# Is it possible to reverse the spreading in space of a particle's wavefunction and if not, are all processes asymmetric in time?

Already more than a year ago, scientists claimed to have reversed the direction of time. What they actually did (see this article) to have reversed the direction of time. Which was hugely exaggerated. The process was simulated on a quantum computer, of which none of its constituents went back in time for the tiniest fraction.

They simulated the motion of an electron in deep space. Normally, the wavefunction of an electron (like any particle) grows wider in space; it gets smeared out. This is logical because the associated function in momentum space has a certain width, which means the electron is in a superposition of a range of momenta, all with their own probability(density). This means the wavefunction corresponding to an electron's position in space is spreading out due to all different velocities. This is an asymmetrical process in time.

The simulation made the electron's spacial wavefunction go back in time for a tiny fraction of a second. One can read in the article:

"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.

Now what I don't understand is how these random fluctuations in the CMBR can, for a tiny moment, reverse the smearing out of the electron, which occurs once in the whole universe in its whole lifespan and has never been observed (which is a sign the normal Schrödinger equation applies). How is a complex conjugated Schrödinger equation involved (if it is), and how is its realization (in which case the motion of a particle evolves according to a complex conjugated equation, which I can't imagine) is connected to the CMBR?

After reading the answer by anna v below (as usual, very informative) answer, I can better ask the question: Is it possible at all to reverse the spreading in space of a particle's wavefunction? If not, does this mean that all processes are asymmetric in time? In 1964 it was shown, by Cronin and Fitch, that the decay of neutral Kaons shows CP-violation. I don't agree with the implications for matter-antimatter asymmetry though because I see the elementary particles as given by Rishon Model as fundamental (and there are equal amounts of them in our Universe). So, can it be possible that the time asymmetry wrt to the smearing out of a particle's wavefunction is the cause for the CPT symmetry?