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The problem of the primitive universe.
...Let us consider a particle at the instant t = 0, or at an instant "close to t = 0". Suppose it emits some signal, for example electromagnetic radiation. This will propagate at the speed c. After time t the spherical wave will have a radius ct, which is called the horizon. But the law of expansion, of the distancing between two particles supposed to be linked to the "cosmic support" (they are said to be comoving) has a parabolic form (this distance grows as t2/3). Going back in time we will always find an epoch t < th where the particles were materially unable to communicate with one another, since they were moving apart "faster than the electromagnetic wave emitted at an instant t close to zero was traveling".
...The image below evokes this autistic state of the universe, the white spheres, linked to each of the particles, representing the volumes in which a neighbor would have to be located for communication to be possible. Alas, they do not interpenetrate, and will not do so until much later.
...It therefore becomes difficult to justify the remarkable homogeneity of the primitive universe, whose fossil trace is the cosmological radiation background at 2.7° K.
...The fashionable theory is that of Linde: inflation, and this is its sole justification. Without going into detail, this theory consists in endowing the primitive universe with a super-cosmological constant (depending on time!), reflecting a "repulsive power of the vacuum" defying all imagination. This then brings about an expansion by a factor of ten to the power of I don't know how many....
The problem of the origin.
What, in fact, is this time t = 0? Does it have any meaning?
...When one goes back in time, the temperature of the "cosmic fluid" increases. The speed of thermal agitation of particles endowed with a non-zero mass also increases. There comes a moment when this speed becomes relativistic. In fact, when t tends toward zero and the temperature T tends toward infinity, the individual energy of the particles tends toward infinity and their speed tends toward c. Proper time follows the law:
...When v tends toward c proper time "freezes in the chronometers". Defining a clock becomes problematic, even conceptually.
...One thus sees that the standard model is far from perfect. The list of problems mentioned is moreover not exhaustive. Fundamental physics knows similar problems. The theory of superstrings goes through an extension of the dimensional context (ten dimensions, for many). But ten-dimensional geometry remains an obscure jungle. If 2d surfaces have lost their mystery, the classification of 3 and 4d hypersurfaces remains to be done.
....Moreover, when one adds dimensions to the cosmos, characteristic lengths appear, associated with each of them. And these are invariably... the Planck length. Now whoever says length says wavelength, which is linked to energy, according to the relation:
...The Planck energy is considerable. To implement it, according to classical techniques, one would need to be able to have an accelerator with the diameter of a galaxy. Experimental physicists throw up their hands.
...The theoretical physicist of Japanese origin, Michio Kaku ("Hyperspace, a scientific odyssey through the 10th dimension", Oxford University Press, 1995), puts forward a tasty personal interpretation: according to him, the theory of superstrings would simply be ahead of its time by a few centuries. At the current stage of technology this would therefore only be a way of entertaining oneself among friends.
The Aspen colloquium.
...In 1996 the famous journal Scientific American published an account of a colloquium on superstrings that had just been held in Aspen, Colorado, under the pen of Madhusree Mukerjee, staff writer. A text worthy of the Marx Brothers:
...As recalled by the author of the article, in 1986 Jeffrey A. Harvey, of the University of Chicago, had been asked to define the theory of superstrings in seven words. His response had then been:
- Oh, Lord, why have you forsaken me?
But the paper indicates that God seems to have answered, through the discovery of a new symmetry: duality.
...Witten, the most optimistic of the superstring men, thinks that this duality will not only lead to the TOE (The theory of everything) but also explain "why the universe is made thus". He thinks that one is converging toward an explanation of the deep nature of quantum mechanics.
...Few people in fact tackle this theory of superstrings, which is indeed so complicated on all levels, including mathematically, that physicists and mathematicians are reluctant to plunge into it.
...The article indicates that this "duality" would make elementary particles and composite objects interchangeable. The specialists then evoke clumps which they attempt to visualize as "hedgehogs". To curl like a hedgehog: to roll oneself into a ball. Other images: those of "spheres studded with vectors", christened "solitons".
...But this duality, if it existed, would remain, specify the authors of this concept, impossible to demonstrate (by duality one must understand "double nature": English dictionary). In the article it is therefore specified that composite structures could be equivalent by being "tangled up" and then become "elementary objects".
The concept of "mirror symmetry" is then bandied about, without great success.
...In 1986 Duff, of Imperial College London, had considered the vibrations of a new entity, "a bubble". Whereas strings wiggled in ten dimensions, bubbles would float in an eleven-dimensional space. Then Duff considered membranes with "five dimensions", an alternative description with respect to strings. He then considered that these membranes could in turn roll up like "the skin of a sausage". And to evoke a "string-string duality".
...In 1995 Witten gave a lecture at Berkeley conjecturing that Duff's bubbles could be the solitons of a particular string corresponding to the ten dimensions.
And Schwarz, of Caltech, (one of the pioneers of the theory) added:
- I should have been a truck driver!
Be that as it may, currently, ten new papers on superstrings appear each day.
A soliton "looks like a hairy caterpillar", bristling with vectors, it is therefore "the dual object of the string".
Duff then proposed a duality of duality, between spaces. And Susskind to comment:
The size and the internal dimension of an object would change "from place to place".
Townsend:
- The membranes, transforming into string solitons, could have the same status as strings. Unfortunately the calculations made with membranes make no sense.
...One then evokes a marriage between strings and black holes. Hawking had indicated that black holes, being capable of emitting particles, would thus lose mass and shrink. If they were initially made of strings ("stringy black holes") their evolution would transform them into objects of zero size: "an extremal black hole looking in fact rather like a particle". Polemic between Susskind and Strominger, on this point:
- Strominger's work is "great", but to call these things black holes is still pushing it a bit.
For information, the title of Strominger's latest paper is: "The world conceived as a hologram".
The latter then evokes the concept of "zero-mass black hole".
Jeffrey A. Harvey, of the University of Chicago, protests at once:
- What does it mean that your black holes with zero mass? Do they move at the speed of the light?
Gary T. Horowitz, of the University of California:
- Oh, baloney!
A little further on one reads that strings "could configure themselves according to their environment", adopting a dynamically correct solution (...). And Strominger to add:
- Somewhere in the universe there could exist portions of space in the form of droplets, in which black holes, on entering, would transform into strings, and vice-versa. In our environment these droplets could seem to navigate in virtual universes, which would exist for an infinitesimal lapse of time, since they would disappear at once, before one could observe them.
...But no one seems to believe anymore that "the solution is around the corner", despite Witten's assertion, who had bet an ice cream cone that the theory would be ripe by the end of the century.
And t'Hoff to reply with acidity:
- When the string people take stock, they always tend to inflate their results. They simply blindly believe in their theory.
In this arena of superstrings, the young and the less young rub shoulders.
Sidney R. Coleman, of Harvard:
- At my age you tend to emit a lot of gas. I'd rather not.
Sheldon L. Glashow agrees that "nothing has moved in this theory":
End of the colloquium. Night falls, says the author of the article, and Susskind to let drop:
- I personally think it's a lot of crap!
Despite this crisis some think that everything will eventually work out. Dark matter will be detected. The theory of everything will eventually emerge, against a background of ten-dimensional superstrings.
...While awaiting this blessed epoch, this golden age of knowledge, the theoretical developments that will follow are, all in all, neither better nor worse than everything relating to dark matter and superstrings.
Before attacking the presentation of our work, an account of a discussion with J.M. Souriau (4/1/98).
(perhaps a beginning of an explanation of the current situation).
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You think we are living through a period of stagnation, in fundamental physics?
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Since the fifties, Feynmann and quantum electrodynamics, it's flat. Quantum electrodynamics, it works, but to tell the truth one doesn't really know why. That remains to be found. Apart from that nothing really striking has been found.
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But has the world of science known periods of stagnation of the fundamental, of the same kind. In the last century?
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There seems to be a sort of alternation of leaps forward, in the fundamental domain and in technological exploitation, as if people could not do both at once. The invention of the Jacquard loom (1752-1834), for example, reflects a mechanized relay between manual labor and the production of objects (it is also the beginning.... of computing). In Physics, in 1788, you have Lagrange's Analytical Mechanics. At the turn of the century Navier invents fluid mechanics, Fourier, the theory of heat, harmonic analysis, Fresnel advances fundamental optics.
Between 1815 and, say, 1870, it is a techno period. Steam engine, therefore setting machines in motion by a chemical energy and no longer human or animal. There is also electricity. Gramme invents the dynamo in 1845. Jules Verne, around 1870, makes himself the bard of these technological applications. There is also the development of chemistry, of the railway, of the telephone, the electric production of light. But between 1815 and 1870 it is rather an era of technological applications.
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And when does it start up again?
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Around 1870 it is the birth of crystallography and the beginning of atomic theory, which appears, at that time, as a speculative hypothesis. There is also Maxwell.
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And groups?
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Groups are born with crystallography. Sophus Lie, Klein, it's around 1870. The starting point of group theory is crystallography. At the turn of the century it is the atom.
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And in your opinion does it continue until 1950?
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Afterwards, it is above all techno, applied research. In physics, the big leap forward is computing, whose explosion, moreover, no one had been capable of foreseeing.
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And since 1950, everything has again refocused on technology. And the fundamental bears the cost.
End of this digression. .
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