12
G. Altarelli and S. Forte
problem of the formulation of a quantum theory of gravitational interactions is
one of the central problems of contemporary theoretical physics. But quantum
effects in gravity become only important for energy concentrations in space-time
which are not in practice accessible to experimentation in the laboratory. Thus the
search for the correct theory can only be done by a purely speculative approach.
All attempts at a description of quantum gravity in terms of a well defined and
computable local field theory along similar lines as for the SM have so far failed to
lead to a satisfactory framework. Rather, at present the most complete and plausible
description of quantum gravity is a theory formulated in terms of non pointlike
basic objects, the so called “strings”, extended over distances much shorter than
those experimentally accessible, that live in a space-time with 10 or 11 dimensions.
The additional dimensions beyond the familiar 4 are, typically, compactified which
means that they are curled up with a curvature radius of the order of the string
dimensions. Present string theory is an all-comprehensive framework that suggests
a unified description of all interactions together with gravity of which the SM would
be only a low energy or large distance approximation.
A fundamental principle of quantum mechanics, the Heisenberg indetermination
principle, implies that, for studying particles with spatial dimensions of order x or
interactions taking place at distances of order x, one needs as a probe a beam of
particles (typically produced by an accelerator) with impulse p ¯
h//x, where ¯
h
is the reduced Planck constant ( ¯
h = h/2π). Accelerators presently in operation or
available in the near future, like the Large Hadron Collider at CERN near Geneva,
allow to study collisions between two particles with total center of mass energy up
to 2E ∼ 2pc 14 TeV. These machines, in principle, can allow to study physics
down to distances x 10 −18 cm. Thus, on the basis of results from experiments
at existing accelerators, we can confirm that, down to distances of that order of
magnitude, indeed electrons, quarks and all the fundamental SM particles do not
show an appreciable internal structure and look elementary and pointlike. We expect
that quantum effects in gravity will certainly become important at distances x
10 −33 cm corresponding to energies up to E ∼ M P l c 2 ∼ 10 19 GeV, where M P l
is the Planck mass, related to Newton constant by G N = ¯
hc/M 2
P l . At such short
distances the particles that so far appeared as pointlike could well reveal an extended
structure, like for strings, and be described by a more detailed theoretical framework
of which the local quantum field theory description of the SM would be just a low
energy/large distance limit.
From the first few moments of the Universe, after the Big Bang, the temperature
of the cosmic background went down gradually, starting from kT ∼ M P l c 2 , where
k = 8.617 . . . 10 −5 eV K −1 is the Boltzmann constant, down to the present situation
where T ∼ 2.725 K. Then all stages of high energy physics from string theory,
which is a purely speculative framework, down to the SM phenomenology, which is
directly accessible to experiment and well tested, are essential for the reconstruction
of the evolution of the Universe starting from the Big Bang. This is the basis for the
ever increasing relation between high energy physics and cosmology.
G. Altarelli and S. Forte
problem of the formulation of a quantum theory of gravitational interactions is
one of the central problems of contemporary theoretical physics. But quantum
effects in gravity become only important for energy concentrations in space-time
which are not in practice accessible to experimentation in the laboratory. Thus the
search for the correct theory can only be done by a purely speculative approach.
All attempts at a description of quantum gravity in terms of a well defined and
computable local field theory along similar lines as for the SM have so far failed to
lead to a satisfactory framework. Rather, at present the most complete and plausible
description of quantum gravity is a theory formulated in terms of non pointlike
basic objects, the so called “strings”, extended over distances much shorter than
those experimentally accessible, that live in a space-time with 10 or 11 dimensions.
The additional dimensions beyond the familiar 4 are, typically, compactified which
means that they are curled up with a curvature radius of the order of the string
dimensions. Present string theory is an all-comprehensive framework that suggests
a unified description of all interactions together with gravity of which the SM would
be only a low energy or large distance approximation.
A fundamental principle of quantum mechanics, the Heisenberg indetermination
principle, implies that, for studying particles with spatial dimensions of order x or
interactions taking place at distances of order x, one needs as a probe a beam of
particles (typically produced by an accelerator) with impulse p ¯
h//x, where ¯
h
is the reduced Planck constant ( ¯
h = h/2π). Accelerators presently in operation or
available in the near future, like the Large Hadron Collider at CERN near Geneva,
allow to study collisions between two particles with total center of mass energy up
to 2E ∼ 2pc 14 TeV. These machines, in principle, can allow to study physics
down to distances x 10 −18 cm. Thus, on the basis of results from experiments
at existing accelerators, we can confirm that, down to distances of that order of
magnitude, indeed electrons, quarks and all the fundamental SM particles do not
show an appreciable internal structure and look elementary and pointlike. We expect
that quantum effects in gravity will certainly become important at distances x
10 −33 cm corresponding to energies up to E ∼ M P l c 2 ∼ 10 19 GeV, where M P l
is the Planck mass, related to Newton constant by G N = ¯
hc/M 2
P l . At such short
distances the particles that so far appeared as pointlike could well reveal an extended
structure, like for strings, and be described by a more detailed theoretical framework
of which the local quantum field theory description of the SM would be just a low
energy/large distance limit.
From the first few moments of the Universe, after the Big Bang, the temperature
of the cosmic background went down gradually, starting from kT ∼ M P l c 2 , where
k = 8.617 . . . 10 −5 eV K −1 is the Boltzmann constant, down to the present situation
where T ∼ 2.725 K. Then all stages of high energy physics from string theory,
which is a purely speculative framework, down to the SM phenomenology, which is
directly accessible to experiment and well tested, are essential for the reconstruction
of the evolution of the Universe starting from the Big Bang. This is the basis for the
ever increasing relation between high energy physics and cosmology.