John West wrote:

A third alternative, which may do better with relativity but doesn't help against Tom's argument, is the Growing Salami Theory (which some call the Growing Block).

Why would the Growing Salami Theory (GST) do any better with special relativity (SR)?

GST would entail a preferred reference frame — namely, the unique inertial frame in which the events with time coordinate t = 0 (the present, say) are all on the "leading face" of the Salami.  Furthermore, if you are in any other inertial reference frame, then, while you are on the leading face, some of the events that are in your past (t < 0) aren't yet in the Salami, while some of the events in your future (t > 0) are already in the Salami, "behind" the leading face.

In other words, some events that are non-existent (assuming GST) right now will prove in the future to have happened prior to right now.

If SR and GST are both true, then the exists/doesn't-exist-yet border is sweeping through events transversely to the past/future border (unless you happen to be in that one preferred reference frame).  That is, you don't have that "the past exists, while the future doesn't."  Instead you have, "some of the past exists, while the rest doesn't, and some of the future exists, while the rest doesn't".  The distinction between what is in the Salami and what isn't doesn't coincide with whatever distinguishes the past from the future.

Last edited by Tyrrell McAllister (2/02/2016 8:10 pm)

Thanks for the quotes, John.  A few responses to Forrest:

By not positing a flat boundary we avoid any commitment to a privileged frame of reference

This does eliminate the privileged-reference-frame problem.  However, it makes his theory seem less and less like a theory of time.  The modern physical definition of time is still essentially Aristotle's: Time is a measure of motion. When we play out the implications in special relativity of this definition of time, we find that the locus of events taking place "at the same time" is flat. (See the "appendix" below for a totally skippable justification of that claim.)

So, if the boundary of the Growing Block is not flat, then it is not behaving like time, defined as a measure of motion.  Therefore, a theory about the Growing boundary isn't a theory about time as such.  It's a theory about something else (such as "becoming", maybe).   It might even be best to think of this "something else" as having only an incidental relationship to time.

'[N]owb' is frame-independent, and so presentists and no-futurists have a much more intuitive way of thinking, not available to the likes of Braddon-Mitchell. For the question 'Is Plato still alive nowb?' admits of a definite answer.

This is a bad example, unless I'm missing his point.  For, Braddon-Mitchell can reply that the question "Is Plato still alive nowi?" also has a definite answer, if uttered here-and-now.  Plato's death occurred in the backward light cone of here-and-now.  So, if you are here-and-now, then Plato's death is in your past regardless of your reference frame.  It is true that Relativity makes the orderings of some events depend on your reference frame.  Nonetheless, the pair {Plato's death, here-and-now} cannot be reordered by changing frames.  Every reference frame will agree that Plato's death happened before here-and-now.

If we adopt the interpretation of Relativity in which we ignore frames of reference and think of Space-time rather than Space and Time, then the indexical 'nowi' should not be taken as frame-relative but rather as 'here-nowi'. For the whole idea of introducing frame-relative simultaneity is foreign to that interpretation.

Consequently Parmenideans who adopt this interpretation of relativity should eliminate all talk of what is happening now at a distance.

I disagree.  Spacetime isn't just a 4-dimensional manifold of events.  Spacetime also includes the light cones (and backward light cones) with apexes at these events.  These light cones are an integral part of the structure of spacetime in special relativity, even at its most Parmenidean.

Now, given these light cones, any pair of points A and B in spacetime determine a reference frame, provided only that one of the points is in the future light cone of the other.  I won't go into details (unless someone wants me to), but I will say that these reference frames are determined entirely by the geometry of the light cones at A and B and, hence, by the structure of spacetime itself.

Thus, there is no need to add reference frames as an additional structure on top of spacetime.  Reference frames are already implicit in "Parmenidean" spacetime alone, because they are implicit in the geometry of the light cones.  Each such reference frame then determines an indexical 'nowi' at each event in the usual way.  The upshot is that Parmenideans have just as much right to talk about reference frames and the frame-relative nowi as anyone else.

Appendix: Here is why the locus of events happening "at the same time", qua measure of motion, must be flat.

Imagine building a large sphere in outer space surrounding yourself.  Suppose that the internal surface of the sphere is mirrored.  Now float to the center of the sphere. Adjust your velocity until you and the sphere are stationary with respect to each other.  Quickly flick a light bulb on-and-off, so that a pulse of light emanates in every direction from your position at the center.  Wait until the pulse reaches the boundary of the sphere, bounces off, and re-converges on your position.  Since you are at the center of the sphere, you will see the pulse arrive at your location from every direction at the same instant.

Now think back to when the pulse was just reaching the boundary of the sphere.  Time, qua measure of motion, should have the following properties:

1. The pulse reached every point on the boundary at the same time (qua measure of motion).
2. This would have been true no matter where or how big you had built the sphere.

But these two claims together, within the context of special relativity, entail that the locus of events "at the same time" is flat.

Note that there is nothing special about light in this story.  You could have projected any physical process, as long as it was the same process, traveling through the same conditions, being projected in every direction.