a117

With only positive masses the Einstein's equation is :

(95)

S = c
T

where S is a geometric tensor and T the
"energy-matter" tensor. We can express in a form where r
( matter-density) and p (pressure) appear explicitely.
In classical relativity both are positive.

Now call r+ and
p+ the contributions
due to positive masses. Call T+ the
tensor built with these quantities.

Negative mass-density r- <
0 and negative pressure p-
< 0 , due to negative masses would give a tensor T-.

Then the corresponding field equation becomes :

(96)

S = c
(T+ + T-)

The unsolved problems in today's astrophysics and cosmology.

There are a lot of unsolved problems in these two fields.
We are not going to recall the whole story of astronomy and cosmology here.
Spectroscopic method, combined to Doppler effect measurements gave important
data on chemical compositions and temperature of stellar chromospheres.

Cepheids, used as distance standards, make possible distance
evaluation up to tens of millions light years.

Differential geometry tools gave a new insight on cosmology
( field equation, metric) and explained the red shift phenomenon and the cosmic
background radiation.

Nuclear physics produced stellar models, both for their
origin, working and evolution ( but we saw in a preceding section that the
solar neutrino deficit arises a serious problem about these stellar models
).

Nuclear physics explains the presence and relative abundance
of primitive helium in the universe.

But :

• We have no theoretical model explaining galactic dynamics.
  In this field our approach is still fully empirical.

• We don't know how galaxies form and why they have such
  specific masses, nor how they change in time. The spiral structure is not
  really understoood. Its real origin remains controversial.

• All galaxies should have exploded since billions of
  years ( missing mass effect ). The rotation curve, with large peripheric velocities,
  is still a mystery.

• Same missing mass problem about clusters of galaxies.

• Many galaxies are very irregular. Years ago, the British
  astronomer Sir James Jeans used to say :

When we see such distorted patterns we cannot resist
the idea that some powerfull underlying and completely unknown forces causes
that.

• It seems to be a problem about the age of the universe,
  from Hubbles' constant measurement, compared to the estimated age of the oldest
  stars of our galaxy (which belong to globular clusters, like Hercules'cluster).

• The VLS ( very large structure ) of the universe is
  still an unsolved problem. We don't know why the galaxies take place around
  big voids, 100 years light span.

• The quasar's energy source is still unknown.

• Halton Arp has found many systems of galaxies whose
  red shifts violate the Hubble's law.

• Nature of the "gamma flashes" : Unknown.

• Neutron stars were predicted and many hundreds were
  found. This model owns a critical mass : about 2.5 solar mass. No neutron
  star could exist, with higher mass, for internal pressure force could no longer
  balance the gravitational force, so that the object would collapse.

Such conditions must exist, somewhere in the universe.
For example as the result of the merging of a couple of neutron stars. The
"classical answer" is the so-called black hole. Some astronomers "explain"
all kinds of phenomena with such objects. Giant black holes must be
present at the center of galaxies or at the center of clusters of galaxies.
They "explain" the QSO phenomenon. They "explain" almost everything.

But direct observations look very rare. Why so few candidates
?

When an object really exists, after a time, astronomers
find many. Example : supernovæ, rotating neutron stars (pulsars). Why
so few black hole candidates ?

Furthermore, the geometry of the black hole is a solution
of the Einstein equation when the second member vanishes, when T =
0. Which means that this solution describes a portion of the universe where
no energy-matter is present. The field equation reduces to :
(97)

S = 0

• Back to the standard model, why the early universe (whose
  image is given by the cosmic background radiation) looks so uniform ? From
  the model, in the early time, particles of the universe could not interact,
  for the "horison" ct was smaller than the mean distance between them. So,
  what caused today's observed remarkable homogeneity of the cbr ?

• What is "time", close to "t=0" ? Does this question
  makes any sense ?

Walking back to the most distant past, physicists reach
high energy conditions, and the problems they meet seem to be comparable to
today's crisis of high energy physics :

- What do we talk about ?

• Who knows that the Einstein's equation, supporting the
  Standard Model, does not take account of electromagnetic phenomenon ? The
  link between gravitation and light theory is not built yet. The same gap between
  quantum world and gravitation ( what is a graviton ? ).

Fifty years of null-physics.

This title seems very provocative. Today's technological
progress is very impressive.Theoretical physicists dream about the "Theory
of Everything" (TOE) ". The success of quantum mechanics delude researchers.
Do you know that we have no way to predict the masses of particles. The Quark
model looks like Ptolemaic system.

Centuries ago, Ptolemy found a system able to describe
the paths of planets in the sky, through a complex system of circles. This
was very efficient, to predict eclipses, for example. At the end this model
used 48 circles. Before Copenician era. When the young King of Spain learned
the Ptolemaic model from his teatcher, he said :

- Gosh, if the Lord asked me advice before creating
all that, I should have recommended something simpler !

False things can efficiently work during centuries. That's
why the solar neutrino deficit, evoked in a preceeding section, is so fascinating
: quantum mechanics cannot explain it. That's the very first time the quantum
machinery jams.

Some look in the direction of superstring theory, which
is based on group theory. Superstring men think that everything in the world
could correspond to different structures of a 10-dimensional entity, "space".
In 1714 the German philosopher and mathematicain Gottfried Wilhem Leinitz
proposed something similar in his book, Monadologia. Leibnitz thought that
"everything was made of "monads". The world should be some sort of organized
system of monads, but he could not develop his idea.

Superstring men search their modern ten dimensional monad.

All this gives rise to truly surrealistic exchanges in
colloquia, like that which recently took place in Aspen, Colorado. The news
paper Scientific American reported in its edition of January 1996, in an article
entitled "Explaining everything," by Madhusree Mukerjee, staff writer.

Seeking this magical object supposed to organize the ten-dimensional
universe, some people speak about "studded spheres," hedgehogs bristling with
vectors, or "hairy caterpillars," membranes with five dimensions (Duff, of
London's Imperial College), capable of rolling onto themselves "like the skin
of a sausage."

Schwarz, of Caltech (one of the pioneers of the theory),
adds, "I should have been a truck driver!"

Others speak of "black holes with zero mass."

Jeffrey A. Harvey, of the University of Chicago, cried
out:

"Does that mean that your black holes have zero mass?
Do they move at the speed of light?"

"No, they have nothing, no momentum," Gary T. Horowitz
of the University of California at Santa Barbara turns to reply.

"Oh, baloney!" That was Leonard Susskind of Stanford.

They have no energy, no momentum -- there's nothing there!"
Harvey protests.

Strominger: "Somewhere in the universe portions of space
might exist in the shape of little drops, entering into which black holes
would be transformed into strings, and vice-versa. In our environment these
little drops could seem to navigate in virtual universes, which would exist
for an infinitesimal period of time, since they would immediately disappear,
before they could be observed.

Susskind: "I personally think it's a lot of crap."

In 1986 someone asked a researcher to sum up the "Theory
of Everything" in seven words, and he answered:

• Oh, Lord, why have you forsaken me?

All this is interesting, but it's not over, as we can see.
Never in the history of physics has a body of theory given rise to such convulsions
as now, when ten articles are being published on the subject every day. And
we cannot say whether the mountain will give birth to a mouse or the mouse
to a mountain.