A proposal for exploring quantum theory in curved spacetime in lab

Gravity curves spacetime. In regions where the de Broglie wavelength is very small compared to the curvature of spacetime, the wave equations in flat spacetime can be generalized to curved spacetime. The validity of the formulation when the de Broglie wavelength becomes comparable to the curvature is an open question. To test these formulations experimentally, huge energy of the order of the Planck mass would be required. Euclideanized spacetime is used to model thermal systems. In this work, an equivalence between spatial variation of temperature in thermal baths and curvature of Euclideanized spacetime is propounded. The variation in temperature is recast as a variation in the metric. The Dirac equation is then solved in this curved Euclideanized spacetime. The curvature in Euclideanized spacetime can be obtained in Chromodynamic or Electromagnetic scale energies. If this equivalence is correct, it could provide a platform to experimentally explore quantum mechanics in curved spacetime.