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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 it in a form where r (matter-density) and p (pressure) appear explicitly. 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 many unsolved problems in these two fields. We are not going to recall the whole story of astronomy and cosmology here. The spectroscopic method, combined with Doppler effect measurements, gave important data on the chemical composition and temperature of stellar chromospheres.
Cepheids, used as distance standards, make it possible to evaluate distances up to tens of millions of light years.
Differential geometry tools gave a new insight into 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 previous section that the solar neutrino deficit raises a serious problem about these stellar models).
Nuclear physics explains the presence and relative abundance of primitive helium in the universe.
But:
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We have no theoretical model explaining galactic dynamics. In this field our approach is still fully empirical.
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We don't know how galaxies form and why they have such specific masses, nor how they change over time. The spiral structure is not really understood. Its real origin remains controversial.
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All galaxies should have exploded since billions of years (missing mass effect). The rotation curve, with large peripheral velocities, is still a mystery.
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Same missing mass problem about clusters of galaxies.
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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 powerful underlying and completely unknown forces causes that. * * - It seems to be a problem about the age of the universe, from Hubble's constant measurement, compared to the estimated age of the oldest stars of our galaxy (which belong to globular clusters, like Hercules' cluster).
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The VLS (very large structure) of the universe is still an unsolved problem. We don't know why the galaxies are located around big voids, 100 million light years in size.
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The quasar's energy source is still unknown.
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Halton Arp has found many systems of galaxies whose red shifts violate the Hubble's law.
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Nature of the "gamma flashes": unknown.
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Neutron stars were predicted and many hundreds were found. This model has a critical mass: about 2.5 solar masses. No neutron star could exist with a 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: supernovae, 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
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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 "horizon" ct was smaller than the mean distance between them. So, what caused today's observed remarkable homogeneity of the cbr?
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What is "time", close to "t=0"? Does this question make 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 deluded 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 Copernican era. When the young King of Spain learned the Ptolemaic model from his teacher, 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 previous 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 mathematician Gottfried Wilhelm Leibniz proposed something similar in his book, Monadologia. Leibniz 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 newspaper 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.