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

by Brian Greene

In the golden age of cosmology, some of the wildest ideas may actually be testable.

Dark Matter, Dark Energy, and the Future of the Universe

So, if not protons and neutrons, what constitutes the dark matter? As of today, no one knows, but there is no shortage of proposals. The candidates’ names run the gamut from axions to zinos, and whoever finds the answer will surely pay a visit to Stockholm.

The precision measurements initiated by COBE and since bettered by WMAP strongly support the proposition that space is flat. Not only does this match the theoretical expectations coming from inflationary models, but it also jibes perfectly with the supernova results. As we’ve seen, a spatially flat universe requires the total mass/energy density to equal the critical density. With ordinary and dark matter contributing about 30 percent and dark energy contributing about 70 percent, everything hangs together impressively.

Space, Time, and Speculation

Will we one day be masters of space and time and do things that for now are only part of science fiction? No one knows. But let’s see how far we’ve gotten and what it might take to succeed.

Teleporters and Time Machines

TRAVELING THROUGH SPACE AND TIME

Teleportation in a Quantum World

When, if ever, should an exact replica be identified, called, considered, or treated as if it were the original? The second is the question of whether it’s possible, even in principle, to examine an object and determine its composition with complete accuracy so that we can draw up a perfect blueprint with which to reconstitute it.

To replicate we must observe, so we know what to replicate. But the act of observation causes change, so if we replicate what we see, we will not replicate what was there before we looked.

According to quantum mechanics, every electron in the universe is identical to every other, in that they all have exactly the same mass, exactly the same electric charge, exactly the same weak and strong nuclear force properties, and exactly the same total spin. Moreover, our well-tested quantum mechanical description says that these exhaust the attributes that an electron can possess; electrons are all identical with regard to these properties, and there are no other properties to consider. In the same sense, every up-quark is the same as every other, every down-quark is the same as every other, every photon is the same as every other, and so on for all other particle species.

What can differ between two particles of the same species are the probabilities that they are located at various positions, the probabilities that their spins are pointing in particular directions, and the probabilities that they have particular velocities and energies. Or, as physicists say more succinctly, the two particles can be in different quantum states.

But if two particles of the same species are in the same quantum state—except, possibly, for one particle having a high likelihood of being here while the other particle has a high likelihood of being over there—the laws of quantum mechanics ensure that they are indistinguishable, not just in practice but in principle. They are perfect twins. If someone were to exchange the particles’ positions (more precisely, exchange the two particles’ probabilities of being located at any given position), there’d be absolutely no way to tell.

Thoughts, memories, emotions, and judgments have a physical basis in the human body’s atomic and molecular properties; an identical quantum state of these elementary constituents should entail an identical conscious being.

Quantum Entanglement and Quantum Teleportation

The disruption caused by measurement prevents us from determining Photon A’s quantum state, but in the approach described, we don’t need to know the photon’s quantum state in order to teleport it. We need to know only an aspect of its quantum state—what we learn from the joint measurement with Photon B. Quantum entanglement with distant Photon C fills in the rest.

Realistic Teleportation

From our current vantage point, a dispassionate assessment would conclude that teleporting a macroscopic object, at least in the manner so far employed for a single particle, is eons—if not an eternity—away.

The Puzzles of Time Travel

When it comes to time, we get dragged along in one direction, whether we like it or not.

I find the nearest Internet café and get online to see what advances have been made in string theory. And do I get a splendid surprise. I read that all open issues in string theory have been resolved. The theory has been completely worked out and successfully used to explain all known particle properties. Incontrovertible evidence for the extra dimensions has been found, and the theory’s predictions of supersymmetric partner particles—their masses, electric charges, and so on— have just been confirmed, spot on, by the Large Hadron Collider. There is no longer any doubt: string theory is the unified theory of the universe.

In your dreams, Brian. In your dreams.

Rethinking the Puzzles

Free Will, Many Worlds, and Time Travel

Is Time Travel to the Past Possible?

Blueprint for a Wormhole Time Machine

Building a Wormhole Time Machine

Some physicists have suggested that tiny wormholes might be plentiful in the microscopic makeup of the spatial fabric, being continually produced by quantum fluctuations of the gravitational field.

The bottom line is that intentional acquisition of a macroscopic wormhole is a fantasy that, at best, is a very long way from being realized.

First, in the 1960s, Wheeler and Robert Fuller showed, using the equations of general relativity, that wormholes are unstable. Their walls tend to collapse inward in a fraction of a second, which eliminates their utility for any kind of travel.

Visser has calculated that the amount of negative energy needed to keep open a one-meter-wide wormhole is roughly equal in magnitude to the total energy produced by the sun over about 10 billion years.15)

Cosmic Rubbernecking

The time machines that have thus far been proposed do not allow travel to a time prior to the construction of the first time machine itself.

I count myself among the sober physicists who feel intuitively that we will one day rule out time travel to the past. But until there’s definitive proof, I think it justified and appropriate to keep an open mind. At the very least, researchers focusing on these issues are substantially deepening our understanding of space and time in extreme circumstances. At the very best, they may be taking the first critical steps toward integrating us into the spacetime superhighway.

The Future of an Allusion

PROSPECTS FOR SPACE AND TIME

Physicists spend a large part of their lives in a state of confusion. It’s an occupational hazard. To excel in physics is to embrace doubt wh...

What is the next chapter in spacetime’s story?

Are Space and Time Fundamental Concepts?

spacetime may be an illusion—

Just as the hardness of a cannonball, the smell of the rose, and the speed of the cheetah disappear when you examine matter at the atomic and subatomic level, space and time may similarly dissolve when scrutinized with the most fundamental formulation of nature’s laws.

Quantum Averaging

Space and time may only be approximate, collective conceptions, extremely useful in analyzing the universe on all but ultramicroscopic scales, yet as illusory as a family with 2.2 children.

A second and related insight is that the increasingly intense quantum jitters that arise on decreasing scales suggest that the notion of being able to divide distances or durations into ever smaller units likely comes to an end at around the Planck length (10−33 centimeters) and Planck time (10−43 seconds).

It seems likely, therefore, that the appearance of the fundamental spacetime constituents—whatever they may be—is altered significantly through the averaging process by which they yield the spacetime of common experience.

Thus, looking for familiar spacetime in the deepest laws of nature may be like trying to take in Beethoven’s Ninth Symphony solely note by single note or one of Monet’s haystack paintings solely brushstroke by single brushstroke.

Geometry in Translation

The dictionary that translates questions posed in one string theory into different questions posed in another string theory also translates the geometry of the extra dimensions in the first theory into a different extra-dimensionalgeometry in the second theory.

In short, a given string theory with curled-up dimensions in one geometrical form is equivalent to—is a translation of— another string theory with curled-up dimensions in a different geometrical form.

A given string theory with extra dimensions curled up into a particular Calabi-Yau shape gets translated by the dictionary into a different string theory with extra dimensions curled up into a different Calabi-Yau shape (one that is called the mirror or dual of the original). In these cases, not only can the sizes of the Calabi-Yaus differ, but so can their shapes, including the number and variety of their holes. But the translation dictionary ensures that they differ in just the right way, so that even though the extra dimensions have different sizes and shapes, the physics following from each theory is absolutely identical. (There are two types of holes in a given Calabi-Yau shape, but it turns out that string vibrational patterns—and hence physical implications—are sensitive only to the difference between the number of holes of each type. So if one Calabi-Yau has, say, two holes of the first kind and five of the second, while another Calabi-Yau has five holes of the first kind and two of the second, then even though they differ as geometrical shapes, they can give rise to identical physics.44)