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On Grave Matters About Gravity

Gravity is the force law that acts universally on all forms of matter and energy. If something exists, it must gravitate. Furthermore, gravity exerts the same acceleration on objects of different masses and energies! A feather is pulled by the Earth with the same acceleration as is an elephant - even a rather large elephant with weight management issues. This is known as the "equivalence principle": the principle that the amount of stuff within an object - i.e. its inertial mass - is directly related to the amount that gravitates - i.e. its gravitational mass.

These universal aspects of gravity lead Einstein to propose that gravity is really not a force, but the result of distortions in distances in space. Since all objects have to sail through time and space in a universal way, if the fabric of space-time gets deformed, all things moving on it feel it and can get deflected through a common trajectory. This is the framework of General Relativity: gravity is the curvature of space-time itself; things appear to change course under a gravitational "force" simply because the fabric over which they move is distorted by nearby massive objects. The first video shows a cartoon of this idea. 

Very recently, the string theorist Erik Verlinde proposed an intriguing new perspective on gravity - one that further capitalizes on the universal character of this force law. Verlinde proposed that gravity may be a statistical effect, an entropic force - not a fundamental one akin to electromagnetism. He illustrates his proposal through an analogy with other known entropic effects such as osmosis or polymer dynamics.

In the second video, we see the well-known processes of diffusion and osmosis. When two different solutions of salt water of different concentrations are separated by a semipermeable membrane, over time the two sides equilibrate in salt density. The details of any fundamental force laws acting between the molecules of the water and salt are not important. The water from the less dense solution flows towards the higher density side for statistical reasons: the flow would maximize the level of disorder or entropy in the system (see previous post on the arrow of time). Simply put, the configuration of equilibrated uniform solutions is a more likely arrangement of water and salt molecules and hence will be attained eventually due to statistical considerations. We could be misled to think of this process as one driven by some force that pushes water from one side to the other. However, we should know that this "force" is not a fundamental one, but a fictitious one: it is statistically driven, a collective effect, entropic in origin. This was a larger dose of biology than I intended… so, let's quickly move onto the physics of gravity.

Verlinde proposes that gravity is also an entropic effect rather than a fundamental force law. This is motivated from recent results in string theory, but it can in fact be phrased in an independent and self-contained manner. The universal attributes of gravity encourage such a general scheme or interpretation. And recent suggestions from string theory about gravity having a "holographic" nature further bolster it (I'll write more about this in a future post). 

Verlinde's proposal may suggest that there is no reason to worry about developing a theory of quantum gravity - a rather elusive project of theoretical physics for decades that has only recently been realized within string theory. If gravity is a statistical effect, perhaps there is no sense to worry about its quantum realm at small distances - as much as we would want to worry about forces between molecules in a gas in an effort to understand osmosis. Hence also lies the problem with Verlinde's proposal. At the end of the day, this proposal amounts to the following curious observation: that gravity at large distances has all the hallmarks of a statistical effect. This is not inconsistent however with any microscopic formulation of gravity through string theory - nor does it preclude its need for understanding the small scale structure of space-time… The proposal is a statement about long distance gravity only. It is still an intriguing exercise since it attempts to identify a minimal set of independent physical principles that can realize the well-known long distance attributes of gravity from a statistical point of view.

So, the entropic proposal for gravity to me is simply an interesting story - with a great deal of elegance and pedagogical value. However, it is not a framework that can complete or replace a description of space-time at the smallest distances - a description of quantum gravity. Quoting the ghost of Niels Bohr from a century ago, the proposal is crazy - but it is not crazy enough to be correct…

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