# Why did the apple fall from the tree, vis-à-vis the second law of thermodynamics?

Newton came up with gravity to explain apple falling from the tree, what would Gibbs have thought?

The second law states that entropy of the universe, in general increases. This is relatively easy to see when you expand a gas or dissolve salt in water but how is entropy increasing by the falling of the apple. Of course the potential energy of the apple is decreasing but the second law has no mention of potential energies or forces.

So how do you explain this or like charges repelling or any other macroscopic phenomena not related to gases or chemical reactions and processes?

• Why do you think that the second law of thermodynamics would be sufficient to prescribe how an object should move? Commented Jul 30, 2020 at 12:09
• I dont know, thats what I was asking. Commented Jul 31, 2020 at 2:37
• @ManitAgarwal-Elpsycongroo Please use apostrophes, ', rather than grave accents, , for contractions. As you may have noticed, SE uses the grave accent to indicate Code Formatting Commented Jul 31, 2020 at 10:56

## 4 Answers

The second law says that the entropy of the universe cannot decrease. In this situation Gibbs would say that the entropy of a freely falling apple does not change. Indeed the situation is completely time reversible. If you reverse time in this situation you go from a apple accelerating down under gravity to an apple decelerating under gravity as it travels up, exactly as if it had been thrown from the ground. There is no thermodynamics here, which is what you would expect.

Now an apple breaking off a tree or hitting the ground do generate some entropy, related to the breaking of the apple's stem, the deformation of the ground and the dissipation of whatever energy is left over as thermal energy.

• If the motion of the apple in the earths gravitational field is completely equivalent in every direction, then why does the apple fall ? Commented Jul 30, 2020 at 12:03
• @ManitAgarwal Because of the initial conditions. Commented Jul 30, 2020 at 12:42
• So does that mean thermodynamics is insufficient to model the behaviour of anything except gases? Commented Jul 31, 2020 at 2:35
• I get the point of simplifying things, but statements like "There is no thermodynamics here" are a bit much for me...
– Will
Commented Jul 31, 2020 at 2:56
• @ManitAgarwal-Elpsycongroo thermodynamics is insufficient to model the behaviour of anything at all, including gases! Thermodynamics puts constraints on what can happen (the entropy can't decrease, the total energy can't change), but to know what actually will happen you need more information. For a gas at equilibrium you need the heat capacity, and for a falling apple you need Newton's laws. Neither of those things can be derived from thermodynamics alone - you always have to use thermodynamics in conjunction with other physical knowledge. Commented Jul 31, 2020 at 5:51

To add to BySymmetry's answer, I would like to provide a quote from Eddington's "The Nature of the Physical World"$$^*$$, in which he discusses the link between the second law of thermodynamics and our perception of "time's arrow".

There is only one law of Nature⎯the second law of thermodynamics⎯which recognizes a distinction between past and future more profound than the difference between plus and minus. It stands aloof from all the rest. But this law has no application to the behavior of a single individual.

In your case, the "single individual" is the apple moving in the presence of the gravitational field.

One must remember that entropy, temperature, etc. are concepts from statistical mechanics; which we apply to ensembles of many, many constituents because to track each part individually would be utterly impossible. Therefore, it is not very meaningful to apply the ideas of "entropy" or "temperature" to a system of one or even two bodies. As Eddington also says in the above reference:

it must be remembered that many properties of a body, e.g. temperature cannot be regarded as controlling the behavior of a single individual.

So, I might go one step further from BySymmetry's answer and say that Gibbs would have found the question to be somewhat meaningless.

$$^*$$This is a great text to read that, while over 90 years old, gives an accessible overview of many areas in physics and specifically gives good intuition behind entropy. It also has one of my favorite quotes:

The law that entropy always increases⎯the second law of thermodynamics⎯holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations⎯then so much the worse for Maxwell’s equations. If it is found to be contradicted by observations⎯well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.

The question that the second law of thermodynamics really addresses is not "why does the apple fall from the tree" but instead "why, having fallen from the tree, does the apple not leap back into the tree again ?". When you throw a stone into a pond it causes ripples which expand outwards. That is not mysterious. What is mysterious is that we never see ripples which converge on the stone and then project it back to your hand. That is what the second law of thermodynamics answers.

If you want to know how falling of an apple increases entropy, you can think about it like this: When an Apple falls, it interacts with the earth through the gravitational fields and thus force carriers are continuously exchanged between them. The re-arrangement of the net energy of system and force carriers makes it chaotic, thus entropy increases.

The same theory applies to electromagnetic forces of attraction and repulsion.

• This is incorrect. Force carriers being exchanged does not change the net energy of the system. Commented Jul 30, 2020 at 23:13