Space, time, and arrows

This post is a continuation on the duality of space and time. The basis of space is distance (or length) and the basis of time is duration. It must be emphasized that both distance and duration are scalars, i.e., they have magnitude but no direction. They are not one-dimensional because that would entail direction, represented by a positive and negative quantity. So scalars are non-negative real numbers (zero is a degenerate case).

Consider two sentences: “The Arcade building was a block long.” “They were stuck in traffic on Lake Shore Drive for 12 hours.” The first sentence expresses a distance and the second expresses a duration. Note that both sentences use the past tense. In the present tense the Arcade building in Chicago’s Pullman district doesn’t exist because it was demolished in 1926, and the mammoth traffic jam on Chicago’s Lake Shore Drive in February 2011 is over. This parallel shows that anyone who wants to say the past time is in the opposite direction from the present time could equally well say that past space is, too.

The problem is Arthur Eddington’s “arrow of time” which says time is one-way or asymmetric. But time in this sense has to do with tense, not duration, and has no application to space and time. Note that more recent work on “arrows of time” has focused on thermodynamics, causality, etc., and not on space and time.

What, then, is the meaning of a time line that goes from negative to zero to positive? If “now” is at the zero point, isn’t the negative part in the past? In fact, this is no different from a “space line” that goes from negative to zero to positive with “here” at the zero point. The location of a point in the past would be negative, but that does not lead us to say that space is one-way or asymmetric.

Putting “-t” into an equation of physics does not change the tense or make the present precede the past. It simply reverses the direction of the duration. If “+t” is to the right, then “-t” is to the left.