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Gravity-induced decay



I suggest an object acted on by classical (i.e. non-coherent) force, in gravitational field, unavoidably decays. I estimate decay rates in some scenarios.
Gravity-induced decay
Sergei Viznyuk
I suggest an object acted on by classical (i.e. non-coherent) force, in
gravitational field, unavoidably decays. I estimate decay rates in some scenarios.
Quantum phase shift between superposed states with different space geometries in
gravitational field inspired interest (Penrose, 1996) as well as controversy (Gao, 2013; Bonder,
Okon, & Sudarsky, 2016; Pikovski, Zych, Costa, & Brukner, 2015) since at least early 1960-ies
when (Feynman, 1962) first talked about role of gravity in breakdown of quantum mechanical
behavior. Despite the controversy, the nature of the phenomenon appears mundane: the states with
different space geometries in gravitational field experience phase shift with respect to each other.
If the shift is larger than the de-Broglie wave packet length the interference between packets with
different space geometries vanishes. It is the same effect as disappearance of interference pattern
in two-slit experiment when difference in optical lengths between two paths exceeds the coherence
length of the light source (Figger, Meschede, & Zimmermann, 2002). In such case, wave packets
(e.g. laser pulses) appear as if they travel down only one of the paths, as do classical particles.
However, the interference amplitude can be easily restored by introducing phase delay into one of
the optical paths. Perhaps one should not equate phase shift between wave packets or decrease in
interference amplitude with true de-coherence, which is an irreversible loss of phase relationships
between constituent states.
The observable effect of true de-coherence is disintegration of the object into wave packets
with no phase relationship between the packets. Such packets behave as separate objects.
True de-coherence arises if phases of constituent pure states no longer predictably relate to
each other, e.g. as a result of random dispersion. Random phase dispersion can be associated with:
1. Scattering (Uys, et al., 2010; Schlosshauer, 2007)
2. Brownian motion (Paz, 1994; Hornberger, 2009)
3. Dispersive media (Antonelli & al, 2011; Salemian & Mohammadnejad, 2011)
In this article I look into phase dispersion introduced by non-coherent coupling between external
non-gravitational fields and object’s constituent pure states, in the presence of gravitational field.
According to (Einstein, 1907) equivalence principle, the effect of the external non-gravitational
force on the object at rest in a [uniform] gravitational field is indistinguishable from the effect of
the same force on the object away from gravitating bodies, in object’s [accelerating] reference
frame. Thus, the influence of non-gravitational fields does not depend on presence of [uniform]
gravity. The inevitable conclusion is that any change to the state of the object, such as phase
dispersion between constituent pure states, can only be caused by non-gravitational fields:
It is clear, …, that, while some kind of decoherence might happen in specific
experimental situations, gravity, … is never the agent that causes the effect.
(Bonder, Okon, & Sudarsky, 2016)
Nevertheless, I suggest, gravity plays an important role, by establishing preferred basis in system’s
state vector space. Phase dispersion by coherent coupling between external field and pure states
retains coherence of the wave packet. If coupling is non-coherent, as e.g. with environment heat
bath, the phase dispersion includes random phase noise which, over sufficiently long time, results
in true de-coherence of the wave packet, and decay of the object is represents.
To demonstrate the principal feature, consider the object is in a stable state if no external
fields. If object is free-falling in a gravitational field, with respect to lab frame the state is a
superposition of eigenstates of Hamiltonian with field, i.e. in the preferred basis:
Thus in a lab, is no longer a static state, as can be seen from solution to Schrodinger’s equation:
 
An observer performing measurement of object’s vertical coordinate will find the expectation
value change according to:
, where
A two-level system is sufficient to demonstrate the main feature (Viznyuk, 2014):
From (4) the relation with acceleration of gravity is:
, where  ought to be taken as a distance (radius) to the center of gravity at ,
and  
Now consider the object is acted on by an external non-gravitational forces keeping the
object around fixed position in a lab frame. If external fields couple coherently, the evolution of
object’s state is still described by (2), where are eigenstates of Hamiltonian with all fields
included. With non-coherent coupling, the phases of -states no longer relate to each other as
Instead, non-coherent coupling can be modelled as a random phase walk, with phase
difference  changing by   during single act of interaction with external
field. Here  has a meaning of mean free time between interactions, with   
being a
scattering rate. During time there is   scattering events, each with probability
 
to increment phase difference  by  in positive or negative direction. After 
scattering events phase difference  will be within standard deviation  of its coherent
value, where 
is the variance of binomial distribution 
 . So, instead of
(6), for non-coherent coupling I have:
  
Once random dispersion (7) grows to  the , -states can be considered de-coherent
with respect to each other. From here I estimate time for the object to decay, considering it a
simple two-level system as in (4), (5):
, and decay rate
Eqs. (7-8) has been derived in approximation of large number of scattering events per rotation
period  
, i.e. in approximation . In the opposite case I expect: as .
The inverse proportionality of decay rate on de-coherent scattering rate in (8) can be viewed
as manifestation of quantum Zeno effect (Misra B., 1977). Each scattering event constitutes the
measurement by the environment. The more frequent are the measurements performed on the
object, the more likely the object will be found in its initial state after fixed elapsed time.
Furthermore, the effect may not even be so “quantum” in nature. I can simulate it using the
following experiment: take a [fragile] wine glass and try to keep it vertically around the same
height with respect to lab floor by applying periodic kicks from below using some hard-surface
object, e.g. a wood board. In the mean free time between the kicks the wine glass will be in free
fall. The more frequent are the kicks, the lesser distance the wine glass will fall in between the
kicks, the lesser is the force of each kick required to return the wine glass to its initial position. In
the limit of infinite frequency of kicks, the wine glass will be simply standing steady on hard
surface. It can stay in such position forever. However, if the frequency of kicks is decreased, in
the mean free time the wine glass would fall greater distance. Each kick would have to be stronger
to return wine glass to its initial position; and with stronger kick it is more likely the wine glass
would eventually break into smaller pieces. As I expect, there is also a second limit, when ;
; corresponding to the case when wine glass is allowed to fall indefinitely without
experiencing kicks, and that would preserve wine glass too.
It is conceivable (8) could be applicable to any object, including elementary particles which
are otherwise considered stable, such as electrons and protons. I shall estimate from (8) in some
scenarios, using input parameters from the cited sources:
Distance to the
center of gravity ()
Acceleration of
gravity ()
Scattering rate
Decay time
electron in Sun’s
 [21]
 [10]
electron in Sun’s
 [21]
 [10]
24 years
proton in Sun’s core
at the maximum
gravity location
 [18]
 [9]
 s
With solar mass distribution (Stix, 2004), the gravity reaches maximum of  at about
 of solar radius from the center of the Sun. The proton collision rate in Sun’s core is estimated
from  (Knapp, 2011) to  (Mullan, 2009). Thus from (8) the decay rate of
protons in Sun’s core could range from  to . The claimed hydrogen
fusion rate of  (Knapp, 2011; Mullan, 2009) in Sun’s core lays right in that
range. If the presented reasoning is valid, the thermonuclear fusion might not be the primary factor
behind Sun’s radiative output. Indeed, as radiative modes have higher entropy than heavy nuclei
the Second Law of Thermodynamics favors Sun evaporating into thermal radiation rather than
forming iron core and turning into a white dwarf or neutron star, a relatively low entropy states.
Also, the presented estimates show the proposed particle decay rates in Sun’s corona are many
orders of magnitude higher than in Sun’s photosphere, which may explain why the temperature of
Sun’s corona is , and up to  in the hottest regions, in comparison with
photosphere which is about .
1. Adelberger, E., et al. (1998) Solar Fusion Cross Sections. arXiv:astro-ph/9805121
2. Antonelli, C.; Shtaif, M.; Brodsky, M. (2011) Sudden Death of Entanglement Induced by
Polarization Mode Dispersion, Phys. Rev. Lett., 106 (8) 080404,
3. Bonder, Y., Okon, E., Sudarsky, D. (2016) Can gravity account for the emergence of
classicality? arXiv:1509.04363 [gr-qc]
4. Einstrein, A. (1907) On the Relativity Principle and the ConclusionsDrawn from It. Jahrbuch
der Radioaktivität und Elektronik, 4, 411-462.
5. Feynman, R., Morinigo, F., Wagner, W., Hatfield, B., & Pines, D. (2002). Feynman Lectures
On Gravitation. Westview Press, ISBN 0-8133-4038-1.
6. Figger H., Meschede D., Zimmermann C. (2002) Laser Physics at the Limits. Springer, ISBN
7. Gao, S. (2013). Does gravity induce wavefunction collapse? arXiv:1305.2192 [quant-ph].
8. Hornberger, K. (2009) Introduction to Decoherence Theory, Lect. Notes Phys. 768, 221276,
doi:10.1007/978-3-540-88169-8, arXiv:quant-ph/0612118
9. Knapp, J. (2011) The physics of fusion in stars.
10. Miralles, M.P., Almeida, J.S. (2011) The Sun, the Solar Wind, and the Heliosphere, Springer,
ISBN 978-90-481-9786-6.
11. Misra B., Sudarshan E.C.G. (1997) The Zeno's paradox in quantum theory. J. Math. Phys.
18(4) 756-763.
12. Mullan, D.J. (2009) Physics of the Sun. CRC Press, ISBN 13-978-1-4200-8308-8.
13. Paz, J.P. (1994) Decoherence in Quantum Brownian Motion. arXiv:gr-qc/9402007v1
14. Penrose R. (1996) On Gravity's Role in Quantum State Reduction. General Relativity and
Gravitation, 28(5), 581-600.
15. Pikovski, I., Zych, M., Costa, F., & Brukner, C. (2015). Universal decoherence due to
gravitational time dilation. Nature Physics, 11, 668-672. doi:10.1038/nphys3366
16. Salemian, S., Mohammadnejad, S. (2011) Analysis of polarization mode dispersion effect on
quantum state decoherence in fiber-based optical quantum communication, Proceedings of
the 2011 11th International Conference on Telecommunications (ConTEL), IEEE, 511-516,
ISBN: 978-3-85125-161-6516
17. Schlosshauer, M. (2007) Decoherence and the quantum-to-classical transition, Springer,
ISBN 978-3-540-35773-5.
18. Stix, M. (2004) The Sun. An Introduction.Springer, ISBN 978-3-642-62477-3.
19. Uys, H., et al. (2010) Decoherence due to Elastic Rayleigh Scattering. Phys.Rev.Letters,
105, 200401, doi:10.1103/PhysRevLett.105.200401.
20. Viznyuk, S. (2014). New QM framework,
21. Wikipedia (2016) Sun.
... The boost involves acceleration from 0 to 1 . It is done through the action of a classical force, always accompanied by decoherence [21]. An assumption that one can reconcile extraction of information, implied by the boost transformation, with unitarity, leads to a collection of paradoxes, see, e.g., Lecture IV in [22]. ...
... It has been shown[21] the measurements in gravitational field result in decoherence and object's [state] decay ...
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I show any theory assuming state of an object, or even object’s existence, will be at odds with empirical evidence. I discuss QM relation with special relativity (SR). I argue all paradoxes are artifacts of factitious assumptions
... , where ( • ) is a characteristic decoherence time; ℰ is in joules ( ), and ℎ is in ( • ). The expression (10) for transition rate, containing ℰ 2 in one form or another, is present in a number of QM artifacts, from Fermi's golden rule [9], to Planck's radiation law [10], to the predicted gravityinduced decay [11]. ...
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I show the unitarily equivalent solutions of Schrödinger equation predict different measurement results in different observation bases. I identify the criterion for choosing an observation basis in which the predicted measurement results are consistent with observed macroscopic behavior
... Quantum de-coherence has received an extensive coverage in last decades. A link between de-coherence and decay has been suggested [50]. De-coherence between knowledge vectors is not unlike the spontaneous collapse of wave function, a subject of a number of collapse theories [51]. ...
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A recent debate has ensued over the claim in Ref. 1 that systems with internal degrees of freedom undergo a universal, gravity-induced, type of decoherence that explains their quantum-to-classical transition. Such decoherence is supposed to arise from the different gravitational redshifts experienced by such systems when placed in a superposition of two wave packets at different heights in a gravitational field. Here we investigate some aspects of the discussion with the aid of simple examples. In particular, we first resolve an apparent conflict between the reported results and the equivalence principle by noting that the static and free fall descriptions focus on states associated with different hypersurfaces. Next, we emphasize that predictions regarding the observability of interference become relevant only in the context of concrete experimental settings. As a result, we caution against hasty claims of universal validity. Finally, we dispute the claim that, at least in the scenarios discussed in Ref. 1, gravitation is responsible for the reported results and we question the alleged ability of decoherence to explain the quantum-to-classical transition. In consequence, we argue against the extraordinary assertion in Ref. 1 that gravity can account for the emergence of classicality.
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Conference Paper
The implementation of quantum communication protocols in long optical fibers is limited by several decoherence mechanisms. In this contribution we review this mechanisms and analysis their effect on the quantum states. Because of asymmetry in the real fibers, the two orthogonal polarization modes are propagated at different phase and group velocities. The difference in group velocities results in Polarization Mode Dispersion (PMD). It is created by random fluctuations of the residual birefringence in optical fibers, such that the State of Polarization (SOP) of an optical signal will turn randomly over time, in an unpredictable way. In optical quantum communication, quantum state measurement is necessary. The bottleneck for communication between far apart nodes is the increasing of the error probability with the length of the channel connecting the nodes. For an optical fiber, the value of absorption and depolarization of a photon (i.e., the qubit) increases exponentially with the length of the fiber.
We seek a quantum‐theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seems to pose a paradox which we call Zeno’s paradox in quantum theory. The relation of this result to that of some previous works and its implications and possible resolutions are briefly discussed. The mathematical transcription of the above‐mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the general formulation and the proof given here are believed to be new. We also note that the known ’’no‐go’’ theorem concerning the semigroup law for the reduced evolution of any physical system (including decaying systems) is subsumed under our theorem as a direct corollary.
We describe the aims and contents of the book entitled “The Sun, the Solar Wind, and the Heliosphere”. This is a volume in the IAGA Special Book Series dedicated to the science covered by IAGA Division IV, Solar Wind and Interplanetary Field. The book features review articles on topics from the interior of the Sun to the outermost regions of the heliosphere. In addition, we highlight some of the results presented during the Division IV symposia at the 11th Scientific Assembly of IAGA in Sopron, Hungary, which was planned simultaneously with this book.
This is an introduction to the theory of decoherence with an emphasis on its microscopic origins and on a dynamic description. The text corresponds to a chapter soon to be published in: A. Buchleitner, C. Viviescas, and M. Tiersch (Eds.), Entanglement and Decoherence. Foundations and Modern Trends, Lecture Notes in Physics, Vol 768, Springer, Berlin (2009)
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