of thermodynamics, allowing perpetual motion machines [@Dubovsky; @Eling].

Principle of equivalence \[equiv\]
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The principle of equivalence takes a number of different guises, not all exactly equivalent. For our purposes, the most relevant version is the universality of free fall, with its implication that all forms of matter couple to gravity with equal strength. As Feynman emphasized [@Feynman], this universality implies a spin two graviton: energy falls with the same acceleration as mass, and the unique Lorentz covariant combination of mass and energy density, the stress-energy tensor, couples to spin two. A model of emergent gravity must thus ensure that

1.  only one massless spin two field is relevant;

2.  this field couples with equal strength to all matter;

3.  any spin zero or spin one components of the interaction are absent or strongly suppressed. (In some models [@Zhang], higher spin interactions must also be suppressed.)

The principle of equivalence is extremely well tested from millimeter to Solar System distances [@Will; @EotWash], so while the very short and long distance behavior may differ, these requirements are quite strong.

In type I models, the would-be gravitational degrees of freedom typically have no initial connection to the geometry; their role as a 