The Fabric of the Cosmos: Space, Time, and the Texture of Reality

by Brian Greene

Through the gravitational force, we could both influence and be influenced by the extra dimensions. Gravity, in such a scenario, would provide our sole means for interacting beyond our three space dimensions.

Gravity and Large Extra Dimensions

Large Extra Dimensions and Large Strings

Ignatios Antoniadis, together with Arkani-Hamed, Dimopoulos, and Dvali, realized that in the braneworld scenario even unexcited, low-energy strings can be much larger than previously thought. In fact, the two scales—the size of extra dimensions and the size of strings—are closely related.

The weakness of gravity translates into the string’s being very short, about the Planck length (10−33 centimeters). But this conclusion is highly dependent on the size of the extra dimensions. The reason is that in string/M-theory, the strength of the gravitational force we observe in our three extended dimensions represents an interplay between two factors. One factor is the intrinsic, fundamental strength of the gravitational force. The second factor is the size of the extra dimensions. The larger the extra dimensions, the more gravity can spill into them and the weaker its force will appear in the familiar dimensions.

But now, if we work in the braneworld scenario and allow the extra dimensions to be much larger than had previously been considered, the observed feebleness of gravity no longer means that it’s intrinsically weak. Instead, gravity could be a relatively powerful force that appears weak only because the relatively large extra dimensions, like large pipes, dilute its intrinsic strength. Following this line of reasoning, if gravity is much stronger than once thought, the strings can be much longer than once thought, too.

Dimopoulos and his collaborators have argued that existing experimental results, both from particle physics and from astrophysics, show that unexcited strings can’t be larger than about a billionth of a billionth of a meter (10−18 meters). While small by everyday standards, this is about a hundred million billion (1017) times larger than the Planck length—nearly a hundred million billion times larger than previously thought.

String Theory Confronts Experiment?

If strings are as large as a billionth of a billionth (10−18) of a meter, the particles corresponding to the higher harmonic vibrations in Figure 12.4 will not have enormous masses, in excess of the Planck mass, as in the standard scenario. Instead, their masses will be only a thousand to a few thousand times that of a proton, and that’s low enough to be within reach of the Large Hadron Collider now being built at CERN.

Calculations show that the Large Hadron Collider may have just enough squeezing power to create a cornucopia of microscopic black holes through high-energy collisions between protons.7

Braneworld Cosmology

If a theory can make it in the extreme conditions characteristic of the universe’s earliest moments, it can make it anywhere.

Cyclic Cosmology

Rather than positing a beginning, a middle, and an end, a cyclic cosmology imagines that the world changes through time much as the moon changes through phases: after it has passed through a complete sequence, conditions are ripe for everything to start afresh and initiate yet another cycle.

These are the major stages in the cyclic model (also known tenderly as the big splat). Its premise—colliding braneworlds—is very different from that of the successful inflationary theory, but there are, nevertheless, significant points of contact between the two approaches. That both rely on quantum agitation to generate initial nonuniformities is one essential similarity.

A Brief Assessment

New Visions of Spacetime

The braneworld scenario and the cyclic cosmological model it spawned are both highly speculative. I have discussed them here not so much because I feel certain that they are correct, as because I want to illustrate the striking new ways of thinking about the space we inhabit and the evolution it has experienced that have been inspired by string/M-theory.

REALITY AND IMAGINATION

Up in the Heavens and Down in the Earth EXPERIMENTING WITH SPACE AND TIME

And so, with a fair bit more luck, some imaginative and innovative ideas regarding unification, the nature of space and time, and our cosmic origins may finally be tested.

Einstein in Drag

According to general relativity, the water in Newton’s bucket, spinning in an otherwise empty universe, would take on a concave shape, and this conflicts with Mach’s purely relational perspective, since it implies an absolute notion of acceleration. Even so, general relativity does incorporate some aspects of Mach’s viewpoint, and within the next few years a more than $500 million experiment that has been in development for close to forty years will test one of the most prominent Machian features.

Austrian researchers Joseph Lense and Hans Thirring used general relativity to show that just as a massive object warps space and time—like a bowling ball resting on a trampoline—so a rotating object drags space (and time) around it, like a spinning stone immersed in a bucket of syrup. This is known as frame dragging and implies, for example, that an asteroid freely falling toward a rapidly rotating neutron star or black hole will get caught up in a whirlpool of spinning space and be whipped around as it journeys downward. The effect is called frame dragging because from the point of view of the asteroid—from its frame of reference—it isn’t being whipped around at all. Instead, it’s falling straight down along the spatial grid, but because space is swirling (as in Figure 14.1) the grid gets twisted, so the meaning of “straight down” differs from what you’d expect based on a distant, nonswirling perspective.

Herbert Pfister and K. Braun, showed that space inside the hollow sphere would be dragged by the rotational motion and set into a whirlpool-like spin.1

What the Pfister and Braun results show is that a sufficiently massive rotating sphere is able to completely block the usual influence of the space that lies beyond the sphere itself.)

Schiff and Pugh realized that according to Newtonian physics, a spinning gyroscope—a spinning wheel that’s attached to an axis—floating in orbit high above the earth’s surface would point in a fixed and unchanging direction. But, according to general relativity, its axis would rotate ever so slightly because of the earth’s dragging of space. Since the earth’s mass is puny in comparison with the hypothetical hollow sphere used in the Pfister and Braun calculation above, the degree of frame dragging caused by the earth’s rotation is tiny. The detailed calculations showed that if the gyroscope’s spin axis were initially directed toward a chosen reference star, a year later, slowly swirling space would shift the direction of its axis by about a hundred-thousandth of a degree.

Catching the Wave

Many physicists tried to prove that the supposed waves in space amounted to a misinterpretation of the mathematics of general relativity. But in due course, the theoretical analyses converged on the correct conclusion: gravitational waves are real, and space can ripple.

practice, no one has been able to do this, so no one has directly detected a gravitational wave.

LIGO did it! Whoo-hoo!

The scientists who designed and built the Laser Interferometer GravitationalWave Observatory (LIGO) (being run jointly by the California Institute of Technology and the Massachusetts Institute of Technology and funded by the National Science Foundation) have risen to the challenge. LIGO is impressive and the expected sensitivity is astounding. It consists of two hollow tubes, each four kilometers long and a bit over a meter wide, which are arranged in a giant L. Laser light simultaneously shot down vacuum tunnels inside each tube, and reflected back by highly polished mirrors, is used to measure the relative length of each to fantastic accuracy. The idea is that should a gravitational wave roll by, it will stretch one tube relative to the other, and if the stretching is big enough, scientists will be able to detect it.

To capitalize on this, the LIGO experimenters actually direct the laser beams to bounce back and forth between mirrors at opposite ends of each tube more than a hundred times on each run, increasing the roundtrip distance being monitored to about 800 kilometers per beam. With such clever tricks and engineering feats, LIGO should be able to detect any change in the tube lengths that exceeds a trillionth of the thickness of a human hair—a hundred millionth the size of an atom.

Oh, and there are actually two of these L-shaped devices. One is in Livingston, Louisiana, and the other is about 2,000 miles away in Hanford, Washington. If a gravity wave from some distant astrophysical hullabaloo rolls by earth, it should affect each detector identically, so any wave caught by one experiment had better also show up in the other.

collisions between black holes.

a pair of colliding black holes would mimic the trill of a sparrow that’s received a sharp blow to the chest.

LIGO thereby marks a significant turning point in the way we examine the cosmos.

For millennia we have looked into the cosmos; now it’s as if, for the first time in human history, we will listen to it.

The Hunt for Extra Dimensions

For Shapere and Feng, the origin of super-energetic cosmic ray particles was of secondary concern. They realized that regardless of where such particles come from, if gravity on microscopic scales is far stronger than formerly thought, the highest-energy cosmic ray particles might have just enough oomph to create tiny black holes when they violently slam into the upper atmosphere.

Finding the remains of black holes produced in cosmic ray collisions is certainly a long shot, but success would open the first experimental window on extra dimensions, black holes, string theory, and quantum gravity.

The idea is a sophisticated variant on the “space-between-the-cushions” explanation for the loose coins missing from your pocket.

No doubt, when it comes to extra dimensions, I’m biased. I’ve worked on aspects of extra dimensions for more than fifteen years, so they hold a special place in my heart. But, with that confession as a qualifier, it’s hard for me to imagine a discovery that would be more exciting than finding evidence for dimensions beyond the three with which we’re all familiar. To my mind, there is currently no other serious proposal whose confirmation would so thoroughly shake the foundation of physics and so thoroughly establish that we must be willing to question basic, seemingly self-evident, elements of reality.

The Higgs, Supersymmetry, and String Theory

The detection of Higgs particles would be a major milestone, as it would confirm the existence of a species of field that theoretical particle physicists and cosmologists have invoked for decades, without any supporting experimental evidence.

It's been found! Whoo-hoo!

On the other hand, if the braneworld scenario is correct, upcoming accelerator experiments do have the potential of confirming string theory.

Cosmic Origins

The influx of precision data has winnowed the field of cosmological proposals, with the inflationary model being, far and away, the leading contender. But as we mentioned in Chapter 10, inflationary cosmology is not a unique theory. Theorists have proposed many different versions (old inflation, new inflation, warm inflation, hybrid inflation, hyperinflation, assisted inflation, eternal inflation, extended inflation, chaotic inflation, double inflation, weak-scale inflation, hypernatural inflation, to name just a few), each involving the hallmark brief burst of rapid expansion, but all differing in detail (in the number of fields and their potential energy shapes, in which fields get perched on plateaus, and so on). These differences give rise to slightly different predictions for the properties of the microwave background radiation (different fields with different energies have slightly different quantum fluctuations). Comparison with the WMAP and Planck data should be able to rule out many proposals, substantially refining our understanding.

Steinhardt, Turok, and their collaborators have argued that the inhomogeneities generate temperature deviations of the same form as those emerging from the inflationary framework, and hence, with today’s data, the cyclic model offers an equally viable explanation of the observations.

Since ripples in space are nothing but gravitational waves (as in our earlier discussion of LIGO), the inflationary framework predicts that gravitational waves were produced in the earliest moments of the universe.8 These are often called primordial gravitational waves, to distinguish them from those generated more recently by violent astrophysical events.

It is unlikely that LIGO will be sensitive enough to detect inflation’s predicted gravitational waves, but it is possible that they will be observed indirectly either by Planck or by another satellite experiment called the Cosmic Microwave Background Polarization experiment (CMBPol) that is now being planned. Planck, and CMBPol in particular, will not focus solely on temperature variations of the microwave background radiation, but will also measure polarization, the average spin directions of the microwave photons detected. Through a chain of reasoning too involved to cover here, it turns out that gravitational waves from the bang would leave a distinct imprint on the polarization of the microwave background radiation, perhaps an imprint large enough to be measured.