The Arrow of Time - A Coin Toss Away from Disorder

Written by: Arman Momeni

The universe tends towards disorder.

Disorder:

The Second Law of Thermodynamics states that the entropy of the ENTIRE universe, considering the universe as an isolated system, always increases over time. Or in other words, each reaction that occurs adds to the universe’s entropy. And, in dramatic terms, with every passing day, the universe becomes more and more disordered.

An isolated system is one that cannot exchange either matter or energy with its surrounding. Given that the universe comprises virtually EVERYTHING known to existence, it physically is unable to exchange anything with any external sources – given that there are none.

In statistical mechanics, entropy measures the number of different ways a system can be arranged, thus a measure of “disorder.” Disorder increases over time, as energy disperses, and systems dissolve and meld into chaos. The more disordered something is, the higher its entropy.

A Coin Toss:

Let’s look at Entropy from the analogy of a coin toss. If we have a single coin and we flip it, the result is either heads or tails – there is no disorder. A non-disordered state would be a case were every coin is the same face – either all heads or all tails. If we are to now add another coin, there are 4 possible outcomes.  

1.     HH (both coins are heads)

2.     HT (the first coin is heads, and the second coin is tails)

3.     TH (the first coin is tails, and the second coin is heads)

4.     TT (both coins are tails)

There is a 50% chance that both coins will be heads or both coins will be tails, but there is also a 50% chance that the system will be disordered, thus the entropy of the system is greater than that of one coin. Now, let’s add 2 more coins. With 4 coins there are 16 possible outcomes.

1.     HHH

2.     HHHT

3.     HHTH

4.     HHTT

5.     HTHH

6.     HTHT

7.     HTTH

8.     HTTT

9.     THHH

10.  THHT

11.  THTH

12.  THTT

13.  TTHH

14.  TTHT

15.  TTTH

16.  TTTT

As we can see, there are still only 2 outcomes where the system is ordered, and all coins are either heads or tails. However, what’s changed is that instead of 2 unordered/disordered outcomes, there are now 14. There is a 1/8 probability that the system will be ordered and 7/8 probability that the system will be disordered. Are you starting to see a trend? The more coins we add, the greater our system becomes, and the more it becomes disordered. If I were to have one thousands coins there is a 1/500 chance that the system is ordered, and a 499/500 chance that the system is disordered. If I were to have one million coins there is 2 scenarios where the system is ordered, and well, 999998 where the system isn’t. Thus, we see that as reactions occur in the universe, and we leave our indelible footprints on existence, randomness increases. The universe is not necessarily guaranteed to be disordered, but as we saw with the probabilities, it certainly tends to disorder.

Significance:
So, the universe is disordered – why is entropy significant – so what?

Entropy is one of the few concepts that proves the existence of time – or the flow of it at least. The “Arrow of Time” is the conspicuous name given to the idea that time is not symmetrical and only flows in one, linear direction – forward. Time is non-reversible, we cannot go back in time, we cannot ultimately reverse reactions and entropy always increases.

The “Arrow of Time” provides solace (and worry) in the idea that with each passing moment, the only constant is change. Everything changes, and once these changes occur, there is nothing that can be done to undo them – the universe’s entropy has been forever changed. But we cannot be intimidated by change, change is a fundamental, crucial, and beautiful part of humanity. We all age with each passing day, and there is no way to reverse that aging. At the same time, however, with each passing day, people are born, and new lives are brought into the universe. Entropy makes our lives both a joy and a tragedy. The flow of time – the “Arrow of Time” always helps point us to the future, the certainty that we cannot change the past should motivate us to look into the future and focus only on what we can control.

Entropy shows us to take advantage of life as we know it. Life is messy. Life poses randomness. Life is cluttered. Life is disordered. But just as a book doesn’t start to finish, humans are not born to die. We are born to embody the universe’s entropy - to love, to cry, to laugh, to feel, to learn. We are born to live.

Works Cited:

Farnam Street. (2021, February 12). Entropy: The hidden force that complicates life. https://fs.blog/entropy/

Libretexts. (2023, January 30). 2nd law of Thermodynamics. Chemistry LibreTexts. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Thermodynamics/The_Four_Laws_of_Thermodynamics/Second_Law_of_Thermodynamics