Einstein's New Clothes

Einstein introduced his theory of General Relativity in his seminal
paper in 1917. Building up on Special Relativity, which describes a
dynamical system under the assumption that no body can move faster
than the speed of light, General Relativity was meant to include the
forces of gravity and accelerated frames into Special Relativity. One
of its basic assumption was the equivalence principle, i.e. that the
instance of mass as a source of the gravitational field, is the same
as the instance of mass as the measure of "resistance" a body exerts
if one tries to distort it from linear unaccelerated motion. The onset of Special
Relativity is that light propagates with a constant speed along the
shortest distance between two points A and B. This is for our everyday
experience a straight line, however in the presence of massive bodies
light propagates along geodesics in a curved space. This is just like
for long distance flights which follow the shorter parts of great circles
along the surface of the earth.

Hence, according to General Relativity, if light seemingly deviates from a straight path,
space must be curved. This happens in the close vicinity of large masses,
and the effect is a valuable tool in modern astrophysics, known as
gravitational lensing.

From it's beginning one of the amazing results was that General
Relativity seemed to describe a dynamically evolving Universe. The
dynamics of the large scale motion of the Universe is described by
Einstein's equation of gravity, which relates the geometry of the
Universe to its energy (matter) contents. Einstein, who firmly
believed at the time that the Universe should be a static entity,
could only accommodate this by introducing a term which carefully
balanced the other energy constituents. He called this term the
cosmological constant, because the energy associated with it, has the
peculiar feature that even if the Universe expands, it's density stays
constant.

In 1929 Hubble discovered his famous law, that the further away
galaxies are from us the faster they are receding. This was later
confirmed by Sandage and others and is continued to be tested by the
Hubble Space Telescope to unprecedented distances.

Einstein realized that the Universe
must be expanding and the the Universe is NOT static. He
threw the cosmological constant out of the window, and according to Gamow
Einstein called the introduction of the
cosmological constant its greatest blunder. Nevertheless the inclusion
of a cosmological constant in the equations of General Relativity is
mathematically sound and no fudge factor.

In 1933 Fritz Zwicky observed the Coma Cluster and noticed that
outlying galaxies where moving much faster than would be expected for
the sum of the mass of galaxies further inside. He hence estimated
that the cluster must consist of 90% dark matter which we can not
observe directly.

At the beginning of the 1970s Vera Rubin made the
discovery that the velocity of hydrogen clouds in galaxies does not
decrease with distance from the center, as would be expected from the
distribution of visible stars. Hence, galaxies, like clusters must
also contain some form of dark matter.

In 1997 Cosmology experienced another surprising turn. With the
observation of imploding stars (Type Ia Supernovae for the experts),
which are as bright as an entire galaxy, the Supernovae Cosmology
Project and the High-z Supernovae Search Team announced, that they
found evidence that the expansion of the Universe is speeding up.
What was measured was the receding velocity of the host galaxies of
the Supernovae, i.e. their redshift and the brightness of the
Supernovae. The brightness can be related to the distance of the
Supernovae, with the simple fact that more distance objects appear
fainter. Hence we can plot a distance - redshift diagram. Since the
receding velocity (or redshift) is related to its distance, via
Einstein's equations of General Relativity, and hence to the energy
(matter) contents in the Universe, one can probe cosmological models
in this way. The outcome was shocking:

A cosmology with a cosmological constant seem to be a much better
explanation of the data. In a sense it was discovered that expansion
rate of the Universe at early times was slower than it is now, hence
we require some source for this cosmic speed up. Einstein's balancing
term was swiftly remembered. What, if we actually over-balance the
ordinary matter terms with the cosmological constant ? Instead of
obtaining a static Universe, we obtain one which expands in an
accelerated fashion.
The early findings of the Supernovae teams are now confirmed by
observations of the cosmic microwave background, together with large
scale structure and clusters of galaxies (Wilkinson Microwave Anisotropy Probe ,
2 degree Field Galaxy Redshift Survey , Sloan Digital Sky Survey , Chandra Satellite).

However we are now faced with the fact that 95% (!) of the Universe
are made of a form of energy, or matter, which we have hardly an
inkling what the stuff actually is made of. Only 5% is made of matter
we have observed directly in Nature. 25% reside in form of
dark matter, which is only very weakly, if at all, interacting with
"natural" forms of matter. However fundamental physics, like
Supersymmetry, predicts a plethora of particles, which are valid dark
matter candidates. The situation is far more grim for the 70% which
are responsible for cosmic acceleration and are usually called dark
energy. There are some interesting description, like scalar field
Quintessence models, but most of them are made up more or less ad hoc
and have no sound footing in fundamental physics.

We are in a situation now, that if we believe
Einstein's Equation of Gravity, 95% of the Universe are unknown to us.
This reminds me of the fairy tale by Hans Christian Anderson, "The
Emperor's New Clothes", where everybody admires the new suit of the
emperor, which according to the crooked tailors is only visible to
smart people. Until a little kid shouts: "But he [the emperor] has nothing
on at all".

This is setting the scene for a new approach to gravity. The earliest
published approaches to an alternative description of General
Relativity were done by Pasqual Jordan in 1945. In 1961 Brans and
Dicke studied a similar theory, which effectively resulted in a theory
of General Relativity with a varying gravitational constant.
Since Brans and Dicke wrote their paper about an extension of Einstein
gravity with higher order curvature terms, theorists in the back of their
minds are aware that Einstein's theory of gravity might not be the
final answer. However Einstein's general relativity is an incredible
successful theory, which so far has stood all direct, albeit local
tests, like the perihel precession of mercury. Hence any valid
extension of gravity has to pass these tests as well.
The gravity in galaxies and clusters of galaxies is mainly governed by
Newtonian mechanics, however with the addition of a dark matter
halo as mentioned above. Milgrom [1983] however introduced a
different explanation. What if Newtonian dynamics is modified on large
scales and hence explains the rotation curves of galaxies without the
introduction of dark matter. These theories are usually called MOND
(the German word for 'moon' incidently), for Modified Newtonian
Dynamics. However, the problem is that Einstein's General Relativity
reproduces in it's low mass limit Newton's dynamics. That is why it is
incredibly hard to experience any effect of General Relativity on
Earth. Up until two years ago their was no mathematically
sound theory which produced a relativistic extension of MOND. However,
Bekenstein introduced a mathematically consistent theory of MOND in
the beginning of 2004. This theory is able to reproduce the galactic
rotation curves
without introducing dark matter. But it is significantly different
from Einstein's General Relativity. An even bolder, but nevertheless,
valid step is to try and explain the accelerated expansion of the
Universe by modifying the laws of gravity. These approaches contain
higher orders of the curvature of the
Universe. An interesting class of these was recently suggested by
Carroll and collaborators. In this case the inverse of the curvature
is included into the set up of the equations which describe
gravity. In this case, the dominant effect is at large scales where
the Universe is apparently flat and there is zero curvature. It can be
shown that some of these models lead to accelerated expansion and also
pass solar system tests. A different approach is to try and explain these
modifications of gravity in our four dimensional space-time with
higher dimensional world models. So called Brane Worlds which could appear
from compactifications of 11-dimensional theories to our four
dimensions could lead in fact to modifications of of the equations
which govern the the dynamical evolution of a 4-dimensional world. In
this case a straight forward extension of General Relativity holds at
the higher dimensions and our low dimensional Physics is just some
effective theory as a result of the compactification.

The exciting prospects for the future are that there is a hand full of
missions and observations planned which would allow the
distinction between dark energy and modified gravity. One such probe
is the "Dark Energy Survey" which is led by Fermilab scientist, with
collaborators from other US institutions and Europe. The "Dark Energy
Survey" tries to test dark energy models simultaneously with four
different astrophysical probes. Some of these respond differently to
modified gravity than to dark energy. The combination of all four
probes might be able to distinguish between modified gravity models
and dark energy approaches. In the end the "Dark Energy Survey" might
be able to show if Einstein is in fact naked or has indeed a multi
layered suit whose fabric needs to be revealed.

If you would like to read more about me and my research have a look on my Quantum Diaries Blog

Comments

[Robert B. Peake]

A great summary! I had not encountered the idea of MOND before.

This is certainly an interesting time in which to live!

It is somewhat amazing to me that humans are ingenious enough to figure out these mysteries of the Universe.