Then what, exactly, is time dilation as caused by high-fractional relativistic velocities?
8.3 Time, Space, and Relativity
Interactions without gravity are described by special relativity, while interactions in
the presence of massive systems are described by general relativity. The parameters used to measure the states of relativistic systems, are no longer invariant, apart from some constants like the speed of light or the spatial constant p; the information which is received, is distorted compared to the information which is emitted. The covariance of the parameters is caused by:
• The high speed of the object relative to the observer (relativistic speed).
• The propagation of information at the speed of light.
• Gravity during interactions with massive systems.
8.3.1 Special Relativity
The theory was published in 1905 by Albert Einstein (1879–1955). Information,
emitted by a relativistic object is distorted when it reaches the laboratory; con-
versely, information emitted by the laboratory is distorted when it reaches the relativistic system. The parameters lose their invariance: the object looks smaller, its mass and its temperature look higher, etc. In relativity, parameters are covariant.
Time seems to flow more slowly, durations look longer, and chronological age thus increases more slowly. In contrast, biological age and aging increase more quickly because of gravitational stress, which is not taken into account in theoretical
physics.
The formulas we owe to the French mathematician Henri Poincaré (1854–1912)
and the Dutch physicist Hendrik Lorentz (1853–1928) restore values of the data
provided by the relativistic system, given values of the received data. Let us look at
the alterations of space and time:
• The contraction of the length of an object is such that
l0 ¼ l 1 -
v2
=c2 1=2
in which “l” is the real length of the object and “l′” is the length of the object when it is observed from the laboratory.
• The dilatation of duration of an event is such that
t
0 ¼ t 1 -
v2
=c2 -
1=2
in which “t” is the duration of a relativistic event and “t′” is the duration measured
with the laboratory clock.
A traveler moving at speed v = c/2 (150 000 km/s) sees the scientist in the
laboratory smaller than he is: 1 m 47 instead of 1 m 70. According to calculations,
the scientist is 13.4 % less aged (theoretical chronological age); in fact, the traveler
will not be able to see this, because less aged does not mean younger (biological
age): the scientist does not rejuvenate. The phenomenon is reciprocal: the scientist
makes the same findings about the traveler (Fig. 8.1). Ultimately, they both pre-
serve their respective integrity. These relativistic mirages are caused by the co-
variance of the parameters.
The lifetime of the p+ meson is 2.5 10−8 s in its own reference frame, but in a
synchrotron where its speed is increased to 0.99995 c, the lifetime observed is c. 2.5
10−6 s. It seems that its life lasts 100 times longer at this speed: this feeling is belied
by the relativistic correction of the measures ([3]: Ch. III).
It was essential to rebuild a parametric invariance; we observe with interest that
this achieved thanks to a mathematical combination of the two abstract parameters
whose physical inexistence has been demonstrated:
ds2 ¼ c2
dt2 -
dx2 þ dy2 þ dz2
The time parameter “dt” and the space parameters “dx”, “dy”, and “dz” are no
longer invariant. The new invariant parameter “ds” is called the elementary interval
of spacetime, due to Minkowski.1 This is an original concept which replaces time
and space and remains to be defined.
According to the definitions of time and space, two states of a relativistic system
allow us to define the invariant concept of spacetime interval: this concept is more
Propagation
REFERENCE <--------------------------> RELATIVISTIC
of information
LABORATORY <------------------------> SYSTEM
at speed of light
Fig. 8.1 Reciprocity of the covariance of parameters
1
Hermann Minkowski, Baltic mathématician (1864-1909).
From
The Invention of Time and Space by Patrice F. Dassonville
The cut and paste from the book has mangled the formula and at 2am on holiday in Bali I'm to lazy to try to fix it but I hope you get a feel from the text
Cheers
