I decided to interrupt what I had planned to write in order to address one issue I've been asked about over the weekend, specifically if a paper that appeared on arXiv in April 2014 titled "Cosmology from Quantum Potential" had shown the universe is eternal. One of the authors Ahmed Fang Ali is also the author of other another publications arguing that a speculative approach to quantum gravity called "Rainbow Gravity" lends further credence to pre-Big Bang eternal cosmologies.

The argument they make involves replacing geodesics in cosmology with the particle trajectories of Bohmian mechanics, these trajectories have certain properties that prevent their paths from crossing and so prevents them from forming an initial singularity.

Bohmian mechanics is an alternative to ordinary quantum theory that in addition to postulating a wave function that evolves according to some dynamic equation (Schrodinger, Dirac, Klein-Gordan etc,) posulates classical variables (coordinates on a phase space), like the position and momentum of individual particles, depending on the variant of the model, the particle trajectories are guided by either a force unique in the theory called the "quantum potential"

Physicists understand that Bohmian particles have "surrealist trajectors" that behave antithetical to how we'd expect from classical mechanics or intuition. The origin of this weird behaviour comes from the fact that Bohmian mechanics is contextual, the value an experimenter gets when they measure the spin of a particle depends on which component of the wave function it corresponds to and the device with which its measured. The particle cannot change which component its in, this combination makes Bohmian mechanics "first order deterministic" when mathematicians map these trajectories on a configuration space they cannot cross.

Singularity theorems in cosmology, from Penrose-Hawking onwards attempt to demonstrate that the paths of particles or "geodesics" terminate in the early universe due to the effects of gravity. They bunch in a tiny, infinitely dense region from which its impossible to extend the geodesic any further. The authors of the paper argue that if geodesics are replaced by Bohmian trajectories then they should "bounce" before forming a singularity and therefore you can extend spacetime indefinitely into the past.

They state ". . . the trajectories as opposed to geodesics do not converge and there is no counter part of geodesic incompleteness, or the classical singularity theorems, and singularities such as the big bang or big crunch are in fact avoided." The authors go on to add a quantum correction to the Raychaudhuri equation (QRE) which describes the evolution of a congruence of curves, from which they derive the second Friedman equation. With terms predicting the observed value of the cosmological constant and a radiation term eliminating the Big Bang singularity. This understanding of the QRE seems to me just bizarre. The equation is a kinematic equation, and yet the authors are using to describe dynamics. They only achieve these results by assuming that certain quantities in cosmology are identical to other parameters. For example they identify theta the expansion parameter with 3

The penultimate finding of their paper came when they inverted and integrated the Hubble constant. In astrophysics this gives you the age of the Universe

With the Bohmian correction added, they find that the inversion tends toward infinity. So the universe is geodesically complete and eternal. I have some concern that the correction they use for QRE cannot always be interpreted as "timelike" and refer to duration with the additional terms it may well have to flip into "spacelike" with a vector describing displacement, which serves to make the proposal unrealistic. I have however seen people apply Bohmian mechanics to cosmology before, for example Craig Callender and Robert Weingard convincingly solved the problem of time in quantum gravity within their model.

But I'm mostly sceptical in so far as I don't believe many physicists take Bohm's alternative very seriously. The interpretation is fraught with problems for example in standard quantum theory, one can only describe a system when the particles are travelling much slower than the speed of light and when none of the particles are decaying into other particles. For these special cases you describe the system in terms of fields using quantum field theory, which on a fixed space time background is determined by local physics with no dependence on the structure of space time globally, this requirement is equivalent to the principle of locality so it's important for a consistent unification with general relativity that our interpretation of quantum mechanics is also local. But Bohm's guidance wave equation is known to contain explicit non localities.

What's more is that Bohmian mechanics denies a lot of the symmetry, for the theory physicists have to pick out a preferred basis (momentum or position) in the Hilbert space which is unnatural. Picking out a particular field configuration is more natural for field theories. Furthermore due to the guidance equation the wave function causally influences the particles even though it's not modeled "in space" but the particles are causally effete in influencing the wave function. Because it's such a bizarre and at times nonsensical approach that breaks so many important principles physicists don't care for it very much. As I've argued before I believe the Consistent Histories approach is a much more natural interpretation for doing cosmology.

The argument they make involves replacing geodesics in cosmology with the particle trajectories of Bohmian mechanics, these trajectories have certain properties that prevent their paths from crossing and so prevents them from forming an initial singularity.

Bohmian mechanics is an alternative to ordinary quantum theory that in addition to postulating a wave function that evolves according to some dynamic equation (Schrodinger, Dirac, Klein-Gordan etc,) posulates classical variables (coordinates on a phase space), like the position and momentum of individual particles, depending on the variant of the model, the particle trajectories are guided by either a force unique in the theory called the "quantum potential"

**Q**or by the gradient of the phase of the wave function, which evolve according toPhysicists understand that Bohmian particles have "surrealist trajectors" that behave antithetical to how we'd expect from classical mechanics or intuition. The origin of this weird behaviour comes from the fact that Bohmian mechanics is contextual, the value an experimenter gets when they measure the spin of a particle depends on which component of the wave function it corresponds to and the device with which its measured. The particle cannot change which component its in, this combination makes Bohmian mechanics "first order deterministic" when mathematicians map these trajectories on a configuration space they cannot cross.

Singularity theorems in cosmology, from Penrose-Hawking onwards attempt to demonstrate that the paths of particles or "geodesics" terminate in the early universe due to the effects of gravity. They bunch in a tiny, infinitely dense region from which its impossible to extend the geodesic any further. The authors of the paper argue that if geodesics are replaced by Bohmian trajectories then they should "bounce" before forming a singularity and therefore you can extend spacetime indefinitely into the past.

They state ". . . the trajectories as opposed to geodesics do not converge and there is no counter part of geodesic incompleteness, or the classical singularity theorems, and singularities such as the big bang or big crunch are in fact avoided." The authors go on to add a quantum correction to the Raychaudhuri equation (QRE) which describes the evolution of a congruence of curves, from which they derive the second Friedman equation. With terms predicting the observed value of the cosmological constant and a radiation term eliminating the Big Bang singularity. This understanding of the QRE seems to me just bizarre. The equation is a kinematic equation, and yet the authors are using to describe dynamics. They only achieve these results by assuming that certain quantities in cosmology are identical to other parameters. For example they identify theta the expansion parameter with 3

*H*(Hubble constant) I don't see how this can be justified given that it leads to suspicious calculations.The penultimate finding of their paper came when they inverted and integrated the Hubble constant. In astrophysics this gives you the age of the Universe

But I'm mostly sceptical in so far as I don't believe many physicists take Bohm's alternative very seriously. The interpretation is fraught with problems for example in standard quantum theory, one can only describe a system when the particles are travelling much slower than the speed of light and when none of the particles are decaying into other particles. For these special cases you describe the system in terms of fields using quantum field theory, which on a fixed space time background is determined by local physics with no dependence on the structure of space time globally, this requirement is equivalent to the principle of locality so it's important for a consistent unification with general relativity that our interpretation of quantum mechanics is also local. But Bohm's guidance wave equation is known to contain explicit non localities.

The guidance wave equation connects the position of all particles and in this sense is said to be non local and requires us to pick out a preferred frame in which these signals propagate. In contradiction to the principle of relativity. Bohmian mechanics is also more complicated than standard theory because now we differentiate for the motion of particles following a classical trajectory as well as the additional evolution of the wave function described by the Schrodinger equation.

What's more is that Bohmian mechanics denies a lot of the symmetry, for the theory physicists have to pick out a preferred basis (momentum or position) in the Hilbert space which is unnatural. Picking out a particular field configuration is more natural for field theories. Furthermore due to the guidance equation the wave function causally influences the particles even though it's not modeled "in space" but the particles are causally effete in influencing the wave function. Because it's such a bizarre and at times nonsensical approach that breaks so many important principles physicists don't care for it very much. As I've argued before I believe the Consistent Histories approach is a much more natural interpretation for doing cosmology.

## Comments

## Post a Comment