## Wednesday, November 30, 2011

### Gravity

Of all the four fundamental forces, the force of gravity is the one most familiar to our daily experience. We are even born with innate sense of this force. It is called the Moro reflex, demonstrated in this brief video:

This basic and primitive reflex is a response to a sudden loss of support, of falling in other words, and it is built into us in incomplete form as early as 28 weeks gestation. By week 34 it is fully developed, and by around 3 to 6 months of age it disappears once again. By then, we are well into exploring the force of gravity by dropping objects and watching them fall, and soon after, we are falling down ourselves as we learn to walk. Throughout our lives we experience the force of gravity and without it, we can quickly become disorientated, as test pilots and astronauts can attest.

And yet, gravity, for all its familiarity, is the least understood fundamental force. In this article we will explore how it works and how it fits into current theories about forces and the particles that mediate them. In the process we will acquaint ourselves with the mystery of gravity, a mystery that will inevitably lead us to a larger ultimate mystery.

You've Come a Long Way Baby: The Changing Face of Gravity

Newton's Gravity

In the late1600's we thought we had the force of gravity all wrapped up. Isaac Newton famously sat under an apple tree and when an apple fell on his head he had an epiphany, or so the legend goes: Apples fall to the ground because they are attracted to it. And the ground is also attracted to the apples. In 1687, he published this idea in his Theory of Universal Gravitation. Gravity, he discovered, is a predictable force of attraction that acts on all matter in the universe. It is directly proportional to the mass of the objects in question and is inversely proportional to their distance from each other. Newton's  law of universal gravitation looks like this:

where F is the gravitational force between the masses,
G is the gravitational constant,
m1 and m2 are the masses of the two objects,
And r is the distance between.

G, the gravitational constant, with a value of approximately 6.67 x 10-11N (m/kg)2, appeared in Newton's equation but it was not actually measured until 71 years after his death, by Henry Cavendish in 1798. Newton simply knew that the values were proportional to each other and so a constant of some kind was needed to express this relationship (and he was genius enough to know this would be a very small number).

Cavendish set out to confirm Newton's theory and to confirm his constant, G. It was no easy task because this constant, as you saw, is an extremely small value. He ingeniously created a torsion balance, shown in this diagram:
Two masses are suspended at either end of a bar, which is suspended from the ceiling by a thin wire. Attached to this wire is a mirror off which a beam of light is reflected. When he brought a third mass close to one of the suspended masses, it attracted one of the ends of the torsion balance causing the whole thing to rotate, slightly changing the direction of the beam of light. By carefully measuring the angle of deflection he could measure the extent to which two known masses attracted each other and he could get a value for G to within 1%. What's so cool about this experiment is that such a simple apparatus can measure a force so infinitesimally small. We can only feel Earth's gravitational attraction to us because Earth's mass is so big, and that is why in everyday life everything seems to fall to Earth. In fact, Newton's apple and the Earth fall toward each other and Newton understood that. He also understood that the distance of projectiles depended on both Earth's gravity and their velocity. If a projectile were shot out horizontally with increasing velocity its trajectory would become longer and longer and eventually, with enough velocity, it would never hit the ground. It would, in essence, be in orbit around Earth. And this is how the Moon orbits Earth. The Moon is constantly falling to Earth but its velocity keeps it in orbit. If the Moon's mass increased or it's orbit slowed down, it's orbit would decay and it would eventually slam into Earth. This brief 2-minute video explains this concept of orbit:

He quickly realized he could use this value, and the acceleration due to gravity worked out by Galileo in the 1600's, to accurately measure Earth's mass. Soon, scientists were using the formula to predict the behaviours of planets, comets and asteroids. It was used to predict the presence of the planet, Neptune, as well as the trajectory of Halley's comet. It was a brilliant step forward but it was not to be the final word on gravity as Albert Einstein, a little over 100 years later, would demonstrate.

Einstein's Gravity

For over 200 years, Newton's theory of universal gravitation remained unquestioned - it was very successful at describing the motion of objects. Gravity, according to scientists in this age, was an attractive force between masses that acted universally across the universe.

In the early 1900's, however, this nicely sewn up theory began to unravel when Albert Einstein, dealing with the ramifications of a universal speed limit on light, realized that if light speed could not change then space and time had to. He then set about attempting to describe this elastic space-time that this theory of special relativity required. He formulated a mathematical framework for space-time, an invisible framework that underlies the universe, which can be stretched, twisted and warped. If you would like to know more about this discovery, I explore Einstein's space-time in my article called "Time."

Einstein soon realized that not only were time and space themselves at the mercy of space-time stretching, so was gravity. In fact, gravity was the stretching, or the shape of space-time. This would become the seed of his theory of general relativity.

This clip from the NOVA series, The Elegant Universe, describes how our understanding of gravity evolved from Newton's time into Einstein's theory of gravity, with a slightly different twist than what I have outlined here:

We experience gravity as the motion of objects following the curvatures of space-time. This concept challenges the idea that gravity is a force at all, and we will explore this implication in greater detail soon.

You may have seen diagrams in which heavy objects, Earth for example, bend this space-time fabric. In fact, NASA physicists are measuring that curvature right now using the Gravity Probe B. This is a diagram of space-time curved around Earth and the probe:

They are finding that there is indeed a space-time vortex around Earth and its shape matches Einstein's theoretical predictions. As you think about space-time, please keep in mind that this diagram shows us a 3-dimensional curvature. In reality, the curvature is 4-dimensional, through the 3 dimensions of space and 1 dimension of time. This 4-dimensional shape is impossible for us to visualize. Its geometry is instead described using mathematical formulas.

Einstein expanded his theory of special relativity to describe the behavior of masses in space-time, and he called this new theory general relativity (the earlier link above brings you to an introduction, click here for a more in-depth discussion). In a nutshell, mass causes space-time to curve. Do you see how this new concept does away with Newton's idea of an attractive force between masses? For most of our everyday experience, Newton seems right - gravity appears to act as an attractive force - but that is only how it appears. The idea that outer space, seemingly an empty vacuum, has a built-in structure that can be altered according to certain rules is still very weird to us. If you have read some of my earlier articles, you might not be so shocked, however - remember how perfectly empty vacuums, at their tiniest fundamental level, teem with unpredictable quantum fluctuations? Einstein's bizarre idea of space-time broke the way for us to re-visit the mysteries of the universe from a new perspective. Weaving this new perspective together with a quantum mechanical description of the universe, which is, itself, utterly mysterious at its core, means that we must weave two very weird and mysterious concepts together in order to approach the heart of gravity. Let's take this one step at a time and begin where it all started, with general relativity.

General Relativity

To understand gravity we must learn the basic ideas behind general relativity, and in order to appreciate general relativity, we must abandon our old notions of space and time and embrace space-time. You may want to begin by thinking of space-time as an invisible stream flowing ever onward, bending in response to objects in its path, carrying everything in the universe along with it as it twists and turns, as was elegantly described by physicist Hans von Baeyer.

This theory can be daunting but I hope to guide you toward an intuitive feel for how it works. Einstein took his theory of special relativity and expanded it to take into account areas that are accelerating with respect to each other. Recall that relativity is all about which frame of reference you are measuring something from. In physics we call these areas non-inertial frames of reference. This theory is written out as a set of field equations that describe and relate the curvature and the distribution of matter within space-time. These equations can be used to represent the geometry of space-time, much like the diagram of Earth shown above. In developing general relativity, Einstein had to refine his concept of space-time into these much more mathematically precise field equations. He also developed the idea that all space-time coordinates, all parts of space-time, are treated equally by the laws of physics. Like the speed of light, the laws of physics are treated as universal throughout the universe. This means that, for example, a skydiver in free fall, experiencing an acceleration of 1 g (9.8 m/s2) is experiencing exactly the same thing as an astronaut in a spaceship that is accelerating at a rate of 1 g through empty space. As the skydiver falls toward Earth, he is falling, in a sense, toward a space-time "dent," Earth's dent. In the accelerating spaceship, where there are no dents, that is, no curvatures of space-time caused by nearby planets or stars, the geometry of space-time would appear to curve into exactly the same shape as it's curved around Earth. This is the essence of relativity.

Objects with mass curve space-time and they also follow the shortest path as they move through space-time. The orbits of planets around the Sun are examples of objects taking the shortest paths, the paths that require the least amount of energy. In physics, this path is called a geodesic.

Light also follows the curves of space-time. In 1919, not long after Einstein published his theory of general relativity, astronomer Arthur Eddington measured the deflection of light caused by the Sun during a solar eclipse, precisely matching Einstein's prediction.

Gravitational Time Dilation

Einstein's theory of special relativity predicts that time is relative - it appears to slow down at very high relative velocities. When this theory is expanded and refined into general relativity, gravity, or the curvature of space-time by mass, will also appear to slow down, or dilate, time. Gravity also stretches or shrinks distances perpendicular to the gravitational field. To outside observers, time would even appear to slow to a stop at the event horizon of a black hole, which curves space-time so intensely that the curvature becomes infinite. Nothing, not even light, can escape this maximum curvature of space-time. To learn more about black holes, please see my article called Stellar Objects Part 5: Black Holes. We should keep in mind that black holes are theoretical. No black holes have yet been directly observed but there is growing physical evidence for them based on their predicted effects on the motion of nearby stars and other bodies.

Gravitational Waves

Einstein's field equations also predict that the motion of a mass through space-time will cause a disturbance in it, an oscillation that travels at the speed of light. These waves travel right through matter, but their strength weakens proportionally to the their distance from their source. Such a wave will alternately stretch and shrink distances as it travels, but this is a very subtle effect. Even if a quite strong gravitational wave travelled through Earth, it would affect distances on the scale of the diameter of an atom. Gravitational waves also exhibit another strange quality: If an object itself emits gravitational waves, its mass is predicted to decrease. You might recall that, according to special relativity, mass is dependent on the velocity of the observer. This is called relativistic mass, and it stems from Einstein's concept of mass-energy equivalence. In contrast, an object's rest mass is its Newtonian, or invariant, mass. These two definitions of mass play a functional role in particle physics where particles are accelerated to enormous velocities. Gravitational waves have been documented. The 1993 Nobel Prize in Physics went to two researchers, Russell Hulse and Joseph Taylor who were able to prove that a binary system consisting of two neutron stars orbiting each other, called PSR1913+16, emits gravitational waves. As I mentioned, mass and energy are equivalent. The orbital period of one of the stars is decreasing at precisely the rate predicted if the system were losing mass/energy by radiating gravitational waves.

You may want to think of gravitational waves like this: An object with mass creates a curvature in space-time. If that object moves around through space-time, that curvature changes to reflect its changing location. Under certain circumstances, if that object is accelerated, it can generate a disturbance in space-time that spreads like ripples on a pond. These are gravitational waves, also called gravitational radiation. You might be wondering what these special circumstances are. Acceleration that is not perfectly symmetric (such as an expanding and contracting sphere) or cylindrically symmetric (like a spinning disc or sphere) can generate gravitational waves. I can use a spinning dumbbell as an analogy. If the dumbbell spins like wheels on an axis, it won't generate any gravitational waves but if it tumbles end over end (like the neutron star binary system), it will. The faster it tumbles, the greater the gravitational radiation it will give off. As you might imagine, astrophysicists are busy right now looking for gravitational radiation signatures of various objects such as supernovae, provided the explosion is not symmetrical. These signatures might also provide information about the mysterious black holes mentioned earlier, and about the Big Bang itself. Remember the example of the spaceship accelerating a 1 g, where space-time would appear to curve? That ship is creating gravitational waves but they would be extremely small and virtually undetectable, even right at the source, the ship itself.

An experiment under development to measure gravitational waves is a joint NASA/ESA effort called the Laser Interferometer Space Antenna. This is an artist's conception of how it will work:

Each of three spacecraft will be placed in an individual Earth-like orbit around the Sun, flying in a triangular formation with equal arms of 5 million km. The spacecraft will measure tiny warps in space-time caused by gravitational waves as they pass through the triangle, compressing and stretching it. The shape and timing of waves will be measured and they will hopefully help us learn about the systems that created them.

Gravitational Lensing

Light follows the curves of space-time. In 1919, Eddington proved it, as we learned earlier. This phenomenon is called gravitational lensing. Because light is deflected in a gravitational field, light from a very distant object can reach an observer along two or more paths. As a result, an observer could see the same object in two or more places in the night sky. A famous example is called the Einstein Cross, shown here:

This is a gravitationally lensed quasar, four images of it, around a foreground galaxy. The gravitational field of the galaxy (400 million light years away) bends the light from the more distant quasar (8 billion light years away). It is important to remember that light is simply following the space-time geometry. The photons themselves have no mass and they are not attracted or pulled in by large masses nearby. This is exactly why photons are lost in a black hole. The black hole doesn't suck them in - the photons are simply moving through the extreme space-time geometry that the black hole creates. From each photon's point of view it is traveling in a straight line. Again, this is the nature of relativity.

Quantum Gravity

General relativity, though modern, is an example of a classical theory - it does not take into account quantum mechanical effects. A quantum version of general relativity is modern physic's version of the Holy Grail. It has been an incredible ongoing challenge to formulate this quantum version. However, two theories, string theory and loop quantum gravity, show some promise toward developing a theory of quantum gravity. We will explore their promise and their pitfalls in a moment but first, I would like to stress the enormity that an ultimate break-through represents to the scientific community, and to all of our understanding of how the universe works.

The "Holy Grail" - a Word of Caution

Quantum Gravity, General Relativity and the Graviton

Physicists are in hot pursuit of a workable theory that describes gravity at the quantum level. The other three fundamental forces (strong, weak and electromagnetic) can all be described in the language of quantum mechanics. Gravity, for several reasons, is not nearly so easy to pin down. For example, these three forces are measurable at the level of the very small but gravity is so much weaker - for practical purposes, gravity can even be excluded from quantum mechanics equations, and it currently is. We have no experimental evidence for gravity operating at the quantum level. However, physical behaviours on the scale of the very large, such as how stars and galaxies work, depend almost entirely on the physics of gravity. Our ability to describe the behaviour of gravity breaks down when we talk about very large masses squeezed into very small volumes (black holes, the Big Bang). Neither general relativity nor quantum mechanics can be used alone to describe it - both are required together and we do not have the theoretical framework to do that. We have a problem of scale when we try to design experiments that test quantum gravity. We also have a problem of assumptions on how the universe works. For example, quantum mechanics depends on quantum field theory in which each fundamental force is mediated or carried out by a particle within the flat space-time described by special relativity. Gravity, on the other hand, is modeled on the curvature of space-time. According to general relativity, space-time geometry is dynamic - it can't be independently pinned down to any kind of fixed background (the consequences of this are profound and they still have yet to be worked out! - this is what makes general relativity so hard to grasp). Quantum mechanics, in contrast, depends on a fixed background (loop quantum theory attempts to come up with a quantum dynamics framework that is background-independent as we will soon see). When the equations for quantum mechanics are combined with those describing general relativity, you get infinite values that don't cancel out. Another way of putting this problem is that under low energies, quantum gravity reduces down to gravity as defined by general relativity but at very high energies, such as within black holes, gravity cannot be described because quantum effects tend to take over and those infinite values tend to take over the equations used to describe it. Physicists have been reworking these equations, some of which are very complex, for decades in an attempt to put them together in a sensible way with some limited success. For example, the structure of general relativity can be shown to follow, at least in an incomplete way, from the quantum mechanics of a theoretical massless spin-2 particle, and this has been named the graviton. It would be the force carrier or mediator particle for the gravitational field. Gravitons are special in that they play a role, unlike the particles mediating the other fundamental forces, in defining the space-time in which the other particles carry out their various functions. The existence of a graviton agrees with both string theory and loop quantum theory (in fact these two theories require it), which I will describe next, beginning with strings.

String Theory

What is gravity according to string theory and how does it propose to knit two mutually exclusive views of the universe together?

String theory originated as a theory that describes the strong force but researchers soon realized that the graviton, as well as all other mass and force particles, could be described mathematically as strings. Here, the condensation of certain vibration modes of a very tiny 1-dimensional string is equivalent to the modification of an original background, that being a field. It is a weak form of background dependence, which makes it not quite perfect for some theorists. A quantum theory of gravity should be background-independent. An exchange of gravitons should be equivalent to a change in background. This is a fancy way of saying that gravity itself is the curvature, the change, in space-time. You can't superimpose this on another field. Another pesky problem is that string theory comes in several equally workable forms, and no one knows what this means. Finally, the strings we are talking about are infinitesimally small, so small it is almost impossible to imagine how physicists could prove it experimentally. String theory itself, since its inception in 1969, has had its golden moments when everyone wanted to study it as well as its doldrums when no respectable researcher would touch it with a ten-foot pole. Right now, many prominent physicists, such as Stephen Hawking, Edward Witten and Leonard Susskind, believe it has some real potential toward combining quantum mechanics and general relativity into one grand scheme. Hawking goes as far as to say that M-theory, one kind of string theory, is the only plausible candidate for a unified theory. Richard Feynman and Sheldon Glashow, however, view it as more philosophy than science - what good is a theory that can never be verified through experiment? Is that not the heart of physics, that which distinguishes it from other "softer" sciences?

What exactly is string theory? Other models consider particles to be either zero-dimensional points or billiard-type balls. In string theory, particles are very tiny (Planck-length) 1-dimensional strings. This diagram gives you an idea of how these fundamental strings make up matter, for example:

(1) denotes matter (diamond, made up of carbon atoms), (2) is the molecular structure composed of atoms, (3) is a single carbon atom. (4) is an electron, (5) are the 3 quarks within a single nucleon (either a proton or a neutron), and (6) shows us that quarks and electrons are ultimately made up of strings.

These strings can vibrate at various frequencies and it is the vibrational mode that characterizes the string as matter, light or energy. It gives the particle its charge, mass and spin. The universe, according to string theory, is a symphony. According to most string theories, the theoretical graviton is a closed string loop in an especially low-energy vibrational state, and this loop traces out the surface of a kind of graph called a worldsheet. In this case, because the graviton string is a closed loop, its worldsheet is a pipe shape with no boundaries. Gravitons are surface waves across this shape. Some theorists believe that we live in a three-dimensional subspace of space-time, which can consist of as many as 11 dimensions. Because gravitons have no boundaries, they can move freely between and around our brane, as it is called, and this "leakage" of gravitons from this brane into higher-dimensional space could explain why gravity is so much weaker than the other three fundamental forces. As well, gravitons from other branes adjacent to ours could help explain what we call dark matter. This idea requires us to re-visualize the universe as consisting of four unfolded dimensions of space-time as well as up to 7 tightly folded up dimensions. We do not experience these higher dimensions but they may play a vital role in quantum behaviours. An analogy is a garden hose. To us from a distance it appears as a 1-dimensional line. As we draw nearer, we realize it is two-dimensional; it has width and length. As we get even closer, we see that it clearly has three dimensions - length, width and depth, or a circumference. In a similar way, we do not see or experience all the extra dimensions in which a graviton string can potentially move across. Although string theory is far from being experimentally verified, it has a certain elegance that is hard to ignore.

Loop Quantum Gravity

If the notion of extra dimensions of space-time is not palatable to you, consider loop quantum gravity. First formulated in the 1980's and a major contender for quantum gravity, this theory incorporates general relativity and also quantizes space and time (helping it fit into quantum mechanics), without resorting to extra dimensions.

Loop quantum gravity attempts to formulate a quantum theory for gravity based directly on Einstein's geometrical description of space-time. Remember that Einstein did not think of gravity as a force, unlike the strong, weak and electromagnetic forces. He thought of gravity as a property of space-time itself. This theory has its problems just as string theory does, but it goes a considerable way toward describing space-time in the language of quantum mechanics. It is very appealing because it does not require any major reworking of either quantum mechanics or general relativity. It sort of takes them as they are and works from that - and we don't need to add extra dimensions or other exotica to this concept in order for it to work, with one strange little exception as we will soon find out.

Many people, including me, find this theory complex and difficult to understand but let's give it a try. In general relativity, space-time is a smooth continuum - you can theoretically divide it into smaller and smaller volumes ad infinitum. Loop quantum theory, because it is a quantum theory, breaks down this smooth space-time into a discrete basic structure, as it must, but this structure is a bit more complex than just sliced up single discrete units. This theory calls space-time fabric a spin network that is made up of lines and nodes. You can visualize it as a string of Christmas lights except that instead of a single string, each light (called a node) is connected to many other lights (other nodes), shown here:

(Courtesy: Einsteinonline.com)

These nodes carry numerical values, so, depending on the number, they stand for space-time volume building blocks of different sizes. The smallest possible volume, or unit, of space-time is a region containing only a single node of lowest possible value. Adding nodes or increasing their values increases the size of the building block. You can think of space-time a bit like a set of Lego blocks, and the smallest unit is like the tiny one-piecer. This one-piecer has a numerical value associated with a massless spin-2 particle, a graviton. And this graviton, not surprisingly, is roughly the cube of a Planck length (10-33 cm).

This means that the smallest volume of space-time is this Planck volume and all theoretically measurable volumes are multiples of this volume. They are quantized, in other words, much like electron energies are quantized inside atoms. Long-wavelength gravitational waves in otherwise flat space-time can be described as excitations of these quantum states. It has the nice side effect of doing away with singularities such as the Big Bang and black holes, with infinite mass crammed into a point of zero volume. Because space-time is not localized to a single point, the spin network described here has been coined spin foam, analogous to but not quite the same as the quantum foam I have mentioned in other articles. I could say that string theory also does away with singularities, owing to its one-dimensional strings. The problem with this is that string theory is not entirely background-independent and so we can't make that claim so enthusiastically since it doesn't provide us with a complete picture of space-time itself. Loop quantum theory can also describe black hole radiation and the relationship between a black hole's entropy and its surface area.

Loop quantum gravity has a gigantic plus going for it - we can potentially obtain some direct physical evidence for this smallest unit of theoretical volume in space-time. The light from gamma ray bursts, for example, should scatter off the discrete structure of the quantum geometry of space-time, much like light scattering off molecules in the air  as it passes through it, but on a much smaller scale, the Planck scale, about 10-20 the diameter of a single proton. This means that the effect we can expect is extremely tiny. Fortunately, we have gamma ray bursts that we can measure from great distances, billions of light-years away, and over these distances the tiny quantum effect is amplified to the point where it could be measured.

According to this theory, each gamma photon occupies a region of lines at each instant as it moves through the spin network. This discrete nature of space-time should cause higher energy photons to move through slightly faster than lower energy photons. There is a potential fly in this promising ointment, however, and it has to do with the speed of light. Einstein's theory of special relativity tells us that light has a speed limit. In technical terms we say it obeys Lorentz invariance - it is the same for all observers and for all energies of light photons. This has been experimentally verified with great precision. Loop quantum theory, on the other hand, predicts that this invariance breaks down as we approach Planck scale so that high-energy photons should travel faster than low-energy photons. This effect seems to bring special relativity into question. However, Richard Feynman, using quantum electrodynamics, showed us that, at the quantum level, photons could travel faster than the speed of light, as well as slower, and that these strange occurrences disappear as the scale is increased (see my article on the nature of light).

A gamma ray burst is perfect for amplifying these expected but tiny speed differences. Astrophysicists found just such a perfect burst in 2009 using the Fermi Gamma-ray Space Telescope. They focused on a single very energetic (31 GeV) photon from gamma ray burst GRB 090510. It was a brief burst but it should have given measurable results - and they were disappointing - all the photons (of varying energies) of the burst, including the very energetic one, arrived at exactly the same time. What this means is that they need more testing using data from other gamma bursts. It is also possible that the researchers timing assumptions need to be fine-tuned. The researchers, in their paper on this experiment, suggested various explanations for this result, one of which is that high-energy photons might be released earlier than lower-energy ones. I sense a hint of panic in these explanations. Every researcher involved in quantum gravity theory wants to be the one to find the Holy Grail and the competition is fierce. All is not lost: there may be yet another way to test loop quantum theory. Researchers in France and the US have come up with a theory that evaporating black holes, in addition to emitting Hawking radiation should emit one or two distinct loop quantum signatures as well, depending on the size of the black hole. The challenge now will be finding evaporating black holes to test this theory.

Negative Gravity?

The equations that describe general relativity cannot construct a negative geometry unless a theoretical negative mass, which the equations do not rule out, is introduced. This negative mass would produce a repulsive gravitational field. Do we have any contenders for negative mass?

Antimatter?

It is important to distinguish negative mass with antimatter. The rules of CPT symmetry tell us that antimatter, while opposite in charge and magnetic moment from ordinary matter, has positive energy content and reacts to gravity just like ordinary matter does.

Dark Matter?

Dark matter, which you may have heard about, is matter that neither emits nor scatters electromagnetic radiation. This matter does not appear to interact with itself or other forms of matter (with the exception of possible weakly interacting particles which physicists are now trying to detect). Its interaction with gravity gives us a way of indirectly detecting it, through its gravitational effects. The orbital velocities of galaxies within clusters are too high to account for the mass we can measure. Dark matter is believed to make up over 80% of all the matter in the universe. This matter, just like ordinary matter and antimatter, reacts positively to gravity.

Thus, we do not have any contenders for negative mass. This hasn't stopped many researchers over the decades from attempting to demonstrate the existence of negative or anti-gravity, but none have been successful. The idea of negative gravity was, in fact, dead until 1998, when a new form of energy was suddenly plunked down on the table for consideration. It began when astrophysicists were shocked to discover that the universe is expanding at an increasing rate. Only a force that opposes the force of gravity could cause masses such as galaxies, which are moving away from each other, to accelerate rather than eventually slow down and begin to collapse back in toward each other. All the mass in the universe should be self-attracting, slowing down the expansion. A force with negative pressure seems to be involved and it has been coined dark energy. This new energy presents physicists with an enormous new challenge that brings our current understanding of fundamental forces, and gravity itself, into question.

Dark Energy

In the 1930's, contrary to Einstein's view of a static universe, Edwin Hubble discovered that the universe is expanding. This expansion is now thought to be driven by vacuum energy. Even completely empty space contains a minimum energy, which exerts negative pressure. Only recently did we know that the rate of expansion is increasing. The question is whether vacuum energy contributes to accelerating expansion or not. According to one theory, called the cosmological constant theory, it does. The cosmological constant gives us a value for the universe's vacuum energy.

At this point, you might wonder how the notion of negative pressure fits into general relativity. This is explained by something called the Stress-energy tensor, which is the physical quantity that causes matter to generate a gravitational effect. The Stress-energy tensor contains not only the energy or matter density of a substance but its pressure and viscosity as well. It gives us a more refined description of how matter interacts with gravity. Using this approach, cosmologist Marco Spaans suggests that the cosmological constant (vacuum energy) could be increasing as the number of black holes in the universe increases. The quantum properties of their particular space-time could, in theory, squeeze out vacuum energy, contributing to ever-increasing vacuum energy, and therefore, accelerating expansion of the universe.

However, in order for the cosmological constant theory to explain accelerating expansion, it must predict a constant that describes the rate of acceleration we measure. Most quantum field theories predict a constant that is 100 orders of magnitude too big. Other theories predict as constant of zero. It is a very economical theory because one numerical value could explain many different kinds of data from the WMAP data to recent supernovae data but unless a better value can be found this theory has limited usefulness.

A competing theory of dark energy is that of quintessence. Here, the potential energy of a dynamic field, which acts like a perfect fluid, could account for the acceleration. The field can vary in space and time. Quintessence itself can be attractive or repulsive depending on the ratio of potential energy to kinetic energy in the universe. As this ratio changes, the expansion rate of the universe changes. The quintessence field has a density that closely tracks, but is slightly less than, the radiation density of the universe until a point in the universe's evolution when matter and radiation equal each other in total energy density. A this point quintessence begins to act more and more like the repulsive dark energy that seems to dominate the universe today (74% of the total mass/energy of the universe). Some theorists are currently interested in trying to link quintessence with inflation, the early extreme expansion of the universe, in the hope that one theory could ultimately explain both phenomena. Subtle measurable violations of Einstein's equivalence principle (this is the principle that?s says that a spaceship accelerating at 1 g is equivalent to a skydiver in free fall accelerating at 1 g) and measurable variation in fundamental constants in space or time could be used as evidence for this theory, but no evidence has yet been found.

Dark energy may be a property of space-time itself, as hinted at by the cosmological constant theory. It could be a new dynamic fluid of some unknown composition as postulated by the quintessence model. It could also be telling us that Einstein's theory of gravity is incomplete because it does not describe the changing behavior of the universe over time. As to the question of whether dark energy is actually negative gravity, we cannot really say until we understand either the forces and fields involved or the space-time fabric itself, or both, better. Obviously, dark energy is a giant hurdle we need to overcome before we can approach any universal theory of everything.

Conclusion

Over the past few years, the hard work of scientists has given us much food for thought, refining our concept of gravity toward a eventual understanding that may weave it into an elegant fabric of space-time as well as give it its home within the quantum mechanical model of particle physics. Researchers may indeed find the ultimate answer to the question of what this universe is ultimately made of, the "theory of everything." We seem to be close, and far away, at the same time.

It is still appropriate to learn first about Newtonian gravity in school science, to know its history and get a good theoretical background. It is also important that as scientific explorers we build our knowledge from a firm foundation. But I hope we appreciate too that Newtonian gravity represents a door just ajar onto great mysteries of gravity and ultimately the mystery of the universe itself. As we learn about gravity, we may begin to deepen our appreciation for how scientific understanding is refined and built up through hard work and imagination, and how fragile those theories we build can be.