Entropische Gravitation

Verlinde's statistical description of gravity as an entropic force leads to the correct inverse square distance law of attraction between classical bodies.

Entropic gravity is a hypothesis in modern physics that describes gravity as an entropic force; not a fundamental interaction mediated by a quantum field theory and a gauge particle (like photons for the electromagnetic force and gluons for the color force), but a probabilistic consequence of physical systems' tendency to increase their entropy. The proposal has been intensely contested in the physics community but it has also sparked a new line of research into thermodynamic properties of gravity.

Origin

The probabilistic description of gravity has a history that goes back at least to research on black hole thermodynamics by Bekenstein and Hawking in the mid-1970s. These studies suggest a deep connection between gravity and thermodynamics, which describes the behavior of heat and gasesVorlage:Fact. In 1995, Jacobson demonstrated that the Einstein field equations describing relativistic gravitation can be derived by combining general thermodynamic considerations with the equivalence principle. Subsequently, other physicists began to explore links between gravity and entropy.

Erik Verlinde's theory

In 2009, Erik Verlinde disclosed a conceptual model that describes gravity as an entropic force. On January 6, 2010 he published a preprint of a 29 page paper titled On the Origin of Gravity and the Laws of Newton. The paper was published in the Journal of High Energy Physics in April 2011. Reversing the logic of over 300 years, it argued that gravity is a consequence of the "information associated with the positions of material bodies". This model combines the thermodynamic approach to gravity with Gerardus 't Hooft's holographic principle. It implies that gravity is not a fundamental interaction, but an emergent phenomenon which arises from the statistical behavior of microscopic degrees of freedom encoded on a holographic screen. The paper drew a variety of responses from the scientific community. Andrew Strominger, a string theorist at Harvard said “Some people have said it can’t be right, others that it’s right and we already knew it — that it’s right and profound, right and trivial."

In July 2011 Verlinde presented the further development of his ideas in a contribution to the Strings 2011 conference, including an explanation for the origin of dark matter.

Verlinde's article also attracted a large amount of media exposure, and led to immediate follow-up work in cosmology, the dark energy hypothesis, cosmological acceleration, cosmological inflation, and loop quantum gravity. Also, a specific microscopic model has been proposed that indeed leads to entropic gravity emerging at large scales.

Criticism and experimental tests

Verlinde's proposal makes a number of assumptions about the microscopic foundations of space-time, the most important of which is that the degrees of freedom that are leading to the emergence of gravity can be enumerated on holographic screens, the surface of which contains all relevant physical information about the volume they enclose. Using a very straight forward argument about the entropy contained on these screens and the change to this entropy in the presence of masses, he then proceeds to derive the consequences of thermodynamics for masses contained in these volumes, which allows him to derive Newtonian gravity, as well as the equations of general relativity.

Logically this line of argument is similar to the derivation of classical mechanics from Newton's Laws or from an equivalent variational principle, as it is done in standard textbooks on classical mechanics, or the derivation of the consequences of Lorentz Invariance by Einstein, which lead to the predictions of special relativity. The essential difference between Entropic Gravity and established theories like classical mechanics and relativity is that no experimental evidence for or against the concept of holographic screens exists, while all the axioms of classical mechanics and relativity have been very thoroughly vetted by observations and precision experiments.

Since Verlinde's derivation does not predict any new physics, its assumptions and methods of derivation are essentially equivalent to existing physical theories, the most important of which is General Relativity. Except for non-trivial technical questions relating to the mathematical details of the derivation, it can therefore be understood as an interpretation of General Relativity in terms of information on holographic screens.

Early attempts at criticizing Entropic Gravity with experiments, like e.g. in the paper by Archil Kobakhidze on the basis that it fails to explain gravitational bound states of neutron observed in the experiments with ultracold neutrons completely fail to treat it for what it is, a re-interpretation of existing, experimentally well tested theories, in new terms. Kobakhidze's conclusions were disputed in a follow-up paper. and Chaichian, Oksanen and Tureanu deliver much better technical arguments with respect to omissions in the hand-waving nature of Verlinde's original paper. In a recent paper Kobakhidze argues that the counter to his argument against entropic gravity is invalid, but fundamentally misses the point, again, since he invalidates only his own assumption of what holographic screens mean in Schroedinger Quantum Mechanics, which, by definition, is not a suitable framework for the analysis of gravity, as it can not incorporate the effects of curved space-time on quantum systems.

A much more profound criticism of Entropic Gravity in the Newtonian limit based on technical grounds was given by Matt Visser in . He derives general mathematical properties of entropy and temperature functions as used in Verlinde's model for the case of conservative forces in classical mechanics. The main result of his general analysis allows for the modeling of wide classes of conservative forces, at the cost of mostly non-physical entropy and temperature functions. He comes to the conclusion that Verlinde's analysis bypasses these problems by reducing the general case to single particle scenarios, highly symmetric potentials and special choices of holographic screens. But he notes that even in the case of inverse square laws, generalized entropic force formulas lead to physically undesirable requirements, negating most of the potential advantages of Verlinde's proposal. He concludes

"There is no reasonable doubt concerning the physical reality of entropic forces, and no reasonable doubt that classical (and semi-classical) general relativity is closely related to thermodynamics [52–55]. Based on the work of Jacobson [1–6], Padmanabhan [7– 12], and others, there are also good reasons to suspect a thermodynamic interpretation of the fully relativistic Einstein equations might be possible. Whether the specific proposals of Verlinde [26] are anywhere near as fundamental is yet to be seen — the rather baroque construction needed to accurately reproduce n-body Newtonian gravity in a Verlinde-like setting certainly gives one pause."

Visser's criticism does, however, not address entropic gravity as a source of curved space-time, which requires a different mathematical treatment from that relating to conservative forces and classical potentials.

An example of the intense debate that Verlinde has provoked is "Comments on and Comments on Comments on Verlinde's paper 'On the Origin of Gravity and the Laws of Newton'"

On one hand, even a workable Entropic Gravity model shares the fate of all currently untestable models, which are judged by the physics community based on personal preferences and technical arguments (which nature may or may not respect), it does, however, have a major advantage over e.g. quantum field theories of gravity because of its extreme simplicity, which allows for rapid progress in the exploration of the basic idea behind it. Similar examples of conceptually very clean and simple descriptions for complex phenomena can be found in e.g. the Landau Theory of second order phase transitions, which can be used very successfully to describe and explore many types of systems without the need for complete microscopic models. Landau Theory does, however, not remove the necessity for the extremely complex microscopic treatment of phase transitions in general, which very much resembles and is deeply related to quantum field theory problems. Similarly one can not expect Entropic Gravity to provide all the answers to what the actual microscopic origins of the degrees of freedom on holographic screens is, should they turn out to be part of an experimentally supported mesoscopic description of space-time. The hope expressed by Verlinde and other protagonists of this approach is that it is sufficiently powerful to motivate the physics community to invest in research into space-time and gravity as emerging phenomena, which would be a strong deviation from the quantum field and string approach that has dominated the last half century of research.

See also

• Entropic elasticity of an ideal chain
• Entropic force
• Gravitation
• Induced gravity

Further reading

• It from bit - Entropic gravity for pedestrians, J. Koelman
• Gravity: the inside story, T Padmanabhan