If x^0 = 1 and y^0 = 1, then neither equation can be worked in reverse, because, starting with “1”, there would be no way of knowing if one should arrive at x or y.
Even as events you are going to end up with X/Y as some complex function including time.
Lets throw a rock off a cliff and give you two functions one from the start and one from the end
function X = function(mt, ut + 1/2at^2);Definitions:
m = horizontal velocity I threw rock at
u = vertical velocity I threw rock at (unlikely I got it perfectly horizontal)
a = gravity AKA 9.8 m/s/s
t = time from launch
function Y = function(-mt, -ut - 1/2at^2);
It's the car in reverse problem again see the appearance of the negative signs. Time still goes forward but your motion numbers need negatives.
Now lets write a function Z from the END TIME so time will go backwards
function Z = function(mt, ut - 1/2at^2);
Here t = time from land ... so launch time -5 seconds.
This one is a mix of signs created because the square of a negative number is positive t^2
The point here is Function X, Y & Z are all perfectly valid mathematical functions describing our observation and nothing in mathematics is going to help you work out which way time should go.
Thus I reasoned that neither equation (nor any n^0) would work if time were reversed.
Do you see you kicked an own goal .. what you actually proved was you can't distinguish
Function X ^ 0 = Function Y ^ 0 = Function Z ^ 0 = 1
The answer seemed to be non-conservation of the information: did we start from x or y?
That is the problem but you haven't solved it and about now you should realize there are infact infinite functions not just X & Y.
You snubbed all the points in the middle who are demanding they are actually the start, and time runs both ways. I mean Bill S has a history and a future, you even measure them from present (10 min ago, 15 minutes from now etc)
In classical physics they bring in cause and effect. So time starts at a cause and and effect follows. Many layman get comfortable and trapped in that, the Flat Earth effect what you sense does not make it so. So we need to look at all data and make sure it isn't an illusion, yourself is the easiest person to fool ringing in our ears.
Relativity brings in the problem that one mans cause is another mans effect, two observers don't see things the same.
So we put the restriction cause must precede effect only according to inertial observers. So you will see cause before effect only on things in your inertial frame. Einstein struggled with anguish over some of this stuff and where it lead himself because he wanted to keep cause and effect.
QM introduces us the waveform and it connects the cause and effect and as per Relativity in some instances they can be in reversed time order, making the two theories at least compatible at this level. The connection between two events is the QM wave and it doesn't have an absolute direction that must come from elsewhere.
Now those new B meson experiments are the first sign of hope that we can identify microstate processes that are not time symmetrical and the compounding effect will explain the direction of time for macro objects like us.