A clever new paper explores the notion that the reduced Planck's constant in the quantum analogy to Newton's constant for macroscopic quantities though a hybrid quantity that generalized the Compton wavelength and the Schwarzschild radius. This allows for a linkage between the Einstein equations and the Dirac equation.(adsbygoogle = window.adsbygoogle || []).push({});

Tejinder P. Singh, "A new length scale, and modified Einstein-Cartan-Dirac equations for a point mass" (May 15, 2017). We have recently proposed a new action principle for combining Einstein equations and the Dirac equation for a point mass. We used a length scale LCS, dubbed the Compton-Schwarzschild length, to which the Compton wavelength and Schwarzschild radius are small mass and large mass approximations, respectively. Here we write down the field equations which follow from this action. We argue that the large mass limit yields Einstein equations, provided we assume wave function collapse and localisation for large masses. The small mass limit yields the Dirac equation.

We explain why the Kerr-Newman black hole has the same gyromagnetic ratio as the Dirac electron, both being twice the classical value.

The small mass limit also provides compelling reasons for introducing torsion, which is sourced by the spin density of the Dirac field. There is thus a symmetry between torsion and gravity: torsion couples to quantum objects through Planck's constant ℏ (but not G) and is important in the microscopic limit. Whereas gravity couples to classical matter, as usual, through Newton's gravitational constant G (but not ℏ), and is important in the macroscopic limit.

We construct the Einstein-Cartan-Dirac equations which include the length LCS. We find a potentially significant change in the coupling constant of the torsion driven cubic non-linear self-interaction term in the Dirac-Hehl-Datta equation.We speculate on the possibility that gravity is not a fundamental interaction, but emerges as a consequence of wave function collapse, and that the gravitational constant maybe expressible in terms of Planck's constant and the parameters of dynamical collapse models.

The initial insight is that:

What do folks think? Compton wavelength and Schwarzschild radius for a point mass m have a peculiar relation to each other, in that their product remains constant at the square of Planck length, as the value of m is changed. Compton wavelength dominates Schwarzschild radius in the quantum regime m < m_{Pl,}and vice versa in the classical regime m > m_{Pl.}It seems a reasonable possibility that these two lengths are limiting cases of a unified expression for one length depending on mass, and having a minimum at around Planck length L_{Pl.}

Are they onto something or too clever by half?

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# I Is Gravity Dynamically Emergent From Wave Function Collapse?

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