Spacetime fluctuations as deBroglieBohm quantum potential
If randomness of quantum world is simply the result of random (from our perspective) inflow of gravity waves then the whole mystery is suddenly solved.
The difficulty of finding the unified theory has deep sources in humans’ inability to look from outside of their brains — abstract from what they have learned since birth, what they are used to and what perceptions are engraved in our nature. We always tend to draw conclusions that are self-oriented.
From Earth-centric theories to Copenhagen interpretation of Quantum Mechanics many theories had been flawed by the conscious or unconscious anthropocentrism. Whenever researchers had not known anything they immediately introduced concepts of infinities, continuums, intrinsic randomness, multiple dimensions, multiple universes, etc. We have been doing it since the “Turtles all the way down” and we cannot get rid of it till today. The only way to break the impasse in Physics is to get rid of anthropocentrism and accept the discomfort that world is not how we perceive it. If we put aside anthropocentrism, our perception of time, mass and velocities and take into account well proven general relativity and quantum mechanics predictions one should definitely put some effort to check the hypothesis of spacetime fluctuations predicted by GR to play a quantum potential role in the modified deBroglie-Bohm interpretation of QM. This paper is an introductory analysis of such “Spacetime Quantum Potential” (SQP) hypothesis for General Relativity and Quantum
Quantum theory although is greatly successful should not be named a theory but more a framework that needs interpretation and only when such interpretation is proven it will deserve a status of a ‘theory’. Copenhagen interpretation is an anthropocentric explanation that is not falsifiable  as it refers to the consciousness of the observer. This gets even more complicated when conscious observer is not sure what he/she has observed. One of the examples here could be an experiment when measurement device generates a sound signal upon some quantum
originated event and our conscious observer Bob is half deaf. This can bring to the situation that Bob has heard the signal (meaning wave function collapsed) and after a moment he
realizes that not, he has not really heard anything so makes the wave function to decollapse. Only the strong personalities like Bohr and Heisenberg were able to defend it and give the status of theory but this interpretation does not describe the world as it is but describes the knowledge of the observer about the system in the form of the probability being a normalized square of the wave function:
As per Bell and Durr/Goldstein/Zanghi  quantum mechanics does not contain means of describing the classical world in any approximate sense. Either wave function is not all there is, or Schrodinger equation is wrong. Bohmian mechanics based on deBroglie made a great step to enhance Schrodinger with guiding wave but the mysterious source of Quantum Potential and it’s overallowed speed of influence show there is some additional work needed which this paper gives a direction to.
Spacetime fluctuations as the source of the de Broglie’s-Bohm quantum potential
In 1926, Schrodinger published An Undulatory Theory of the Mechanics of Atoms and Molecules , where, inspired by de Broglie’s work [6, 7, 8], he described material points (such as electrons or protons) in terms of a wave solution of the following (wave) equation:
Later on in 1952 Bohm inspired by the deBroglie’s wave theory published  his interpretation of the quantum mechanics by introduction of quantum potential on the polar form of the wave function:
Eq. (5) is the modified Hamilton-Jacobi equation with additional term Q that represents quantum potential known as Hamilton-Jacobi-Bohm. Q here is the function of the real part of wave function and indirectly of the position and time. There are two significant problems with this interpretation:
- quantum potential influences particles instantly
- quantum potential influences particle and does not have reciprocal action
Additionally it is unclear what is the real source of the quantum potential (which obviously makes it comfortable for human minds to assume it is an intrinsic feature of the world…).
Holland has shown that there are alternative forms of Hamiltonian that produce the same results as deBroglie-Bohm theory and that in this context deBroglie-Bohm interpretation is not unique.
In this paper we will analyse new QM interpretation — SQP which locally produces the same result as classical QM interpretation but different (which makes it falsifiable) on a larger scale.
Derivation of SQP interpreted quantum mechanics from classical mechanics
In the SQP interpretation Bohm’s quantum potential Q represents the random inflow of spacetime fluctuations. As SQP inflows with the maximum velocity c it can be considered locally as the random function of time only — SQP(t). It is important to notice that in this interpretation Q (SQP) is not a result (function) of R but the other way around. R is a result of SQP acting in a special way on the particle and it can be considered as the amplitude of displacement in spacetime. Let’s assume that this displacement function reacts to the inflow in the way that:
R.h.s. does not depend on , so it is in fact time dependent constant and in this case equation (7) can be written for a particular moment of time as:
whose general solution for individual coordinate x is:
therefore the probability density (dispersion being result of incoming spacetime fluctuations SQP) of measuring a particle in the given location in a particular moment of time is:
It is worth to note that the bigger mass the smaller dispersion of location being result of incoming SQP.
SQP as the newly interpreted Q in Hamilton-Jacobi-Bohm equation gives then the same results as QM (and Bohm) in case of the mass of apparatus significantly larger than mass of the observed particle but if they are comparable(even quantum small!) we will arrive to the classical mechanics situation because impact of incoming SQP will be similar on both.
Under this hypothesis, so called hidden variables are not features of a particle but are inflows of spacetime fluctuations that influence behavior of particles and obviously measurement results. Such type of hidden variable was not in scope of neither von Neumann or Kochen and Specker .
It is now widely known fact that von Neumann’s proof included assumption that narrowed the classes of hidden variables to those that follow quantum kinematical framework. Therefore neither Bohm’s theory nor hypothesis of this paper is excluded by von Neumann’s logic .
SQP is also excluded from Kochen and Specker as it clearly contradicts Kochen and Specker’s base assumption:
“All observables defined for a QM system have definite values at all times”
Where is the classical limit then?
There is no classical limit in this interpretation but there is a smooth increase of the visibility of quantum randomness the bigger the difference in masses between measurement apparatus and measured particle/object. This is because k (eq. 11) is proportional to mass and inversely proportional to the dispersion function R (eq. 10). Furthermore if h becomes zero (eq. 12) then dispersion disappears and we get to the classical world.
Where does randomness come from then?
Einstein could not believe that God played dice and was on the realists side who preferred to believe in determinism — as he together with Podolsky and Rosen expressed in the form of hidden variables in the famous EPR paper . John Bell in 1964  proved that the only way hidden variables could explain QM is if they were non-local. SQP hypothesis from this paper shows that they both were right. There is a ‘global determinism’ because SQP is generated by the matter but locally it is seen as indeterministic (random) as it travels to the measurement place with the maximum speed c and cannot be predicted / precalculated before it arrives — ‘local indeterminism’. This is exactly what Bell predicted:
“So I could imagine the situation where we do have hidden variables, and we do have again determinism, but not predictability”
What is measurement then?
Measurement process definition in SQP interpretation is the same like in the deBroglie-Bohm interpretation. Every measurement impacts the result and impacts particle state but there is nothing like a wave function collapse as there is nothing special in the measurement process — neither that performed by intelligent nor by nonintelligent person.
What is entanglement then?
Under the Copenhagen interpretation entanglement is a special state of two or more particles that makes their quantum state impossible to describe or analyze independently. The measurement of one instantly impacts the other.
DeBroglie-Bohm interpretation did not accept the specialty of the measurement process but instead introduced Quantum Potential that instantly impacts other particles. Both interpretations contain — as Einstein described it — ‘spooky action at a distance’.
Under the SQP interpretation there are hidden variables but those hidden variables describe not the state of the particle but how the particle reacts on the incoming ‘non-local’ spacetime fluctuations. Those fluctuations then are the loophole in the loophole-free Aspect’s experiment.
How to test SQP hypothesis?
There are at least two ways to test this hypothesis:
- (difficult) measure particle with apparatus of comparable mass
- (easier) compare QM predictions and SQP predictions on long distance EPR experiment. Long distance here means that incoming spacetime fluctuations (SQP) would affect differently each of the measured entangled particles — which is the distance larger than the length of gravity waves (i.e. larger than 1000km)
 Lee Smolin. Scientific alternatives to the anthropic principle. (2004)
 J. S. Bell: Speakable and Unspeakable in Quantum Mechanics. Cambridge University Press (1987)
 D. D¨urr, S. Goldstein, and N. Zangh`ı: Quantum Physics Without Quantum Philosophy. Heidelberg: Springer-Verlag (2013)
 Oriols, Xavier and Jordi Mompart (eds), 2012, Applied Bohmian Mechanics: From Nanoscale Systems to Cosmology, Singapore: Pan Stanford Publishing.
 E. Schr¨odinger, An Undulatory Theory of the Mechanics of Atoms and Molecules, Physical Review 28, 1049 (1926).
 L. de Broglie, Recherches sur la th´eorie des quantas, Ann. de Physique 3, 22 (1925).
 L. de Broglie La m´ecanique ondulatorie et la structure atomique de la mati`ere et du rayonnement, Journal de Physique et du Radium 8, 225 (1927)
 L. de Broglie, Recherches sur la th´eorie des quantas, PhD thesis, University of Paris (1924)
 D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables I, Phys. Rev. 85, 166 (1952).
 D. Bohm, A suggested interpretation of the quantum theory in terms of “hidden” variables II, Phys. Rev. 85, 180, (1952)
 P. Holland, Hamiltonian theory of wave and particle in quantum mechanics. I. Liouville’s theorem and the interpretation of the de Broglie-Bohm theory (2001)
 P.Holland, Hamiltonian theory of wave and particle in quantum mechanics. II: Hamilton-Jacobi theory and particle back-reaction
 Dieks, Dennis. Von Neumann’s Impossibility Proof: Mathematics in the Service of Rhetorics. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics. 60. 10.1016/j.shpsb.2017.01.008. (2016)
 Held, Carsten, “The Kochen-Specker Theorem”, The Stanford Encyclopedia of Philosophy (Spring 2018 Edition), Edward N. Zalta (ed.)
 A. Einstein, B. Podolsky, and N. Rosen, Can Quantum Mechanical Description of the Physical Reality Be Considered Complete? Physics Review 47, 777 (1935).
 J. S. Bell, On the Einstein Podolsky Rosen Paradox Physics 1, 195 (1964).
 Aspect, A. Viewpoint: Closing the Door on Einstein and Bohr’s Quantum Debate. Physics 2016, 8, 123.(2016)