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We know that time flows from the past to the future. We remember the past and make predictions about the future. You stir cream in your coffee, and it mixes in. It doesn't un-mix.
The classical understanding of the nature of time is that time is absolute - that time ticks by the seconds, minutes, hours, and years at the same rate for everyone.
The directionality of time comes from the idea in classical physics called the 'second law of thermodynamics', which states that a quantity called 'entropy' (which is a measure of the disorder of a system) always increases.
Because of the equations of special relativity and the nature of the speed of light, Einstein was forced to let go of the Newtonian idea of absolute time.
Einstein taught that time and space are connected. Space and time are relative. It ticks at different rates for different people, depending on your frame of reference. It's malleable and stretchable.
But Einstein takes it further with his 'general theory of relativity' and says what Newton taught about the invisible force of gravity pulling objects together is really about the shape of space-time.
Clocks tick at different rates depending on where they are in Earth's gravitational field.
From Einstein's perspective, time is integral to reality itself. Looking at the way the equations of quantum mechanics evolve in time, you could run the tape forwards or backwards without knowing the difference. Time is a parameter in the quantum world. It is just a number.
But quantum systems are not isolated, they are always interacting with their surroundings, which gives a direction to time.
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