I think that time is strongly related with the events in one system.every event corespons to its own moment in time like this:
say one system is regulated with this law F=PS
F=force
P=presure
S=surface
the three (F,P,S) is legal event if it respects the law
say you start from (F1,P1,S1) and endup in (F2,P2,S2)
the vector (dF,dP,dS)
in (F1,P1,S1) is (P1*dS+S1*dP,dP,dS)
and
in (F2,P2,S2) is (-P2*dS-S2*dP,-dP,-dS)
if you want the shortest distance from event1 to event2 you have to set a plane thru event1, event2 parallel with the straith line from event1 to event2.so it has to be
F=a(P1*dS+S1*dP)-b(P2*dS+S2*dP)=ab*dP*dS and
P=(a-b)dP and
S=(a-b)dS or
a(dF,dP,dS)(1)-b(dF,dP,dS)(2)=(F,P,S)
(there are also other ways of finding the shortest legal trajectory)
now find b(a);
b1=-0.5(P1/dP)-0.5(S1/dS)-0.5*sqrt(sqr((P1/dP)+(S1/dS))-8a);
b2=-0.5(P1/dP)-0.5(S1/dS)+0.5*sqrt(sqr((P1/dP)+(S1/dS))-8a);
now you get:
b=f(a)
F=f1(a,P1,P2,S1,S2)
P=f2(a,P1,P2)
S=f3(a,S1,S2)
where a is pure number and it is the quantum of time.
assign seconds to a and you get dimension time.
NOW da>0 MEANS FORWARD IN TIME WHILE da<0 MEANS BACKWARD IN TIME.
da=0 means time is frozen/no changes.
you see my concept of time is slightly different from the common one.