Spacetime

Newtonian Space-and-time, Neo-Newtonian Spacetime, and Spacetime of Special Relativity (pp. 202-209)

ª@
Newtonian space-and-time
Neo-Newtonian spacetime

Minkowski spacetime

(special relativity)
absolute temporal separation
OK
OK
NO
absolute spatial position
OK
NO
NO
absolute velocity
OK
NO
NO, except for the velocity of light
absolute acceleration
OK
OK, if "inertial" motion is introduced (by definition)

OK in the sense that noninertial motion can be distinguished; and if an inertial frame is chosen, the magnitude of acceleration can be defined as an invariant quantity.

But otherwise absolute magnitude of acceleration is meaningless except for zero.

Added March 23, 2001:

The preceding comparison needs supplement; John Earman (World Enough and Space-Time, 1989, ch. 2) pointed out six kinds of classical space-time:

  1. Machian space-time, which assumes absolute simulataneity and a Euclidean metric structure for each instantaneous space (i.e. a slice of space-time at an instant), and in which a relative distance between two particles is invariant.
  2. Leibnizian space-time, which adds time metric to Machian space-time, and consequently relative velocities and accelerations also become invariant.
  3. Maxwellian space-time, which adds a standard of rotation to Leibnizian space-time; that is, you choose a rigid frame and declares that this is nonrotating. This makes the difference between linear motion and rotation, and rotation of an extended body becomes invariant, although acceleration in general of a body is not meaningful.
  4. Neo-Newtonian or Galilean space-time (now familiar to you), which is obtained by adding inertial structure to Maxwellian space-time, and acceleration becomes invariant.
  5. Full Newtonian space-time, which assumes absolute space in addition to Neo-Newtonian space-time. Thus velocity also becomes invariant.
  6. Aristotelian space-time further assumes a single spatial origin (see Aristotelian Space) , so that a distance from the origin (i.e. the center of the universe) becomes invariant. However, in this context you have to ignore both the "natural" difference between celestial region and sublunar region, and the finiteness of the universe, contrary to Aristotle's own assertion! Earman's idea is a "modernized Aristotelian view", for limited use only.

In any case, this finer distinction throws some good light on the classical debates on relationism-absolutism of space and time.

BACK TO SPACETIME

Last modified March 27, 2003. (c) Soshichi Uchii

suchii@bun.kyoto-u.ac.jp