But *a Bohm ‘trajectory’ is the average of an ensemble of actual individual stochastic Feynman paths*
@philipthrift On Saturday, August 24, 2019 at 2:18:34 PM UTC-5, Brent wrote: > > > > On 8/24/2019 6:11 AM, Philip Thrift wrote: > > > The "quantum potential" should be approached instead via > > > But Feynman paths can cross. > > Brent > > > *Feynman Paths and Weak Values* > Robert Flack, Basil J. Hiley > > https://pdfs.semanticscholar.org/5e42/85d4e8ca27499a0e6a3b24e5d4b5111bb40d.pdf > (Published in Entropy 2018) > > There has been a recent revival of interest in the notion of a > ‘trajectory’ of a quantum particle. In this paper, we detail the > relationship between Dirac’s ideas, Feynman paths and the Bohm approach. > The key to the relationship is the weak value of the momentum which Feynman > calls a transition probability amplitude. With this identification we are > able to conclude that a Bohm ‘trajectory’ is the average of an ensemble of > actual individual stochastic Feynman paths. This implies that they can be > interpreted as *the mean momentum flow of a set of individual quantum > processes* and not the path of an individual particle. (This enables us > to give a clearer account of the experimental two-slit results of Kocsis et > al.) > > The approach outlined in this paper shows that the basic assumption made > in Bohmian mechanics, namely, that each particle follows one of the > ensemble of ‘trajectories’ (calculated by Philippidis et al.) cannot be > maintained. *Rather the trajectories should be interpreted as a > statistical **average of the momentum flow of a basic underlying > stochastic process.* > > > @philipthrift > > > > On Saturday, August 24, 2019 at 5:59:53 AM UTC-5, Lawrence Crowell wrote: >> >> One obvious possible problem is that this employs Bohm QM. If you take >> the Klein-Gordon equation and do the Bohm calculation you find that the >> putative particle moves faster than light.This is one reason it is so >> commonly said Bohm QM is not compatible with special relativity. Then to >> try to work with general relativity is going to be a far bigger tangle to >> work through. >> >> LC >> >> On Saturday, August 24, 2019 at 2:53:06 AM UTC-5, Philip Thrift wrote: >>> >>> >>> >>> https://arxiv.org/abs/1404.3093 : >>> >>> *Cosmology from quantum potential* >>> Ahmed Farag Ali, Saurya Das >>> >>> *It was shown recently that replacing classical geodesics with quantal >>> (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri >>> equation (QRE). In this article we derive the second order Friedmann >>> equations from the QRE, and show that this also contains a couple of >>> quantum correction terms, the first of which can be interpreted as >>> cosmological constant (and gives a correct estimate of its observed value), >>> while the second as a radiation term in the early universe, which gets rid >>> of the big-bang singularity and predicts an infinite age of our universe.* >>> >>> >>> >>> >>> https://www.physics-astronomy.org/2019/08/no-big-bang-quantum-equation-predicts.html >>> >>> *No Big Bang? Quantum Equation Predicts Universe Has No Beginning* >>> >>> ... >>> >>> In their paper, Ali and Das applied these Bohmian trajectories to an >>> equation developed in the 1950s by physicist Amal Kumar Raychaudhuri at >>> Presidency University in Kolkata, India. Raychaudhuri was also Das's >>> teacher when he was an undergraduate student of that institution in the >>> '90s. >>> >>> Using the quantum-corrected Raychaudhuri equation, Ali and Das derived >>> quantum-corrected Friedmann equations, which describe the expansion and >>> evolution of universe (including the Big Bang) within the context of >>> general relativity. Although it's not a true theory of quantum gravity, the >>> model does contain elements from both quantum theory and general >>> relativity. Ali and Das also expect their results to hold even if and when >>> a full theory of quantum gravity is formulated. >>> >>> In addition to not predicting a Big Bang singularity, the new model does >>> not predict a "big crunch" singularity, either. In general relativity, one >>> possible fate of the universe is that it starts to shrink until it >>> collapses in on itself in a big crunch and becomes an infinitely dense >>> point once again. >>> >>> Ali and Das explain in their paper that their model avoids singularities >>> because of a key difference between classical geodesics and Bohmian >>> trajectories. Classical geodesics eventually cross each other, and the >>> points at which they converge are singularities. In contrast, Bohmian >>> trajectories never cross each other, so singularities do not appear in the >>> equations. >>> >>> In cosmological terms, the scientists explain that the quantum >>> corrections can be thought of as a cosmological constant term (without the >>> need for dark energy) and a radiation term. These terms keep the universe >>> at a finite size, and therefore give it an infinite age. The terms also >>> make predictions that agree closely with current observations of the >>> cosmological constant and density of the universe. >>> >>> In physical terms, the model describes the universe as being filled with >>> a quantum fluid. The scientists propose that this fluid might be composed >>> of gravitons—hypothetical massless particles that mediate the force of >>> gravity. If they exist, gravitons are thought to play a key role in a >>> theory of quantum gravity. >>> >>> In a related paper, Das and another collaborator, Rajat Bhaduri of >>> McMaster University, Canada, have lent further credence to this model. They >>> show that gravitons can form a Bose-Einstein condensate (named after >>> Einstein and another Indian physicist, Satyendranath Bose) at temperatures >>> that were present in the universe at all epochs. >>> >>> Motivated by the model's potential to resolve the Big Bang singularity >>> and account for dark matter and dark energy, the physicists plan to analyze >>> their model more rigorously in the future. Their future work includes >>> redoing their study while taking into account small inhomogeneous and >>> anisotropic perturbations, but they do not expect small perturbations to >>> significantly affect the results. >>> >>> "It is satisfying to note that such straightforward corrections can >>> potentially resolve so many issues at once," Das said. >>> >>> >>> (The cosmos is made of fluid? So Thales was right.) >>> >>> @philipthrift >>> >> > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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