Thursday, February 27, 2014

On Non-Eternities And The Nature of Time


Pondering the question of what non-eternity is, and whether or not it is a logically coherent idea, has lead me to make some observations about the nature of time.

What is a non-eternity?  For non-eternity to exist, all time everywhere and for all things that exist, have existed, or will ever exist, must have a beginning and an end.  More generally speaking, the extent and influence of time must be bounded at both ends, in a non-eternity.  Time bounded at only one end (for example, having a beginning but no end) might be a different type of eternity from time without beginning or end, but it is still an eternity, by definition.  Supposing it is possible for time to be bounded, what are the ways in which a boundary might be imposed on it?

A non-eternity can be conceptualized as a line segment.  It has a beginning and an end, and time flows from the beginning to the end.  Join the opposite ends of the line segment, and you have a circle.  In a circular topology of time, identical events are repeated ceaselessly.  Although time in a circular flow never begins or ends, the endless perfect repetition places a boundary on time.  It is therefore reasonable to label the circle a "non-eternity." In an earlier post, I referred to a "circular eternity" so and am being deliberately inconsistent with that earlier terminology here.  This is merely a matter of semantics.

Upon further reflection, it is somewhat inappropriate to call a universe in which only a finite amount of change is possible an "eternity," even if endlessly repeated.  On the contrary, it may be logical to define a non-eternity as a universe in which only a finite amount of change is possible.  In that case we would have to be very careful about how "an amount of change" is defined, clearly, mere repetition could not increase an amount of change.  On the other hand, an eternity might be defined as universe without both an end, and a beginning, of time.  Under that definition, circular time might be considered an eternity; however, every moment of a circular time is both an end, and a beginning, to the rest of the time circle.  So calling a time circle a non-eternity seems justifiable, under both definitions.

The analogies of a line segment and circle might be extended to additional dimensions with additional details.  For example, a sphere or a toroidal helix (see illustration above) might be imagined instead of a circle.  However, the topologies of a line segment or a circle represent essential ways that time can be bounded. 

The Impossibility Of  Distinguishing Linear and Circular Non-Eternities 

If the line represents the flow of time, and time can flow only in the forward direction, the two geometries of a line segment and a circle are indistinguishable to any finite being in the continuum.  In other words, a circular non-eternity and a linear non-eternity are indistinguishable to beings existing in them.  Both are bounded; the linear non-eternity by a beginning and end of time, and the circular non-eternity by infinitely repeating the same sequence of events through a sort of curvature in time.  Each transit of the time circle is identical to every other transit, and therefore time in a sense is continually reset or restarted.  There can be no change in knowledge from one cycle to the next in a circular eternity, or else the cycles are not identical.  Since there can be no change in knowledge between cycles without destroying circularity, a temporal being in a circular eternity can never know whether it is transiting an eternally repeated cycle of a time circle, or just taking a single, unique trip along a time segment.  To the temporal being, each experience is and must be exactly the same.

A temporal being in a non-eternal time segment might observe an approach of the end of time.  For example, it might be observed that time was gradually slowing everywhere in space, and therefore it may be anticipated that an end of time is drawing near.  But the temporal being can never know whether time has ended, or is just temporarily stopped.  If time stops and never restarts, the temporal being will never know.  If time stops and restarts in a way that preserves at least some information through the stoppage, that is just time behaving eccentrically along its merry way.  If time stops in a way that destroys all information in existence, and then restarts after all information is destroyed, no temporal being in a later cycle can recover information from the previous cycle.  Such stopping and restarting may be the same, topologically speaking, as time reversing and returning everything to its original state.  For the new temporal beings, time will appear to have started at the beginning of the cycle in which the beings exist.

On Different Flow Rates

It has been observed that the speed of light in a vacuum is everywhere the same regardless of the velocity or acceleration of its frame of reference.  From this observation, Einstein deduced that time and space form a sort of continuum.  One aspect of this continuum is that differences in the momentum history of objects can cause corresponding differences in the relative amounts of time experienced by each object.  In other words, time flows at uneven rates.  For example, suppose Bob stays on planet Earth, while his brother Ted accelerates away from Earth to visit Sirius, and then accelerates back from Sirius to return to Earth, before Bob dies.  When Bob and Ted are reunited, they will discover that Bob has experienced more time waiting on Earth, than Ted has during his journey to Sirius and back.  The logical reasons for this odd result are explained clearly here.  If we accept the logical conclusion, the fact that objects in space can experience the flow of time at different rates tells us nothing obvious about the end or beginning of time itself.  But it might hint at a better understanding of what time is.

Time As The Possibility Of Change

Time is, in a sense, the possibility of change.  A photon emitted without any subsequent interaction with matter or energy travels at the speed of light and exists unchanged except for its position in space.  It will experience neither time nor change so long as its velocity is exactly 'c'.  Unless and until it interacts with the universe and changes state, time for the photon does not pass.  Time nonetheless exists, in a sense, for the lonely photon so long as there is a possibility that the photon can change its state.  Generally speaking the constant change in its position and the existence of the universe implies that such a possibility -- that the photon will experience time and change at some time in the future -- cannot be ruled out.

Supposing that time flows forward only and is the aspect of the universe providing the possibility of change.  It follows that, even if at some time in the past the universe was not experiencing any change, the fact that it is presently experiencing change proves that it has always been possible for change to occur.  Therefore time, defined as the possibility of change, has always existed.

If at some future time the entire universe ceases to experience the flow of time and reaches a state in which any further change is utterly impossible, time will have ceased to exist.  In such case, time will have passed from eternal existence into oblivion.  That is, time might have an end but cannot have had any beginning.  It has always existed but might someday end.

The possibility of an End of Time seems unlikely, but perhaps cannot be entirely ruled out logically.  Even if this strange topology (an end but no beginning) cannot be proven illogical, time will always have existed and is therefore eternal in the sense of having no beginning.  Even supposing it cannot be proved that the universe will never reach a state in which all future change is impossible, logic proves that the past, future change has always been possible and therefore time (in the sense of an enabler of change) has always existed. 

Although we can prove that change has always been possible, no one can prove that future change is impossible.  Suppose the universe is trending towards absolute stillness, meaning the absence of all change.  The trend can be observed while time and change still exist, but nothing can be observed or known once perfect stillness is achieved.  Nothing whatsoever can be done.  It cannot be known whether absolute stillness in the end of time is unchangeable, or merely unchanging.  Unless the stillness is absolutely and necessarily permanent, then time has not ended. 

Therefore if we define time as the possibility of change, non-eternity is not a logically coherent idea, because we can deduce that the possibility of change must have always existed.  We can also deduce that it is unknowable whether or not time (as possibility of change) will ever end.  If it is not impossible for time to have an end but no beginning, it is at the very least quite surprising.  Even in that case, however, time as the possibility of change has always existed, so there can be no non-eternity.

However, this definition of time seems a bit like a rhetorical trick.  If there was zero change anywhere and forever before the present epoch of change, then the universe was preceded by a changeless void, a nullity in which nothing ever existed or happened.  In that case it may be more satisfying to say that time did not exist until  the earliest change occurred.  Perhaps time is better defined as change itself.

Time As Change Itself

If time is defined not as the possibility of change, but as change itself, we may have to wrestle with more difficult logical conundrums.  This definition may require accepting that time is capable of passing into and out of existence more easily than the downstroke beat of a bee's wing.  For example, if time did not exist before the earliest change, it sprang into existence with the first change.  If in a trillionth to the trillionth power of a nanosecond, no change occurs anywhere in the universe, then time has flashed out of existence for that brief instant.  And at countless other instants in every second of time.

If time is change itself and cannot be divided more finely than a certain amount, then time is quantized.  If time is quantized, the minimum quantum of time must be non-zero, and each time quantum must be separated from its neighbors by some quantity of no-time or absolute stillness.  If there is no stillness between adjacent time quanta, then time is continuous, and not quantized.  Quantization by definition requires some separation between adjacent quanta, or else the quanta run into each other and cannot be distinguished from a continuum.  Since change cannot occur without passage of time, this would mean that a phase of absolute stillness must, in a sense, occur between each tick of the quantum clock.  Quantized time in a sense must wink in, and out, or existence between each tick.  This is so, because the state of the universe must be exactly the same at the end of each time quantum as at the beginning of the next, and no change can occur except within a time quantum.  So, if time is quantized, each unit of time experiences time extinction events equal in number to the unit of time divided by the time quantum.

If space has some minimum quantum while time does not, there must be some tiny slice of time over which no change within any quanta of space is possible.   Within time slices that are sufficiently small, there is not enough time for particles in adjacent but different quanta of space to interact.  Thus, no change can occur in countless tiny time slices of any given time interval.

Conversely, if change must occur somewhere in the universe at every instant of time no matter how finely divided, then at least one changeable quality of the universe must subsist in an infinitely divisible matrix.  The only apparent candidate for such a matrix is space, alternatives such as "ether" having been shown inconsistent with experimental observations.  Change cannot occur without some space for particles to evolve in.  Even if it is hypothesized that a particle is a point occupying zero space, it cannot interact with anything else without some space to propagate through.

If space is infinitely divisible, every particle no matter how small encompasses an infinitely divisible volume of space, unless the particle occupies no space at all.  Suppose, for example, that a "quark" is the fundamental particle.  If each quark encompasses an infinitely divisible volume of space, it must either be perfectly homogenous throughout its entire volume, or have a structure that includes some smaller, more fundamental thing.  If the quark must be perfectly homogenous, it encompasses a volume of space in which no change that would disrupt its internal homogeneity can occur; such that it must change instantaneously or not at all.  If the quark has internal structure, either there is some smaller fundamental, necessarily homogenous thing that is too small for us to detect making it up, or there is no fundamental particle at all and every structure is infinitely complex. Some theorize that quarks encompass no space at all, and exist as "point-like" particles. Point-like particles occupy no space, and thus allow existence of arbitrarily small structures.  An infinite number of points can be packed in an arbitrarily close arrangement, if there is no lower limit to the scale of space.

Thus, if space is infinitely divisible, there is no scale to the universe, which is infinitely complex and extends from from the infinitely tiny to the infinitely large.  If there is no lower limit to the divisibility of space, an infinite amount of change can occur during what seems, at larger scales, to be a finite amount of time, due to this infinite complexity.  Each subatomic particle can encompass a universe of smaller changes, each sub-atomic particle of that smaller universe can encompass its own universe of smaller changes, and so on up and down the scale of space.  Tiny universes with tiny persons can be born, evolve, and die in the span of a heartbeat in our world -- while even tinier universes similarly pass during heartbeats of the tiny persons.  Both time and space would have no discernible scale. Such a reality is not consistent with our experience, because the universe as we know it does exhibit scale.  Subatomic particles exhibit different structures and behaviors than atoms, molecules, collections of atoms and molecules, cells, animals, worlds, solar systems, galaxies, and on up the scale.  There do seem to be upper and lower limits to this scale.  Perhaps the scale we observe in the universe is an illusion peculiar to our particular location in a sort of infinite fractal.  If so, we might reasonably be deluded into believing that space and time are not infinitely divisible.

Based on observations of universal scale, but not to a logical certainty, our apparent universe includes periods of change surrounded by timeless instances of changelessness ("no-time").  If time is defined as change itself, time is continually stopping and starting.  When stopped universally, time (defined as change itself) does not exist at all.

Instantaneous Change

Can change occur instantaneously, therefore proving that time cannot be defined as change or the possibility of change?  Logically, all change requires the passage of time.  If something exists in a first state, and then changes into a second state, the question of how much time the change required is immaterial.  It is sufficient that at an earlier time the thing existed in a first state, and at a later time it existed in a different state. The presence of time is needed to enable a thing to change from one state into a different state.

If a thing merely exists in two or more different states simultaneously, it is not changing.  Existing in two states simultaneously does not require any time.  For example, an unchanging photon may exist as both a particle and a wave without any need for time.  As Relativity teaches, light can exist unchanging in no-time, such as when moving at velocity 'c' in a vacuum.  It cannot be observed without interacting with something else, and thus, being changed and made subject to time.  Once observed and made to experience time, it can and does change into one or the other of a particle or a wave.

Schrodinger's cat cannot really be both alive and dead at the same time, because it observes itself at some conscious or subconscious level, during macro-time.  But all living things passing in and out of no-time may exist in superimposed states of life and death during those timeless leaps.  Also, it may be that information can be preserved by a thing entering no-time in two or more simultaneous states.  If so, it may be possible to prove that non-eternity does not exist, even in a universe with scales of space and time.

Conclusion

If we define time as change itself, and accept our observation that the universe has scale as valid, we can deduce that periods of change in the universe are like islands rising from an ocean of absolute stillness in which no change occurs. 

We cannot deduce how our epoch will end, or whether other epochs existed prior to our own.  Surmising that our own epoch is like a vast chain of islands representing change in an ocean of changelessness, we might reasonably imagine that our own "island chain" (epoch) may be separated from other epochs by an ocean of timelessness.  But we will never find any evidence to support such an imagining, unless we can discover a record that can be proved to have been created in an earlier epoch.

Until then, we live in a universe of unknown age and origin, progressing towards the unknown. If time is change, non-eternity is not logically impossible, but neither is it required.

Friday, February 14, 2014

Valentine's Day


If ever love could reach across an ocean,
And back across a wide expanse of time,
Sowing seeds of hope in the driest desert --
Such love is ours, my love, your story true.

If love is just a feeling with no power
to act at all beyond our mere beliefs;
From you pours forth that power with amazement,
Your touch, your voice, your words, make me believe.

Be love what ever knows no computation,
And what ever breaks all chains of time;
O, may such love be in us ever growing,
With wonders new until our bodies rest.

Monday, January 20, 2014

On Different Types of Eternities




Supposing there is nothing in the universe outside of time, such that everything that can exist (the "universe"), exists in time, and that time has no beginning or end, then we can make some statements about eternity.  If time itself has a beginning and an end, then there is no eternity.  We cannot know whether eternity exists, but if it exists we can deduce its possible structures. 

We can deduce that, if eternity exists, the three possible types of generally non-random eternities are linear, circular, and spiral.  We can deduce that we exist in a generally non-random universe, because we observe that the universe changes, at least some of the time, non-randomly.  Each state of the universe is correlated to a prior state in a way that preserves information, for at least our epoch.  So if eternity exists, it is generally non-random at least some of the time.

A linear eternity is one in which whatever has happened before, never happens again in exactly the same way.  One can roll snake-eyes twice in a row, or a million times in a row, but the universe changes in countless ways between each roll of the dice.  Cycles can exist, but the universe never repeats the same pattern of successive states, unless for a finite period by random happenstance. Generally, the universe never obtains exactly the same state as any prior state.  However, if the universe is finite while time is infinite, it is inevitable that prior states will be replicated in the future.  In a linear eternity, there is no predictable pattern to replication, if replication occurs.  Occasionally, randomness or something indistinguishable from randomness must occur between successive states, breaking correlation of the state to its parent state.  For example, at the instant of a big bang, randomness (or some other force, e.g., "infinite creativity" or "free will") can give rise to a new and different cycle unlike any previous cycle.

A  circular eternity is one in which each state of the universe is repeated forever and ever at successive times.  For example, every "big bang" is followed by a "big crunch" (or by some other destiny), after which there is a new big bang and everything that happened in the earlier universe is replicated exactly again.  A never-ending series of big bangs each leading to an everlasting expansion and nested inside one another is another example of a circular eternity.  This would be a structure a bit like a perpetual ripple on the surface of a pond.  Whatever its structure, the characteristic feature of a circular eternity is that every state that the universe obtains is identically repeated at successive later times.  There is no randomness because every state of the universe is perfectly correlated to every other state.  There is no randomness, no creativity, no free will; only the pulsing of a never ending wave.

A spiral eternity is one in which states of the universe are repeated in successive cycles, but each successive cycle differs from its most recent prior counterpart in some correlated way.  There is loss of information between cycles injected by forces such as randomness or free will, but not a total loss.  The next cycle remains a recognizable child of its most recent parent.  Like the linear eternity, there is no discernible pattern to replication (if replication occurs); like the circular eternity, successive cycles are discernibly related. 

Besides linear, circular, and spiral eternities, eternity could also behave like combination of these types, for example linear sometimes, and circular or spiral sometimes, but in the ultimate analysis it must be one of these three.  This conclusion follows from the starting assumptions that time has no end, time is necessary to enable change, and that at least some changes in the universe are not random.  If time has a beginning but no end, then the eternities are the same as for time without beginning or end, once begun.  If time has an end but no beginning, that is an impossibility.  Although we can deduce the possible structures of eternity, we cannot discover empirically whether or not eternity is linear, circular, or spiral.


We (i.e., finite beings) cannot ever know by empirical science whether eternity is linear, circular, or spiral, or whether eternity exists at all.  No matter how long our period of scientific observation endures, it is always finite.  Therefore we can never know whether what we observe will remain so forever, or only for a temporary phase.  For example, if we observe the universe expanding, we cannot know that it will never contract later on.  If we see entropy always increasing, we cannot know that universal laws will not change so that entropy seems to be always decreasing during some future time. 

To empirically determine the structure of eternity, it would be necessary for a part of the universe to exist outside of time, and for communication to be possible between the part of the universe subject to time, and that part outside of time.  More on this in a subsequent post.

Knowledge of whether eternity exists, and if it exists is linear, circular or spiral, are rather small examples of knowledge beyond all possible reach of empirical observations.  For convenience, we might refer to things that we know must be real, but cannot be known scientifically, as holy things.  This is not inconsistent with the biblical meaning of "holy."  In the biblical sense, holy means set apart from the mundane, empirical world. 

In modern times, most people spend almost no time thinking about or discussing holy things.  It feels a bit strange and useless.  Many people profess the rather bleak belief that everything about our existence can be known empirically, but this belief cannot be true.  There are many things that logically must be real, but cannot be known empirically.  For example, we can know we exist, but we cannot know whether we exist in a time dimension that is eternal, or if eternity exists, whether its structure is linear, circular, or spiral.  Although logical hypotheses about eternity are not empirically testable, they are no less logical for that.  And being no less logical, they are no less possible and true.

Mathematicians have spent a great deal of time thinking about infinities, if not eternities, and practical applications have even been developed from such thinking.  Mathematical infinities are not exactly the same as eternities, however.  Eternities deal with the destiny of the universe, and the human race as part of that universe.  Holy eternities have a special significance to ethics, because eternities enmesh related concepts like free will, predestination, and destiny, that are important in ethics.  In other words, metaphysics is not entirely useless.  In future posts, we will attempt to derive some use from it.


Friday, December 6, 2013

I Lit A Match


I lit a match
one bright day,
and failed to see cast light.

Its flame was feeble
in the glare,
and brought nothing to my sight.

I lit a match
one dark night,
and was astonished by its flare.

What things hidden
sprang to sight!
Never shall I despair.

Tuesday, October 22, 2013

The Call of Righteousness

Athiest, you are called by your Reason to righteousness;
Christian, you are called by your Lord.

Muslim, you are called by the prophet Mohamed;
Jew, you are called by Yahweh;

Bhuddist, you are called by your Teachers,
Hindu, you are called by your Gods;

Believers, of many diverse faiths
Called, one and all by one call.

Called to peace, the peace of the righteous;
Peace, without murder or war.

Peace, with freedom and justice abundant;
Peace, for ever and for all.

Wednesday, October 16, 2013

Germany

In the north lands, long ago
There stood a land of freedom;
Mythical though it may be,
I sing of ancient Germany.

"Of the people," Deutschland means;
And so the tribes did spread;
Across the forests, snows, and plains;
Often invaded, never conquered.

In Deutschland, all were mostly free,
Mothers were mostly honored;
Within each tribe all freely traded,
Courage and valor mattered.

So Deutschland stayed, in first version:
Repelling each Roman incursion,
Despoiling their eagles of war,
While worshiping the German Thor.

Until Rome decayed, and
In swept, or crept the German tribes,
to sit upon the ancient thrones,
and pillage what remained.

And so did Deutschland finally lose
Its freedoms held so dear;
By feasting on the dying beast,
It enlivened and became her.

This song in German tongue
Does mourn that mad temptation;
Sing it loud with heart and lung,
And warn of repetition.

Refrain:
Tho' Germany the free is lost,
Its children kept in chains:
May myths of captors be forgot,
May freedom live again.

About the OMG JC Musings

From now on, posts that do not fit neatly into the story line of UWBAAB will be collected under the link OMG JC Musings.  This stands for Open-Minded Germanic Judeo-Christian Musings (or if you prefer, the O My God Jesus Christ Musings).  I hope you find the musings interesting, edifying, and uplifting.

Posts in UWBAAB story line are collected under the UWBAAB link.