Understanding Carlo Rovelli's theory on the emergence of time

My head has been cooked since reading The Order of Time by Carlo Rovelli. I’ll write my understanding of it here in my own words in the hope that someone might one day read this and correct me if I’m mistaken.

His theory is an attempt to explain the emergence of time as we experience it. It comes after having deconstructed our incorrect perception of time as fundamental feature of the Universe, and having been left in ‘a Universe without time’.

Establishing the root of all temporality

First we dip down to the quantum level to look for temporality at the lowest level that we can observe .

  1. The fabric of spacetime materialises as the result of interactions at the quantum level.

  2. These interactions are not linear and do not have a direction in ‘time’. The happenings of the Universe are a collection of events that are not ordered in time.

  3. There is, however, an implied order at the quantum level due to quantum noncommutativity; the order in which you do things results in different outcomes.

  4. Mathematician Alain Connes has shown that there is a kind of ‘temporal flow’ which is implicity defined by this noncommutativity. This could be the root of all temporal order in the Universe.

  5. Later it is established that in order for things to ‘flow’ through time, we must have an incomplete understanding of a system that does not take its microscopic state into account. At the quantum level, a similar incomplete understanding is maintained by quantum indeterminacy.

Where time emerges in our world

Now we look for where this temporality manifests itself at a more recognisable scale.

  1. The second law of thermodynamics (the law of entropy) is the only physical law in which the direction of time matters; it does not work in reverse. It is bound to the same passing of time that we are.

  2. Entropy increases as a system moves from ordered states into more chaotic ones. What is ordered (low entropy) and what is chaotic (high entropy) is matter of perspective. It depends on the configurations that you recognise as ordered. Therefore, entropy is a relative quantity. The same way that an object’s speed depends on the perspective of its observer, so too does a system’s entropy.

  3. Entropy arises from an incomplete, or “macroscopic”, view of a system. We are unable to distinguish between the many microscopic states that give rise to water, we just see the macroscopic view of water. If we saw the state of a system in microscopic detail, none of the configurations would be particular or special; they would all be equal. For particularity to exist, we must “group” together indistinguishable microscopic states into macroscopic ones. Entropy would not exist without this particularity afforded to us by our incomplete view.

  4. At the microscopic level of a system, everything is a variable like any other; everything changes all the time. It is only in our macroscopic abstraction of that system that a specific variable emerges which behaves like time. Things don’t change because of some underlying time that is passing. Instead, as things change, a variable which behaves like time emerges as a result of our abstraction.

  5. This variable is what powers our perception of time. It is coined as ‘thermal time’.

Stitching the two together

  1. The ‘temporal flow’ implicitly defined by quantum noncommutativity mentioned earlier, and the ‘thermal time’ determined by a macroscopic state are aspects of the same phenomenon.

  2. Here the theory dips into territory that is far beyond my comprehension. Both of these ‘temporal flows’ are equivalent “up to certain internal symmetries”. My understanding of this is that, depending on some assumptions that I do not understand and therefore will assume are not universally agreed upon, the algebra that models the relationship between these flows (internal automorphisms) can be reduced so that there is a single variable that represents ‘time’.

  3. This is what connects everything together; the time we experience through entropy increasing is an aspect of the same phenomenon that gives rise to deepest root of temporality we can observe.

How we experience time passing

  1. Energy degrades into heat as entropy increases. This leaves behind a trace we can recognise. For a moving object, energy is transferred into heat through friction, and an object that was once moving stops moving.

  2. Our concepts of past and future emerge as a result of these traces left behind by increasing entropy. There are traces of the past but not of the future because entropy was lower in the past, and we see the traces left by it increasing. This essentially is the passing of time that we experience.

  3. Every interaction our nervous system has with the outside world records things like this. We see where things were and how they interacted with other things because of the traces left behind by energy degrading into heat (increasing entropy).

  4. We form memories from these collective interactions in our brains. Our brain can be thought of as a machine that continually records all of the traces left behind by increasing entropy in order to better predict the future.

  5. Our perception of the present moment emerges from recording events that extend through time. Our brain creates the concept of duration from these periodic recordings. This implies the existence of a present moment to us when there is not one, only what has been and what is to come. When you stop and listen to time passing, it is entropy increasing that you hear.

If you understand this better than I do and have spotted any errors or misunderstandings, please let me know.