Of Brane New World!

With them and with other observations such as the cosmic microwave background radiation, we may be able to determine whether we are or not living on a brane. If we do, it will presumably be because the anthropic principle picks out brane models from the vast zoo of universes allowed by M-theory. We could well paraphrase Miranda in Shakespeare’s The Tempest:

O Brane new world
That has such creatures in’t.


That is the universe in a nutshell. (Stephen Hawking [1])

It has been the most cherished dream of man ever since he evolved into homosapien to comprehend the world in which he lived. Astronomy and cosmology are thus the oldest sciences which fascinated the human imagination. Every bit of information which was discovered or explained by the human intellect thus became part of the monumental contributions to science. Among them were the discovery that the earth is round and not flat, explanation of the eclipses, gradual development of cosmological theories and models to explain the movement of the planets, so on and so forth. The road of discovery was never straight nor the shortest. Aristotle’s postulate that earth was the center of the universe remained an obstacle for further development for several centuries until finally Copernicus replaced it with the heliocentric theory.

Until the beginning of the twentieth century, it was believed that the universe was static and eternal. It was always there in the same form and size. Einstein arbitrarily crafted his cosmological constant to get a static universe from his theory of relativity which correctly predicted expanding universe. Within a decade however, Hubbell showed on the basis of his astronomical observations that the universe was actually expanding. All hell broke loose.

To understand the origination of our universe, Einstein’s theory of general relativity was the best tool available until the first half of the twentieth century. His theory was used to reverse the process of the evolution of the universe in time to see how it (universe) began at t=0. Immediately, a theoretical problem cropped up. At t=0, the theory predicted infinite density of the mass of the universe. The universe was reduced to a dimensionless point. Infinity is the nightmare of the physicists; further progress was thus blocked. You could reverse the time clock up to an infinitesimal amount but you could not go back to absolute zero. In ordinary language, you could not comprehend how the universe began but once it began you could build a theoretical framework allowing you to make predictions.

The structure of the universe at t=0 was called a singularity. When the scientific progress is blocked by horrible creatures like infinity, the scientists don’t call it off but continue searching and sniffing for other useful approaches. Can we make a detour around the singularity? Yes, but then we cannot explain how the universe began.

Einstein’s theory of relativity works superbly in a smooth continuum of space. Close to t=0, the continuum breaks down and the space becomes ‘grainy’. What does it tell? That we cannot use theory of relativity for the universe at its birth. Some other theory is needed.

The other theory which had come into being at the beginning of the twentieth century was the theory of quantum mechanics and it was fundamentally different from the theory of relativity. Theory of quantum mechanics dealt with the structure of the matter. Its daily bread and butter were elementary particles many of which were no longer elementary because finer matter was discovered of which they were made. A whole zoo of new elementary particles was discovered.

Were the theories of relativity and quantum mechanics related to each other? Could they be unified in the same way that theories of electromagnetism and gravitation were unified by theory of relativity? Many scientists believed so but no method of unification could be determined for this task. Einstein spent better part of his later life in this engagement but he died without success. He was trying to unify gravity with the other fundamental forces which is extremely difficult and still remains a challenge to the brainiest physicists and mathematicians who are engaged day and night in finding the ultimate solution.

Salam and Weinberg independently chose to unify the electromagnetic and the weak forces and were successful. Later on, the strong nuclear force was also tamed and unified with the electroweak force. The force of gravitation continued defying unification.

The string theory came into being quite accidentally. In 1968, Gabrielli Veneziano concocted a mathematical formula that described the likelihood for different things to come out in different directions when two particles collided. It was a mathematical formula without any physical insights. Susskind imparted a physical insight to it. He realized that Veneziano’s formula described “what happens when two little loops of string come together, join, oscillate a little bit, and then go flying off.” Almost at the same time, Yoichiro Nambu had the same insight.

Interest in the string theory started with new hopes. But many lost faith in it when they realized that the theory worked only in ten dimensions which looked weird and unrealistic in the beginning. Susskind who was a particle physicist lost interest in it when he discovered that “when the theory was solved it included forces between particles that were like gravitational forces. This theory was not behaving like nuclear physics – like it was supposed to behave. It was behaving like Newtonian gravity.” This very feature became the forte of the string theory because by virtue of this property it could provide a bridge between theories of gravitation and quantum mechanics.

Another strong point of the theory was that it dealt with strings and not points; infinities were thus avoided naturally. The original theory suffered from some other defects also which were overcome by combining super symmetry with the string theory. The resultant theory was called superstring theory. However the ultimate goal still remained elusive and out of reach particularly when it was discovered that there were in fact five different superstring theories instead of one.

In 1995, Ed Witten removed the uncertainty from the string theory when he showed that all of the five theories were indeed different reflections of the same fundamental theory. They were so to say five translations in different languages of the same masterpiece. This theory was called the M-theory and it needed eleven dimensions instead of ten to produce solutions.

It was realized that the different material particles were the manifestations of the vibrations of tiny strings. To build a picture of the universe however one doesn’t need to remain confined to strings. The M-theory worked with the membranes which was shortened to branes. A membrane is a two dimensional sheet like surface. Theories of higher dimensions were called 3-branes, 4-branes, or p-branes where p is an integer between one and ten. The eleventh dimension is that of the time. A multidimensional brane can be as big as our universe. The string theory is a 1-brane theory.

Different people understand differently as to what a brane is. K.C.Cole (2) quoted different views as follows:

“Essentially, a brane is a discontinuity in spacetime, a boundary where things meet, like the surface of a pond where the water meets the sky.
It’s a defect in the quantum fabric, said Ruth Gregory of the University of Durham in Britain. On one side of the defect would be the vacuum of empty space. A vacuum with somewhat different properties might exist on the other side………
A brane doesn’t always divide one thing from another. It may just be a condensation of stuff, a localized lump of energy and curvature that likes to hang together, Stanford university physicist Steve Shenker said.”

Lisa Randall of Harvard university and Raman Sundrum of Johns Hopkins university realized and explained that branes could be infinitely large and yet remain invisible. This is because light can not travel out of one brane into another. “We can’t hear anything outside because sound travels through matter and matter is stuck to our brane. We can’t use radioactivity to sense what’s beyond, or even break through nuclear bombs because nuclear forces are also firmly nailed to our brane. There could be a big blue elephant sitting not a millimeter away in another dimension but we wouldn’t know it’s there because everything we use to ‘see’ is stuck to our brane,”.

String Theory Landscape and Anthropic Principle

The string theory appears to be the best available tool for the purpose of unification and thus holds a key for the answers to many important cosmological questions one of which is the origination of our universe. It has its own subtleties which are a serious challenge to the ingenuity and creativeness of the physicists. According to Fernando Quevedo (3), “..even if the (string) theory is unique, the number of different universes that appears as solutions to its equations is extremely large. One solution, for example, is a flat Minkowski space-time in 10 dimensions. Another is a universe similar to ours that has four flat space-time dimensions and an additional six dimensions that are curled up at extremely small scale. These ‘hidden’ dimensions correspond to a class of spaces known as Calabi-Yau spaces. The crux of string theory is that these 6D spaces can fix the physical properties of the observable universe such as the type and number of elementary particles and the forces that act between them. There are at least 10,000 Calabi-Yau spaces, each of which is defined by a number of parameters called moduli that determine its size and shape. Each value of these parameters gives rise to different physics in the 4D observable world, but the trouble is that all values are equally valid solutions.”

And there is such a large number of solutions, millions of millions of them, which create “an extremely rich landscape with many mountains, valleys, oceans, and even volcanoes.” Describing this scenario little differently, Susskind (4) wrote, “The reason that there is so much diversity in string theory is because the theory has an enormous number of what I call moving parts, things you can tinker with.” If the predictions of the string theory regarding diversity and multiplicity of universes in a megaverse are correct, the questions which have troubled many physicists are in Susskind’s words: “..why was the (our) universe made in such a way as to be just right for people to live in it…why certain quantities that go into our physical laws of nature are exactly what they are, and if this is just an accident. Is it an accident that they are finely tuned, precisely, sometimes on a knife’s edge, just so that the world could accommodate us?” These questions are entwined with what is popularly called the anthropic principle. Again, in Susskind’s words, “The kind of answer that this or that is true because if it were not true there would be no body to ask the question, is called the anthropic principle.”

The creation scientists have used the anthropic principle rather forcefully to advance their argument for the ‘intelligently designed’ universe. According to them, God set the values of the universal constants in precisely such a manner that the universe could support human life. The physicists hate the anthropic principle. They suggest that there are all kinds of universes with different fundamental laws of nature and different values for the universal constants and majority of those universes are such that can not support human life. One of such millions of universes is ours which can support human life. Our universe is a statistical probability and not necessarily the result of any intelligent design. According to this line of thinking, our universe is only one of many that can support human life. It is not that it was designed intentionally so. If it couldn’t support human life, we wouldn’t be here to ask this question.



References

1.Stephen Hawking, “The Universe in a Nutshell,” Bantam
Books, New York, 2001, p. 200.
2.K.C. Cole, “Strings and Branes: So What Do We Know?”
http://www.csudh.edu/dearhabermas/stringtheorybk01.htm
3. Fernando Quevedo, “The String-Theory Landscape,”
Physicsweb, November 2003, http://www.physicsweb.org/articles/world/16/11/3.
4.Lenny Susskind, “Edge: The Landscape,”
http://www.edge.org/3rd_culture/susskind03/susskind_index. html