Abstract We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schrödinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub-Planckian phenomenology.
Abstract We show that quantum fluids enable experimental analogs of relativistic orbital precession in the presence of non-paraxial effects. The analysis is performed by the hydrodynamic limit of the Schrödinger equation. The non-commutating variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is formally identical to the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton’s theory. In our case, the corrections are due to the modified uncertainty principle. The results may enable novel relativistic analogs in the laboratory, also including sub-Planckian phenomenology.
Modified uncertainty principle and non-commutative variables may phenomenologically account for quantum gravity effects, independently of the considered theory of quantum gravity. We show that quantum fluids enable experimental analogs and direct tests of the modified uncertainty principle expected to be valid at the Planck scale. We consider a quantum clock realized by a long-lasting quantum fluid wave-packet orbiting in a trapping potential. We investigate the hydrodynamics of the Schrödinger equation encompassing kinetic terms due to Planck-scale effects. We study the resulting generalized mechanics and validate the predictions by quantum simulations. Wave-packet orbiting generates a continuous amplification of the quantum gravity effects. The non-commutative variables in the phase-space produce a precession and an acceleration of the orbital motion. The precession of the orbit is strongly resembling the famous orbital precession of the perihelion of Mercury used by Einstein to validate the corrections of general relativity to Newton's theory. In our case, the corrections are due to the modified uncertainty principle. The results can be employed to emulate quantum gravity in the laboratory, or to realize human-scale experiments to determine bounds for the most studied quantum-gravity models and probe Planckian physics.
Abstract In general relativity, the dynamics of objects is governed by the curvature of spacetime, which is caused by the presence of matter and energy. In contrast, in quantum mechanics, the dynamics is governed by the wavefunction, which completely describes the behavior of the particles. There is an ongoing effort to explore analogs of space and spacetime curvature in the context of quantum mechanics. Such analogies may reveal a deeper structure of quantum reality and its possible relations with Einstein’s theory of gravity. In this note, by coupling the non-relativistic Schrödinger equation with the heat equation and using the hydrodynamical formulation of quantum mechanics, we find that the dynamics of the particle is fully characterized by the normalized curvature of the wavefunction’s amplitude. Such a curvature obtains an analogy to the Ricci curvature of curved space in a Riemannian manifold. The proposed geometric correspondence provides a new pathway to explore quantum dynamics through the lens of differential geometry, the language of general relativity.
We show that quasi-paraxial fluids of light propagating in nonlinear Kerr media naturally experience an effective gauge field arising from the intrinsic spin-orbit interaction of light encoded in Maxwell equations. By deriving the leading nonparaxial corrections to the nonlinear Schrödinger equation governing the fluid evolution, we find that, for circularly polarized beams, these corrections generate an effective Lorentz force that modifies the fluid dynamics. Remarkably, the corresponding gauge field is not externally imposed but self-consistently generated by the fluid itself, with its sign controlled by the light helicity and its magnitude governed by the spatial variations of the nonlinear refractive index. We illustrate the physical consequences of this gauge field in two configurations: the chiral deformation of normal and superfluid flows past an obstacle, accompanied by a transverse spin Hall force, and the cumulative precession of an optical wave packet trapped in a focusing fluid.
Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper examines under which conditions a classical fluid model may reproduce the simplest formulations of both theories. By identifying the angular momentum of irrotational vortices in an inviscid, barotropic, isothermal fluid with sound speed c with the reduced Planck constant, and incorporating Korteweg capillary stress, a complex wave equation describing the momentum and continuity fields of a vortex is obtained. When uniform convection is introduced, the weak field approximation of this wave equation is equivalent to Schrödinger’s equation. The model is shown to yield classical analogues for de Broglie wavelength, the Einstein–Planck relation, the Born rule and the uncertainty principle. Accounting for the retarded propagation of the wavefield of a vortex in convection yields the Lorentz transformation and the Klein–Gordon equation, with Schrödinger’s equation appearing as the low-Mach-number limit. These results demonstrate that, under explicit assumptions, a classical continuum can reproduce quantum and relativistic theory in their simplest form, without assuming the postulates principal to those theories.
In this paper, the deformed Special Relativity, which leads to an essentially new theoretical context of quantum mechanics, is presented. The formulation of the theory arises from a straightforward analogy with the Special Relativity, but its foundations are laid through the hypothesis on breakdown of the velocity-momentum parallelism which affects onto the Einstein equivalence principle between mass and energy of a relativistic particle. Furthermore, the derivation is based on the technique of an eikonal equation whose well-confirmed physical role lays the foundations of both optics and quantum mechanics. As a result, we receive the angular deformation of Special Relativity which clearly depicts the new deformation-based theoretical foundations of physics, and, moreover, offers both constructive and consistent phenomenological discussion of the theoretical issues such like imaginary mass and formal superluminal motion predicted in Special Relativity for this case. In the context of the relativistic theory, presence of deformation does not break the Poincaré invariance, in particular the Lorentz symmetry, and provides essential modifications of both bosons described through the Klein-Gordon equation and fermions satisfying the Dirac equation. On the other hand, on the level of discussion of quantum theory, there arises the concept of emergent deformed space-time, wherein the presence of angular deformation elucidates a certain new insight into the nature of spin, as well as both the Heisenberg uncertainty principle and the Schrödinger wave equation.
It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudo-spin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analogue systems. While this result is general, present day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as 87Rb, 7Li, 14K (Newton-Cartan), and 23Na (Einstein-Hilbert).