DICTIONARY OF GEOPHYSICS, ASTROPHYSICS, and ASTRONOMY

a propagation velocity, c, which is numerically
equal to the observed speed of the light.
Minkowksi, Lorentz, and especially Einstein
in his 1905 exposition, modified concepts of
space and time in a way that accommodates
the fact that every observer, regardless of his
motion, will always measure exactly the same
speed for light as experimentally observed by
Michelson and Morley. To accomplish this required
accepting that time is involved in Lorentz
transformation, the change of coordinate frame
between moving observers, just as spatial position
is involved. The Lorentz transformation
also predicts length contraction, time dilation,
and relativistic mass increase, and led Einstein
to his famous result E=mc 2 .
A consequence of the universality of the
speed of light is that velocities are not additive.
If the system B (say, an airliner) moves with respect
to the system A (say, the surface of the
Earth) with a given velocity v1 (say, 900 km/h)
and an object C (say, a flight attendant) moves in
the same direction with a velocity v2 (suppose,
4 km/h), then the velocity of the object C with
respect to the system A is not simply v1 + v2,
v1+v2
but V =
1+(v1v2/c2 , where c is the velocity
)
of light (in the example given, the flight attendant
moves with respect to the surface of the
Earth with the velocity 904 ·(1 − 0.31 · 10−12 )
km/h). As is seen from the example, at velocities
encountered in everyday life the corrections
provided by special relativity to Newton’s mechanics
are negligible. However, for velocities
large compared toc, the difference is profound.
In particular, if v2 =c, then V =c. Also, if
v1 ≤c andv2 ≤c, thenV≤c, i.e., the velocity
of light cannot be exceeded by adding velocities
smaller than c. The geometric arena of special
relativity is not the three-dimensional EuclideanspacefamiliarfromNewton’stheory,
but
a four-dimensional Minkowski spacetime. The
Euclidean space is contained in the Minkowski
spacetime as the subspace of constant time, but
it is not universally defined, i.e., every observer
will see a different Euclidean space in his/her
own reference system. See Lorentz transformation,
Michelson–Morley experiment.
specific The adjective used to express a quantity
per unit mass.
© 2001 by CRC Press LLC
specific photosynthetic rate
specific absorption coefficient The absorption
coefficient [m −1 ] per unit mass of material,
e.g., for unit chlorophyll a concentration (Units:
[mg chl a m −3 ]); one obtains a specific absorption
coefficient with units [m 2 (mg chl a) −1 ].
specific discharge See Darcy velocity.
specific energy A term used in the study of
open channel flow to denote the energy of a fluid
relative to the channel bottom. Specific energy
is defined as E = y + V 2 /2g, where y is flow
depth, V is flow speed, and g is acceleration of
gravity. Specific energy has units of length and
corresponds to energy per unit weight of fluid.
specific gravity Ratio of the density of a substance
to that of water.
specific heat Specific heats, also called specific
heat capacity or heat capacity, are defined
under constant volume (cv, Cv, also called isochoric
specific heat) and constant pressure (cp,
Cp, also called isobaric specific heat). The constant
volume specific heat of a pure substance
is the change of molecular internal energy u for
a unit mass (or 1 mole) per degree change of
temperature when the end states are equilibrium
states of the same volume:
∂u
∂ū
cv ≡ and Cv ≡ ,
∂T v
∂T v
where cv is for unit mass and Cv is called the
molal specific heat, u is the specific internal energy,
ū is internal energy for 1 mole; Cv = Mcv.
The constant pressure specific heat of a pure substance
is the change of enthalpy for a unit mass
(or 1 mole) between two equilibrium states at
the same pressure per degree change of temperature:
∂h
∂ ¯h
cp ≡ and Cp ≡
∂T p
∂T p
where h = (u+pv) is the specific enthalpy, and
¯h is the enthalpy for 1 mole; Cp = Mcp.
specific humidity The mass of water vapor
per unit mass of air.
specific photosynthetic rate Photosynthetic
rate, net or gross, per unit biomass or per unit
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