Basic Cosmic Brane Theory Revisited

We now revisit basic ideas concerning branes, brane theory.

By way of recapping some of the earlier material I've written on branes, I note the following:

a) The p= 1 brane is a string.

b) The p = 2 brane is a surface or mem-brane.


The basic principle concerning p-branes is one articulated by Stephen Hawking in his book, 'Universe in a Nutshell' (p. 54), that is, there exists no special preference for opting or choosing one type of p-brane over any other. In other words, a kind of "p-brane democracy' inheres, in which all p-branes are equal.

As Hawking also observed (ibid.), all p-branes can be found as solutions of supergravity theories in 10 or 11 dimensions. More importantly, p-branes are peculiar to the low energy limit of superstring theory, with the energy density of the nongravitational fields confined to some p-dimensional subspace of the 9 space dimensions in the theory.

A special class of p-branes in string theory are called D -branes. Roughly speaking, a D -brane is a p-brane where the ends of open strings are localized on the brane. A D -brane is like a collective excitation of strings. All these objects took a long time to be discovered in string theory, because they are buried deep in the mathematics of T-duality.

A much energized use of branes has been in providing descriptions for force interactions and emergence at different scales. For example, in a solution with electric charge, if the energy density in the electromagnetic field was distributed along a line in spacetime, this one-dimensional line would be considered a p-brane with p=1. A two-dimensional interaction would encompass p=2 branes.

Most all of this is now subsumed under what is called "M-Theory". Technically speaking, M theory is the unknown eleven-dimensional theory whose low energy limit is the supergravity theory in eleven dimensions briefly noted above. However, many people have taken to also using M theory to label the unknown theory believed to be the fundamental theory from which the known superstring theories emerge as special limits.

In M -theory, there are also extended objects, but they are called M -branes rather than D -branes. One class of the M -branes in this theory has two space dimensions, and this is called an M2 -brane. Despite this, we still often opt to use D-branes. Why? Mainly practicality! D-branes provide a link between algebraic and differential geometry which is quite natural. Any device or mathematical agent which can provide such a link will be invoked, because of the levels of difficulty in these two mathematical areas.

Now, in the cosmic case we can focus on the diagram shown which shows a simplified 4-step process in the origin of the cosmos based via colliding D-branes. One of these is identical with our own known universe and is designated (A) and another 'shadow' brane exists in close proximity. The proximate brane, as Hawking has noted (op. cit.,p. 183) prevents gravity from spreading too far into extra space dimensions. (He also notes that experiments so far haven't detected branes separated by less than a few mm. )

Now, in phase (2) the two branes are pulled closer by an interbrane force and develop tiny quantized "wrinkles" (which can be thought of as the rudimentary 'seeds' of future galaxies). In phase (3) the branes are actually undergoing a collision and the graphic depicted is meant to show a two-dimensional portrayal of a multi-dimensional encounter. In this collision, an enormous amount of energy is released which is interpreted as 'the Big Bang'.

By phase (4) the branes have separated and stretch and smooth out as they do so (note - galaxies or what will become such, are shown in the image). Also, the cosmos will be seen to be expanding as we see it today. Eventually, of course, the two branes are pulled back again and another collision is induced, and so another Big Bang. This is why the model based upon these interacting branes is called a "cyclic" or "Big Bounce" model. Further, in this model, the universe not only existed before the Big Bang (as a 'known universe brane') but retains the memory of what went before.

More to the point, if brane dynamics governs the recycling of Big Bangs, then it may not even matter what the cosmic density itself is in our own universe - say attaining a density such that all the matter re-collapses (unlikely given the universe's expansion seems to be accelerating). But if the action of a shadow brane is ultimately responsible for recycling the issue is essentially moot or out of our knowledge domain, in terms of definitely knowing that the universe will re-collapse or not!

Thus, even if our own cosmic energy density, r <   r (c), the critical density needed for re-collapse, the interaction of a nearby "shadow" brane in an inter-brane collision may still provide it!

Alan Lightman's New Book Validates Transgressive Nature of the 'Multiverse'

MIT physicist -cum-novelist Alan Lightman's new book , “The Accidental Universe: The World You Thought You Knew,” explores the way recent (and not-so-recent) discoveries and theories in physics and cosmology affect our take on the big questions. Often these happen to be questions he additionally explores in his novels, i.e. the meaning of life, the nature of morality, the importance of love and the general human condition including whether there is any ulterior 'purpose' to life.

Lightman's book is presented as a collection of essays but for me the one that struck the biggest chord was the first which gives the book its title ('The Accidental Universe - The World You Thought You Knew'). Therein, Lightman explains the emerging consensus among theoretical physicists that our own universe is only one among countless alternate universes, universes where the properties of matter and energy may differ significantly from our own. Physicists call this “the multiverse.”


Let's go back to explore more of the multiverse concept as it arises from M-theory. In the diagram below one begins with a zero-dimensional point particle. Let the particle move, say from point x1 to point x2 and it sweeps out a linear  (1-D) ‘string'. Take the 1-dimensional string and move it through space and it sweeps out a 2-dimensional band or what is called a p-brane. Take this p–brane and sweep it out in a perpendicular direction and one obtains a higher (p +1) dimensional world volume.

The quantitative description of brane phenomena is enormously complex and far beyond the scope of this blog, or even a small book. However, some simple insight and appreciation for the complexity can be gained by looking at the simplest brane of all, the D-0 brane consistent with the point particle. Without going into the details of obtaining the (fiber) bundle map, we require for completeness the tachyon field described by the expression for T(x) given in the upper right of Fig. 2, where the summation is taken from u= 1 to u = 9, with x_u the coordinates for the rotation space (group) R(9), and Gamma_u , the matrices needed. Then the tachyon field consistent with the above would be given by the small matrix expression in the upper right of Fig. 2.


For a system of D0- branes,  parameterized by such matrices and defined by the given tachyon field (T(x)), we have a system of 9 x 9 matrices, defined by the large array shown in Fig. 2. Since the fields, and dynamics (as well as the tachyon field) are occurring at the level of the vacuum, that is the first place to start. Thus, to manipulate the D-brane in Fig. 2 it seems clear that energy consonant with a vacuum energy – or more exactly, a vacuum energy density- is needed.

The energy density attendant on vacuum manipulation must have some lower limit, estimated to be ~ 10 ^94 g/cm^3

This is an astounding amount of mass-energy density! To give a rough comparison, the mass of the Sun is 2 x 10^33 g. The mass of the Milky Way galaxy is roughly 10 ^45 g. The mass of 100 billion galaxies the size and mass of the Milky Way is ~ 10^56 g. In other words, the mass density or energy density shown is more than ample to account for an entire universe!

I reiterate here that:

1) D-branes, by definition, are dynamical objects that can fluctuate.

2) The dynamical aspect is a result of the ability of D-branes to couple to closed strings (Fig. 2) Recall here that the latter embody a description of gravity and M-theory proper combines supergravity with Brane theory.

Now, I look at the simplified,  "uniform"  multiverse model - shown in the diagram below-  which might be considered a first iteration to a genuinely realistic multiverse model:

















Each longitude circle is a quotient space q1 and each latitude circle is a quotient space q2. More exactly, q2 denotes the fifth dimensional connector that links multiple "parallel" universes, i.e. for the model shown. Each of these can be represented by one single longitudinal loop marking off a coordinate on q1 (e.g. Θ). Since time can be broken down in fundamental units of  Planck time or tau (τ) then each q1 is theoretically separated from its neighbor universe by one tau. This neighbor is impossible to access from within the fixed coordinate quotient space (q1) but can be accessed if one could find a way to get to q2 and traverse it. Thus, in simplest terms, each “slice” q1 can be regarded as an alternate or parallel universe within the multiverse. (Again, the model shown is only for discussion purposes and may not in any way correlate to the actual multiverse!)


More explicitly, one may adopt absolute toroidal (Θ,φ) coordinates to locate events in the multiverse system. There are a number of fascinating aspects of this model. First, the toroidal hypersphere implies an endlessly repeating universe that is the same in each new cycle[1] - instead of being different (i.e. with different physical constants as the reprocessed mode, e.g. of physicist John Wheeler demands). The key to this aspect is the fact that the radius R remains constant.

A second intriguing aspect is that the exact same point of space-time occurs for each "beginning" (Big Bang) and "end" ("Big Crunch"). This point is easily identified in the diagram as the most constricted part of the interior "hour-glass" shape defining the inner wall of the torus-hypersphere. Third, the overall configuration is exactly the same as that defined for the high-energy "twistors" used in the 1980's by Roger Penrose and his colleagues at Oxford.[2] The twistors are discrete points of space, each defined by 4 real numbers and 4 imaginary numbers.

The physical differences manifested via the generation of different universes in Lightman's generic  multiverse  (contrasted with the one I've depicted) would obviously be  much more significant , since each one would exhibit a  completely different assembly of 'universal' constants. Thus, no two component universes would be expected to be duplicates, given inherent differences, say in the fine structure constant, the Newtonian gravitational constant (G), and the charge to mass ratio for the electron, e/m.   Certain other factors, such as the critical ratio w (= (p / rho) = -1 ) would also determine the amount of dark energy in a given universe. Depending on whether w is a little bit greater or lesser — poof!- in one universe you have some degree of 'order' and matter, in another nothing. Thus,  there could well be an infinite, or nearly infinite, number of universes, in which there exists nothing but a cold 'fog' of evenly dispersed particles. In others, there may be only a single, tiny, infinitely dense point. In this milieu ours is merely one of a few universes configured so as to allow life.

All this implies that ours is an accidental universe, rather than  one that's emerged as a result of inexorable and inevitable set laws which have been discovered and understood by humanity. As the  Nobel-winning physicist Steven Weinberg put it, “We now find ourselves at a historic fork in the road we travel to understand the laws of nature. If the multiverse idea is correct, the style of fundamental physics will be radically changed.”

One might go so far as to even say the multiverse concept is transgressive at its core. As Lightman himself has put it, "the philosophical ethos of science is torn from its roots.” That ethos rests on the conviction that science is moving us toward a more and more complete understanding of the laws of nature and that “these basic principles are so restrictive that only one self-consistent universe is possible, like a crossword puzzle with only one solution.”

But if an infinite or nearly infinite number of self-consistent universes exist that all goes out the proverbial window. And the laws that may apply in our universe are as useless as a hammer without a handle in any other.

Needless to say, the multiverse also offers a refutation of the concept of Intelligent Design.  If an infinite or nearly infinite number of universes within it are merely cold, dark voids then wherefore the "designer"? In fact, he, she or it isn't needed at all because the very creation of the multiverse via vacuum energy in a spontaneous quantum fluctuation makes it redundant. But again, if the designer isn't evident in most of the cosmi, why the need to postulate it? Just so one of the infinite number of universes can be said to have one? That's totally ludicrous.

Yes, as Lightman has conceded (interview with salon.com), it may be very hard to test for, far less prove that a multiverse exists. But at least the concept offers a superior natural alternative to the supernatural bollocks spouted by diehard religionists.  In any case, a multiverse such as described is far easier to swallow (and based on rational -mathematical principles)  than an infinite Being who supposedly controls everything  and is everywhere, but yet is powerless to stop evil - whether  human (such as the beheadings of infants now going on in the Central African Republic)  or natural, such as the tsunami that killed over 200,000 in 2004..

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[1] This could also be interpreted as a "timeless" universe. See, e.g. Rucker, R.: 1977, Geometry, Relativity and the Fourth Dimension, Dover Publications, New York, p. 105. According to Rucker:"There is no last time around or next time around because nothing is moving...we feel that we are going through time but that is an illusion."

[2] For an excellent article on twistors, see: Spinning New Realities, by R.L. Forward, in Science 80 (December, 1980), p. 40.

Re-Examining Brane Theory in a Cosmic Light

Just over three years ago, in July, 2008, I began to examine branes as possible agents in explaining the UFO phenomenon. Now, I'd like to recap some brane theory to see how it is applied to the cosmic scene, and especially in how collidng branes can account for a Big Bang.

By way of recapping some of the earlier material, I noted the following:

a) The p= 1 brane is a string.

b) The p = 2 brane is a surface or mem-brane.

The basic principle concerning p-branes is one articulated by Stephen Hawking in his book, 'Universe in a Nutshell' (p. 54), that is, there exists no special preference for opting or choosing one type of p-brane over any other. In other words, a kind of "p-brane democracy' inheres, in which all p-branes are equal. As Hawking also observed (ibid.), all p-branes can be found as solutions of supergravity theories in 10 or 11 dimensions. More importantly, p-branes are peculiar to the low energy limit of superstring theory, with the energy density of the nongravitational fields confined to some p-dimensional subspace of the 9 space dimensions in the theory.

A special class of p-branes in string theory are called D -branes. Roughly speaking, a D -brane is a p-brane where the ends of open strings are localized on the brane. A D -brane is like a collective excitation of strings. All these objects took a long time to be discovered in string theory, because they are buried deep in the mathematics of T-duality.

A much energized use of branes has been in providing descriptions for force interactions and emergence at different scales. For example, in a solution with electric charge, if the energy density in the electromagnetic field was distributed along a line in spacetime, this one-dimensional line would be considered a p-brane with p=1. A two-dimensionall interaction would encompass p=2 branes.

Most all of this is now subsumed under what is called "M-Theory". Technically speaking, M theory is is the unknown eleven-dimensional theory whose low energy limit is the supergravity th-eory in eleven dimensions briefly noted above. However, many people have taken to also using M theory to label the unknown theory believed to be the fundamental theory from which the known superstring theories emerge as special limits.

In M -theory, there are also extended objects, but they are called M -branes rather than D -branes. One class of the M -branes in this theory has two space dimensions, and this is called an M2 -brane. Despite this, we still often opt to use D-branes. Why? Mainly practicality! D-branes provide a link between algebraic and differential geometry which is quite natural. Any device or mathematical agent which can provide such a link will be invoked, because of the levels of difficulty in these two mathematical areas.

Now, in the cosmic case we can focus on the diagram shown which shows a simplified 4-step process in the origin of the cosmos based via colliding D-branes. One of these is identical with our own known universe and is designated (A) and another 'shadow' brane exists in close proximity. The proximate brane, as Hawking has noted (op. cit.,p. 183) prevents gravity from spreading too far into extra space dimensions. (He also notes that experiments so far haven't detected branes separated by less than a few mm. )

Now, in phase (2) the two branes are pulled closer by an interbrane force and develop tiny quantized "wrinkles" (which can be thought of as the rudimentary 'seeds' of future galaxies). In phase (3) the branes are actually undergoing a collision and the graphic depicted is meant to show a two-dimensional portrayal of a multi-dimensional encounter. In this collision, an enormous amount of energy is released which is interpreted as 'the Big Bang'.

By phase (4) the branes have separated and stretch and smooth out as they do so (note - galaxies or what will become such, are shown in the image). Also, the cosmos will be seen to be expanding as we see it today. Eventually, of course, the two branes are pulled back again and another collision is induced, and so another Big Bang. This is why the model based upon these interacting branes is called a "cyclic" or "Big Bounce" model. Further, in this model, the universe not only existed before the Big Bang (as a 'known universe brane') but retains the memory of what went before.

More to the point, if brane dynamics governs the recycling of Big Bangs, then it may not even matter what the cosmic density itself is in our own universe - say attaining a density such that all the matter re-collapses (unlikely given the universe's expansion seems to be accelerating). But if the action of a shadow brane is ultimately responsible for recycling the issue is essentially moot or out of our knowledge domain, in terms of definitely knowing that the universe will re-collapse or not!

Thus, even if our own cosmic energy density, rho < rho(c), the critical density needed for re-collapse, the interaction of a nearby "shadow" brane in an inter-brane collision may still provide it!