  I suggest that the Spin-Statistics connection is a consequence of the phase
shifts on quantum scattering amplitudes due to the induced gravitomagnetic
field of the whole Universe at critical density. This connection was recently
brought out in the context of a new theory of relativity in flat space with
matter, called Cosmic Relativity (gr-qc/0406023). This prediction of the
correct gravitational phases is a consequence of any relativistic gravitation
theory in the presence of the massive Universe. This can also be interpreted as
related to the Mach's principle applied to quantum phenomena. Perhaps this is
the simplest valid proof of the Spin-Statistics Theorem, and it finally
identifies the physical origin of the connection.
