First, what phenomenon are we even talking about? It’s important to start here. I’m going to start somewhat cavalierly: Motion is a state of affairs in which, if we measure two variables, X and T, where X is the position on some arbitrary dimension relative to some arbitrary point using some arbitrary scale, and T is the position in “time” as measured by a clock (also arbitrary), we can observe that X varies with T.
Notice there are actually two distinct phenomena here: There is the fact that “X” changed, which I am going to talk about. Then there is the fact that “T” changed, which I will talk about later. For now, it is taken as a given that “time passes”. In particular, the value “T” refers to the measurement of a clock whose position is given by X.
Taking “T” as a dimension for the purposes of our discussion here, what this means is that motion is a state of affairs in which a change in position in time additionally creates a change in position in space; that is, motion is a state of affairs in which a spacial dimension, and the time dimension, are not independent variables. Indeed, special relativity gives us precisely the degree to which they are dependent on one another.
Consider geometries which are consistent with this behavior; if we hold motion in time as a given—that is, if we assume that the value on the clock will change—then the geometry can be a simple rotation.
However, suppose we don’t hold motion in time as a given. What geometry are we describing then? I think we’re looking at a three-dimensional geometry for this case, rather than a four-dimensional geometry.
What does it mean, for a thing to move?
First, what phenomenon are we even talking about? It’s important to start here. I’m going to start somewhat cavalierly: Motion is a state of affairs in which, if we measure two variables, X and T, where X is the position on some arbitrary dimension relative to some arbitrary point using some arbitrary scale, and T is the position in “time” as measured by a clock (also arbitrary), we can observe that X varies with T.
Notice there are actually two distinct phenomena here: There is the fact that “X” changed, which I am going to talk about. Then there is the fact that “T” changed, which I will talk about later. For now, it is taken as a given that “time passes”. In particular, the value “T” refers to the measurement of a clock whose position is given by X.
Taking “T” as a dimension for the purposes of our discussion here, what this means is that motion is a state of affairs in which a change in position in time additionally creates a change in position in space; that is, motion is a state of affairs in which a spacial dimension, and the time dimension, are not independent variables. Indeed, special relativity gives us precisely the degree to which they are dependent on one another.
Consider geometries which are consistent with this behavior; if we hold motion in time as a given—that is, if we assume that the value on the clock will change—then the geometry can be a simple rotation.
However, suppose we don’t hold motion in time as a given. What geometry are we describing then? I think we’re looking at a three-dimensional geometry for this case, rather than a four-dimensional geometry.