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
<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
<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
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