Gravitation of ultra-relativistic barionic matter. Implications for weak equivalence principle.

Previously it was found that the non-barionic matter inside the stars will be gravitating much stronger per  mc² compare to the barionic matter (2*n² stronger, where n is the effective refraction coefficient for the light in the fully ionized plasma) [1]. For the high-energy gamma-quanta the effective gravitation is only 2 times stronger (this is because of the general relativity prediction  for the deviation of the light beam near the sun being twice the Newton value - the experimental fact confirming general theory of relativity).

However, any barionic matter composed of ordinary particles (electrons, protons, neutrons, neutrinos) which is the main composition of the star (fully ionized plasma) when heated to tens of million degrees (Suns core) will be closer to relativistic compare to cold barionic matter. Ultra-relativistic matter will have the energy-pulse relation E=pc (here E-energy, p=pulse, c- speed of light) exactly like photons and thus it should behave exactly like photons and gravitate like photons (twice the Newton value). 

Indeed, accurate calculations based on general relativity were performed few decades ago and confirmed, that the ultra-relativistic particle  will be deflected by the gravity exactly like photons (very small difference is present, of course, because they do have rest mass) [2].

However, the star is almost entirely composed from very hot matter (fully ionized plasma at temperature of ten of millions degrees). Application of the formula output procedure described in [1] to the ultra-relativistic particle (it is exactly like photons but the refraction coefficient is 1, the particle is moving with ~ speed of light) will lead to the increase of the gravitational force experienced by the star as a whole. 

Exactly how big is this contribution? The rest energy of the proton is 1.5*10exp(-10) J and for electron it is 8.2*10exp(-14) J. Assuming the kinetic energy of the electron or proton is still governed by the Boltzman formula E=3/2*kT, the kinetic energy of the particles inside the star core would be 2.1*10exp(-16) J - still to small to claim the particles are ultra-relativistic.

In this case the gravitational properties of the star barionic matter will be between the Newton limit (cold barionic matter) and Einstein limit (ultra-relativistic barionic matter). Application of the formula from [2] for the intermediate region lead to the following approximation: for the slow particles the gravity increase would be proportional to 1+v²/c²=1+mv²/mc²=1+2E_k/E_o

For the protons this means the change in gravity of only 1.4*10exp(-6). That would be too little to explain the presence of dark matter (most probably another, non-barionic matter responsible, see [1, 3,4], but clearly means that weak equivalence principle is not valid for star considered as a whole. 

References.

1. http://tipikin.blogspot.com/2019/10/stars-are-full-of-trapped-light-may.html

2. D.Fargion "Deflection of Massive Neutrinos by Gravitational Fields" // Lettere al Nouvo Cimento, Vol.31, No 2, 1981

https://www.researchgate.net/publication/

227245454_Deflection_of_massive_neutrinos_by_gravitational_fields

3. http://tipikin.blogspot.com/2019/12/light-matter-attraction-as-driving.html

4. http://tipikin.blogspot.com/2019/09/accelerated-rotation-of-star-because-of.html

5. 

Increase of the yield of the elementary particles created at collider through manipulations with quantum vacuum. A chemical approach to the elementary particle physics.

The modern accelerators reached complexity level enough for more intricate manipulations with generated elementary particles. In modern approach the beams are interacting and the results of the strike is analyzed. Essentially this is close to the way the free radicals were created in the chemical experiments decades ago: powerful laser strike breaks away chemical bonds with generation of assembly of unstable chemical products (ions, free radicals, ion-radicals) which are to be analyzed spectroscopically. 

Researchers quickly realized, that in some cases the concentration of the unstable particles may be greatly increased if they quickly frozen inside some neutral matrix (liquid helium, liquid neon, liquid argon or liquid nitrogen). Such matrix isolation at helium temperature prevents any mobility and thus allows accumulation of the unstable products in high concentrations.

Such approach needs, of course, some manipulations with the molecular beams: not simply strike them with laser pulse, but do in the presence of the cold medium, so that the products created are delivered to the isolation matrix fast enough.

The only "isolation matrix" available in high-energy physics is quark-gluon plasma. So the idea of the future accelerator would be the cross-accelerator: in the reaction chamber the first beam prepares the spot of quark-gluon plasma and the second, more powerful beam will generate the elementary particles inside such a spot in the correct time: just before adronisation (cooling) of the quark-gluon plasma.

Why would new particles be created:

1.The quark-gluon plasma is kind of primordial quantum vacuum - the type of the vacuum existing soon after the big bang. Thus all four forces are closer to each other compare to modern quantum vacuum and the yield of the exotic particles responsible for unification of forces (including gravitational force) is expected to be higher.

2.Despite all those exotic particles are expected to be extremely short-lived, they must have at least some time in modern quantum vacuum. So if they are created just before adronisation of the quark-gluon plasma, they are to be cooled to modern quantum vacuum temperatures before they decay (obviously the decay time in the primordial quantum vacuum also is shorter compare to the modern quantum vacuum because of its temperature).

3.Possibly any interaction with parts of the quark-gluon adronising parts may accelerate cooling thus increasing the life-time (pretty much  like weak complexes between the highly reactive free radical and neutral molecule in the isolating matrix spread the wavefunction thus lowering the energy).

4.Future computers will be powerful enough to see the signs of the new particles in the mess created by the adronized quark-gluon plasma. Undoubtedly the interpretation of the results will be much more difficult.

Such experiments may seems to be far future for now, but in design of the future chambers it may be necessary already now to add the additional input window for the future crossed path of the preparation beam. It is expected that by the time the next generation of the accelerators is ready the concept of complex manipulation with the quantum vacuum (preheating of the quantum vacuum in the place of the particle generation) will be already developed to the level of possible implementation.

The particular particles of the interest from author point of view would be antigravitational Higgs boson [1]. The absence of the symmetry between matter and antimatter is not understood, but presumably the absence of the symmetry between matter and gravitational antimatter will be even worse (the gravitational force was split from the unified force first). So even inside the primordial quantum vacuum the probability of generation of any antigravitational particle (like antigravitational Higgs boson [1]) is really small. Correspondingly the direct observation of such antigravitational particle in the modern quantum vacuum is highly improbable (too long waiting time to see any event). Hopefully the idea of the preheated quantum vacuum  may increase the probability of the creation of such elementary particle and thus improve the chances of its detection in reasonable time.

References.

1.http://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html

Multiple energies photons - may they be seen by two photon absorption spectroscopy?

Two photon absorption spectroscopy is well known non-linear optic phenomena [1]. In this phenomena the virtual level is present which allows to absorb the second photon and thus excite the state with energy equal to two times the energy of the original quantum. The corresponding two-photon excited fluorescence is well known (and now three-photon excited fluorescence is known well). The most important observation connected with multiple quanta absorption is the non-linear dependence on power: this allows easily distinguish it from other phenomena.
The fundamental hypothesis outlined in the previous post [2] concerning the harmonics of de Broglie waves may be also stated for the photon itself. Indeed, the initial hypothesis of Plank concerning the photons [3] was the energy of photons itself is:  E=n*h*ν [3]. From observation of photoelectric effect Einstein deduced the more commonly known rule:  E=h*ν, which eventually lead to the development of the quantum electrodynamics and numerous discoveries. 
However, any mathematical expression is only the approximation to the natural law, and the idea of the photons having energy of only  E=h*ν may be very successful but not finally correct. Indeed, the double energy photon (with  E=2*h*ν) may be so rare that virtually non-observable and thus making the Einstein idea so exceptionally great fit to the natural law that it looks absolute. The double energy photons may easily decay into two ordinary photons or mutate into the photon with double frequency.
Even the probability of the existence of such photons would be governed by the usual Boltzman rule (from [2]):
the population of double energy photons would be exp[-hν/(kT)] less compare to the usual photon. That value for relatively small energy infrared photons (1064 nm wavelength, 1.17 eV ordinary photon energy) would be at room temperature only 2.35*10exp(-20). This means that even such photons exist, they are so rare that virtually non-observable.
However, the two photon excited fluorescence is a convenient way to check theirs presence. Indeed, in addition to the quadratic in power term of such fluorescence (due to virtual levels creation [1]) an extremely small linear in power fluorescence is predicted. This fluorescence is so weak that it is necessary to consider the background created by usual thermal excitation (with some non-zero probability the same excited level may be reached by the usual thermal excitation according to the Boltzman formula P/Po=exp[-E/(kT)].
The trick to subtract background is that the two photon fluorescence is a resonant phenomena. It means that for the deviation of the wavelength from the resonant value it will quickly disappear. Since for the linear phenomena search the laser should not be powerful (to prevent observation of the more common quadratic in power two photon fluorescence) it may be with tuned frequency and thus allowing to observe the linear in power resonant phenomenon. When the frequency of the laser deviates from the frequency necessary for two quanta fluorescence (this frequency may be obtained from the quadratic term of the induced fluorescence) the observed linear term should quickly disappear (and the thermal background stay the same). 
In summary: the observation of the linear term in the two photon fluorescence is predicted due to hypothetical existence of double energy photons (from Planks rule  E=n*h*ν [3]), the phenomenon would be really weak (20 orders of magnitude weaker compare to one-photon fluorescence at least for infrared photons) but resonant in photon frequency.



References.
1. https://en.wikipedia.org/wiki/Two-photon_absorption
2. https://tipikin.blogspot.com/2020/05/quantization-rule-and-harmonics-of.html
3. http://web.phys.ntnu.no/~stovneng/TFY4165_2013/BlackbodyRadiation.pdf

Quantization rule and harmonics of matter waves.

When modern scientist is recalling the quantization rule for photons, usually the famous E=h*ν is recalled. However, in the original Planck's derivation the more general rule of quantization was assumed: E=n*h*ν [1]. A similar rule of quantization was assumed by Nield Bohr concerning the orbital moment. The values n=2,3,4 .. are responsible for the excited states of the quantum system.
In quantum electrodynamics the quantization rule for electromagnetic field is similar to oscillator:
E=n*h*ν +0.5*h*ν 
At the same time the wavelength of the de Broglie wave has only one value: λ=h/p=h/(m*v)  not λ=n*h/p, where n is a number 1,2,3..., p is the pulse of the particle (applicable for any particle), m - rest mass and v - velocity of the particle (applicable only for non-relativistic case). 
Since the matter waves are not really easy to investigate, it may happened that the de Broglie wavelength also follows the most general rule with the presence of the harmonics:
λ=n*h/p,
But they were simply overlooked and careful experiment would be necessary to discover them.
For de Broglie wave it is would not be easy to find presence of such harmonics, because during the interference experiment they would generate the maxima and minima, which coincide with maxima and minima of the main matter wave. If harmonic is present in the miniscule amount it will lead to some hardly observable effect. 
Let's consider for example the case of only one added harmonic. Let the first harmonic has maximum of 1 and decays as exp(-0.1*m), where m is the interference band number, m=0,1,2,3,4... In this case the amplitudes of the interference bands would be: Io=1, exp(-0.1), exp(-0.2), exp(-0.3), exp(-0.4)=1, 0.905, 0.819, 0.741, 0.670...
Second harmonic of de Broglie wave would have the amplitude of 0.01 and decays with distance away from the center according to the same law exp(-0.1*m), here m is the interference band for the second harmonic, which would coincide with a certain band for first harmonic (because wavelength is exactly 2 times larger). The amplitude would be I=0.01, 0.01*exp(-0.1), 0.01*exp(-0.2)… =0.01, 0.00905, 0.00819 ...
The sum of the amplitudes would be:
1.01; exp(-0.1); exp(-0.2)+0.01*exp(-0.1); exp(-0.3); exp(-0.4)+0.01*exp(-0.2); …..=
1.01; 0.905; 0.828; 0.741; 0.679; …..
In order to distinguish the case of the one and multiple harmonics the ratio of the amplitudes of the consecutive bands may be calculated: bamd1/band0; band2/band1, band3/band2.....
For exactly one de Broglie wavelength that would be monotonic function:
0.905, 0.905, 0.905 …. (constant in this example, because the chosen decay function was exponential)
For the sum of harmonics it would be: ratios are:
0.896; 0.915; 0.895; 0.916 …. - non-monotonic function, the superposition of monotonic function and ao*Cos(pi*m), where m is the interference band number.
The third and higher harmonics will add more "waviness" to the smooth function.
How to estimate the amplitude of the harmonics in matter wave? The idea of evaluation is inferred from the reciprocity principle: the particle is both matter and wave [2]. Assuming the matter wave is something real (similar to a photon, but permanently "attached" to the particle), the probability of the excitation of the second energy level would be similar to the idea proposed by Plank [1]:
population of each next level would follow Boltzmann rule [3]:
-log(N_i/N)~E_i/kT
But what is the expected energy of the initial de Broglie wave? Hypothesizing that  the particle is both matter and wave it is possible to speculate about this value.
Since de Broglie wave is "attached" to the particle, the only velocity it may have is equals to the velocity of particle v. From the general rule connecting velocity, wavelength and frequency of the wave it follows:

v=λ*ν or λ=v/ν
here v is the velocity of the particle, λ is the wavelength, ν is the frequency of the wave.
Substituting λ  into the formula for non-relativistic de Broglie wave:
λ=h/(m*v)   and v/ν=h/(m*v)   
which may be transformed as follows:
mv²=hν  or mv²/2=hν/2
For non-relativistic particle the energy of de Broglie wave can not be larger than the full kinetic energy of the particles and quantized as oscillator (quite reasonable idea, because the zero energy of electromagnetic field has the same value). Assuming the next harmonic will have the energy according to the Planks rule (or quantum electrodynamic rule, similar to oscillator), the difference in energy between two levels for de Broglie wave would be double the kinetic energy of the non-relativistic particle (for relativistic particle the quantization rule is simpler and coincides with the quantization rule for photons).
Than the ratio of the amplitude of the second harmonic of de Broglie wave to the initial amplitude would be equal (from Boltzmann rule): 

I/I_o=exp(-2E_k/kT)
where Ek is the kinetic energy of the non-relativistic particle. For example for electron with possible to reach energy of 0.1 eV, observed at the room temperature (300 K, at this temperature de Broglie wave is still well resolved since 0.1 eV > kT), the ratio would be:

I/I_o=exp(-2E_k/kT)=4.4*10exp(-4)
Which is small, but at numerous averaging is possible to reach and to discover.


References.
1. http://web.phys.ntnu.no/~stovneng/TFY4165_2013/BlackbodyRadiation.pdf
2. https://tipikin.blogspot.com/2019/09/the-possible-way-to-search-for-new.html
3. https://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution

Quantization of the gravitational dipole

At the present time gravity is considered by many scientists as the under-investigated  force of nature due to  its weakness. It is interesting to investigate the hypothetical possibility of the associated with the mass of the elementary particle gravitational dipole. That would be analogous to electric dipole for the electric field and it would reflect the non-uniform distribution of the mass inside the elementary particle.
Since all the physical values which have the dimensions of energy*time (J*s) are quantized (the Plank constant), it would be interesting to see, what physical values may be quantized, too. For example, production m*v*r (mass*velocity*radius is quantized and this is orbital moment). Investigation of quantization of this moment lead to all modern quantum mechanics, started by Niels Bohr. However, the same production may be considered as production of m*r (gravitational dipole, similar to electric dipole  q*r - charge times distance) and velocity v of the particle.
Following Niels Bohr steps, it is possible to suppose that such value is quantized too:
(m*r)*v=n*h
here h is Plank's constant.
It may be rewritten as follows:
m*r=n*h/v,
Since h/(m*v) is the de Broglie wavelength λ
m*r=n*m*(h/m*v)=n*m*λ
It means that the mass of the particle is "spread" in the space as de Broglie wavelength. Here n is the number 1,2,3,4...
The most important consequence of the hypothesis - the gravitational dipole moment is not equal to zero! This is a conclusion similar to de Broglie wavelength - it must exist, due to quantum mechanics the particle can not be represented as a point, therefore the dipole moment can not be zero under any circumstances.
Lets estimate the additional gravitational force due to the gravitational dipole moment of the particle. Lets consider the ball with mass M as the second body (the first body has mass m). The gravitational dipole force between the dipole and spherical mass M is:
Fd=m*r*grad(Eg)
here Fd is the force acting onto the dipole m*r, grad(Eg) is the gradient of the gravitational field, what is equal for the spherical mass to:
grad(Eg)=d/dr(M*G/(R*R))=2*M*G/(R*R*R)
Here G is the gravitational constant, M is the mass of the second body, R is the distance between the centers of the attracting masses. Then the gravitational dipole force may be written as:
Fd=n*m*λ*(2GM/R³)=2n*(λ/R)*(GmM/R²)=2n*(λ/R)*Fg
Here Fg is the classical gravitational force between two spherical masses separated by distance R between centers. For the multiple harmonics of the gravitational dipole  force (n>1) and for very slow electron (de Broglie wavelength is high) it may be comparable with gravitational force and measurable relatively easily - the electrons will be split into several beams. The gravitational force is not quantizied and the same for all electrons, but the dipole gravitational forced is different depending upon n.  
Here comes the different problem discussed in another blog - de Broglie wavelength is unique and not quantizied according to Bohr rule. It may happened that there is no "excited" states for gravitational dipole, only the lowest state exist (n=1).
For the ultraslow electron with the temperature of 1 micro-Kelvin (reachable now in some experiments) the velocity of electron would be 6.7 m/s and de Broglie wavelength is 0.1 mm. For the second body with radius of 0.1 m the ratio of dipole gravitational force to gravitational force is 2*0.0001/0.1=0.002.
The accuracy of the direct measurements of gravitational force today (Kavendish experiment) is much higher than 0.2%, thus making such measurements quite possible. 
Additional alleviation may be from the shape of the second mass - the gradient of the gravitational force, similar to the gradient of the electric field, will be much stronger near the sharp edges, so the manipulation with different shapes of the second body with mass M will allow to amplify the gravitational dipole force while keeping the classical gravitational force the same.

Unification of gravitational and electromagnetic force through quantum vacuum. Modification of Cavendish experiment to observe the influence of quantum vaccum excitation by laser

There is a lot of attempts which were trying to create the complete unified field theory. However, some experiments and observations may help to complete smaller but the most important part - unify gravity with any other fundamental force. The possible way to unify gravity and electromagnetism would be use of idea of common source for both forces - quantum vacuum. Indeed, the idea of the direct influence of the quantum vacuum onto the electromagnetic constants (electric force strength and speed of light) is well established: the virtual pairs of particle-antiparticle (mainly electron-positron) are attenuating the electric field strength (in smaller scale the magnetic field strength) and thus limiting the speed of light. A similar idea about gravity was proposed [1]: a massive pairs particle-gravitational antiparticle in quantum vacuum would be responsible for the main contribution of the gravity strength. However, the charged particles are also having mass and thus more common pairs like positron-electron and proton-antiproton will be influencing the gravity force too. Since the quantum vacuum is the same for both interactions, all of the possible pairs having mass will be responsible for the gravity. But some of such pairs are also having charge. The very strong electric field will be able to polarize the quantum vacuum (electromagnetically responsive part of it), which would influence the speed of light (known phenomenon) and simultaneously the gravitational constant (the phenomenon to be discovered), since any pair which has charge and responded to the electric field has also a mass. In the opposite situation the extremely strong gravitational field excites the quantum vacuum (all of the particles, including those which bear charge) and thus influence the speed of light (this is also known phenomenon - the speed of light is smaller in the vicinity of the star or black hole).
The phenomenon of the influence of the gravity onto the speed of light is well known and usually interpreted as the change of time speed [2]. From quantum vacuum point of view it may be interpreted as the excitation of the quantum vacuum by the strong gravitational field, what leads to the change of the parameters of the electric field constant (permittivity and permeability of free space). Indeed, those parameters are known to be changed in the vicinity of the electron (vacuum screening of electron, see [3], which is a confirmed fact). Why would not strong gravitational field modified the same quantum vacuum in a similar way? All the barionic particles which are responsible for virtual pairs in the quantum vacuum have mass and must respond to the strong gravitational field.
But the gravity is responsible for the presence of space and time in our Universe. As the Universe expands, the gravity potential inside the Universe (away from the black holes and stars) will be smaller and smaller (assuming no new mass is added into the Universe). This will lead to the change of the speed of light (change of both permittivity and permeability of free space) - to the increase of speed of light. This value may be estimated as follows:
Speed of light near the massive ball is (according to Einstein, [2,4]):
c=c_o-2c_o*α
here α=(GM)/(r*c_o*c_o)
Where G is the gravitational constant, M is the mass of the black hole (star), r is the distance from the center of the star and c_o is the speed of light away from the gravitating star. The value of gravitational potential is expressed as follows:
Φ(r)=-GM/r
c=c_o+2*Φ(r)/c_o       
Assuming the whole Universe as a ball partially  filled with mass it would be possible to evaluate the speed of light inside such a ball using the formula for calculation of the potential inside the charged ball (the analogy to electrostatic is straightforward). Electric potential inside the uniformly charged ball is [5]:
ϕ(r)=[k*Q/(2R)]*(3-r²/R²)
Here k is electric field constant, R is radius of ball, r is the distance from the center of the ball, Q is total charge of the ball. Correspondingly for the gravitational potential (for simplicity at the center of the Universe):
Φ=-3GM/(2*R)
Here M is the total mass of the Universe (1.5*10exp(53) kg) , R is the total radius of the Universe (4.4*10exp(26) m) and Φ=-6.82*10exp(16) m²/s² (this parameter is related to the cosmological constant, of course [6]). 
Thus we got an equation for the speed of light in gravitation-free space (virtual place because according to Einstein the space-time itself is created by gravity, no gravity means no space):
c=c_o-6.38*10exp(16)/c_o
Here c is 3*10exp(8) - is the observable speed of light in the present Universe. Solving the quadratic equation, c_o=4.5*10exp(8) - relatively small change because our Universe is already very inflated. 
Assuming no new mass will appear in the Universe, many billions years from now the speed of light will be a just a little larger (if the inflation of the Universe will not influence other properties of the quantum vacuum, for example the probabilities of the appearance of particle-antiparticle pairs).
The difference between the c_o and observed c is due to the polarization of the quantum vacuum by the total masses present in the Universe.
In summary, the same quantum vacuum may be polarized by different fields and this influences the corresponding constants for both electric and gravitational force (because we are talking about the same vacuum). This may help to unify the gravity and electromagnetism
 1. Strong gravitational field polarizes the quantum vacuum and changes electric constant (observed through change of speed of light near the star and black hole) [4]
2. Strong electric field changes the permittivity near the charge ( vacuum screening of electron [3])
3.Perturbation of the quantum vacuum by the electric field should influence the gravitational constant (because the same virtual pairs would be responsible for both forces)
This experiment is the most difficult one, because the gravitational force so much smaller. In a simple way it should be strongly electrically charged objects in Cavendish experiment on gravity [7], but since the electric force is so hugely strongly compare to the gravity, the change in gravity will be completely invisible. Fortunately powerful lasers may already create the electric field strong enough to generate electron-positron pairs (breaking the quantum vacuum) are already available [8]. Illumination of the space between the test masses in Cavendish experiment may create the polarization of the quantum vacuum strong enough to be observed through the measurement of the gravitational constant. 
4.In principle the polarization of the quantum vacuum by the strong gravitational field will lead to the different outcome of the Cavendish experiment. This experiment may be performed in the vicinity of Sun or Jupiter and the observed result will be a little different compare to Earth experiment. Such idea may be even closer to the reality because the satellites traveling close to Sun or large planet are already present.
The discoveries of the more elementary particles which would be present as virtual pairs in the quantum vacuum will eventually allow to calculate exactly the strength of electromagnetic constants and gravitational constant from the same principles and general formulas, effectively unifying both fundamental forces [2].










References.
1.http://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html
2.https://arxiv.org/abs/1401.3110
3.https://arxiv.org/ftp/arxiv/papers/1405/1405.5792.pdf
4.https://www.speed-light.info/speed_of_light_gravity.htm
5.http://www.phys.uri.edu/gerhard/PHY204/tsl94.pdf
6.https://en.wikipedia.org/wiki/Observable_universe
7.https://en.wikipedia.org/wiki/Cavendish_experiment
8.https://www.sciencemag.org/news/2018/01/physicists-are-planning-build-lasers-so-powerful-they-could-rip-apart-empty-space

Inherently quantum phenomena reveal itself in macroscopic world. Idea of correlations instead of science fiction "time line".

Landau-Zener formula manifestation in macroscopic world and impossibility of "time-line".
In deterministic world based on classical mechanics the idea of "time-line" appeared (very popular in science fiction in the sense that it should be preserved). Indeed, the classical mechanics is deterministic. After appearance of quantum mechanics this idea disappeared a instead the idea of multiple worlds appeared. At the present time the idea of quantum Darwinism is popular:
https://en.wikipedia.org/wiki/Quantum_Darwinism
which may seemingly allow to preserve the determinism at least for macroscopic world. Unfortunately some of the inherently probabilistic phenomena, governed by quantum mechanics laws may be traced up to macroscopic world. The easiest example would be the motion of electrostatically charged balls, because the electrostatic force is rather macroscopically significant (the coefficient in Coulomb law is 9*10^9 and the force is acting at long distances compare to the inside the nucleus strong force).  The charge is quantified and even one electron added or subtracted may change the mechanical motion of the macroscopic object and change the history in the most common sense of this world.
Triboelectrization of polymers includes two steps: at the first step the mechanochemical reaction generates free radicals and at the second stage the interaction between the radicals may lead to recombination of them or to the charge transfer between the contacting surfaces [1].
The second step includes the Landau-Zeener process, where the two energy levels quasi-cross each other and as the system moves along the reaction coordinate, the electron may be transferred between the surfaces, thus creating the charge. Landau-Zeener process law is a quantum law and its application will lead to inherently unpredictable charging of the surfaces (mathematically verified stochastic process). For such process the fluctuations are of the value of sqrt(N), where N is the average value of the quantity (like the distance of the travel in the Brownian motion). The most important consequence of Landau-Zeener determined stochasticity is that it has no hidden parameter.
For the relatively weak charge of 1000 electrons the fluctuation would be around 32 electrons. Triboelectrization takes place between the closely placed surfaces, say 3 angstroms apart. In this case the additional electrostatic force due to 32 electrons (this is the unpredictable fluctuation of average charge of 1000 electrons) would be:

F=k*q*q/(r*r)
here k is coefficient in Coulomb law, q is the charge and r is the distance (say 3 A). Calculations for 32 electrons give force of 2.56*10exp(-6) Newton.
Lets consider lottery where the plastic balls are used with mass of 1 g. The additional acceleration of such ball due to the stochastic electrostatic force would be
a=F/m=2.56*10exp(-3) m/s^2
 Being in contact for 1 second the fluctuation in the velocity would be
v=a*t=2.56*10exp(-3) m/s
For the further flying inside the lottery machine for 30 seconds the distance fluctuation is 0.077 m (around 8 cm). Correspondingly the ball will miss the hole and different winning number will appear.
In addition of demonstration that such lottery machine is stochastic on the deepest level possible (no possibility of pre-calculation of the winning number quaranteed by quantum mechanics) it also means the probabilistic events do not stop on microscopic level - they have the way to reveal itself on the macroscopic level as well. Even idea of quantum Darwinism can not return the predictability in the macroscopic world.
From philosophical point of view it means that determinism is not present in our world - it is inherently stochastic. What is preserved is correlations: even in the fully stochastic world there is the range of fluctuations is limited. The correlations between the different values are measurable in the past and due to the laws of correlation function may be used to predict future. This is used by economists to evaluate numerous trends on the market. For example if the consumption of strawberries is increasing consistently for 50 years, the correlation between grows of population and consumption of strawberries is almost 1. By no means may it be that next year it will drop to zero - the correlation function was very strong for around 50 years and it must be equally strong for approximately next decade or so at least.
From science fiction time travel point of view the travel in the past and back into the present will change nothing - the butterfly effect is forbidden by the laws of quantum mechanics. It means that by traveling to the past, doing nothing (no butterfly) and returning back the completely different future will be found. The deviation will depend upon the correlation functions of the event expected and distance in time. For example by traveling back for 50 years and returning to the present minimum changes are expected - the presidents are different, but for example New York is still the largest city of USA (however, some tallest buildings are looking differently and are in a little different places). Since the correlation function associated with city of New York is measured in centuries, 50 years should not lead to big change. The company lifetime is much shorter, so no Google now (but because the Internet has at least comparable lifetime already it must be present and the similar search engine is here, but with different name) etc.
The deeper into the past the travel, the smaller would be the remnant values of correlation function and more changes are to be expected. Traveling back to dinosaur times will lead to the huge change on the return - may be a different species are now making civilization.
The best representation of such attempts may be sci-fi movie "Sliders".
The main conclusion is that contrary to the believe of the scientists of 19th century more and more evidence tells that the world is probabilistic on the deepest level possible. There is no predictable future, but there is also no past at all. History is only recorded in the books, there is no "time-line" at all. The possibility of prediction and use of numerous laws of physics is that the correlation functions for some of them are equal to 1 with enormous accuracy. For example, motion of planets may be predicted forward for billions of years easier. The mechanical motion of macroscopic objects (what lead to the discovery of the Newtons law and the idea of predictability of the motion of any particles) is also very high and predictable - that is why civilization is possible.
Fortunately for everyday life the quantum stochasticity on the macroscopic level is rear. It is only because the electrostatic force is so strong and charge is quantized it is possible in some situations.




References.
1.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2969192