Part 1, which begins our examination of the question 'what is time?' can be viewed here.
Part 2 Some travels through time can be viewed  here.
Part 3 discussing language, sequence and order, can be viewed  here.
Part 4 a brief discussion of clocks, Steno, Foucault and Allais, can be viewed here.
Part 5 a time-free N-body heuristic, can be viewed here.

Note: this blog on time is speculative, not established fact.

A Theory of Time Part 6 : Inertia, Information and The Arrow of Time

Thus far, I have tried to show that the whole notion of time is problematic, that it is not a requirement in a Galilean-Newtonian-Euclidean GNE model of the cosmos.  With one exception: the so-called arrow of time.  Any theory which purports to show what time is, or, as in the case of this occasional blog series, that time has no cosmic reality, must explain the arrow of time within the terms of that theory.  I shall attempt that here.

Inertia

For the purposes of these discussions about time, I define inertia as generalised inertia:

Generalised inertia is a property of mass and of energy such that no entity containing mass or energy can undergo any change of relative location, relative velocity or structural condition without the expenditure of energy.

All physical systems have inertia, and this is projected into all informational systems.  Information transfer is subject to inertia in all systems.  The Nobel Laureate Wilhelm Ostwald gave, in his Nobel lecture, the example of redundant features in biological organisms.  He refers to biological inertia, which might be viewed as a biological mechanism operating in opposition to evolution. 

It is contrary to the nature of organic evolution for such "rudimentary" organs or characteristics to be shed at once. On the contrary they have to be carried for quite a long time and are only discarded after long and difficult evolution.

Wilhelm Ostwald next refers that inertial mechanism to the theories formulated in science:

the new concepts in science which are invariably so formulated as to simulate as closely as possible the existing concepts and therefore from the time of their formation and the ideas then prevailing they absorb a greater or lesser number of "rudimentary" elements which it is the difficult and laborious task of subsequent research to eliminate. For the furtherance of science it is therefore extremely important to recognize the rudimentary elements of an existing concept which
are destined to disappear.

The inertia in concept formulation is a prime example of what I would call the fundamental inertia in the use of language as a means of advancement of knowledge.
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Information.

An entity may be said to contain information if it is in some way unchanging or if it is subject to a regular,  non-random mode of change.

It is possible to view any entity as a packet of information or as a collection of information packets.  For example, a photon is a carrier of information about the chemical nature, gravitational strength and velocity of its source.  These three components are subject to various interpretations by observers, depending on the reference frame of choice.  This choice leads to controversies about interpretations.
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The arrow of time

No information storage, duplication or communication device can ever be perfect.  Our sense of time as a line from past, through present and into the future derives directly from this principle.  Any memory effect, whether as human memory or as photonic or quantum memory is subject to degradation.  Our human ability to extrapolate is also subject to an informational degradation.  Memory of the past is on a surer footing than expectations of the future. 

Human memory, and therefore human history,  is an eclectic  mix of recorded information, interpolation and extrapolation.  Human future cannot by definition have a stored informational content.  It follows that there can be no interpolation.  Future events can only be extrapolated by the projection of a trend.  But that trend can only be obtained by comparing past with present, comparing an already decaying memory with the 'now'.  The future is but an imperfect shadow thrown by the light of memory onto the viewing screen of consciousness.

The information stored in any entity has a utility as 'truth' which decays gradually into a 'job done' list and rapidly into a 'to do' list, like a heavily skewed triangular waveform.

When we humans try to reconstruct the past, we can only do so from a perspective of current knowledge.  But inextricably entwined with that 'knowledge' is a vast store of interpolation and extrapolation created by previous reconstructors.  We communicate with our past through a mist of misconceptions.  We only rarely challenge these retro-acting preconceptions.  An idea from the dawn of history may be accepted as fact only because it was never challenged.  But once challenged, with proofs, it may come to be accepted.

In a social environment, memory is extended to tribe memory, but by the very act of extension is irredeemably degraded.

The communication between the past and the present is always polluted by interference from the noise of hindsight.

I am grateful to Laurence Arnold  for this perspective.

The arrow of time

Whenever information is stored or transmitted there is a chance for error.  In making a copy of some thing,  the information in one entity is transmitted to, and stored in, a second entity.  Every subsequent copy of a copy is degraded.  In the real world, perfect replication of any entity by means of the fundamental building blocks of nature is impossible.

In biology, the impossibility of perfect replication can add to the other mechanisms of genetic and epigenetic evolution.  In language, the degradation of information leads to words changing in sound, spelling and meaning as they are replicated between users.  In mechanical systems, I propose, the degradation of information leads to decay of oscillations and orbits, if these are viewed in terms of the exchange of information between physical entities.

If an entity has a robust means of storing information about its past attributes, then it is less affected by the degradation of information.  But it can never be exempt from that degradation.  And so, a living thing, having a robust 'memory' of its own structure (DNA) , can recover from damage.  But it cannot do so indefinitely.  A rubber ball can bounce repeatedly against a surface in a gravitational field , using its 3-dimensional molecular structure as a memory of previous location.  But information must be degraded, and the ball must come to a halt.

When an entity is subjected to a force, and the force overwhelms the memory capacity of the entity, then the entity is unable to respond elastically to the force.  The limited memory cannot store sufficient information to map the effect of the force on the entity.  Any effect on the entity is non-reversible.  The entity may even be shattered into smaller entities, none of which has a memory capacity sufficient even to cause it to recognise and attach itself to its historical neighbour.

That is the Humpty Dumpty effect of the degradation of information.

In the GNE information storage model, the degradation of information is the mechanism of the arrow of time.
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In the next part, I shall discuss the role of gravity in a time-free GNE information-storage model, and  discuss the gyroscope and Foucault pendulum in further detail.