Time Travel Quantum Mechanical B. S. By Brian Simpson

     The media have reported that physicists have engaged in a time travel experiment, using quantum mechanics, which is the next best thing to miracles and magic, and wow, it is science wrapped in complex mathematics so anything goes:
  https://phys.org/news/2019-03-physicists-reverse-quantum.html
  https://www.naturalnews.com/2019-07-24-quantum-computer-time-machine-russian-physicists.html
  https://arxiv.org/pdf/1712.10057.pdf

     The paper operates in the context of whether there are violations of the “arrow of time,” that we observe, for example, a burning cigarette turning to ash, but not the reverse. The ash does not spontaneously reconstruct back into the cigarette. There is an identification of the arrow of time with time travel; that if an experiment showed the analogue to the cigarette ash reconstructing itself, then time would be reversed. They then show that there is an exotic experiment in quantum mechanics, the theory of the actions of elementary matter, that allows this.

“Quantum physicists from MIPT decided to check if time could spontaneously reverse itself at least for an individual particle and for a tiny fraction of a second. That is, instead of colliding billiard balls, they examined a solitary electron in empty interstellar space. "Suppose the electron is localized when we begin observing it. This means that we're pretty sure about its position in space. The laws of quantum mechanics prevent us from knowing it with absolute precision, but we can outline a small region where the electron is localized," says study co-author Andrey Lebedev from MIPT and ETH Zurich. The physicist explains that the evolution of the electron state is governed by Schrödinger's equation. Although it makes no distinction between the future and the past, the region of space containing the electron will spread out very quickly. That is, the system tends to become more chaotic. The uncertainty of the electron's position is growing. This is analogous to the increasing disorder in a large-scale system—such as a billiard table—due to the second law of thermodynamics. "However, Schrödinger's equation is reversible," adds Valerii Vinokur, a co-author of the paper, from the Argonne National Laboratory, U.S. "Mathematically, it means that under a certain transformation called complex conjugation, the equation will describe a 'smeared' electron localizing back into a small region of space over the same time period." Although this phenomenon is not observed in nature, it could theoretically happen due to a random fluctuation in the cosmic microwave background permeating the universe. The team set out to calculate the probability to observe an electron "smeared out" over a fraction of a second spontaneously localizing into its recent past. It turned out that even across the entire lifetime of the universe—13.7 billion years—observing 10 billion freshly localized electrons every second, the reverse evolution of the particle's state would only happen once. And even then, the electron would travel no more than a mere one ten-billionth of a second into the past.”

     Now, the assumption here is that a violation of the arrow of time would indicate time travel, but that is a logical error. It is the passage of time which lies behind the arrow of time, and is not defined by the arrow. How to define time is a major philosophical problem, but these experiments do not exhibit time travel anymore than say the abstract possibility of the molecules in a bath tub of warm water suddenly separating back into cold at one end and hot at the other, which is at least logically, and theoretically possible, but not observed, due to the low probability of the event. A mere reversal of a causal process therefore does not prove that time travel occurred.

     In conclusion: a violation of what is a statistical law anyway, for a very short time period, does not refute the second law of thermodynamics, nor does it show time travel.
  http://www.informationphilosopher.com/problems/arrow_of_time/

“Would time itself be reversed if we could make the entropy decrease? That is unlikely, since entropy decrease anywhere (creating negative entropy or negentropy, a term coined by Leon Brillouin) must be accompanied by an increase elsewhere, to satisfy the second law. Otherwise we could use the local reduction in the entropy to build a perpetual motion machine. Put another way, if we could reverse the time, would entropy decrease? What can time reversal really mean? A thought experiment suggests not. Consider a closed perfume bottle inside a large empty container. Remove the bottle top and what would happen assuming that time is flowing backwards? It seems likely that the perfume molecules would leave the bottle whatever time is doing. For Aristotle, time was a measure of motion and change and for practical purposes, many scientists have thought that time reversal is approximated by the reversal of all the velocities or momenta of material particles at an instant, starting from their current positions. If we could reverse the motions of every material body (a practical impossibility, and perhaps a violation of Heisenberg's uncertainty principle), would that make the entropy decrease? Ludwig Boltzmann agreed that it might, but only for a while. His intuition was that a system could not return to a highly ordered original state, such as every molecule back in the perfume bottle.”

  https://theconversation.com/what-is-time-and-why-does-it-move-forward-55065