### Entropic Gravity

October 26, 2010 Isaac Newton witnessed the falling of an apple and he was inspired to formulate his theory of universal gravitation. Despite the popular myth, the apple didn't hit him in the head physically. It only hit him in the head "physics-ally." His theory was published in his 1687 book, Philosophiae Naturalis Principia Mathematica, known simply as "Principia." In the Principia, Newton "explained" gravity in one sense, by giving equations that predict its manifestation. He didn't explain gravity in the other sense; that is, what caused gravity. By way of excuse, he gave the following:"I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. In this philosophy particular propositions are inferred from the phenomena, and afterwards rendered general by induction." [1,2]All this was written in Latin, and the phrase, Hypotheses non fingo, "I do not feign hypotheses," is often translated as "I frame no hypothesis." I mentioned all this in a previous article (The Mind in the Thermostat, September 13, 2007) in which I wrote that this phrase has set the tenor of physics since Newton's time. Physics is the generalization of phenomena, usually via mathematics, and explanations of what causes these phenomena are not required. Gravity is a very strange force. First, it's always attractive; and, second, it's extremely weak. When you think about gravitation, you need to think also about mass. The Large Hadron Collider has been built principally to detect the Higgs Boson, the particle in the Standard Model that gives particles their mass. This explains mass only in the first sense; but that's the type of explanation that physicists have become accustomed to. A novel way of looking at gravity was introduced in 1995 by Theodore Jacobson of the University of Maryland. Jacobson was able to formulate the same relativistic gravitation equations as Einstein by combining thermodynamics and the equivalence of inertial mass and gravitational mass (the equivalence principle).[3] Lee Smolin of the Perimeter Institute for Theoretical Physics, who's controversial in his own right for publication of "The Trouble With Physics,"[4] is quoted in the New York Times as saying that Jacobson's paper is "one of the most important papers of the last 20 years."[5] Jacobson's insight didn't come out of the blue, since Stephen Hawking and Jacob Bekenstein had proposed several decades before that there's a fundamental connection between thermodynamics and the most spectacular manifestations of gravity known, black holes. They conjectured that all the information lost to the universe when matter falls into a black hole is actually still contained at the event horizon that surrounds it. This is known as the holographic principle, since something that's three-dimensional has been encoded in two dimensions, just like a laser holograph in an optics laboratory. Ludwig Boltzmann had much earlier found the connection between information and thermodynamic entropy.

*Artist's representation of matter accretion by a black hole (NASA)*

Then, early this year, Erik Verlinde a Dutch theoretical physicist at the University of Amsterdam, published an lengthy paper on the arXiv physics preprint server entitled, "On the Origin of Gravity and the Laws of Newton."[6] Verlinde's proposal is that gravity is not a force, but merely an expression of the thermodynamic imperative that the universe seeks a more disordered state. From our four-dimensional viewpoint, this looks like a force, but the prime mover is something much more fundamental. As Verlinde states in the abstract to his paper,

"Gravity is explained as an entropic force caused by changes in the information associated with the positions of material bodies."If all this sounds a little fuzzy, join the club. Physicists are still debating what all this means, exactly, and I'm not about to match wits with a string theorist.[7-9] If you're looking for a current example of Thomas Kuhn's paradigm shifting, this might be it. A paradigm shift seems to be needed. Two cosmic manifestations of gravitational significance, dark energy, which is pulling the universe apart, and dark matter, which holds galaxies together, are presently unexplained. Thanu Padmanabhan of the Inter-University Centre for Astronomy and Astrophysics, University of Pune, India, and one of the commentators on Verlinde's arXiv paper,[7] is quoted in the New York Times as saying that Verlinde's entropic force idea lacked mathematical rigor.[5] Verlinde has posted what amounts to an FAQ site for his paper,[10] and it will be interesting to see how this entropic gravity idea develops.

### References:

- I. Bernard Cohen and Anne Whitman, translators, "Philosophiae Naturalis Principia Mathematica, General Scholium (Isaac Newton)," Third edition, University of California Press (1999, ISBN 0-520-08817-4), p. 943. Latin facsimile of the entire edition is available here.
- "Rationem vero harum gravitatis proprietatum ex phaenomenis nondum potui deducere, & hypotheses non fingo. Quicquid enim ex phaenomenis non deducitur, hypothesis vocanda est; & hypotheses seu metaphysicae, seu physicae, seu qualitatum occultarum, seu mechanicae, in philosophia experimentali locum non habent. In hac philosophia propositiones deducuntur ex phaenomenis, & redduntur generales per inductionem."
- Ted Jacobson, "Thermodynamics of Spacetime: The Einstein Equation of State," arXiv Preprint Server, June 6, 1995).
- Lee Smolin, "The Trouble With Physics: The Rise of String Theory, The Fall of a Science, and What Comes Next," (Houghton Mifflin Harcourt, September 19, 2006), pp. 416.
- Dennis Overbye, "A Scientist Takes On Gravity," New York Times, July 12, 2010.
- ,Erik P. Verlinde, "On the Origin of Gravity and the Laws of Newton," arXiv Preprint Server, January 6, 2010.
- ,T.Padmanabhan, "Thermodynamical Aspects of Gravity: New insights," arXiv Preprint Server, January 19, 2010.
- ,Sheldon Gao, "Comment on 'On the Origin of Gravity and the Laws of Newton' by Erik P. Verlinde," arXiv Preprint Server, February 13, 2010.
- ,Sabine Hossenfelder, "Comments on and Comments on Comments on Verlinde's paper 'On the Origin of Gravity and the Laws of Newton'," arXiv Preprint Server, March 4, 2010.
- Erik Verlinde, Entropic forces and the 2nd law of thermodynamics (Web Site).

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Linked Keywords: Isaac Newton; universal gravitation; Philosophiae Naturalis Principia Mathematica; gravity; Hypotheses non fingo; phenomenon; mass; Large Hadron Collider; Higgs Boson; Standard Model; Theodore Jacobson; University of Maryland; relativistic gravitation equations; Einstein; thermodynamics; inertial mass; gravitational mass; equivalence principle; Lee Smolin; Perimeter Institute for Theoretical Physics; Stephen Hawking; Jacob Bekenstein; black holes; event horizon; holographic principle; laser holograph; Ludwig Boltzmann; Boltzmann's entropy formula; thermodynamic entropy; Erik Verlinde; Dutch; University of Amsterdam; arXiv physics preprint server; spacetime; four-dimensional; prime mover; string theorist; Thomas Kuhn; paradigm shift; dark energy; dark matter; galaxies; Inter-University Centre for Astronomy and Astrophysics; University of Pune; entropic gravity.

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