I just want to point out some interesting properties of this definition of time: Let time_C refer to the classical notion of time in a dynamical system, and time_FFS the notion defined in this article.
1. Suppose we have a field on space-time generated by a typical differential dynamical law that satisfies time_C-reversal symmetry, and suppose we factorize its histories according to the states of the system at time_C t=0. Then time_FFS doesn’t make a distinction between the “positive” and “negative” part of the time_C. That is, if x is some position (choose a reference frame), then the position (x,2) in space-time (i.e. the value of the field at position x at time_C 2) is later in time_FFS than (x,1), but (x,-2) is also later in time than (x,-1). In this sense, the time_FFS notion of time seems to naturally capture the time-reversal symmetry in the laws of physics: Intuitively, if we start at the big bang, and go “backward in time” we are just as much going into the future as we are if we would go “forward in time”. Both directions are the future.
2. However, more weirdly, time_FFS also allows a comparison between the negative-time_C and positive-time_C events. Namely, (x,1) happens before_FFS (x,-2) while (x, −1) happens before_FFS (x,2). I am not sure what to make of this, or whether we should make anything of it.
3. Suppose a computer is implemented in the physical world and implements a deterministic function f:X→Y, AND we restrict to the set of histories in which this computer actually does this computation. Now let x denote the variable that captures what input is given to this computer (meaning, the data stored in the input register at one particular instance of running this algorithm), and y similarly denote the variable that captures what the output is, then y occurs (weakly) earlier_FFS than x, even though the variable x is defined to be earlier than y (more precisely, to directly apply the definitions of x and y to check their value in a particular history h would involve doing a check for x at a time_C that is earlier_C than the check for y). I’m not sure what to make of this, though it kind of seems like a feature not a bug. If we don’t restrict to the set of histories in which the computer does the computation, I’m pretty sure this result disappears, which makes me think this is actually a desirable property of the theory.
I just want to point out some interesting properties of this definition of time: Let time_C refer to the classical notion of time in a dynamical system, and time_FFS the notion defined in this article.
1. Suppose we have a field on space-time generated by a typical differential dynamical law that satisfies time_C-reversal symmetry, and suppose we factorize its histories according to the states of the system at time_C t=0. Then time_FFS doesn’t make a distinction between the “positive” and “negative” part of the time_C. That is, if x is some position (choose a reference frame), then the position (x,2) in space-time (i.e. the value of the field at position x at time_C 2) is later in time_FFS than (x,1), but (x,-2) is also later in time than (x,-1). In this sense, the time_FFS notion of time seems to naturally capture the time-reversal symmetry in the laws of physics: Intuitively, if we start at the big bang, and go “backward in time” we are just as much going into the future as we are if we would go “forward in time”. Both directions are the future.
2. However, more weirdly, time_FFS also allows a comparison between the negative-time_C and positive-time_C events. Namely, (x,1) happens before_FFS (x,-2) while (x, −1) happens before_FFS (x,2). I am not sure what to make of this, or whether we should make anything of it.
3. Suppose a computer is implemented in the physical world and implements a deterministic function f:X→Y, AND we restrict to the set of histories in which this computer actually does this computation. Now let x denote the variable that captures what input is given to this computer (meaning, the data stored in the input register at one particular instance of running this algorithm), and y similarly denote the variable that captures what the output is, then y occurs (weakly) earlier_FFS than x, even though the variable x is defined to be earlier than y (more precisely, to directly apply the definitions of x and y to check their value in a particular history h would involve doing a check for x at a time_C that is earlier_C than the check for y). I’m not sure what to make of this, though it kind of seems like a feature not a bug. If we don’t restrict to the set of histories in which the computer does the computation, I’m pretty sure this result disappears, which makes me think this is actually a desirable property of the theory.