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spacetime interval
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GorillaPhysicist
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Mon Aug 06 2001 at 18:27:07
Under the
Lorentz Transformation
,
space
and
time
intervals turn out not to be
invariant
. The
transformation
, and the
relativity of simultaneity
lead
observer
s in
intertial frames of reference
to see
length contraction
and
time dilation
, given by the
gamma factor
of (1-v
2
/c
2
)
-1/2
.
The
spacetime
interval
is the
quanitity
that
is
invariant under the Lorentz Transformation, it gives a '
distance
' in
4-space
of two
event
s. The
interval
/\
s is given by:
/\
s
2
= (c
/\
t)
2
-(
/\
x
2
+
/\
y
2
+
/\
z
2
)
When c
/\
t is greater than
/\
x
2
+
/\
y
2
+
/\
z
2
, the spacetime interval is said to be '
timelike
'. If those two are equal, the interval is '
lightlike
'. And if c
/\
t is less than
/\
x
2
+
/\
y
2
+
/\
z
2
, the spacetime interval is '
spacelike
', and could constitute part of the
world line
of a
particle
with
rest mass
.
printable version
chaos
four space
Lorentz invariant
Lorentz transformation
command mode
proper
Klein-Gordon Equation
OO
PFE
Inertial frame of reference
length contraction
time dilation
delta
Heisenberg Uncertainty Principle
invariant
squared
relativity
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