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
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