Dear professor Cristian Corda:
I am a physician specialized as a psychiatrist. I'm clarifying this point, just to also make understandable that I don't know almost nothing of physics and also of mathematics. But when I read the title of your essay: "Time dependent Schrödinger equation for black hole evaporation: no information loss" I ask myself how physicists can work for years and years, on and around something, than no physicist since the discipline began as such, knew or know what "time" is, your essay refer to a subject, that supposedly depend on "time". I know that physics don't know its definition neither its more important experimental meaning. So how a physicist can understand Schrödinger equation if they don't know what is "time" from which the equation suppose to depend.
I know that physicists when referring to "time" they in fact are referring mainly to the measuring of "duration", they can't take "time" as a physic entity and relate its properties with any other physical entity properties like gravity for example, just because nobody know what "time" properties are.
I know that you also can depend of something that you don't know and that you don't understand, but become workable for you all, because the reliable and exact measuring of "duration". Medicine also used plants to cure people without knowing why these were effective, and even that, they kept using it.
But physics is not like medicine, is among the exact sciences. As I said when in physics people refer to "time", they mainly believe they are referring to measuring "duration", the problem is, that they don't know what is "duration" either, because this one is define as a period of "time" and if you don't know the meaning of "time" you don't know the meaning of "duration" either.
So you don't think that could be useful to know from what is depending Schrödinger equation. As a physicist you think that could be possible that depend from a quality or property of every physical existing thing like "motion", which when is "constant" or "uniform" as in celestial bodies and clocks, can be use to measure now days, with great precision, the periods of change and transformation allowed by "motion"? That now on we can call "duration"?.
With my best whishes
Héctor Daniel Gianni