## Introduction

We now know all of the four fundamental forces of nature. The most universal of which is clearly gravity.

Gravity is intimately connected with the nature of space-time as explained by Einstein. At large distances, gravity dominates while at smaller scales, it is very weak. And thus it is considerably harder to combine gravity with quantum mechanics than other forces for a grand unified theory. The attempts to unify gravity with other forces at microscopic level may not be the right approach as it leads to many contradictions and paradoxes.

The second law of Thermodynamics states, “In any cyclic process the entropy will either increase or remain the same.” [1] Entropy is a measure of disorder or multiplicity of a system, or the amount of energy unavailable to do work. For an isolated system, the natural course of events takes it to a more disordered and higher entropic state.

Gravity, on the other hand, knows attraction only and thus tends to keep the things in orderly state by keeping them close to one another and thus reducing the volume occupied as well as the possibilities of the possible states.

In this paper, we try to draw a hypothesis on the relation between gravity and entropy, which is based on questions like “Do gravity and entropy complement each other?”, “Can one exist without the other?” and “Is there any common denominator between the two?”

We make the modern theory of “Entropic Gravity” our assumption, which states that gravity is an entropic force and not a fundamental interaction but a consequence of physical systems’ natural tendency to increase their entropy.

We conclude by stating a relation between entropy and gravity and discussing its implications.

**Fundamental Forces of Nature**

All the forces of nature can be simplified down to four most fundamental of forces, which are gravitational, electromagnetic, strong nuclear and weak nuclear. The holy grail of physicists has been to unify all of these forces in one all-encompassing theory, often termed as grand unified theory or theory of everything. It has not been possible to successfully unify gravity with the other three fundamental forces unified, which leads to the possibility that combining gravity with other forces at microscopic levels may not be the right approach after all.

**Entropic Force and Gravity**

Interest in the concept of entropic forces has risen considerably since 2011 when E. Verlinde proposed to interpret the force in Newton’s second law and gravity as entropic forces. An entropic force in a system is a force that results from the entire system’s thermodynamic tendency to increase its entropy, rather than from a particular underlying microscopic force. [2]

In statistical mechanics, entropic force is an effective macroscopic force that originates in a system with many degrees of freedom by the statistical tendency to increase its entropy. There is no fundamental field associated with entropic force

In 2009, Erik Verlinde argued that gravity can be explained as an entropic force. [3] He claimed that gravity is a consequence of the “information associated with the positions of material bodies”.

The entropy of a Black Hole can be computed by quantum gravity theories. From quantum gravity calculations, it turns out that the entropy of a Black Hole is proportional to the surface of its event horizon. [5]

**Space and Information**

Space gives meaning to position and momentum, which implies that space is a storage for information associated usually with matter. Considering the statistical view of entropy, the number of possibilities of micro-states of information depends on the size of the storage i.e. space considered.

For those that are technically inclined, the exact statistical definition is

Entropy = (Boltzmann’s constant k) x logarithm of number of possible states

Since the logarithm of a number always increases as the number increases, we see that the more possible states that the system can be in, the greater the entropy. In our case, the larger the space, the larger is the number of possible states and hence the greater is the entropy. Therefore, if an isolated system expands, its entropy increases.

## Entropy of the Expanding Universe

Modern cosmology states that the universe is accelerating and expanding continuously and therefore has its entropy being increased every moment. It is moving from a less entropic to a more entropic state. During this expansion, some particles may stumble upon one another and will have gravitational attraction between them, thus getting ordered. Entropy may decrease at that particular portion of space but it is at the expense of increase in entropy in its surroundings so that the net entropy increases. Moreover, as the universe is expanding, the effective gravity is decreasing (in accordance with Newton’s law of universal gravitation) because of increase in distances among matter.

**Gravity and Disorder**

Gravity tries to keep things together through attraction and thus tends to lower statistical entropy. The universal law of increasing entropy (2nd law of thermodynamics) states that the entropy of an isolated system which is not in equilibrium will tend to increase with time, approaching a maximum value at equilibrium. At equilibrium, entropy change is zero. If we assume the universe to be an isolated system, once it attains equilibrium i.e. maximum entropy, the gravity has to vanish from it altogether because if it does not, the entropy will start moving from high to low and time’s arrow will reverse. Another possibility is that the net effect of entropy due to gravity and the net effect of entropy because of expansion of the universe have to cancel each other at equilibrium, which is a rare possibility since the net effect of gravitational entropy is negligible as compared to the latter one.

**Gravity as an Outcome of Entropy**

If the first possibility is indeed true, the next question is: what triggers the gravity to disappear? Maximum entropy does that.

Considering the weak effect of gravitational entropy, the big bang, and the 13.8 billion years age of the universe [4], we say that gravity and entropy have a reciprocal existence, meaning that increase in one causes decrease in the other. And the universe, as we currently know it, is moving from lowest entropy and strongest gravity i.e. just before big bang toward highest entropy and weakest gravity. In other words, entropy was all gravity in the beginning and gravity is changing into entropy, and perhaps this change is called time or time’s arrow.

## Conclusion

We have claimed that entropy and gravity are one and the same thing i.e. they are inter-convertible, just like mass and energy are. But due to some reason, the conversion from gravity into entropy is or seems to be uni-directional, which we call time’s arrow. It gives rise to the question: will the time’s arrow reverse direction once maximum entropy is attained, revealing that it is a slow oscillation of inter-conversion between entropy and gravity? Will there be an anti big bang and another big bang after that? We do not know yet.

## 13 thoughts on “On the Relation of Entropy with Gravity”

The idea is very interesting! I also developed it in the previous years, unfortunately rarely in English, with few such notifications (from August 2016):

https://www.academia.edu/27650508/Entropy_and_Inertia

These days I wrote the book “Nature of Time – information of matter” (only in pdf file, internet, on Serbian, 290 pages, ), the physics and especially mechanics based on the principle of probability, information, and entropy, which has too many math. Its simpler version is the book “Space-time’’ recently published in Serbian, with a rough translation here:

https://www.scribd.com/document/349336253/Principles

I’d like to hear some opinions about that.

I found your paper very interesting. I have similar views concerning gravity and entropy.

I would say that these two terms are one and the same. Is it possible that the force of gravity is caused by the entropic energy variation of matter? Example: for the Earth; all of the atoms accelerating towards it’s center. * F = ma could be written: as the energy of matter tends to zero potential, it’s kinetic energy increases causing it to accelerate.

* replaced “force of gravity” by it’s cause: Ep (potential energy tends to zero).

This theory implies that the universe is accelerating because it’s energy content is transforming to reach zero potential. Could it be something like: Ep = ma and E = mc² being a limit?

Forces are the result of energy’s interactions.

The arrow of time, entropy increase, closed universe, no physical constants, curved space-time, conservation of energy, and cyclic universe are part of this theory.

Thank you for considering this and would appreciate your comments.

I thought maybe I would summarize my previous comments by stating that Gravity implies the weakening of the strong force with time.

May I add the following: The acceleration of a mass is the indication of it’s entropy. For example, the Earth has gone through warming and glaciation periods over it’s history. I would attribute this to the change in velocity of the solar system in it’s trajectory in the galaxy.

I hope If you don’t mind if I continue adding comments.

In this theory of entropy increase with time, the changing position of a body in space following the entropic arrow of time, defines it’s changing energy state. An atom at the surface of the Earth and one 100 km below (or above) the surface do not have the same energy state. The arrow of time points towards the center of a mass where potential energy and degrees of freedom tend to zero.

Another example would be a hydrogen atom at the surface of the Earth and one in the Sun. The Sun being the center of mass of the solar system.

This theory links space (Universe) with energy’s availability to do work with time. If the Big Bang had a definite amount of energy, then the universe is not infinite. The Universe’s volume changes with it’s entropy with time. For the Universe to be infinite, the amount of energy released at the moment of the Big Bang, would have needed to be infinite as well.

The conclusion of the WMAP results, a flat & infinite universe would be wrong according to this.

If I continue along these lines … an accelerated atom caused by it’s entropy change (aging Universe), produces a magnetic field which in turn is caused by the weakening of the strong force holding the nucleus together. The energy flow within the atom towards zero potential is what brings about electromagnetic forces (and magnetic fields). Therefore gravity (entropy) and electromagnetic forces are part of the same phenomenon.

The weakening of the strong force is what favors molecular bonding. This would explain why Earth’s atmosphere has a boundary.This would also be the reason for Plate tectonics: the accelerating atom moving towards the center of the Earth as it sheds energy in the process.

Observation: The helix shape of DNA has the same configuration than that of the motion of the planets’ helical path take around the sun as the solar system orbits the center of the galaxy. I would suggest that gravity (entropy) is the cause for both. The natural entropic motion of atoms with time.

The major points for the hypothesis of this theory:

1) Energy is the basic component in the universe.

2) There is a definite amount of energy in the universe (closed system).

3) An accelerating universe implies an irreversible change of it’s energy state with time.

4) The entropic change in energy state of the universe permits the evolution of any system within it. This results in the forces needed for life, planetary motion, etc.

– Gravity is a non-equilibrium force which allows the flow of energy from the atom to its surroundings.

This theory would have a different version from Einstein’s thought experiment: “what would it be like to ride alongside a lightbeam.”

If the environment you were in was accelerated to the speed of light due to higher entropy, the structural integrity of the atom would be compromised and therefore only energy would fill this part of space. You could not ride alongside a lightbeam.

The path that takes a subatomic particle after it’s collision in a particle accelerator and that of the motion of atoms moving towards the center of the galaxy is the same: a spiral towards zero potential energy. The spiral is entropy’s signature which indicates matter converting into energy with time. A fraction of a second for the particle and billions of years for the sun. The unravelling of the atom into disorganized energy is complete once it reaches the center of the galaxy.

Without the flow of energy from the atom, there would be no work performed, no motion, no change in the universe.