Please look into for satisfactory answer:

ISBN-13 978-1-4020-4025-2 (e-book).

@P. K. Karmakar: Could you please provide a title or a link to a place offering this e-book? On Amazon, Alibris, and Abebooks, and a few others, this ISBN yields no search results.

Thanks for further interest. The book reference is as follows.

R.W. Carroll, Fluctuations, Information, Gravity and the Quantum Potential (Springer, Netherlands, 2006).

Dear Mikael,

What you wrote:

So a microscopic system on the other hand, like an electron, can exist in more than one location until its space-time curvature separation reaches the collapse threshold, which could be a thousands of years from the emergence of its superposition.

Cannot be true because, among other things the conservation of the electric charge is lost.

Daniel Baldomir I appreciate your answer but would be happy if you could elaborate a bit more as to why you think so. Indeed, standard interpretation predicts violations of conservation laws... but exact decoherence fixes that, or do you think these kind of solutions to the conservation problem are flawed? Do you agree with any of the current interpretations of Quantum Mechanics, or do you think something is missing in all of them? What's your solution :) ? Muchas gracias, profesor! Esperando su respuesta.

May I mention my own preprint arXiv:1808.02089, published in Phys.Rev.A 98, 032508 (2018).

Dear Mikael,

The main difficulty is when you assume the same electron in many different locations. One immediate consequence is the lost of charge conservation of the electron, which has a quantized charge and well localized following the continuity equation.

It is true that there is a problem associated to measurement in QM and in fact related with the idea that this theory is not fully local. It is well known the problems that Einstein had with Bohr on this subject and which carry to that we know EPR issue. This difficulty of the Copenhagen interpretation of QM appeared impossible to test decisively until 1964, when John Bell of CERN showed theoretically that a statistical test with an EPR-like experiment could quantitatively compare predictions made by quantum mechanics. I think that these was a good phenomenological result for QM and these experiments were even improved 20 years later

A. Aspect, P. Grangier, and G. Roger, “Experimental Tests of Realistic Local Theories via Bell’s Theorem,” Phys. Rev. Lett. 47, 460 (1981); “Experimental Realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: a New Violation of Bell’s Inequalities,” Phys. Rev. Lett. 49, 91 (1982); “Experimental Test of Bell’s Inequalities Using Time-Varying Analyzers,” Phys. Rev. Lett. 49,

1804 (1982)

But the problem still follows in QM. What produces such an abrupt change of the entity’s state after measurement? Why such change is non-deterministic and irreversible? Why the Born statistical rule is so successful in determining the probabilities of the different possible outcomes?. These basic questions are not solved within QM and in spite of being the most successful theory in predicting new real physical behaviours it needs to go further to understand it fully. This is not a question of models as the de Broglie-Bohm where in fact tries to find hidden variables, but to enlarge the well developed Quantum Mechanics which is teached in every university of the world.

Well, if I may add, in my preprint I compare various versions of the Penrose conjecture, including a new (proposed) one, to experiment, including the famous COW experiment (Colella Overhauler Werner), whose direct significance to the experimental verification (or falsification, with "greetings from Karl Popper") o the Penrose conjecture may not have been fully appreciated in the literature up to this point.

I find it curious that classical probability collapses to certainty after I throw a dice and observe the outcome and no one worries about that, but when it comes to quantum mechanics, lots of people get upset with the analogous process. It's not correct to reply that it's because of non-locality, because I can have classical probabilities assigned non-locally as well. I think it's because too many people objectivize quantum wavefunctions as if they were real things. They are not. They are mathematical representations of empirical context. Another conceptual error along the same lines is to talk about objects such as electrons with no reference to any of the observers and apparatus required to justify that. It's a small step from there to metaphysics.

Dear George,

There are many fundamental differences between the dice and the wave function. The dice information is not contained within a differential equation which depends of physical variables as the potentials and so on, while the wave function follows a differential equation (Schrödinger, Dirac ...). That is to say, although the wave function is an amplitude of probability, it has a guiding equation which is in certain form a deterministic equation.

Dear Daniel,

I think you may have forgotten about the Einstein–Smoluchowski Diffusion Equation, which is a differential equation for a classical probability wave in a diffusing system. Classically, I could label one of the particles, then throw it into a room and allow it to be pushed around randomly. I could then calculate the probability distribution at a subsequent time, then find that particle. The probability distribution immediately collapses. The probability distribution has no objective physical existence per se. Same thing in quantum theory, unless you have Bohmian-Vigier tendencies. Probability is a manifestation of context and ignorance, not a property of an object.

Dear George,

The Einstein–Smoluchowski Diffusion Equation is a pure classical effect for explaining the Brownian motion of a particle within a certain diffusion medium. This dynamics can be included leading by Langevin equation or may be even related with a Fokker-Planck equation that describes the time evolution of the probability density function of the velocity of a particle under the influence of drag forces. This is always in a pure classical context where the stochastic behaviour can be directly related with forces or diffusion coeficients.

This is obviously very far Physics that the one of the wave function where the probability is reached by the its square (or modulus). For instance the uncertain principle of Quantum Mechanics relating action complementary varialbles has no parallel in the above classical physical context. The comparition of Einstein diffusion equation is not possible with quantum mechanics behaviour and no also with the possible ontic wave function. For instance the orbitals of one atom would be impossible to be calculated using just stochastic equations because the medium of the electrons would be the vacuum and the interaction just Coulombic one. Trying to translate the Born mechanism within a pure statistical interpretation is too simple for Quantum World and the Collapse of the wave function is with a very different scope too.

Dear Daniel Baldomir,

You have changed the topic away from probability collapse, because I think you have no response to my original statement that no one finds probability collapse an issue in classical theory whilst a subset of theorists find the same phenomenon an issue in quantum theory. Those theorists tend to neglect the crucial role of the observer in all of this.

As far as I can see, no one in this present discussion has advocated using classical stochastic equations to discuss atomic orbitals, or to calculate Born probabilities. The issue here is the interpretation of probability collapse, not the derivation of those probabilities.

Dear George,

I think that I didn't change your question-answer summarized in your last sentences:

I think you may have forgotten about the Einstein–Smoluchowski Diffusion Equation, which is a differential equation for a classical probability wave in a diffusing system.......The probability distribution has no objective physical existence per se... Probability is a manifestation of context and ignorance, not a property of an object.

1. I have tried to show you the difference of classical stochacastics equations and quantum mechanis or quantum field theory. But it seems that I was not successful with my explanation because you follow with the same arguments.

2. Physically it is very different a Brownian motion of particles in a medium subdued at forces than the motion of quantum motion of particles in vacuum. In the first place there is a source of the stochastic motion due to the molecular forces while in the second the reason is purely physical and universal without needing the assumption of medium.

3. For instance, Quantum Mechanics allows to explain how is possible to have electric chages moving with one acceleration around a nucleous (some of them relativistics) without decaying due to Larmor's relativistic law or to have a gap band energy in a semiconductor very well determined between two states of energy. This is absolutely out of the pure statistical concept that you assume for one state. There many other points but I think these are enough for showing the differences between Born interpretation and classical statistics.