What is Space? Part II

Space-Time: The Final Frontier

Written by Sten Odenwald. Copyright (C) 1995 Sky Publishing Corporation. See February 1996 issue.
THE NIGHT SKY, when you think about it, is one of the strangest sights imaginable. The pinpoint stars that catch your eye are all but swallowed up by the black nothingness of space – an entity billions of light-years deep with which we here on Earth have no direct ex- perience.
What is empty space, really? At first the question seems silly. There’s nothing to it! But look again in light of what modern physics knows and suspects, and the nature of space emerges as one of the most important “sleeper” issues growing for the last 50 years. “Nature abhors a vacuum,” proclaimed Aristotle more than 2,300 years ago. Today physicists are discovering that this is true in ways the ancient Greeks could never have imagined.

True, the cosmos consists overwhelmingly of vacuum. Yet vacuum itself is proving not to be empty at all. It is much more complex than most people would guess. “But surely,” you might ask, “if you take a container and remove everything from inside it – every atom, every photon – there will be nothing left?” Not by a long shot. Since the 1920s physicists have recognized that on a microscopic scale, the vacuum itself is alive with activity. Moreover, this network of activity may extend right down to include the very structure of space-time itself. The fine structure of the vacuum may ultimately hold the keys to some of the deepest questions facing physics – from why elementary particles have the properties they do, to the cause of the Big Bang and the likelihood of other universes outside our own.


The state of the art in physics – our deepest current understanding of the world – is embodied in the so-called Standard Model, in which all matter and forces are accounted for by an astonishingly few types of particles (see Sky & Telescope – December 1987, page 582). Six quarks and six leptons make up all possible forms of matter. In practice just two of the quarks (the up and down) and one lepton (the electron) account for everything in the world except for a few whiffs of exotica known only to high-energy physicists. The 12 particles of matter (and their 12 corresponding particles of antimatter, or antiparticles) are acted upon by “messenger particles” that carry all the known forces. The photon mediates the electromagnetic force, including all the familiar chemical and structural forces around us on Earth. The members of the gluon family carry the strong force that binds neutrons and protons together in atomic nuclei. The W’, W-, and Zo mediate the weak nuclear force, and the as-yet-undiscovered graviton is believed to carry the force of gravity.

Every possible event involving the 12 matter particles can be completely explained as an exchange of messenger particles. During some of these events, for example when electrons accelerate in a radio-transmitter antenna, messenger particles (in this case photons) materialize and travel through space. At other times, however, the messengers remain almost entirely hidden within the interacting system. When the messengers exist in this hidden form, they are called “virtual particles.” Virtual particles may seem ghostly and unreal by everyday standards. But real they are. Moreover, they are not limited to their role of mediating interactions. Virtual particles can also pop in and out of empty space all by themselves.

Quantum mechanics, the rulebook of the Standard Model, states as a bedrock principle that you need a certain length of time to measure a particle’s energy or mass to a given degree of accuracy. The shorter the observation time, the more uncertain the measurement. If the time is very brief, the uncertainty becomes larger than the particie’s entire mass, and you cannot say whether or not the particle is there at all. The lighter the particle, the longer its uncertainty time. In the case of an electron-positron pair, the uncertainty time scale is about 10^-21″ seconds.

On time scales shorter than this, virtual electrons and positrons can, and do, pop in and out of nothingness like peas in a shell game. It’s as if, just because you can’t say a particle doesn’t exist when you look very briefly, then in a sense it does. This is not mere theorizing. In 1958 a tabletop experiment demonstrated the “Casimir effect,” measuring the force caused by virtual particles appearing and vanishing in total vacuum through the attraction they caused between two parallel metal plates. If the vacuum were truly empty the plates should not have attracted, but the incessant dance of virtual particles in the space between them produces a detectable effect.

Every particle – matter as well as messenger – seems to display a virtual form, each seething in greater or lesser abundances in what physicists call the “physical vacuum.” When it comes to affecting the ordinary world, moreover, virtual particles may do much more than just mediate forces. Some, in fact, may cause matter to have the property we call mass. The electron is the simplest of matter particles. Our knowledge of the physical world rests upon a solid understanding of its properties. Yet despite its abundance in the circuitry around us, the electron harbors an enigma. The fact that it has mass cannot be explained in the Standard Model, at least the parts of it that have been experimentally verified. More than 30 years ago particle physicist Peter Higgs suggested that the existence of mass has to do with a new ingredient of nature that is now called the Higgs field, which provides a new type of messenger particle that interacts with the electron to make it “weigh.”

The Higgs field has yet to be discovered, but many physicists expect it to exist everywhere in the physical vacuum, ensuring through its interactions with electrons and other particles that they will display mass. Even now, particle accelerators at CERN in Switzerland and at Fermilab near Chicago are straining at their maximum capabilities to cause just one “Higgs boson,” the presumed messenger particle for this field, to break loose from the vacuum and leave a detectable trace. Success would provide a triumphant completion of the Standard Model.

So to answer our question about whether a container of empty space is truly empty, the best anyone can do is remove the normal, physical particles that nature allows us to see and manipulate. The virtual particles can never be evicted. And in addition there may exist the ever-present Higgs field.


For most of this century, physicists have struggled to bring gravity into the scheme of forces that are mediated by virtual messenger particles. To put this another way, the theory of general relativity, which shows the force of gravity to be a curvature of space-time, needs to be integrated with quantum mechanics, which shows forces to be virtual particle exchanges. Working on the assumption that such a marriage is possible, physicists named gravity’s messenger particle the graviton. But general relativity requires that gravitons be more than just quanta of gravity. In essence, gravitons define the structure of space-time itself.

The reconciliation of quantum mechanics and general relativity may lead us to dramatically new notions of the nature of space and time. Some theorists have suggested that points in space-time become defined only when a particle (such as a graviton or photon) interacts with other particles. In this view, what they are doing between interactions is a nonphysical question, since only an interaction defines a measurable time and place. Gravitational forces (and thus gravitons) exert an influence at distances much larger than the subatomic realm, as anyone who has fallen down a flight of stairs can attest. But only at an extremely small scale – the Planck length of 10^-33 centimeters – does the quantum nature of gravity become important.

Suppose you could magically look through a microscope that magnified an atomic nucleus to be some 10 light-years across. Under this magnification the smallest gravitons – that is, the most energetic and massive ones – would be about a millimeter in size. Here we might see a strange world in which space-time itself was defined by gravitons intersecting and looping around each other. In a similar vein, Roger Penrose has suggested that the gravitational field and space-time are built up from still more primitive mathematical entities called twistors, and that “ultimately the [space-time] concept may possibly be eliminated from the basis of physical theory altogether.” In essence, space and time become factored out as less- than-fundamental parts of the physical world.

In such a view, only the interactions between twistors, or perhaps gravitons, define when and where space-time is and is not. Are there gaps in the physical vacuum, voids of true and absolute nothing where space and time themselves do not exist?

Another viewpoint on the structure of space-time is offered by “superstring theory.” String theories posit that the fundamental objects of nature are one-dimensional lines rather than points; the “elementary” particles we measure are only oscillations of these strings. Superstring theory only seems to work, however, if space-time has not just four dimensions (three of space and one of time), but 10 dimensions. This hardly seems like the world we live in. To hide the extra six dimensions, mathematicians roll them up into conceptual corners that go by such cryptic names as “Calabi-Yau manifolds” and “orbifold space.” A recent textbook on the subject concludes on a wistful note that “if the string idea is correct, we may never catch more than a glimpse of the full ex- tent of reality.”

More recently, theorists Carlo Rovelli (University of Pittsburgh) and Lee Smolin (Pennsylvania State University) completed their analysis of a quantum gravity model developed by Abhay Ashtekar at Syracuse University in 1985. Unlike string theory, Ashtekar’s work applies only to gravity. However, it posits that at the Planck scale, space-time dissolves into a network of “loops” that are held together by knots. Somewhat like a chain-mail coat used by knights of yore, space-time resembles a fabric fashioned in four dimensions from these tiny one-dimensional loops and knots of energy.

Is this the way the world really is on its most fundamental level, or have mathematicians become detached from reality? Superstring theory has enticed physicists for over a decade now because it hints at a super unification of all four fundamental forces of nature. But it remains frustratingly hard to plant anchors down from these cloud castles into the real world of observation and experiment. The famous remark that superstring theory is “a piece of 21st- century physics that accidentally fell into the 20th century” captures both the excitement and frustration of workers stuck with 20th-century tools.

Surprisingly, string theory, Ashtekar’s loopy space-time, and twistors are not entirely independent ways of looking at space-time. In 1986 theorists discovered that superstrings have some things in common with twistors. A deep connection had been uncovered between two very different, independent theories. Like two teams of tunnelers starting on opposite sides of a mountain, they had met at the middle – a sign, perhaps, that they are dealing with a single real mountain, not separate ones in their own imaginations. And in 1995 Rovelli and Smolin also found that their graviton loops are very closely related to both the twistors and superstrings, though not identical in all respects.


Space-time could be strange in other ways too. Theorist John A. Wheeler (In- stitute for Advanced Study) has long advocated that at the Planck scale, space-time has a complex shape that changes from instant to instant. Wheeler called his picture “space-time foam” – a sea of quantum black holes and worm holes appearing and vanishing on a time scale of about 10^-43″ seconds. This is the Planck time, the time it takes light to cross the Planck length. Shorter than that, time, like space, presumably cannot exist – or, at least, our everyday notions of them cease to be valid.

Wheeler’s idea of space-time foam is a natural extrapolation from the idea of virtual particles. According to quantum mechanics, the higher the energy and mass of a particle, the smaller it must appear. A virtual particle as small as 10^-33″ cm, lasting only 10^-43 second, has so great a mass (10^-5 gram) in such a tiny volume that its own surface gravity would give it an escape velocity greater than the speed of light. In other words, it is a tiny black hole. But a black hole is not an ordinary object sitting in space- time like a particle; it is a structure of distorted, convoluted space-time itself. Although the consequences of such phe- nomena are not understood, it is rea- sonable to assume that these virtual par- ticles dramatically distort all space-time at the Planck scale.

If we take this reasoning at face value, and consider the decades-old experiments proving that the virtual particle phenomenon in a vacuum is real, it is hard to believe that space-time is smooth at or below the Planck scale. Space must be broken up and quantized. The only question is how. Wheeler’s original idea of space-time foam is especially potent because according to recent proposals by Sidney Coleman (Harvard) and Stephen Hawking (Cambridge University), its worm holes not only connect different points very close together within our space-time, but connect our space-time to other universes that, as far as we are concerned, exist only as ghostly probabilities. These connections to other universes cause the so-called cosmological constant – an annoying intrusion into the equations of cosmology ever since Einstein (see Sky & Telescope- April 1991, page 362) – to neatly vanish within our own universe.

Space-time foam has also been implicated as the spawning ground for baby universes. In several theories explaining the cause of the Big Bang and what came before, big bangs can bud off from a previously existing space-time, break away completely while still microscopic, and inflate with matter to become new universes of their own, completely disconnected (“disjoint”) from their space- time of origin. This process, proposed by Alan Guth (MIT) and others, gives a handle on what many expect to be another key issue of 21st-century physics: was our Big Bang unique? Or was it just a routine spinoff of natural processes happening all the time in some larger, outside realm? (see Sky & Telescope- September 1988, page 253).

Yet there are problems. The amount of latent energy in the quantum fluctuations of space-time foam is staggering: 10^105 ergs per cubic centimeter. This amounts to 10 billion billion times the mass of all the galaxies in the observ- able universe – packed into every cubic centimeter! Fortunately, Mother Nature seems to have devised some means of exactly canceling out this phenomenon to an accuracy of about 120 decimal places. The problem is that we haven’t a clue how.

It’s unnerving to think that in the 16 inches separating this page from your eyes, new big bangs are perhaps being spawned out and away from our quiet space-time every instant. By comparison, it seems positively dull that the photons by which you see this page might be playing a hop-scotch game to avoid gaps where space-time doesn’t exist.


Some physicists have begun to throw cold water on these fantastic ideas. For instance, in 1993 Matt Visser (Washington University) studied the mathematical properties of quantum worm holes and discovered that, once they are formed, they become stable: they can’t foam at all. Kazuo Ghoroku (Fukuoka Institute of Technology, Japan) also found that quantum worm holes become stable even when their interactions with other fields are considered. What Wheeler called space-time foam may be something else entirely.

Among the unresolved problems facing theorists is the nature of time, which has been recognized as inextricably bound up with space ever since Einstein posited a constant speed for light. In general relativity, it isn’t always obvious how to define what we mean by time, especially at the Planck scale where time seems to lose its conventional meaning. Central to any quantum theory is the concept of measurement, but what does this imply for physics at the Planck scale, which sets an ultimate limit to the possibility of measurement? How any of these ideas about space- time can be tested is currently unknown. Some physicists believe this makes these ideas not real scientific inquiry at all. And it’s worth remembering that mathematics can sometimes introduce concepts that are only a means to an end and have no independent reality.

In the abstract world of mathematical symbolism, it isn’t always clear what is real and what’s not. For example, when we do long division on paper to divide 54,162 by 2 to get 27,081, we generate the intermediate numbers 14, 16, and 2, which we then just throw away. Are virtual particles, compact 6-dimensional manifolds, and twistors simply nonphysical means to an end – mere artifacts of how we humans do our mathematics? Particle physicists often have to deal with “ghost fields” that are simply the temporary scaffolding used for calculations, and that vanish when the calculations are complete. Nonphysical devices such as negative probability and faster- than-light tachyon particles are grudgingly tolerated so long as they disappear before the final answers. Even in super- string theory, recent work suggests that it may be possible to build consistent models entirely within ordinary four-dimensional space-time, without recourse to higher dimensions.


So, how should we think of the great, dark void that we gaze into at night? All clues point to space-time being a kind of layer cake of busy phenomena on the submicroscopic scale. The topmost layer contains the quarks and electrons comprising ordinary matter, scattered here and there like raisins in the frosting. These raisins can be plucked away to make a region of space appear empty. The frosting itself consists of virtual particles, primarily those carrying the electromagnetic, weak, and strong forces, filling the vacuum with incessant activity that can never be switched off. Their quantum comings and goings may completely fill space-time so that no points are ever really missing. This layer of the cake of “empty space” seems pretty well established by laboratory experiment.

Beneath this layer we have the domain of the putative Higgs field. No matter where the electron and quark “raisins” go, in this view, there is always a piece of the Higgs field nearby to affect them and give them mass. Below the Higgs layer there may exist other layers, representing fields we have yet to discover. But eventually we arrive at the lowest stratum, that of the gravitational field. There is more of this field wherever mass is present in the layers above it, but there is no place where it is entirely absent. This layer recalls the Babylonian Great Turtle that carried the universe on its back. Without it, all the other layers above would vanish into nothingness.

We know that space-time is quite smooth down to at least the scale of the electron, 10^-20 cm – 10 million times smaller than an atomic nucleus. This is the size limit set for any internal component of the electron, based on careful comparisons between experiment and the predictions of quantum electrodynamics. But near the Planck horizon of 10^-33 cm, space-time must change its structure drastically. It may be a world in which conventional notions of dimensionality, time, and space need to be redefined and possibly eliminated altogether.

The conceit of our universe’s uniqueness may disappear, with big bangs becoming viewed as run-of-the-mill events in some much larger outside realm, and with physical constants being attributed to causes in space-times forever beyond human experience.

There is much that’s spooky about the physical vacuum. This spookiness may be rooted more in the way our brains work than in some objective aspect of nature. Einstein stressed, “Space and time are not conditions in which we live, but modes in which we think.” Our understanding of space remains in its infancy. With Aristotle smiling at us down the centuries, we now see the vacuum as much more than a vacancy. It will take many decades, if not centuries, before a complete understanding of it is fashioned. In the meantime, enjoy the nighttime view!


Davies, Paul. The New Physics. Cambridge: Cambridge University Press, 1989.

Mallove, Eugene. “The Self-Reproducing Universe.” Sky & Telescope, September 1988, page 253.

Matthews, Robert. “Nothing Like a Vacuum.” New Scientist, February 25, 1995, page 30.

Pagels, Heinz. “Perfect Symmetry.” New York: Simon & Schuster, 1985.