Synopsis
Philosophical foundations of spacetime theories
Special-relativistic theories speak the language of uniformly
moving (inertial) observers: the Lorentz coordinates have a
direct metrical interpretation as the distances and times
measured by inertial observers; and the physical quantities of the
theories, when expressed as tensors, refer directly to the
measurements of the inertial observers.
Nevertheless, there is a special interest in the consideration of
accelerated observers, even in a special-relativistic context.
First, accelerated frames are historically the germ from which general
relativity was born: Einstein came to the principle of
equivalence through the investigation of uniformly accelerated
frames, and his primary pretense for the general theory was to extend
the relativity of physical laws from inertial to generic
observers.
Second, there are special topics in relativistic theories (such as
the now-famous Unruh effect, or the problem of radiation
reaction) where a subjective description (made from the point of
view of accelerated observers) is desirable. In collaboration with
Prof. Massimo Pauri, I have studied the physics of accelerated
observers from several points of view.
- We have identified the origin of the Unruh effect (and of its
analog in black-hole spacetimes, the Hawking effect) in the
classical principle of perspectival semantics, according
to which some familiar notions defined in special-relativistic
theories (such as particle and radiation) inevitably
lose their coherence when they are transported to accelerated frames
or to curved spacetimes. [See Refs. 1, 2, 3, 4 below.]
- We have proposed a general scheme to build an accelerated system
of coordinates (Maerzke-Wheeler coordinates) adapted to the
motion of a generic accelerated observer, and we have suggested two
applications for this new system (the first application is related to
the special-relativistic paradox of the twins; the second to
the generalized Unruh effect). [See Refs. 2, 5 below.]
- The definition of coordinate systems (both inertial and
accelerated) is intimately tied to the choice of a relation of
distant simultaneity between events: we have reviewed the
perennial debate (among relativists and philosophers of physics) on
the conventionality of simultaneity in special relativity, and
we have examined the conventionality of Maerzke-Wheeler
simultaneity. [See Ref. 2 below.]