Emergent physics on Mach's principle and the rotating vacuum

G. Jannes^{+}, G. E. Volovik^{*×}

^{+}Modelling & Numerical Simulation Group, Universidad Carlos III de Madrid, 28911 Leganés, Spain

^{*}Low Temperature Laboratory, Aalto University, P.O. Box 15100, FI-00076 Aalto, Finland

^{×}Landau Institute for Theoretical Physics of the RAS, 119334 Moscow, Russia

**Abstract**

Mach's principle applied to rotation can be correct if one takes
into account the rotation of the quantum vacuum together with the Universe.
Whether one can detect the rotation of the vacuum or not depends on its
properties. If the vacuum is fully relativistic at all scales, Mach's
principle should work and one cannot distinguish the rotation: in the
rotating Universe+vacuum, the co-rotating bucket will have a flat surface
(not concave).
However, if there are "quantum gravity" effects which violate Lorentz
invariance at high energy, then the rotation will become observable.
This is demonstrated by analogy in condensed-matter systems, which consist
of two subsystems: superfluid background (analog of vacuum) and
"relativistic" excitations (analog of matter). For the low-energy
(long-wavelength) observer the rotation of the vacuum is not observable. In the
rotating frame, the "relativistic" quasiparticles feel the background as a
Minkowski vacuum, i.e. they do not feel the rotation. Mach's idea of the
relativity of rotational motion does indeed work for them. But rotation
becomes observable by high-energy observers, who can see the quantum gravity
effects.