  A general simple theory for the interspecific allometric scaling is developed
in the $d+1$-dimensional space ($d$ biological lengths and a physiological
time) of metabolic states of organisms. It is assumed that natural selection
shaped the metabolic states in such a way that the mass and energy
$d+1$-densities are size-invariant quantities (independent of body mass). The
different metabolic states (basal and maximum) are described by considering
that the biological lengths and the physiological time are related by different
transport processes of energy and mass. In the basal metabolism, transportation
occurs by ballistic and diffusion processes. In $d=3$, the 3/4 law occurs if
the ballistic movement is the dominant process, while the 2/3 law appears when
both transport processes are equivalent. Accelerated movement during the
biological time is related to the maximum aerobic sustained metabolism, which
is characterized by the scaling exponent $2d/(2d+1)$ (6/7 in $d=3$). The
results are in good agreement with empirical data and a verifiable empirical
prediction about the aorta blood velocity in maximum metabolic rate conditions
is made.
