Erik Verlinde is a String Theorist who recently proposed a theory of gravitation as an emergent entropic force, the entropy being a function of the information stored on holographic screens in higher-dimensional space-time. For the moment, just nod along. A lot of people don't think it makes much sense. According to Verlinde, gravity isn't a fourth fundamental force, it's a consequence of something else. The catch is that his something else is an extended metaphor rather than physics. To see why, we have to have a swift tour of some technical philosophy.
There's distinction between a physical property and a defined property. A physical property is one that exists even if there is no-one or nothing there to measure it: size, weight, mass, electric charge, velocity, being an oxygen atom. A defined property is one that someone needed to think up and define a way of measuring: temperature, decibels, lumens, colour, information, entropy. Many of our physical theories are there to link defined properties with physical ones. We have a theory of temperature as the movement of atoms and molecules, which causes our feelings of hot or cold and makes, amongst other things, thermometers work they way they do. Defined properties don't happen in the world if there are no measurers or definers. If there is no-one to feel the heat, is the kitchen hot? No, but it is full of molecules whizzing all over the place. If a tree falls in the forest and there's no-one there, does it make a sound? No, but it does create a pressure wave in the air (which would be a sound if there was someone there who wasn't deaf). Hold this distinction in mind for a moment.
There are laws of physics, nice-to-have-regularites, models and theorems with empirical content. A nice-to-have-regularity is the one about the speed of sound at sea level on a normal day, or how much effort it takes to cut a wire with a good set of pliers. It's what makes our world predictable and manageable - because you can have a chaotic world that obeys the laws of nature (the atmospheres of Jupiter or Venus, the surface of the Sun). Chemical reactions are nice-to-have regularities. A model is, for instance, Euler's equation for the bending of a beam (the only known instance of a useful fourth-degree differential equation). It starts with assumptions, draws a conclusion and when you measure everything, it works out. A theorem with empirical content is, for instance, information theory and thermodynamics: the terms are defined into existence, and methods of measuring them created to make sure the theorems are true: what you can't guarantee is that the results are useful and interesting. This leaves the laws of physics: these hold all the time, everywhere about everything, and for that reason, they are local and position-indifferent: most laws of physics are equivalent to an instance of the principle of least action.
The laws of physics have to be about physical properties - because they describe how the universe behaves everywhere and all the time, before anyone arrived to define sound, colour or entropy. Models, regularities and theorems with content can be about physical and / or defined properties. Nature doesn't give a hoot about defined properties - we do, cats do, but the dumb stuff that make up us and cats doesn't. Nature works on physical properties.
Verlinde is suggesting that gravity is not a fundamental force, but a consequence of other physical processes: like water pressure, which is a consequence of the mass and velocity of a large number of water molecules. Except his explanation doesn't involve any actual physical properties. Because information, entropy and holographic screens are not physical properties and processes.
Start with "information". As used in these contexts, this is -log(p(x)), where p(x) is the the probability of the event x. The lower the probability, the more information we have when it happens. Probability here is defined in the frequentist sense, as the long-run proportion of the event x happening. Here's where we hit a subtle point: frequencies are "objective" because the counts are a matter of fact, but they are not a physical property of any system, rather, they are the result of the physical properties of that system. The 50% chance of getting heads flipping a fair coin is not a physical property of the coin (and the flipper), it's a consequence of the fact that the centre of gravity of the coin is right in the middle (and of the fact that the flipper picks a random point to apply the force). Taking a mathematical function of a defined property just creates another defined property, so "information" is a defined property.
Entropy is as defined a property as you can get. Whereas the physical explanation of temperature is about the movement and vibration of molecules (physical properties), the physical explanation of entropy is as the proportion of permutations of the particles in a system that leaves certain properties (for instance, its energy and temperature) unchanged: the higher the proportion, the lower the entropy of that state.
The idea of an "entropic force" is that if we subject a system to a slight perturbation, there is a higher probability that it will return to a lower-entropy state than remain in a higher-entropy state. On the outside, this looks like a force - but it isn't. Because the system will remain in the new configuration unless an actual force dislodges it - and that force isn't Nature saying to herself "gee, there are more probable configurations than this one, so I'd better change to one of them". The force is something that, ultimately, will resolve down to lots of quantum mechanics and electromagnetism.
This doesn't mean you can't write down a bunch of equations to define an entropic force and then get gravity out of them - Verlinde does and there's nothing wrong with his maths - though you may find his assumption of some abstruse Black-Hole theory physics less than "first principles". It does mean that those equations might not describe actual physical properties and hence don't describe what happens in Nature. It's the difference between, say, Quantum Mechanics, which tells you not only what the properties of a system are but also why your measuring instruments work for that system, and thermodynamics, which describes the relationships between measurable properties of a system but does not describe what's going on in that system to cause those measurements.
That's what's wrong with Verlinde's paper: there's a lot of mathematics but no actual physics. You can't say "gravity is not a fundamental force, and to prove it I'm going to give you an explanation of it in terms of other things that aren't fundamental forces either". The cutest moment is when he cites the AdS/CFT correspondence and Black Hole theory as "evidence". Last time I looked, speculative physics was neither empirical nor true and so could not be "evidence".
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