Time

Full Title or Meme

Is Time a fundamental part of reality? Or just a result of the evolution of reality? Or just a figment of our imagination?

Context

Time is, above all, a measurement of duration between Events.

• According to St. Thomas Aquinas, concerning temporal things, only present things exist. He said:

  If no one asks me, I know: if I wish to explain it to one that asketh, I know not: yet I say boldly that I know, that if nothing passed away, time past were not; and if nothing were coming, a time to come were not; and if nothing were, time present were not.

Scale

The time of our life is impossibly longer that the life of an electron in a memory registry in the phone in my hand and is impossibly shorter that the life of this world.

Basis

• Time for humans just started with counting days and then separating the days into hours.
• The shortest time interval was the second which, coincidentally, is about one heart beat.
• It has now been determined that any sequences of events can be turned into a "clock". Not all clocks are such obvious time-keepers as a heart beat. If you have a set of irreversible Markovian process, you can turn them into a clock says Marcus Huber at the Austrian Academy of Science.

Direction of Time

Leonard Susskind, Fractal-Flows and Time’s Arrow https://arxiv.org/pdf/1203.6440

This is the written version of a lecture at the KITP workshop on Bits, Branes, and Black Holes. In it I describe work with D. Harlow, S. Shenker, D. Stanford which explains how the tree-like structure of eternal inflation, together with the existence of terminal vacua, leads to an arrow-of-time. Conformal symmetry of the dS/CFT type is inconsistent with an arrow-of-time and must be broken. The presence in the landscape of terminal vacua leads to a new kind of attractor called a fractal-flow, which both breaks conformal symmetry, and creates a directional time-asymmetry. This can be seen from both the local or causal-patch viewpoint, and also from the global or multiversal viewpoint. The resulting picture is consistent with the view recently expressed by Bousso. In the last part of the lecture I illustrate how the tree-model can be useful in explaining the value of the cosmological constant, and the cosmic coincidence problem. The mechanisms are not new but the description is.

The champion for fractals, Benoit Mandelbrot pointed out that material flows around Fractal points are chaotic, and so we might expect that, at the finest granularity, time would not flow evenly but chaotically. It is the expected value of time at higher levels of granularity where we expect the flow of time to be smooth and exactly regular.

Diffusion Equation

The equation does not allow a change of t into -t, the result cannot be compensated by a change of sign of other variables as happens in Maxwell's equations. Hence the solutions exhibit an essential difference of past and future, a definite 'flow of time' as one is used to say-meaning, of course, a flow of events in time. For instance, an elementary solution of (5.2) for the temperature distribution in a thin wire along the x-direction is

T-T0 = C - exp(-cx²/4kt), (5.3) 

or, equivalently of the change of a distribution starting at time 0. This can also be represented by diffusion equation:

∂u/∂t = α∂2u/∂x2

which describes the spreading and leveling out of an initially high concentration or high temperature concentrated at the point x = 0, an obviously irreversible phenomenon.

Time Travel

• Kurt Gödel, a brilliant mathematician, delved into the fascinating realm of time travel. His mathematical insights led to the conclusion that, **theoretically**, time travel is **physically possible**¹. Gödel's work is a testament to the profound interplay between mathematics and the fabric of reality.

In Gödel's universe of mathematical wonder, he demonstrated that given certain conditions, we could traverse time. Imagine stepping into a time machine, not to visit the past or future, but to explore all the myriad paths that existence could take. Gödel's theorem suggests that, with enough time and the right circumstances, we might indeed experience **all possible futures**.

It's a mind-bending concept—one that invites us to ponder the intricacies of causality, destiny, and the very nature of our reality. Gödel's legacy continues to inspire both mathematicians and dreamers alike, as we grapple with the tantalizing possibility of unlocking the secrets of time itself.

So, next time you peel a banana, consider that its length might just be a tiny fraction of the vast tapestry of time and possibility that Gödel's mathematics weaves.

Source: Conversation with Bing, 4/8/2024

(1) The mathematician who worked out how to time travel. https://www.newscientist.com/article/2425623-the-mathematician-who-worked-out-how-to-time-travel/.
(2) Wiles's proof of Fermat's Last Theorem - Wikipedia. https://en.wikipedia.org/wiki/Wiles%27s_proof_of_Fermat%27s_Last_Theorem.
(3) David Hilbert: Mathematical Problems - MacTutor History of Mathematics .... https://mathshistory.st-andrews.ac.uk/Extras/Hilbert_Problems_speech/.

Recurrence

In the context of dynamical systems, the Poincaré recurrence theorem states that certain systems will, after a sufficiently long but finite time, return to a state arbitrarily close to their initial state. (from Wikipedia)

The Poincaré recurrence time is the length of time elapsed until the recurrence. This time may vary greatly depending on the exact initial state and required degree of closeness. The result applies to isolated mechanical systems subject to some constraints, e.g., all particles must be bound to a finite volume. The theorem is commonly discussed in the context of ergodic theory, dynamical systems and statistical mechanics. Systems to which the Poincaré recurrence theorem applies are called Conservative Systems if the time is less than the expected age of the system.