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Introduction. The article that follows this introduction featured in the science section of the 25th December 1999 edition of The Economist magazine. It gives a good idea of how hyperspace is treated in mainstream, leading edge physics.

Hyperspace poses something of a dilemma for modern physics. On one hand it is very useful for explaining how the Universe is constructed at the very smallest level, and it even provides a useful concept for explaining what came "before" the beginning of time (click "stargate" for details µµµ). On the other hand, hyper-dimensional space is incompatible with a Universe of matter as we know it. Computer simulations by anthro-cosmologists of a four dimensional Universe (i.e. with depth, width, breadth and..........lets call it umpth) reveal that stars and planets cannot exist as objects with stable 4-D shapes following stable 4-D orbits. The whole thing just tears itself to pieces.

Mainstream physicists get around this problem by incorporating hyper-dimensional space into matter (and some of the fundamental forces) in the form of "structures" so small that they are incapable of interacting with the bigger picture of the 3-D Universe that we are aware of. This kind of quarantining of hyper-dimensional space from 3-D existence is the basis of String Theory.

The following Economist article describes an exception to this model that helps explain why gravity is such a weak force relative to the amount of matter in the Cosmos. In the Einstein'ian view of the Universe, gravity is a warping in the geometry of space-time caused by the presence of matter. The Hyper-dimensional Theory of Gravity in the article that follows posits that most of the gravitational effect of matter is exerted towards warping hyper-dimensional space.

This theory seems to have strong implications for theories of Zero Point Energy and Richard Hoagland's own hyper-dimensional theories. Quantum physicists predict that even an absolute vacuum at a temperature of absolute zero (i.e. no heat at all) is seething with unimaginable amounts of virtual energy. A mug full of absolutely nothing, they say, has enough energy in it to boil away all the Earth's oceans. A fair hypothesis of where all this hidden energy comes from would be if there existed many hyper-dimensions whose geometries where in conflict with one another and with 3-D space. Hyper-dimensional gravity could be the outside dynamic that keeps these hyper-dimensions in constant turmoil and prevents them from settling into a point of balance. The changing positions of the galaxies, stars and planets would be driving the spatial turmoil in hyperspace through the warping effects of hyper-dimensional gravity - bringing the different geometries of an unknown number of hyper-dimensions perpetually into conflict with one another. This perpetual, twisting dance of hyperspatial geometries would explain the Universe's enormous hidden store of virtual energy. Even the feeble effects of gravitational warping on 3-D space-time is enough to move whole galaxies and compress stars far enough to force nuclear fusion.

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A Matter of Gravity

Newton discovered it. Einstein complicated it. But nobody really understands the force of gravity. Part of the explanation may be that it is not really all here

NOT many people think that a small magnet is performing a remarkable feat when it grabs a nail off a table. Nima Arkani-Hamed, on the other hand, does. The nail, he points out, has the entire mass of the earth tugging down on it through gravity, but this still cannot overcome the force of the magnet. Why is gravity so miserably weak?

This is a question that has puzzled physicists for decades. But two recent papers in Physical Review Letters, by Lisa Randall of Princeton University and Raman Sundrum of Stanford University, suggest an answer. They build on an idea proposed earlier this year by Dr Arkani-Hamed, who works at the University of California, Berkeley, and two of his colleagues: Savas Dimopoulos of Stanford, and Gia Dvali, of New York University. Together, all these physicists believe that the reason gravity is such a weak force in the universe is that it does not actually spend much of its time here.

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Hide and Seek

In the traditional way of looking at things, gravity is one of four fundamental forces that hold the universe together. The other three are the strong nuclear force, which binds the particles in atomic nuclei; the weak nuclear force, which is responsible for some sorts of radioactive decay; and electromagnetism.

All three of these other forces are much more powerful than gravity. But it was not always so. Most physicists believe that, at the time of the Big Bang, when the universe began, all four forces were symmetrical, and thus of equal strength. According to this idea, the different sorts of sub-atomic particle in the early universe were also symmetrical with each other. Soon, however, the elegant symmetry of everything with everything else began to break down. The different sorts of particle and force adopted their modern natures, and gravity dwindled to a pale shadow of its former self.

This theory would be convincing enough were it not for a rather awkward requirement. For gravity to have dwindled as it did, the starting conditions for the universe had to be exactly what they actually turned out to be. Even a minuscule deviation in certain values, such as the mass of an exotic particle called the Higgs boson (which bestows mass on other, more ordinary particles), would have meant that gravity could not have weakened as it did. The result would have been a universe in which stars, planets, human beings and so on could never have come into existence.

Dr Arkani-Hamed describes these highly constrained starting conditions as requiring the universe to be like a pencil balancing on its point—possible in theory, but wildly improbable in practice. He likens previous attempts to explain the so-called hierarchy problem (why gravity is so much weaker than the other three forces) to the creation of a hand designed to hold the pencil up.

Instead, he and his collaborators propose a different explanation. Rather than circumventing the hierarchy problem, they propose to abolish it entirely. In their view, the problem does not exist. The weakness of gravity is an illusion. It actually remains just as strong as it ever was, but not all of its strength is exercised in the perceptible universe. Rather—and in contrast to the other three forces—gravity frequently operates in two or more extra dimensions beyond the commonplace four (the three of distance, plus time). And the longer it spends in these other dimensions, the weaker are its effects in the dimensions inhabited by people.

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Lost in Space

Introducing extra dimensions to account for gravity's weakness may sound loopy, but there is a good precedent. One of the best explanations of why the universe is the way it is—so-called string theory—requires that the universe be, in fact, ten-dimensional.

In string theory, the forces and particles of which the universe is now composed are actually vibrations of tiny strings made from these ten dimensions (six of which are confined to such strings, and thus are not perceivable in the human-scale world). Some strings have ends. Vibrations in these correspond to the strong, weak and electromagnetic forces, and particles that interact through those forces. Others are closed loops. Vibrations in these correspond to gravity.

Another consequence of string theory is that with the addition of an 11th dimension the universe can be divided into so-called membranes. These are regions with fewer dimensions than the space surrounding them. (A familiar analogy might be with a wall, which is a two-dimensional thing in an otherwise three-dimensional room.)

Electromagnetism, and also the strong and weak nuclear forces, are confined to their membranes, and thus to this universe. That is because the ends of the strings of which they are composed tend to "stick" to the membrane in question. But gravitational strings have no sticky ends and can wander freely off into Dr Arkani-Hamed's extra dimensions, where they have no effect on matter stuck to the membranes of the observable universe. That is why gravity appears to be so weak.

The bad news is that the papers by Dr Sundrum and Dr Randall suggest that a consequence of all this is that the extra dimensions into which gravity is wandering might be infinitely large. This means that at least some of the gravitational energy that enters them never comes back. The universe, in other words, may be leaking slowly away.

On the other hand, the good news for physicists is that, if the theory is correct, the loops formed by these extra dimensions, unlike those of standard string theory, will be relatively large. The strings predicted by string theory are so small and convoluted that unwrapping them would require energies that have not existed since shortly after the Big Bang. (This is the main reason why string theory remains just a theory.) Dr Arkani-Hamed's loops, however, may be observable with existing equipment.

That, of course, begs the question of why no one has actually observed the loops already. One possibility is that they are not there, and that Dr Arkani-Hamed is wrong. Another is that too many extra dimensions are involved (the more there are, the smaller the loops will be). But a third is simply that no one has looked for them before, because no one knew they might exist.

And, in truth, they would not be all that easy to blunder across accidentally. Photons—the particles that carry the electromagnetic force—are stuck to their own particular membrane and so cannot interact with Dr Arkani-Hamed's new dimensions. Nor can the more exotic particles responsible for the weak and strong nuclear forces. You have to look using gravity itself. But although the other forces have been probed endlessly, nobody has ever tried measuring gravity accurately over short distances.

Now, that is changing. Experiments currently being undertaken at Stanford, and also by John Price, a physicist at the University of Colorado, will measure the force of gravity over a distance of less than a millimetre (the size of loop expected if there are only two extra gravity-swallowing dimensions). The hope is that the strength of the gravitational field across such short distances will be radically different from that experienced between bodies further apart.

If that does not work, there is a second possibility—to look for the energy leak into the extra dimensions using particle accelerators. At the moment, data collected for other purposes at the Fermi National Laboratory, near Chicago, are being analysed again for signs of a leak. If there are none, a more powerful accelerator may be needed—such as the Large Hadron Collider that is about to be built at the international CERN laboratory, near Geneva.

If that does not find anything, then Dr Arkani-Hamed and his colleagues are wrong, and it may be mere fluke that the universe had exactly the right starting conditions for the emergence of humanity. If they are right, however, that universe may not be around for eternity. It is slowly leaking down a multidimensional plughole.

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Update - 16th February 2002

In mid-February 2002 BBC2 aired a documentary on the latest developments in mainstream hyperdimensional physics. A transcript of the programme can be read by clicking the next "stargate", µµµ.

It turns out that the hyperdimensional theorists have discovered that hyperdimensional gravity theory makes even more sense if the direction of the leakage of gravitational energy is reversed from the direction in The Economist article above. It is now thought that gravity is such a weak force, not because it is leaking out of our three dimensional space into higher dimensions, but because gravity is actually a hyperdimensional force leaking insipidly into our space. This is the first suggestion I've seen in mainstream hyperdimensional physics that large lumps of matter in our Universe (or "brane" as we may now have to learn to call it) act as portals for effects coming from hyperspace. So not only is the weakness of gravity a hyperdimensional effect - but gravity itself seems to be a hyperdimensional effect. This discovery has big implications for Richard Hoagland's theory that rotational systems of matter (stars, planets, solar systems etc.) draw on an additional source of energy through an interaction with high dimensions.

The relevant part of the Horizon programme is given in the transcript below.

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NARRATOR: Randall had been fascinated by an apparently inexplicable phenomenon: the weakness of gravity.

LISA RANDALL: There are various forces we see in nature. Most of them we understand at some level and then there's gravity which seems very different. The gravitational force is extremely weak in comparison with the other forces. Now you might look around and say gravity doesn't seem weak, but if you think about it you have the entire Earth pulling on you and yet you can manage to pick things up.

NIMA ARKANI-HAMED (Harvard University): Gravity certainly does not look weak in everyday life. It's responsible for keeping our feet on the ground and keeping Earth spinning around the Sun and so on, but actually gravity is incredibly weak compared to the, to the other forces. This is easy to appreciate if you take an ordinary refrigerator magnet and stick it on top of a metal pin. We all know this fridge magnet will actually pick that pin up off the table, so that sort of dramatically illustrates how feeble gravity is compared even to the magnetic force of a tiny fridge magnet.

LISA RANDALL: It turns out that there are very new ideas on how to explain the weakness of gravity if we have extra dimensions.

NARRATOR: When M Theory emerged, Randall and her colleagues wondered if it might provide the explanation. Could gravity be leaking from our Universe into the empty space of the eleventh dimensions?

NIMA ARKANI-HAMED: Gravity might only appear to be weak even though it's fundamentally just as strong as everything else because it dilutes its strength out in all these extra dimensions that we can't see.

NARRATOR: Randall tried to calculate how gravity could leak from our membrane Universe into empty space, but she couldn't make it work. Then she heard the theory that there might be another membrane in the eleventh dimension. Now she had a really strange thought. What if gravity wasn't leaking from our Universe but to it? What if it came from that other universe? On that membrane, or brane, gravity would be as strong as the other forces, but by the time it reached us it would only be a faint signal. Now when she reworked her calculations everything fitted exactly.

LISA RANDALL: If you were to imagine that there are two membranes. Say there's one in which we sit and one in which if there's other stuff it sits there, but not our particles, not the stuff that we're made of and not the stuff that we see forces associated with. If we live anywhere else in the extra dimension we would see gravity as very weak because it's mostly spending its time near the other brane. We only see the tail end of gravity.

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