The Khalatnikov lectures on superfluid 4He for students in 1967 at the Kapitza Institute led me to strange connection between superfluid hydrodynamics and general relativity. Later it turned out that in condensed matter it is possible to imitate not only general relativity (in the tetrad form), but also quantum electrodynamics with Weyl and Dirac fermions. The latter follows from the topological properties of the ground state of the system, which are similar in condensed matter and in quantum vacuum. Many different analogies between the condensed matter on one side and relativistic quantum fields and gravity on the other side have been collected in the book [1]. These analogies allowed study the problems of quantum vacuum, such as cosmological constant problem [2] and Hawking radiation [3]. There are several routes to general relativity. In particular, the elasticity theory with the distributed defects can be described in terms of the dimensionful tetrad field [4]. When these dimensionful elasticity tetrads are applied back to general relativity -- the so called superplastic vacuum [5] -- one obtains that the Ricci curvature scalar R, the gravitational Newton constant G, the cosmological constant Λ and masses of particles M become dimensionless [6]. The reason for that is that in the arbitrarily deformed superplastic vacuum, there is no equilibrium size of the elementary cell. Thus the microscopic length scale (such as Planck scale) is absent, and all the distances are measured in terms of the integer positions of the nodes in the crystal. Because of the suppression of dimensionality of physical parameters, the elasticity tetrads are appropriate for the description of the topological terms responsible for the 3+1 quantum Hall effect [6].

References
[1] G.E. Volovik, The Universe in a Helium Droplet, Oxford (2003).
[2] F.R. Klinkhamer and G.E. Volovik, Phys. Rev. D 78, 063528 (2008).
[3] G.E. Volovik, JETP Lett. 90, 1 (2009).
[4] I.E. Dzyaloshinskii and G.E. Volovik, Ann. Phys. 125, 67 (1980).
[5] F.R. Klinkhamer and G.E. Volovik, Pis’ma ZhETF 109, 369 (2019).
[6] J. Nissinen and G.E. Volovik, arXiv:1812.03175.