Quantum Gravity : Mathematical Models and Experimental Bounds

20 Claus Lämmerzahl
The two postulates have some immediate consequences which all can be tested
in experiments:
• The velocity of light, c, does not depend on
– the velocity of the source (what is a statement of the uniqueness of the
phenomenon)
– the velocity of the observer,
– the direction of propagation,
– the polarization or frequency of the light ray.
• The relativity principle implies that
– the limiting velocity of all particles is the speed of light
c = c + = c − = c ν = v max
p
= v max
e
= v grav
(If these velocities are not equal then this defines a preferred frame by
the condition that in this frame both limiting velocities are isotropic.
This is the SR aspect of the THɛµ–formalism (see, e.g., [21, 22] and
references therein. This is in contradiction to the second postulate, with
the consequence that c is universal and, thus, can be interpreted as
geometry.)
– that all physics is the same in all inertial systems, that is, experimental
results do not depend on the
∗ orientation of the laboratory and
∗ on the velocity of the laboratory.
Accordingly, we have the following classes of experiments:
3.3.1. Constancy of c. The independence of the speed of light from the velocity of
the source has been examined by astrophysical observations as well as in laboratory
experiments. We mention just two of them: (i) the observation by Brecher [23] who
analyzed the time of arrival of X–rays emitted from distant a bright star orbiting a
dark, heavy central star. We model a hypothetical dependence of the speed of light
c from the velocity of the source by c ′ = c+κv, wherev is the velocity of the source
and κ some parameter which is 0 in SR and 1 in Galilean kinematics. If the star
is moving away from the Earth, the emitted light is slower than the light emitted
when the star is moving toward the Earth. Therefore, light emitted toward the
Earth may overtake the light emitted earlier. The images of the star seen on Earth
may show an achronological order. Since this has never been observed one can
derive κ ≤ 10 −10 . A laboratory version of this has been carried through at CERN
[24]. Protons hitting a Beryllium target created π 0 mesons possessing a velocity of
v =0.99975c. Theseπ 0 mesons decay within 10 −16 s into photons which velocity
has been measured and compared with the velocity of photons emitted from π 0
mesons at rest. No difference in the speed of the photons has been found leading
to κ ≤ 10 −6 . Though this is not as good as the Brecher result, it shows the result
for a velocity of the source being almost the speed of light. The independence of
the speed of light from the velocity of the source cannot be demonstrated more
convincingly than by this experiment.