# Is Gravity an Entropic Force?

## Abstract

**:**

## 1. Introduction

## 2. Verlinde’s Argument

## 3. Understanding Entropy Force

## 4. Why Gravity Is Not an Entropy Force

## 5. Further Discussions

## Acknowledgments

## References and Notes

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- In the polymer example, the energy of the polymer keeps constant when the entropic force does work (the energy for the work comes from the surrounding heat bath). This dissimilarity reconfirms the conclusion that the screen is not like a polymer.
- Interestingly, [25] showed that if gravity is an entropic force as Verlinde argued, then the Coulomb force should be also an entropic force. But it is well accepted that the Coulomb force is a fundamental interaction transferred by virtual photons. Besides, the directions of the entropic force and the Coulomb force are opposite for two charges with different signatures. This has been identified as the problem of negative electromagnetic temperature [25,26]. As we think, these apparent contradictions also suggest that the idea of gravity as an entropic force is probably wrong. In addition, this result can also be taken as a support for our conclusion that it is gravity (and the Coulomb force) that result in the entropy increase of the screen, not the contrary.
- Note that the energy of the screen only depends on the mass inside it and is irrelevant to the mass of the external particle. Moreover, the entropy of the screen does not include the entropy of gravitational field, and it is only the entropy of matter.
- As a result, the energy and entropy of the gravitational field correspondingly decrease during the process.
- It has been shown that this consistency also has a mathematical origin, and it is a consequence of the specific properties of solutions to the Poisson equation [26].
- Verlinde also discussed this large-distance situation and implicitly presented the right formula ([9], p.10).
- Verlinde also admitted that why his equations come out is because the laws of Newton have been ingredients in the steps that lead to black hole thermodynamics and the holographic principle (see [9], p.9). However, as we have argued, his attempt to reverse this argument was not successful.
- It has been recently claimed that Verlinde’s idea is supported by a mathematical argument based on a discrete group theory [27]. As we think, although the theory might provide a possible mathematical formulation of the holographical principle, it does not necessarily entail that gravity is an entropic force in physics. Besides, it is far from clear whether this formulation can naturally lead to general relativity and quantum field theory as two proper approximations.
- As we think, our physical analysis also applies to the similar arguments proposed by other authors (e.g., [5,6,7,8]). Like Verlinde, Jacobson did not explicitly state the causal relationship between energy flux and entropy change either, though his analysis was more rigorous than Verlinde’s [5]. It seems that Jacobson assumed the right causal chain, i.e., energy flux entropy change, as he said “the entropy is proportional to the horizon area” and “the area increase of a portion of the horizon will be proportional to the energy flux across it”. However, he also reached a similar conclusion that the Einstein equation is a thermodynamics equation of state [5].
- This fact should not surprise us very much, as the thermodynamics of gravitational systems such as a black hole are just derived in terms of general relativity and quantum field theory.
- The argument here might be regarded as a reverse application of the generalized uncertainty principle (see, e.g., [23,24]). But it should be stressed that the existing arguments for the principle are based on the analysis of measurement process, and their conclusion is that it is impossible to measure positions to better precision than a fundamental limit. On the other hand, in the above argument, the position uncertainty or localization length of a particle is objective and real, and the discreteness of spacetime requires that the objective length has a minimum value, which is independent of measurement.
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Gao, S.
Is Gravity an Entropic Force? *Entropy* **2011**, *13*, 936-948.
https://doi.org/10.3390/e13050936

**AMA Style**

Gao S.
Is Gravity an Entropic Force? *Entropy*. 2011; 13(5):936-948.
https://doi.org/10.3390/e13050936

**Chicago/Turabian Style**

Gao, Shan.
2011. "Is Gravity an Entropic Force?" *Entropy* 13, no. 5: 936-948.
https://doi.org/10.3390/e13050936