The arrow of time (4): entropy and reversibility, pictured in designs

So…I do not see any convincing answers in physics to the basic question of `what is time?’. To wrap up this complicated subject for now, I will show some half-designs for the IMAPP symposium (which I did not elaborate on since the Francesco del Cossa design that I showed earlier clearly was superior), and reformulate earlier questions on time and entropy.

The first question already is hard to formulate without falling into much inaccuracy as well as absurdity. But here goes anyway: suppose we have two situations / configurations S1 and S2 of a closed system U [for Universe] such that S1 is exactly the same as S2 in every conceivable non-time-related way (particles, waves, constellations,…down to every last photon). Then I would say that

A: Within U there is no time difference between S1 and S2, in other words they are also time identical.
B: Therefore time in U corresponds to (some measure of) the difference between configurations of U.

Hence my earlier `formula’ ΔTime \approx ΔEntropy.

Thus the question of (ir)reversibility, known as `arrow of time’, in my eyes could well be a tautology. To see this, consider the statement: `we cannot lower the entropy of the system U when going forward in time’. When ΔTime `equals’ ΔEntropy this more or less becomes equivalent to: `we cannot lower the entropy of the system U when the entropy is increasing’…

Also, it raises the question whether time is a `local’ phenomenon (non-uniform). One half-design that I made for the IMAPP symposium centered around this entropy idea:

arrow of time, entropy

(click for enlargement, you might notice different `reversal arrows’ which I added pictorially, to express the questions surrounding this subject)

Next, in my eyes the question of causality and reversibility is intimately connected to our own consciousness. We seem to experience things exclusively in the present, but! we do not even know what `experience’ and `the present’ mean. Anything we experience stems from neurons firing in our brain; anything we see/hear/sense in this way has a time lag as compared to the stimulus which provoked our senses…

Somehow we retain memories (unreliable!) from past events, and we experience time as moving forward, probably because our consciousness is hardwired that way. See Immanuel Kant‘s Kritik der Reinen Vernunft, we quote from wikipedia:

Kant proposed a “Copernican Revolution” in philosophy. Kant argued that our experiences are structured by necessary features of our minds. In his view, the mind shapes and structures experience so that, on an abstract level, all human experience shares certain essential structural features. Among other things, Kant believed that the concepts of space and time are integral to all human experience, as are our concepts of cause and effect.[3] One important consequence of this view is that one never has direct experience of things, the so-called noumenal world, and that what we do experience is the phenomenal world as conveyed by our senses. These claims summarize Kant’s views upon the subject–object problem.

In my humble and ignorant opinion, Kantian philosophy is not eclipsed by Einstein’s relativity and its concomitant spacetime. A real discussion of relativistic spacetime is beyond both me and the scope of this series of blog posts, but perhaps it is relevant to notice that causality in relativistic spacetime hinges on `light cones’ (image by Stib):


When it comes to reversibility and the arrow of time, the Kantian crux seems to me: what do we mean with the word causality?

If our consciousness were hardwired `the other way round’, could we not perceive reality as follows: a billiard ball rolling `kauses’ a billiard cue to hit the ball which in turn `kauses’ a billiard player to appear at the billiard table etc. etc.

With this in mind I made the following Escherian half-design:

arrow of time, Escherian style, frank waaldijk
(click for enlargement)

and since I found this half-design to be too sterile, I also made another one based more on entropy and human experience (which is approximate, vague, sketchy):

arrow of time, Escherian sketch style, frank waaldijk
(click for enlargement)

This last design was a close contender (but lost to the Del Cossa design, see the first posts in this series), however it lacked the depiction of a human interaction, intervention, … I also tried yet another half-design, before finally picking the Del Cossa design:

Centauresse Vezelay, arrow of time, frank waaldijk

(click for enlargement, the arrow shooter comes from a centaur sculpture in the Basilique Sainte-Marie-Madeleine of Vézelay, the original photo was taken by Vassil)

In the end , the Del Cossa design, apart from its visual strength, had another interesting feature which proved decisive: the golden circle held by its arrow-bearing protagonist. To me this circle symbolized both mathematics, and two other conundrums of time: can there be a first moment in time? is time circular (another way of looking at reversibility)?:

arrow of time, frank waaldijk
(click for enlargement, almost final design, just the sponsors omitted)

Hope you enjoyed this cross-over between science, philosophy and graphical design!

Postscript: if you’ve come this far, then the following very recent article should interest you: new quantum theory could explain the flow of time. It seems that every few years or so, a new insight in `the arrow of time’ is claimed…which in a way illustrates how hard the problems surrounding time really are.

Entropy, entanglement, energy dispersal… they all start with an E so perhaps I could just pimp up my `formula’ thus: ΔT = H(ΔE), where H is some appropriate function (multiplication with constant would be nice but is probably far too simplistic).

Isn’t cosmology just the most marvelous religion? The really amazing part of physics to me is that we actually succeed in increasing our capabilities to manipulate Nature, even when (in my eyes) we remain largely ignorant of the real mechanisms at work. On the other hand, I’m highly pessimistic about whether this increase in manipulative activities will be beneficial to humanity, and life on earth in general.

[End of series]


About fwaaldijk

mathematician (foundations & topology in constructive mathematics) and visual artist
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