socratus wrote: Minkowski said "The views of space and time ... are radical.
Henceforth ... only a kind of union of the two will preserve an independent reality."
Minkowski space-time diagram is a graphical representation of events and
sequences of events in space-time
as “seen” by observer at rest.
Such sequences are named wordlines, which provide an illustration of the properties of space and time in the special theory of relativity. It allows a quantitative understanding of the corresponding
actual observation like time dilation and length contraction without mathematical equations.
http://www.math.brown.edu/~banchoff/STG ... kowsk.html
T. Banchoff, Brown U. wrote:If light cones are drawn in the positive and negative time directions from a certain event (E), space-time is separated into three distinct regions: "future", "past", and "meta-present". ...
The meta-present is a mysterious thing. One piece of the meta-present is the present, which are all of the events that lie on a line (or plane) of simultaneity with E--things that are actually happening at the same time.
The author refers to the space between past and future as the "meta-present", because either a) the events have happened, and there is no way for someone at E to know about it or b) the events has not happened, but there is nothing that a person at E can do about it. For all intensive purposes, this is a good working definition of a "kind" of present.
My concern is not with the space twin who is aging slower than his inertial twin. I would like to understand the 'static' observer at O, =E for Prof. Banchoff, and his 'meta-present'.
The diagram is causal and deterministic. However, the universe is not deterministic, even in Minkowski/Einstein. There is a gap at O, that is not explained in the texts. Which is that O is not permanently static. O is just an instantaneous point somewhere in event E. The two are not the same. O is a point, E is an event in space-time. This difference introduces a necessary uncertainty in the universe.
What do you think?