i.e. the theory, not reality, is where time symmetry comes from. and this is also exactly why those theories have predictive capabilities
but reality is still asymetric in the temporal dimension
That's an interesting claim. Do you have any evidence of it?
Oh, wait. Do you actually believe time passes? You're going to need to start by proving we're not in a block universe, then.
As far as I know, there is no such thing as an experiment that can disprove either assertion. As such, they're more claims of faith than claims about reality.
time is asymmetric BY definition. if time weren't asymmetric I would have to call it space instead. (seems like I'm using asymmetry and monotonicity as synonyms)
in my definition, passing is all time can ever do, and it must do it only in the 'same direction'.
finally, in my view it is space which enables backwards and forwards motion.
I don't follow you here. If time were not asymmetric it wouldn't suddenly just be space. What are you actually claiming here?
Sabine made a great episode on this recently, fwiw, and it’s worth watching if the subject interests you.
The Schwarzschild metric for example is expressed in terms of time squared so time itself can take positive or negative values and give the same result. It also allows negative mass but those solutions are not symmetric with positive mass - the rs term that contains mass is not quadratic.
One consequence of this combination is if you consider "negative mass" to be just positive mass operating in reverse time (to avoid having to accept the ugly idea of negative mass in positive time), you end up with asymmetric effects.