not connected by a single series of events, they are not connected to a common third event by separate series of events, nor are both embedded in a common third event. Finally, they do not constitute a third event via the phenomenon of quantum entanglement. What can we say about such an event pair?

We must say that such an event pair does not exist! Or at least we must say that two such events do not share a common universe. (I do not use the word “universe” in the astronomical sense of the word; I use it to mean the entirety of all experience.) They do not exist for one another and there is no conceivable third event for which they both exist.

At best, we could say that they existed in entirely separate and utterly disconnected universes. But since we do not have any reason to believe that such disconnected universes exist (or any idea what it would mean to say that disconnected universes existed) and since, even if they did, we could never have any knowledge of them and they could never impact our universe in any way, such event pairs are non-existent for us. (Recent cosmological considerations of multiverses, bubble universes, etc. do not conflict with this conclusion.)

We may now state the tautological “Principle of Universality”: all actually existing events exist within a common Universe and no event exists outside that Universe.

We may now generalize our conclusions. For any pair of events, one or more of the following must be true:

(1)   The events are sequential.

(2)   They overlap.

(3)   One is embedded in the other.

(4)   They are connected to one another by a series of events.

(5)   They are connected to a common third event by two distinct series of events.

(6)   They are embedded in a common third event.

(7)   They constitute a common third event.

Looking more closely at these modes of relatedness, we can see that they fundamentally resolve into just two modes:

(1)   Serial Connectedness: #1, 4 and 5, above.

(2)   Embedded Connectedness: #3, 6 and 7 above.

(Note that #2 is an intermediate case that shares aspects of #1 and #3; #7 is a special case of #6 in which the third event consists of just the two embedded events.)

This result prompts further reflection. Is one mode of connectedness more fundamental, more sub-structural than the other? In general, an event that exhibits serial connectivity can also exhibit embedded connectivity and vice-a-versa. If we could find a phenomenon that exhibited one of mode of connectivity and excluded the other mode, that would go a long way toward establishing one mode as the more general, more substructural mode. I believe we can identify such a phenomenon but to do so we need to wade into the realm of Quantum Mechanics.

A fundamental principal of Quantum Field Theory (QFT) is that the nature of a single event is not deterministically caused and therefore in some situations is not even knowable. Rather, what does behave deterministically is a system of events which events do not exhibit causal connectedness among themselves.

The 7th mode of connectedness (above) is an example of such a phenomenon. It is a single event comprised of just two embedded events. The two embedded events are entirely disjoint but they are embedded in a common third event. The nature of the third event is perfectly determined but the nature of each of the two embedded events is perfectly undetermined.

The phenomenon of quantum entanglement described here requires as an absolute condition that the two disjoint but embedded events not connect (serially) with any other events. Such connection would collapse the wave packet and destroy the embedding entity.

Any sort of serial connectedness would destroy the embedding event (or prevent its occurance in the first place). But without an embedding event, the two embedded events would not exist in a common universe (since they would lack any connection to one another). Therefore, without quantum entanglement, Universe as we know it would not exist.

While we can observe the effects of quantum entanglement only under very specialized laboratory conditions, we should not conclude from that that such events are rare. I would speculate that Universe consists of more event pairs with “entangled connectedness” that with serial connectedness; but that is mere conjecture.

In any case, the example of entangled connectedness is sufficient to prove that serial connectivity is not a universal characteristic of all events in Universe. Embedded connectivity therefore must be the more general case of connectivity and therefore the sub-structural mode!

Applying the Principle of Universality, we can go further! No event or hierarchy of events may exist outside the universal hierarchy of events. Therefore, every event is embedded in at least one other event except Universe itself. Universe is exempt from this requirement (without contradiction) since by definition there can be no events outside it. (See The Intellectual History of Time in this collection for an alternative approach to this last point.)

How does universal embedded connectivity impact the past-present-future model of time? In a word, it destroys it!

Every event has its own duration. That duration can be dozens of orders of magnitude less than a second…or it can span the entire history of Universe. The duration of each event is that event’s own unique Present. These presents are not primarily arranged according to sequence along a timeline but are embedded in one another according to a hierarchic scheme.

Event A is embedded in Event B which in turn in embedded in Event C. A, B and C each has its own Present but these presents are not related sequentially; they are related hierarchically.

So the present is not a specific region of time. Each event has a Present proper to itself. Sometimes those presents happen to be sequential (tangent), sometimes they happen to overlap, but every present is embedded in the present of at least one other event, unless all presents are embedded in it (i.e. unless it is Universe).

The naïve notion that Present is a point or region of time located somewhere between past and future on a linear continuum turns out to be a fairy tale. It is better to understand Presence as perpendicular to linear time. From any point on the past-future timeline, we can draw a series of concentric semi-circles, each including broader and broader segments of that timeline, each potentially corresponding to the Present of some event.

The perpendicular axis appropriate to the hierarchy of embedded events measures the duration of the event, not its serial order relative to some other event. As we measure magnitude along the hierarchic axis, we subsume larger and larger segments of serial time in single events. single presents.

Ultimately, the timeline itself, Time itself, is embedded in the uber-present we call Universe.

What holds the universe of events together is not a linear sequence of temporal events; it is the hierarchical embedding of events in an ever broadening Present. As our theoretical scheme demonstrates (above), all events ultimately participate in a single, common Present that constitutes the unity of all that is.