Time

I had a discussion with a couple of friends about the new Nolan movie Tenet. We came to a point where we were trying to explain what entropy and time is. (slight spoilers) The main idea of the movie is that objects and people can enter a reversed-entropy state. In this state, the 'entropy' of their existence is moving in the opposite direction of what we view as the normal entropy direction. When trying to how this worked in the movie we came to a point where we thought of time as two lines.

Measure of entropy, right = more entropy, left = less entropy.
-------------------------------------------1----------------------------------------------------
-------------------------------------------2----------------------------------------------------
Image 1 being a person, Amy, and 2 being another person named John. As Amy's and John's entropy changes, their respective position on this timeline moves as well. If both of their entropy changes normally they continue moving on this timeline. However, when Amy and John are having opposite entropy, they first move towards each other and then pass each other.

John & Amy have the same entropy change:

• Starting position for Amy & John in our timeline.

-------------------------------------------1----------------------------------------------------
-------------------------------------------2----------------------------------------------------

• Something changed with Amy and John

---------------------------------------------------1--------------------------------------------
---------------------------------------------------2--------------------------------------------

• Something changed with Amy and John again

---------------------------------------------------------------1--------------------------------
---------------------------------------------------------------2--------------------------------

John & Amy have opposite entropy change:

• Starting position for Amy & John in our timeline

-------------------------1----------------------------------------------------------------------
-----------------------------------------------------------------2------------------------------

• Something changed with Amy and John

---------------------------------------------1--------------------------------------------------
---------------------------------------------2--------------------------------------------------

• Something changed with Amy and John again

-----------------------------------------------------------------1------------------------------
-------------------------2----------------------------------------------------------------------

You might have already come to the same conclusion that we did. What does it mean to Amy and John to be at different places in the same timeline? Does Amy & John disappear when not on the same entropy 'level' (timeline position)?

Before I try to answer these questions I'd like to introduce another model for representing time: Observed change. Imagine a simple universe. This universe consists of two particles whose only properties are its x, and y position in a 2-dimensional grid.

Time step 1:

1 * *
* * *
* 2 *

Oddly enough, these particles are also named Amy & John (1 = Amy, 2 = John). If Amy & John does not change positions, time does not move either. If Amy moves one step to the right, like so:

Time step 2:

* 1 *
* * *
* 2 *

Time has officially moved! What happens if Amy moves back to her original position? I'd argue Amy goes back in time.

Time step 3:

1 * *
* * *
* 2 *

Can we represent this model with a timeline as well? You betcha'.

1-----------------------------------------------------------------------------------------------
Amy is at position 1,1 (top left corner in our universe). We can write this as U(1) (The state of the universe as shown at time step 1.).

-1----------------------------------------------------------------------------------------------
Amy(2) is the exact state of the world when Amy has moved to position 2,1 in our model universe.

If we increase the size of the universe, the number of moving objects or the complexity of the moving objects, it becomes more and more difficult to move 'back' in time.

Also, using this world model shows why the 'double' timeline model does not work when trying to explain Tenet. Only one timeline can exist at once, and a tick in the timeline can be seen as the state of all objects in a universe. If Amy is having her entropy reversed, while Johns entropy is moving as normal, it just means that their states are changing differently. They still exist simultaneously in the universe at all points in the timeline.

Some odd things do occur in our small universe, if the timeline is supposed to represent change of state. If Amy moves one step to the right, one step down, one step to the left and then one step up she ends up in the same state as she started in. This means that the timeline is not as intuitive as we'd like it to be.

1 * *

* * * 1----

* 2 *

* 1 *

* * * -1----

* 2 *

* * *

* 1 * --1---

* 2 *

* * *

1 * * ---1--

* 2 *

1 * *

* * * 1-----

* 2 *

The timeline model doesn't make much sense.

What is interesting with this state model of time, is that it shows why it's close to impossible to travel back in time. To be able to travel back in time, you would need the entire observable universe to 'reverse entropy'. That is, everything in the world would have to change back to the state that they were in, at the moment you want to travel 'back' to. It also shows how traveling forwards in time is much simpler. Traveling forwards in time simply requires you to stop changing, while everything else changes.