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Time
#1
I've been reading a lot on this topic, most notably works of Carlo Rovelli where the question continuously arises in the context of Quantum Gravity, and various texts on Statistical Mechanics and the origins of irreversibility most notably in the book of Price Huw "Time's Arrow and Archimedes' Point". Most of these ideas are things stolen from these. I urge you in particular, if you have some training in physics, to check out this essay by Rovelli which should make for a great bedtime reading.

So let me pose the question: What is time?

Let us look at how we have tracked time:

1- In the past, people used to measure time by looking at positions of shadows.
2- Nowadays, a second is defined in terms of the frequency of an emission of some element (which element and what transmission is not important).

We see that time is always measured in relation to something else that in itself evolves in time. A year is how long it takes for the Earth to go around the Sun. Once again, that's a relational definition.

Is time really absolute? Newton came by and introduced the notion of absolute time and had a lot of success. He presumed there is a clock ticking in the bacgkround, and everything else evolves according to it. Einstein came later on and found that moving clocks will tick faster than clocks at rest. And so there is no absolute clock ticking in the background that everyone will agree on.

Even more radical, was Einstein's discovery that the gravitational field is nothing but spacetime itself. Moreover, In the "canonical" description of gravity, a description where an object called "the Hamiltonian" plays a starring role in determining the time evolution, the Hamiltonian is zero (on the bulk). This means that there's no "time evolution" in the theory.
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We "remember" the past, but not the future. We experience "moving" towards the future, but not the past.

Yet, the fundamental laws of physics seem to show no prejudice towards one direction of time over the other. In fact, in the theory of gravity/spacetime, one needs to artificially insert a time orientation.
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Where then does this feeling of time come from? A common resolution is that time is only a feature of the macroscopic world. In particular, the macroscopic world is additionally governed by the laws of thermodynamics. In particular, the 2nd law states that a quantity called "entropy" of an isolated system cannot decrease in a process that takes you from one state to another. Perhaps then, we can define the "past" to be the set of states where entropy is low, and the future to be the set of states where entropy is high.

One can then think that perhaps our perception of time is purely psychological. We remember the past, because it has lower entropy. In very sloppy terms, entropy is a measure of "disorder" of a system. You reckon if you see a ruined castle that it would be easier to reenact how the castle "was" than it is to imagine how a castle will look like following an earthquake that brings it to ruins. Perhaps, there is only a "now", and the memories of the past are just interpretations and interpolations of the brain of what possible more orderly states could bring you to your current state. Of course, your brain would be much more successful in doing that than to interpolate towards a less orderly state where the possibilities are far more.

The problem now is that entropy depends on the choice of macroscopic variables. For an example, consider bringing a visually impaired person who cannot distinguish different shapes, and a colourblind who cannot distinguish different colours. Bring an ensemble of objects of different shapes and different colours. To the first person, sorting these balls by their colours will make them look most orderly (they observe low entropy), but not so to the second person who will only see a seemingly random arrangement of shapes (they observe high entropy). If however you sort the balls according to their shapes, the situation reverses and now the first person will classify the state as high entropy and the second person will classify it as low entropy.

I'll leave it to you to think about the implications of what this could mean about our perception of time ?_?
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