Emergence of the arrow of time

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There is an informal explanation with an analogy using a card game.
Choosen such (in Richard Feynman philosophy) that it can give as much of an intuitive understanding as possible.

The game of time

Imagine the abstract concept of the present (as in "right now") being represented as an card game.

First of: Note that we pretend to play in a timeless imaginary space "of the gods" if you will.
Ignore the time it takes to draw and lay out cards. Our "arrow of time" will emerge from something else.

There are three players:

  • You (also called passive observer in this game)
  • The dealer (Also called physical law in this game)
  • The system designer

Cards represent so called microstates. A microstate is:

  • the information of the positions and
  • the information of the velocities (plus masses) of all of the particles of the system.

Systems can be arbitrarily chosen in size by the system designer.
Just a few cards, or so many cards that they wouldn't fit in the whole observable universe.
For all games (but one special game called "the whole of reality") you as the player can decide with which system designer to play.

Beside the microstate the cards also feature one of two colors

  • There are green cards
  • There are red cards

Each color represent a very big group of similar (meaning: in some sense close together) "allowed" microstates.
"Allowed" means defined as reachable by the currently active card
The green cards are (per definition) the group of microstates that is bigger.
Well, there may be more then just two groups and blurry areas of microstates with more or less similarity.
But in the end all the eventually blurry sub-grouped mess is just grouped down to only two groups.

There are two decks

  • M: a very big one with all combinatorically possible microstates (including even all those that are not specified being reachable by the current card)
  • N: a big one with all the microstates that are specified to be reachable by the last card you've drawn
    – these reachability specifications on the microstate cards are the rules that the system designer had set up beforehand.

The second deck (the N deck) is constantly updated by the dealer depending on the card that was drawn last.

The rules of the games are simple.
You just draw cards one after the other from the changing N deck and lay them out in a row.
After every drawn card

  • the dealer must check the microstate that you've drawn.
  • the dealer must remove all the microstate cards that are no longer reachable from the newly drawn microstate – cards from N to M
  • the dealer must add all the microstate cards that are newly reachable from the newly drawn microstate – cards from M to N

As the player while playing you must add up all the cards and write the successive sums below.
Green cards count plus one time-unit red cards count minus one time-unit.
Super simple.

Unless the system designer screwed up
you will notice that on average the successive sum of the time-units increases.

Tadaa!! You finally have time. (To almost cite Terry Pratchett)

The reason is simple. When you draw from card decks decks that always have
more green cards inside than red cards (remember the green cards are per definition always the bigger group)
then you obviously will draw more green cards than red ones.

Since the green cards are per definition are the more common cards in all the N decks one encounters, the worst thing that can happen is that red and green cards become equally common. Thus in the worst case the counter will stay around zero. Meaning there is no emergence of time. Then time no longer runs froward. The artificial closed system is already in equilibrium. For the universe that would mean the "heat death". The concept of time ceases to exist. The artificial closed system runs into its own little personal heat death.

The details about how the microstates evolve in our "timeless game space" (and lead to emergence of time):

  • include which microstates the system fundamentally allows
  • include which microstate transitions the system allows from which other microstates
  • are given by what the nature of the system (and thus the system designer for any artificial system) is.

Limits of the analogy

Note that this intuitively graspable game analogy glosses over a lot.

  • Quantum entanglement allowing quantum parallel players?
  • Chaotic multi body problem?

The proper math that goes in exactly is what one deals with in statistical physics.

Related

External links

Here's a fun scene from Terry Pratchetts work:
Discworld intro 5m12s – Death: "At last, I have time."

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