The issue is how does revising the spatial location of now from a continuous spatial volume to a collections of points solve the problem of the relativity of simultaneity. Remember that three-dimensional spatial volumes are represented by one-dimensional lines in a spacetime diagram.

Figure 8

Now and Simultaneity Diagram

In Figure 8 we find the world lines of three objects. In the reference frame of this diagram the green object has a positive velocity, the red object has zero velocity and the blue object has negative velocity. A short segment of the line of simultaneity for each object is shown.

When in the parable of the two clocks we tried to claim that the now time coordinate should be at each clock’s proper time we got into a paradox when the clocks were reunited. If the past-future boundary is not at each object’s proper time, where in time is it. One possibility is that now is off the clock altogether. This thought invokes visions of additional dimensions and possible other complications. There is one particular time that appears to be the same time throughout the universe. That is the time recorded by the cosmic microwave background (CMB) radiation as observed from the commoving reference frame, which we take to be the age of the universe.

There is some logic in claiming that the boundary between past and future for every object lies at the age of the universe. This only requires that we terminate all world lines at the age of the universe, regardless of the elapsed proper time along that world line. Object ages may vary but the age of the universe is… well its universal. This time coordinate for now is an unsubstantiated claim on my part. It is just hard to imagine the universe marching into the future and leaving those objects that are in the universe behind to straggle into the future at various later times. That is why in Figure 8, as well as Figures 2, 5 and 7, I placed all objects at the age of the universe.

To deal with those pesky lines of simultaneity we need to look into the spatial extent of now. Lines of simultaneity are lines of constant time in the diagram reference frame as seen by observers that may be or not be at rest in the reference frame of the spacetime diagram. We got into trouble in Figure 2 because we had two conflicting versions of the past-future boundary shown on the diagram, one a now line and one a line of simultaneity.

If we stop thinking about a past-future boundary that exists over all of space, or even a significant chunk of space and define now as the past-future boundary on the world line of each particle in the universe, then now for each particle occupies a point, not a line, surface or volume. The concept of spatially separated objects sharing the same now disappears and all the events in which a particle is involved must happen at that particle’s location in space (no action at a distance).

Each particle then is free to drift up the t-axis at the speed of light, always at the age of the universe, dragging its own relativistic version of the line of simultaneity with it. Its own age simply reflects the number of stretched time units since its birth, having no necessary connections to the time coordinate of its now. Its line of simultaneity may slope this way or that as the particle zigzags through space without conflict with its own now since the now point is always on the line, and without conflict with the now of another particle because that now does not exist for the original particle. A line of simultaneity is in fact a line of constant time for a particular observer but that observer is not free to assume that his now extends to distant events lying on that line.