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Arrows Of Time - What even is Time?

A short foreword :
This is one of the most exhausting projects I have ever undertaken and had to go through a lot of different sources and materials which I'll cite in the footnotes. There are three parts to this post,

1) The framework for thinking about Time and how it's different from the Time we experience and know about as well as some basics required to move further. This is a suggested Read for everyone and leans slightly towards the technical side.

2) The second Post deals with The Thermodynamic arrow of time and one of the main reasons for me to write about the topic. It deals with the Second Law of Thermodynamics, Entropy, and leans heavily towards the technical side. It contains the Physics aspect of the perception of time

3) The third post deals with the Psychological arrow of time and has the human aspect towards the perception of time. This post is written to explore how time is perceived by different individuals. You can skip directly to this post if you're more interested in this one.

 I hope that this proves to be as interesting to you as it was to me while researching the topic.



1) Framework

Time invites the curiosity and perspectives of everyone, from the philosophers to scientists
to engineers and so forth. Intervals of time have been used in equations to calculate different
aspects of motion, predicting results using data and models and even helps us in understanding
the history of our universe.
But there's an even subtler concept related to time which we often experience in our daily lives, which we
talk about often and yet can't actually conceptualize - Flow of time.
When we talk about flow we usually talk about how "fast" or "slow" is the flow of time. We marvel
at the pace of the flow and use history as a reference to understand, that we move forward.
For the next few posts, I invite you to think about this flow. Specifically, one other characteristic of
the flow that we feel intuitively but can't really describe- the direction of flow.
If we talk about current it flows from high potential to low potential points in a circuit, when we talk
about air it flows from high-pressure regions to low-pressure regions, talk about fluids they flow from
high potential region to low potential region(In this case Potential energy) and similarly from high pressure
to low pressure(Pumps work on this principle).

So, what about Time, we seem to experience the "flow" of time. What is the direction of this "flow"?
This is where the concept of Arrows Of Time was formulated, to understand this supposed direction
of time.
If you've noticed, in Physics, the direction of time is not mentioned, even in the laws of motion.
These laws actually focus on the duration of time and relate events w.r.t what happened now to
what happens next, but they don't really distinguish the direction in terms of forward and backward.
As we progress through the post, please keep asking yourself this question: What is the direction of
time? Where is it moving towards? Do these directions differ w.r.t perspectives?
Is Time special in Doctor Strange's Universe?




Let's talk about the most confusing thing I had to figure out first: Time and how it’s different
from Arrow of time.
Time:
“People like us, who believe in physics know that the distinction between past, present,
and future is only a stubbornly persistent illusion”.
-Einstein
Now, there are a lot of perspectives to the question of what is time, from the stoners
perspective to the philosophers(Often times the same)to the physicists and cosmologist. 
Let’s look at this from the perspective of physics. Since the publishing of Einstein’s relativity
paper, scientists have really looked at the time differently than what was previously thought
according to Newton’s laws. Let’s have a look at the modern-day concept of time. 
Let’s say that you are at your home, sitting at a specific point(Let’s say that it’s your spot)
and has coordinates as (x,y,z) but to distinguish between events happening at that point
we use another coordinate t which is time. This is how we typically describe events as
when (t) and where (x,y,z). Hence time is nothing but a coordinate to describe things in
the universe which stretches out in the universe from -ve infinity to +ve infinity.
But wait, the laws of Newton don’t mention the time to be co-ordinate and that’s where
Newton’s definition of time was proved wrong by Einstein. 
Let us probe this further with the following example I found:[1]
Suppose I set up a coordinate system with myself at the origin, x to the East,y to the North,
and z straight up. For the time, I'll use my wristwatch and suppose you do the same. But
you are in a different country and our two sets of co-ordinates won't match because our
East, North, and Z(or Up ) axis points in different directions.




Hence, spatial co-ordinates are observer-dependent. But time is absolute. Assuming we
both use Greenwich Meridian Time(or some other standard time) we both will agree upon
time, wherever we are on Earth. This is why Newton treated time as special. But Einstein
published his Theory of Relativity and proved that Space and Time are both relative
and the only absolute quantity is the Speed of Light.



Arrows Of Time:
Arrow of time is both a psychological perception and a physical phenomenon
(this is what we will discuss).  So we’ve just discussed the concept of time in physics according
to physicists. But, let’s stop and question for a moment, If time is just a coordinate why can’t we
travel through it as we do in space and how do we explain the  “flow” of time that we experience?
Arrow of time is related to time asymmetry, i.e. time moving in a direction. From Physics perspective
this property is exhibited by all the macroscopic processes(you, me, the universe, etc.) 

T-Symmetry:
T-Symmetry which would come up a lot in further discussions is known as
time-reversal symmetry. Here, any phenomenon which occurs can retrace its steps back
to its original position.
Hence, the entropy(more on this later) is conserved. Let’s make sense of this:


Imagine if we jog from point A(where we are all fresh, filled with energy and have no sweat)
in the diagram below to point C(where we’re tired, sweaty, and smell). Now, according
to T-symmetry, we could actually retrace our steps back from point C to point A and here’s the
catch, we end up in the absolute same conditions and factors as we began(i.e. From sweaty,
smelly and tired to fresh, filled with energy and non-sweaty). In another case, this is called an equilibrium
state where you can end up in the state that you began. Hence, according to the relativity concept,
I’d say the universe should be behaving as T-symmetry, but this from common experience isn’t
possible and the reason is Time Asymmetry and  Second Law of thermodynamics.

If you are interested in a more geeky explanation which involves Gibbs free energy and
correlation b/w reversibility and equilibrium(which is still not absolutely evident but conclusive)
check out this thread[2]

Now that we know about Time, Arrow of Time and T-Symmetry, let’s have a look at the reason
why we experience time flowing in a direction from a physics perspective, why Doctor Strange’s Universe
violates the Second Law and why things have a certain direction in terms of "lifespan".


Footnotes:




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