A Tale Of Romance Between Entropy And Gravity

Our plays, novels, and movies have done an excellent job of documenting the thrills and frills of human romance. But when it comes to documenting the cosmic romance between gravity and entropy, I feel there is much work to be done.

Our scientists have indeed done their job; I have no qualms there. But let’s be honest; scientific texts are not exactly known for their ability to capture metaphorical romances nor is it their goal. Which is why I am writing this series of essays.

We started with the question of whether God created the universe. This led us to explore the role of entropy in the big bang and why the universe creates low entropic phenomena like stars and planets while the cosmic entropy increases.

We just started probing the role of the most fundamental forces in this grand scheme of things:

1. Gravitational forces

2. Nuclear forces

My aim is to explore these forces in this essay. But before I get ahead of myself, let me start with a personal habit of mine.

The Morning Habit

Every morning after I wake up, I boil water in a kettle and make myself a hot drink with some lime/lemon and salt. Some people like tea, some like coffee; I like my hot lemon/lime drink first thing in the morning.

Now, here’s an interesting thought. Let us say that I place my hot drink on a table. Given no other external factors, CAN my hot cup get hotter after five minutes?

Your answer might be:

“No way, our physical laws would not allow that.”

But here’s the thing. Our physical laws DO allow for that to happen. It is just that we do not see it happening. But then, why does that typically not happen? The short answer is: entropy.

Given no other external factors, the entropy of the system tends to increase. In this case, the number of configurations where the heat from the cup transfers to the environment far, far outweigh the configurations that dictate the other way around.

Consequently, given enough time, we can expect the heat transfer to take place until there is an equilibrium where both the cup and the environment share the same temperature.

Now, please hold this phenomenon at the back of your mind as it will play a key role in understanding the cosmic romance between entropy and gravity throughout this essay.

Gravity is a Cumulative Force

In the scenario we just discussed, we never took the effect of gravity into consideration. Why is that?

Does gravity not affect the rate at which the heat transfer happens? Does it not affect how the steam molecules spread within the room? Well, it does. But its effect is what scientists like to call “negligible”.

It is a fancy way of saying that gravity is too weak a force to make a meaningful difference (at least for a qualitative discussion). The counterintuitive bit with gravity is that it is a cumulative force.

Consider a steam molecule. When Earth’s gravity acts on it, each and every molecule of the Earth exerts a very weak pull on it. All these weak forces add up, but since the steam molecule has very little volume, these forces add up to a “negligible” net force.

Now, consider a huge rock. All the molecules of the Earth exert a weak, cumulative pull on the rock as well. Since the cumulative forces have more volume to work with here, they exert a greater pull.

This force (that we call weight) is certainly much greater than that experienced by the steam molecule. But still, in comparison to cosmic scales, it is nothing. You could lift the rock with the help of a hydraulic digger, for instance.

The point that I am getting to here is that we do not see the romantic dance between entropy and gravity at these scales quite as clearly as with much, much grander scales. In cosmic scales, things work strangely and counterintuitively.

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The Cosmic Thought Experiment

Consider a hypothetical cube in space that could fit a million suns. Now, imagine a huge ball of gas floating inside this cube. In this scenario, the effect of gravity DOES matter unlike previously! Let me explain how.

Any given gas molecule within this cube would try to “spread”. In other words, entropy plays its part here just as it did with steam molecules originating from my hot drink.

But the gas molecule has an added challenge in the form of gravity. You see, every other gas molecule in the cube exerts a weak but cumulative pull on the gas molecule trying to disperse.

Since the size of this gas ball is several thousand orders of magnitude greater than that of the earth, the gravitational pull is significantly higher. Consequently, the gas molecule is likely to be pulled towards other molecules exerting the pull.

Eventually, a core of tightly clustered gas molecules forms. But at the same time, there is a counteracting effect at the boundary. The layer of molecules at the boundary continues to spread whilst increasing the volume of the entire gas ball. A volume increase causes the molecules at the boundary to accelerate.

In my essay on why temperature has no upper limit, I explained how temperature is nothing but the measure of molecular speed. This means that the temperature of the boundary increases as the gas ball expands in volume.

Meanwhile, over at the core of the gas ball, as more molecules accumulate, the gravitational pull exceeds a certain threshold rendering it impossible for gas molecules beyond a certain point to escape. Instead, they fall into the core, and accelerate whilst doing so.

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Again, acceleration means there is a temperature increase. In short, the gravity causes the core to shrink more inward and get more compacter. Since the volume of the core decreases, the average molecular speed goes up, and so does the temperature.

Now, when does this process stop? If we go back to the earlier scenario with my hot drink, the heat transfer stopped when an equilibrium was reached where both the cup and the environment shared the same temperature. In our cosmic thought experiment, “equilibrium” is not so simple.

The Dance Between Entropy and Gravity

We have a strange phenomenon occurring here. Because of the added effect of gravity to the entropic tendencies, we have on the one hand, a core that is shrinking in volume and increasing in temperature. On the other hand, we have an outer boundary that is drifting away, increasing its volume, and thereby its temperature as well.

Now, if this scenario were analogous to the one with my hot drink, we could expect the shrinking and growing to stop when both the core and the boundary equalize in temperature and achieve “equilibrium”. But as I had alluded to earlier, this does not happen.

We expect the heat to transfer from the hotter core to the cooler boundary. But we are now dealing with scales where gravity matters. Here, believe it or not, the flow is reversed!

As the boundary of gas molecules gets heat from the core, it expands further. As it expands, it does more work in moving away from the gravitational pull of the core. Consequently, when you do the math, the net effect is that the temperature of the boundary goes down, not up.

If you haven’t realized it yet, we have a self-sustaining phenomenon going on here. As the core shrinks and gains more temperature, it releases more heat, which expands the boundary further. As the boundary expands further, it cools down even further. As the temperature differential between the core and the boundary increases, the cosmic engine starts accelerating!

Now, this process has to stop at some point, right? Everything has an end, after all. Oh, don’t worry, we will get there. But nature has a plot twist at this point.

The Romance that Defies Expectation

As the core compresses beyond a certain threshold, a new force of nature raises its head: the nuclear force. That’s right; when the gravitational pull is so harsh that atoms start smashing and “fusing”, the process of nuclear fusion begins.

As the nuclear fusion proceeds, it produces an outward pressure that is just enough to stop/slow down the compression of the core. We now have a gas ball with a stable and highly energetic core; a cosmic entity that produces great quantities of heat and light.

A star is born!

A star is an orderly phenomenon that is born out of entropic disorder purely because of the involvement of gravitational forces which enforce nuclear fusion at a threshold point.

This is such an impressive realization. I could wrap the essay right here, but I would like to explore one more important question before that.

Does a Star Reduce Entropy or Increase Entropy?

On the one hand, the temperature of the core undergoing nuclear fusion increases, and thereby increases entropy. On the other hand, its volume decreases, thereby decreasing entropy. The question is which of this wins out.

Scientists have crunched the numbers and the net result is that the core reduces entropy.

As far as the boundary is concerned, the volume goes up, thus increasing the entropy. Scientists have crunched the numbers here as well.

It turns out that increase in entropy of the boundary of a star is higher than the decrease in entropy at its core. In other words, the star increases the entropy of the system by merely existing.

This is an even more impressive realization. Again, the only difference between my hot drink and the gas ball is that effect of gravity is “negligible” in the former, whereas it is NOT in the latter. And what a difference it turns out to be!

A wonderful creation of order arises completely naturally from pure disorder. Yet, the sole purpose of existence of this orderly phenomenon is to increase the net disorder of the cosmos. This realization just leaves me in awe!

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Further reading that might interest you: 

• An Entropic Thought Experiment
• Why Does Science Love Simplicity?
• How Easy Is It Really To Predict The Future?

If you would like to support me as an author, consider contributing on Patreon.

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Reference and Credit: Brian Greene