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Misconceiving the Big Bang

The Big Bang was NOT a Fireworks Display!

Written by Sten Odenwald
Copyright (C) 1997. Published in the Washington Post Horizon education supplement on May 14, 1997.

The Big Bang wasn’t really big. Nor was it really a bang. In fact, the event that created the universe and everything in it was a very different kind of phenomenon than most people–or, at least, most nonphysicists–imagine.
Even the name “Big Bang” originally was a put-down cooked up by a scientist who didn’t like the concept when it was first put forth. He favored the idea that the universe had always existed in a much more dignified and fundamentally unchanging, steady state.

But the name stuck, and with it has come the completely wrong impression that the event was like an explosion and that the universe is expanding today because the objects in it are being flung apart like fragments of a detonated bomb.

Virtually every basic aspect of this intuitive image for the Big Bang (we ARE stuck with the name) is incorrect. To understand why, you need to understand Albert Einstein’s general theory of relativity. Or, at least, you need to have a sense of it. That may sound daunting, but general relativity is the most revolutionary scientific advance of the 20th century, and we all ought to acquire some feeling for it before the century ends.

After all, it’s been 82 years since Einstein put forth his theory. It’s been tested in scores of experiments and has always passed with flying colors and is now firmly established as our premier guide to understanding how gravity operates. Moreover, it is part of the foundation of Big Bang cosmology. And it is because of general relativity that we know the Big Bang was (and is, for the event is still going on) nothing like an explosion.

Albert Einstein developed general relativity in order to make his famous theory of special relativity include the effects of gravity. It is a better way than Sir Isaac Newton’s of understanding how gravity works. Like a hungry amoeba, general relativity ( or just GR for short) had absorbed both Einstein’s newly-minted special relativity and Newton’s physics, giving us the means to replicate ALL of the predictions from these two great theories, while extending them into unfamiliar realms of experience. One of these realms was the Black Hole. The other was the shape and evolution of the universe itself.

Big Bang cosmology says that the universe came into existence between 10 to 20 billion years ago, and that from a hot dense state has been expanding and cooling ever since, remains unassailable. Yet, Big Bang cosmology is vulnerable. It is based on GR being accurate over an enormous range of scales in time and space. Just how good is general relativity? So far, GR has made the following specific predictions:

1…The entire orbit of Mercury rotates because of the curved geometry of space near the sun. The amount of ‘perihelion shift’ each century was well known at the time Einstein provided a complete explanation for it in 1915.

2…Light at every frequency can be bent in exactly the same way by gravity. This was confirmed in the 1919 Solar Eclipse for optical light using stars near the Sun’s limb, and in 1969-1975 using radio emissions from star-like quasars also seen near the limb of the Sun. The deflection of the light was exactly as predicted by GR.

3…Clocks run slower in strong gravitational fields. This was confirmed by Robert Pound and George Rebka at Harvard University in 1959, and by Robert Vessot in the 1960’s and 70’s using high-precession hydrogen maser clocks flown on jet planes and on satellites.

4…Gravitational mass and inertial mass are identical. Most recently in 1971, Vladimir Braginsky at Moskow University confirmed GRs prediction of this to within 1 part in a trillion of the exact equality required by GR.

5…Black holes exist. Although these objects have been suspected to exist since they were first introduced to astronomers in the early 1970’s, it is only in 1992 that a critical acceptance threshold was crossed in the astronomical community. It was then that Hubble Space Telescope observations revealed monstrous, billion-sun black holes in the cores of nearby galaxies such as Messier 87, Messier 33 and NGC 4261.

6…Gravity has its own form of radiation which can carry energy. Russel Hulse and Joseph Taylor in 1975 discovered two pulsars orbiting each other, and through careful monitoring of their precise pulses during the next 20 years, confirmed that the system is loosing energy at a rate within 1 percent of the prediction by GR based on the emission of gravitational radiation.

7…A new force exists called ‘gravito-magnetism’. Just as electric and magnetic fields are linked together, according to GR, a spinning body produces a magnetism-like force called gravitomagnetism. GR predicts that rotating bodies not only bend space and time, but also make empty space spin. A NASA satellite called Gravity Probe B will be launched in the next few years to see whether this effect exists. This is a killer. If it is not found, GR is mortally wounded despite its long string of other successes.

8…Space can stretch during the expansion of the universe. This was confirmed by Edwin Hubble’s detection of the recession of the galaxies ca 1929. More recently in 1993, Astronomer Kenneth Kellerman confirmed that the angular sizes of distant radio sources shrink to a minimum then increase at greater distances exactly as expected for a dilating space. This is not predicted by any other cosmological model that does not also include the dilation of space as a real, physical phenomenon.

We have now boxed ourselves into a corner. If we accept the successes of GR, we are forced to see the world and the cosmos through its eyes, and its eyes alone, since it is the theory which satisfies all known tests to date.

So, how should we think about the Big Bang? Our mental ‘fireworks’ image of the Big Bang contains these basic elements: 1) A pre-existing sky or space into which the fragments from the explosion are injected; 2) A pre-existing time we can use to mark when the explosion happened; 3) Individual projectiles moving through space from a common center; 4) A definite moment when the explosion occurred; and 5) Something that started the Big Bang.

All of these elements to our visualization of the Big Bang are completely false according to GR!

Preexisting Space?

There wasn’t any!

The mathematics of GR state specifically and unambiguously that 3-dimensional space was created at the Big Bang itself, at ‘Time Zero’, along with everything else. It was a ‘singular’ event in which the separations between all particles everywhere, vanished. This is just another way of saying that our familiar 3-dimensional space vanished. Theorists studying various prototypes for the Theory of Everything have only modified this statement somewhat. During its earliest moments, the universe may have existed in a nearly incomprehensible state which may have had more than 4 dimensions, or perhaps none at all. Many of these theories of the earliest moments hypothesize a ‘mother space-time’ that begat our own universe, but you cannot at the same time place your minds eye both inside this Mother Spacetime to watch the Big Bang happen, and inside our universe to see the matter flying around. This is exactly what the fireworks display model demands that you do.

Preexisting Time?

There wasn’t any of this either!

Again, GR’s mathematics treats both space and time together as one object called ‘space-time’ which is indivisible. At Time Zero plus a moment, you had a well defined quantity called time. At Time Zero minus a moment, this same quantity changed its character in the mathematics and became ‘imaginary’. This is a mathematical warning flag that something dreadfully unexpected has happened to time as we know it. In a famous quote by Einstein, “…time and space are modes by which we think and not conditions in which we live”. Steven Hawking has looked at the mathematics of this state using the fledgling physics of Quantum Gravity Theory, and confirms that at the Big Bang, time was murdered in the most thorough way imaginable. It may have been converted into just another ‘timeless’ dimension of space…or so the mathematics seems to suggest.

Individual objects moving out from a common center?

Nope!

GR says specifically that space is not a passive stage upon which matter plays out its dance, but is a member of the cast. When you treat both galaxies and space-time together, you get a very different answer for what happens than if you treat them separately, which is what we instinctively always do. Curved space distorts the paths of particles, sometimes in very dramatic ways. If you stepped into a space ship and tried to travel to the edge of the universe and look beyond, it would be impossible. Not only could you not reach a supposed “edge” of the universe no matter how long or how fast you traveled, in a closed universe, you would eventually find yourself arriving where you departed. The curvature of space would bring you right back, in something like the way the curvature of Earth would bring you home if you flew west and never changed course. In other words, the universe has no edge in space. There is nothing beyond the farthest star.

As a mental anchor, many have used the expanding balloon as an analogy to the expanding universe. As seen from any one spot on the balloon’s surface, all other spots rush away from it as the balloon is inflated. There is no one center to the expansion ON THE SURFACE of the balloon that is singled out as the center of the Big Bang. This is very different than the fireworks display which does have a dramatic, common center to the expanding cloud of cinders. The balloon analogy, however, is not perfect, because as we watch the balloon, our vantage point is still within a preexisting larger arena which GR says never existed for the real universe.

The center of the Big Bang was not a point in space, but a point in time! It is a center, not in the fabric of the balloon, but outside it along the 4th dimension…time. We cannot see this point anywhere we look inside the space of our universe out towards the distant galaxies. You can’t see time afterall! We can only see it as we look back in time at the ancient images we get from the most distant objects we can observe. We see a greatly changed, early history of the universe in these images but no unique center to them in space.

It is at this point that common sense must give up its seat on the bus, and yield to the insights provided by GR. And it is at precisely this point that so many non-physicists refuse to be so courteous. And who can blame them? But there’s more to come.

Projectiles moving through space?

Sorry!

GR again has something very troubling to say about this. For millions of years we have learned from experience on the savanas of the African continent and elsewhere, that we can move through space. As we drive down the highway, we have absolutely no doubts what is happening as we traverse the distance between landmarks along the roadside. This knowledge is so primal that we are incapable of mustering much doubt about it. But science is not about confirming our prejudices. It’s about revealing how things actually are.

What if I told you that you could decrease the distance from your house and the Washington Monument by ‘standing still’ and just letting space contract the distance away? GR predicts exactly this new phenomenon, and the universe seems to be the only arena we know today in which it naturally occurs. Like spots glued to the surface of the balloon at eternally fixed latitude and longitude points, the galaxies remain where they are while space dilates between them with the passage of time. There is no reason at all we should find this kind of motion intuitive.

If space is stretching like this, where do the brand new millions of cubic light years come from, from one moment to the next? The answer in GR is that they have always been there. To see how this could happen, I like to think of the shape of our universe as a “Cosmic Watermellon”. The fact that this is only the shape for a ‘closed’ finite universe is only a technicality. Finite watermellons are also cheaper to buy than infinite ones.

GR predicts the entire past, present and future of the universe all at once, and predicts its entire 4-dimensional shape. As we slice the 4-dimensional, Cosmic Watermellon at one end of the cosmic time line, we see 3-dimensional space and its contents soon after the Big Bang. At the other end of the Cosmic Watermellon in the far future, we see the collapse of space and matter just before the Big Crunch. But in between, our slices show the shape of space (closed, spherical volumes) and the locations of galaxies ( at fixed locations) as space dilates from one extreme to the other.

As a particular slice through an ordinary watermellon, we see that its meat has always been present in the complete watermellon. The meat is present as a continuous medium, and we never ask where the meat in a particular slice came from. Cosmologically, GR ask us to please think of 3-dimensional space in the same way. Space, like the meat of the watermellon, has always existed in the complete shape of the universe in 4-dimensions. But it is only in 4-dimensions that the full shape of the universe is revealed. It is a mystery why our consciousness insists on experiencing the universe one moment at a time, and that is why we end up with the paradox of where space comes from. There really is no paradox at all.

Space is not ‘nothing’ according to Einstein, it is merely another name for the gravitational field of the universe. Einstein once said, “Space-time does not claim existence on its own but only as a structural quality of the [gravitational] field”. If you could experimentally turn-off gravity with a switch, space-time would vanish. This is the ultimate demolition experiment known to physics for which an environmental impact statement would most certainly have to be filed.

The gravitational field at one instant is wedded to itself in the next instant by the incessant quantum churnings of the myriad of individual particles that like bees in a swarm, make up the gravitational field itself. In this frothing tumult, the gravitational field is knit together, quantum by quantum, from perhaps even more elemental building blocks, and it is perhaps here that we will find the ultimate origin for the expansion of the universe and the magical stretching of space. We hope the much anticipated Theory of Everything will have more to say about this, but to actually test this theory may require technologies and human resources that we can only dimly dream of.

Was there a definite moment to the Big Bang?

GR is perfectly happy to forecast that our universe emerged from an infinite density, zero-space ‘Singularity’ at Time Zero, but physicists now feel very strongly that this instant was smeared out by any number of quantum mechanical effects, so that we can never speak of a time before about 10^-43 seconds after the Big Bang. Just as Gertrude Stein once remarked about my hometown, Oakland, California that “There is no ‘There’ there”, at 10^-43 seconds, nature may tell us that before the Big Bang, “There was no ‘When’ there” either. The moment dissolves away into some weird quantum fog, and as Steven Hawking speculates, time may actually become bent into a new dimension of space and no longer even definable in this state. Ordinary GR is unable to describe this condition and only some future theory combing GR and quantum mechanics will be able to tell us more. We hope.

Something started the Big Bang!

At last we come to the most difficult issue in modern cosmology. In the fireworks display, we can trace the events leading up to the explosion all the way back to the chemists that created the gunpowder and wrapped the explosives. GR, however, can tell us nothing about the equivalent stages leading up to the Big Bang, and in fact, among its strongest statements is the one that says that time itself may not have existed. How, then, do we speak or think about a condition, or process, that started the whole shebang if we are not even allowed to frame the event as “This happened first…then this…then kerpowie!”? This remains the essential mystery of the Big Bang which seems to doggedly transcend every mathematical description we can create to describe it.

All of the logical frameworks we know about are based on chains of events or states. All of our experiences of such chains in the physical world have been ordered in time. Even when the mathematics and the theory tell us ‘What happened before the Big Bang to start it?’ is not a logical or legitimate question, we insist on viewing this as a proper question to ask of nature, and we expect a firm answer. But like so many other things we have learned this century about the physical world, our gut instincts about which questions ought to have definite answers is often flawed when we explore the extreme limits to our physical world.

I wrote this essay before seeing the new IMAX file at the Air and Space Museum ‘Cosmic Journey”, by far one of the nicest and most heroic movies of its kind I had ever seen. But of course it showed the Big Bang as a fireworks display. No matter. It doesn’t take a rocket scientist to accept the fact that the Big Bang was a spectacular moment in history. What is amazing is that the daring audacity of humans may have demystified some of it, and revealed a universe far stranger than any could have imagined.

Still, we are haunted by our hunches and intuitions gathered over millenia, and under circumstances far removed from the greater physical world we are now exploring. No wonder it all seems so alien and maddeningly complex.

Before the Big Bang

Beyond the Big Bang

Written by Sten Odenwald Copyright (C) 1987, Kalmbach Publishing. Reprinted by permission

Sometime between 15 and 20 billion years ago the universe came into existence. Since the dawn of human awareness, we have grappled with the hows and whys of this event and out of this effort have sprung many ideas. An ancient Egyptian legend describes how the universe was created by Osiris Khepera out of a dark, boundless ocean called Nu and that Osiris Khepera created himself out of this ocean by uttering his own name. Human inventiveness has not stood still in the 5000 years since these ideas were popular. The modern theory of the Big Bang states that our universe evolved from an earlier phase billions of times hotter than the core of our sun and trillions of times denser than the nucleus of an atom. To describe in detail such extreme physical conditions, we must first have a firm understanding of the nature of matter and of the fundamental forces. At the high temperatures likely to have attended the Big Bang, all familiar forms of matter were reduced to their fundamental constituents. The forces of gravity and electromagnetism together with the strong and weak nuclear forces, were the essential means through which the fundamental particles of matter interacted.
The feedback between cosmology and particle physics is nowhere more clearly seen than in the study of the early history of the universe. In October, 1985 the giant accelerator at Fermilab acheived for the first time, the collision of protons and anti-protons at energies of 1.6 trillion electron volts, about 1600 times the rest mass of the proton. This was a unique event because for one split second, on a tiny planet in an undistinguished galaxy, a small window onto the Creation Event was opened for the first time in at least 15 billion years.

THE LIMITS OF CERTAINTY

The persuit by physicists of a single, all encompassing theory capable of describing the four natural forces has, as a by-product, resulted in some surprising glimpses of the Creation Event. Although such a theory remains perhaps several decades from completion, it is generally recognized that such a theory will describe physical conditions so extreme it is quite possible that we may never be able to explore them first- hand, even with the particle accelerators that are being designed today. For example, the Superconducting Supercollider to be built by the early 1990’s will cost 6 billion dollars and it will allow physicists to collide particles at energies of 40 trillion electron volts ( 40,000 GeV) matching the conditions prevailing 10 seconds after the Big Bang. The expected windfall from such an accelerator is enormous and will help to answer many nagging questions now plaguing the theoretical community, but can we afford to invest perhaps vastly larger sums of money to build machines capable of probing the quantum gravity world at 10 GeV? At these energies, the full unification of the natural forces is expected to become directly observable. How curious it is that definite answers to questions such as, ‘What was Creation like?’ and ‘Do electrons and quarks have internal structure?’ are so inextricably intertwined. Our ability to find answers to these two questions, among others, does not seem to be hampered by some metaphysical prohibition, but by the resources our civilization can afford to devote to finding the answers. Fortunatly, the situation is not quite so bleak, for you see, the ‘machine’ has already been ‘built’ and every possible experiment we can ever imagine has already been performed!

WHAT WE THINK WE KNOW

We are living inside the biggest particle accelerator ever created – the universe. Ten billion years before the sun was born, Nature’s experiment in high-energy physics was conducted and the experimental data can now be examined by studying the properties and contents of the universe itself. The collection of fundamental facts that characterize our universe is peculiar in that it derives from a variety of sources. A partial list of these ‘meta-facts’ looks like this:

1) We are here, therefore, some regions of the universe are hospitible to the creation of complex molecules and living, rational organisms.

2) Our Universe has 4 big dimensions and all are increasing in size as the universe expands in time and space.

3) There are 4 dissimilar forces acting in Nature.

4) Only matter dominates; no anti-matter galaxies exist and this matter is built out of 6 quarks and 6 types of leptons.

The task confronting the physicist and the astronomer is to create, hopefully, a single theory consistent with these metafacts that can then be used to derive the secondary characteristics of our universe such as the 2.7 K background radiation, the primordial element abundances, and galaxy formation. The interplay between the study of the macrocosm and the microcosm has now become so intense that astronomers have helped physicists set limits to the number of lepton families — No more than 4 are allowed otherwise the predicted cosmological abundance of helium would seriously disagree with what is observed. Physicists, on the other hand, use the astronomical upper limits to the current value of the cosmological constant to constrain their unification theories.

An extention to the standard Big Bang model called the Inflationary Universe (see The Decay of the False Vacuum) was created by MIT physicist Alan Guth in 1981. This theory combined Grand Unification Theory with cosmology and, if correct, allows astronomers to trace the history of the universe all the way back to 10 seconds after the Big Bang when the strong, weak and electromagnetic forces were unified into a single ‘electro-nuclear’ force. During the 4 years since the Inflationary Universe model was proposed, other theoretical developments have emerged that may help us probe events occurring at an even earlier stage, perhaps even beyond the Creation Event itself. Ten years ago, theoreticians discovered a new class of theories called Supersymmetric Grand Unified Theories ( SUSY GUTs). These theories, of which there are several competing types, have shown great promise in providing physicists with a unified framework for describing not just the electro-nuclear force but also gravity, in addition to the particles they act on (see The Planck Era: March 1984). Unfortunately, as SUSY GUTs were studied more carefully, it was soon discovered that even the most promising candidates for THE Unified Field Theory suffered from certain fundamantal deficiencies. For instance:

1) There were not enough basic fields predicted to accomodate the known particles.

2) Left and right-hand symmetry was mandated so that the weak force, which breaks this symmetry, had to be put in ‘by hand’.

3) Anomalies exist which include the violation of energy conservation and charge.

4) The Cosmological Constant is 10 times larger than present upper limits suggest.

In recent years, considerable effort has gone into extending and modifying the postulates of SUSY GUTs in order to avoid these problems. One avenue has been to question the legitimacy of a very basic premise of the field theories developed heretofore. The most active line of theoretical research in the last 25 years has involved the study of what are called ‘point symmetry groups’. For example, a hexagon rotated by 60 degrees about a point at its center is indistinguishable from one rotated by 120, 180, 240, 300 and 360 degrees. These 6 rotation operations form a mathematical group so that adding or subtracting any two operations always result in a rotation operation that is already a member of the group ( 180 = 120 + 60 etc). The Grand Unification Theories of the electro-nuclear interaction are based on point symmetry groups named SU(3), SU(2) and U(1) which represent analogous ‘rotations’ in a more complex mathematical space. In the context of ponderable matter, point symmetry groups are also the mathematical statement of what we believe to be the structure of the fundamental particles of matter, namely, that particles are point-like having no physical size at all. But what if this isn’t so? The best that experimental physics has to offer is that the electron which is one of a family of 6 known Leptons, behaves like a point particle at scales down to 10 cm, but that’s still an enormous distance compared to the gravitational Planck scale of 10 cm where complete unification with gravity is expected to occur.

By assuming that fundamental particles have internal structure, Michael Green at Queen Mary College and John Schwartz at Caltech made a remarkable series of discoveries which were anounced in the journal NATURE in April 1985. They proposed that, if a point particle were replaced by a vibrating ‘string’ moving through a 10-dimensional spacetime, many of the problems plaguing SUSY GUTs seemed to vanish miraculously. What’s more, of all the possible kinds of ‘Superstring’ theories, there were only two ( called SO(32) and E8 x E8′) that were: 1) Consistent with both the principles of relativity and quantum mechanics,2) Allowed for the asymmetry between left and right-handed processes and, 3) Were free of anomalies. Both versions were also found to have enough room in them for 496 different types of fields; enough to accomodate all of the known fundamental particles and then some! Superstring theories also have very few adjustable parameters and from them, certain quantum gravity calculations can be performed that give finite answers instead of infinite ones. In spite of their theoretical successes, Superstring theories suffer from the difficulty that the lightest Superstring particles will be completely massless while the next more massive generation will have masses of 10 GeV. It is not even clear how these supermassive string particles are related to the known particles which are virtually massless by comparison (a proton has a mass of 1 GeV!). It is also not known if the 496 different particles will cover the entire mass range between 0 and 10 GeV. It is possible that they may group themselves into two families with masses clustered around these two extreems. In the later instance, experimental physicists may literally run out of new particles to discover until accelerators powerful enough to create supermassive particles can be built.

An attractive feature of the SO(32) model, which represents particles as open-ended strings, is that gravity has to be included from the start in order to make the theory internally consistent and capable of yielding finite predictions. It is also a theory that reduces to ordinary point field theories at energies below 10 GeV. The complimentary theory, E8 x E8′, is the only other superstring theory that seems to work as well as SO(32) and treats particles as though they were closed strings without bare endpoints. This model is believed to show the greatest promise for describing real physical particles. It also includes gravity, but unlike SO(32), E8 x E8′ does seem to reduce at low energy, to the symmetry groups associated with the strong, weak and electromagnetic interactions, namely, SU(3), SU(2) and U(1).

If E8 x E8′ is destined to be the ‘ultimate, unified field theory’, there are some additional surprises in store for us. Each group, E8 and E8′, can be reduced mathematically to the products of the groups that represent the strong, weak and electromagnetic forces; SU(3) x SU(2) x U(1). If the E8 group corresponds to the known particles what does E8′ represent? In terms of its mathematical properties, symmetry considerations alone seem to require that the E8′ group should be a mirror image of E8. If E8 contains the groups SU(3), SU(2) and U(1) then E8′ contains SU(3)’, SU(2)’ and U(1)’. The primed fields in E8′ would have the same properties as those we ascribe to the strong, weak and electromagnetic forces. The E8′ particle fields may correspond to a completly different kind of matter, whose properties are as different from matter and anti-matter as ordinary matter is from anti-matter! ‘Shadow Matter’ as it has been called by Edward Kolb, David Seckel and Michael Turner at Fermilab, may actually co-exist with our own – possibly accounting for the missing mass necessary to close the universe. Shadow matter is only detectable by its gravitational influence and is totally invisible because the shadow world electromagnetic force (shadow light) does not interact with any of the particles in the normal world.

BEYOND SPACE AND TIME

The quest for a mathematical description of the physical world uniting the apparent differences between the known particles and forces, has led physicists to the remarkable conclusion that the universe inhabits not just the 4 dimensions of space and time, but a much larger arena whose dimensionality may be enormous (see Does Space Have More Than 3 Dimensions?). Both the Superstring theories and SUSY GUTs agree that our physical world has to have more than the 4 dimensions we are accustomed to thinking about. A remarkable feature of Superstring theory is that of all the possible dimensionalities for spacetime, only in 10-dimensions ( 9 space dimensions and 1 time dimension) will the theory lead to a computationally finite and internally consistent model for the physical world that includes the weak interaction from the outset, and where all of the troublesome anomalies cancil exactly. In such a 10-dimensional world, it is envisioned that 6 dimensions are now wrapped-up or ‘compactified’ into miniscule spheres that accompany the 4 coordinates of every point in spacetime. What would a description of the early universe look like from this new viewpoint? The 6 internal dimensions are believed to have a size of order 10 cm.

As we follow the history of the universe back in time, the 3 large dimensions of space rapidly shrink until eventually they become only 10 cm in extent. This happened during the Planck Era at a time, 10 seconds after the Creation Event. The appearance of the universe under these conditions is almost unimaginable. Today as we look out at the most distant quasar, we see them at distances of billions of lightyears. During the Planck Era, the matter comprising these distant systems was only 10 cm away from the material that makes-up your own body!

What was so special about this era that only 4 of the 10 dimensions were singled-out to grow to their enormous present size?. Why not 3 ( 2 space + 1 time) or 5 ( 4 space + 1 time)? Physicists have not as yet been able to develope an explanation for this fundamental mystery of our plenum, on the other hand, it may just be that had the dimensional breakdown of spacetime been other than ‘4 + 6’, the physical laws we are the products of, would have been totally inhospitable to life as we know it.

As we relentlessly follow the history of the universe to even earlier times, the universe seems to enter a progressively more and more symmetric state. The universe at 10 seconds after the Big Bang may have been populated by supermassive particles with masses of 10^15 GeV or about 10^-13 grams each. These particles ultimatly decayed into the familiar quarks and leptons once the universe had grown colder as it expanded. In addition, there may only have been a single kind of ‘superforce’ acting on these particles; a force whose character contained all of the individual attributes we now associate with gravity, electromagnetism and the strong and weak nuclear forces. Since the particles carrying the ‘superforce’ had masses similar to those of the supermassive particles co-existing then, the distinction between the force-carriers and the particles they act on probably broke-down completely and the world became fully supersymmetric.

To go beyond the Planck Era may require a radical alteration in our conventional way of thinking about time and space. Only glimpses of the appropriate way to think about this multidimensional landscape can be found in the equations and theories of modern-day physics. Beyond the Planck Era, all 10 dimensions (and perhaps others) become co-equal at least in terms of their physical size. The supermassive Superstring particles begin to take-on more of the characteristics of fluctuations in the geometry of spacetime than as distinguishable, ingredients in the primordial, cosmological ‘soup’. There was no single, unique geometry for spacetime but, instead, an ever-changing quantum interplay between spacetimes with an unlimited range in geometry. Like sound waves that combine with one another to produce interference and reinforcement, the spacetime that emerged from the Planck Era is thought to be the result of the superposition of an infin ite number of alternate spacetime geometries which, when added together, produced the spacetime that we are now a part of.

Was there light? Since the majority of the photons were probably not created in large numbers until at least the beginning of the Inflationary Epoc, 10^-36 seconds after the Big Bang, it is not unthinkable that during its earliest moments, the universe was born out of darkness rather than in a blinding flash of light. All that existed in this darkness before the advent of light, was an empty space out of which our 10-dimensional spacetime would later emerge. Of course, under these conditions it is unclear just how we should continue to think about time itself.

In terms of the theories available today, it may well be that the particular dimension we call Time had a definite zero point so that we can not even speak logically about what happened before time existed. The concept of ‘before’ is based on the presumption of time ordering. A traveler standing on the north pole can never move to a position on the earth that is 1 mile north of north! Nevertheless, out of ingrained habit, we speak of the time before the genesis of the universe when time didn’t exist and ask, “What happened before the Big Bang?”. The list of physicists investigating this ‘state’ has grown enormously over the last 15 years. The number of physicists, worldwide, that publish research on this topic is only slightly more than 200 out of a world population of 5 billion!

QUANTUM COSMOLOGY

In the early 1970’s Y. Zel’dovitch and A. Starobinski of the USSR along with Edward Tryon at Hunter College proposed that the universe emerged from a fluctuation in the vacuum. This vacuum fluctuation ‘ran away’ with itself, creating all the known particles out of empty space at the ‘instant’ of no-time. To understand what this means requires the application of a fundamental fact of relativistic quantum physics discovered during the latter half of the 1920’s. Vacuum fluctuations are a direct consequence of Heisenberg’s Uncertainty Principle which limits how well we can simultaneously know a particle’s momentum and location (or its total energy and lifetime). What we call empty space or the physical vacuum is a Newtonian fiction like absolute space and time. Rather than a barren stage on which matter plays-out its role, empty space is known to be filled with ‘virtual particles’ that spontaneously appear and disappear beyond the ability of any physical measurement to detect directly. From these ghost particles, a variety of very subtle phenomena can be predicted with amazing accuracy. Depending on the total rest mass energy of the virtual particles created in the vacuum fluctuation, they may live for a specific lifetime before Heisenberg’s Uncertainty Principle demands that they vanish back into the nothingness of the vacuum state. In such a quantum world, less massive virtual particles can live longer than more massive ones. Edward Tyron proposed that the universe is just a particularly long-lived vacuum fluctuation differing only in magnitude from those which occur imperceptably all around us. The reason the universe is so long lived in spite of its enormous mass is that the positive energy latent in all the matter in the universe is offset by the negative potential energy of the gravitational field of the universe. The total energy of the universe is, therefore, exactly zero and its maximum lifetime as a ‘quantum fluctuation’ could be enormous and even infinite! According to Tryon, “The Universe is simply one of those things which happens from time to time.”

This proposal by Tryon was regarded with some scepticism and even amusement by astronomers, and was not persued much further. This was a fate that had also befallen the work on 5-dimensional general relativity by Theodore Kaluza and Oskar Klein during the 1920’s which was only resurrected in the late 1970’s as a potent remedy for the ills plaguing supersymmetry theory.

In 1978, R. Brout, P. Englert, E. Gunzig and P. Spindel at the University of Brussels, proposed that the fluctuation that led to the creation of our universe started out in an empty, flat, 4-dimensional spacetime. The fluctuation in space began weakly, creating perhaps a single matter- antimatter pair of supermassive particles with masses of 10^19 GeV. The existence of this ‘first pair’ stimulated the creation from the vacuum of more particle-antiparticle pairs which stimulated the production of still others and so on. Space became highly curved and exploded, disgorging all of the superparticles which later decayed into the familiar leptons, quarks and photons.

Heinz Pagels and David Atkatz at Rockefeller University in 1981 proposed that the triggering agent behind the Creation Event was a tunneling phenomenon of the vacuum from a higher-energy state to a lower energy state. Unlike the Brout-Englert-Gunzig-Spindel model which started from a flat spacetime, Pagels and Atkatz took the complimentary approach that the original nothingness from which the universe emerged was a spatially closed, compact empty space, in other words, it had a geometry like the 2-D surface of a sphere. but the dimensionality of its surface was much higher than 2. Again this space contained no matter what-so-ever. The characteristics (as yet unknown) of the tunneling process determined, perhaps in a random way, how the dimensionality of spacetime would ‘crystallize’ into the 6+4 combination that represents the plenum of our universe.

Alex Vilenkin at Tufts University proposed in 1983 that our spacetime was created out of a ‘nothingness’ so complete that even its dimensionality was undefined. In 1984, Steven Hawkings at Cambridge and James Hartle at UCSB came to a similar conclusion through a series of quantum mechanical calculations. They described the geometric state of the universe in terms of a wavefunction which specified the probability for spacetime to have one of an infinite number of possible geometries. A major problem with the ordinary Big Bang theory was that the universe emerged from a state where space and time vanished and the density of the universe became infinite; a state called the Singularity. Hawkings and Hartle were able to show that this Big Bang singularity represented a specific kind of geometry which would become smeared-out in spacetime due to quantum indeterminacy. The universe seemed to emerge from a non-singular state of ‘nothingness’ similar to the undefined state proposed by Vilenkin. The physicist Frank Wilczyk expresses this remarkable situation the best by saying that, ” The reason that there is Something rather than Nothing is that Nothing is unstable.”

PERFECT SYMMETRY

Theories like those of SUSY GUTS and Superstrings seem to suggest that just a few moments after Creation, the laws of physics and the content of the world were in a highly symmetric state; one superforce and perhaps one kind of superparticle. The only thing breaking the perfect symmetry of this era was the definite direction and character of the dimension called Time. Before Creation, the primordial symmetry may have been so perfect that, as Vilenkin proposed, the dimensionality of space was itself undefined. To describe this state is a daunting challenge in semantics and mathematics because the mathematical act of specifying its dimensionality would have implied the selection of one possibility from all others and thereby breaking the perfect symmetry of this state. There were, presumably, no particles of matter or even photons of light then, because these particles were born from the vacuum fluctuations in the fabric of spacetime that attended the creation of the universe. In such a world, nothing happens because all ‘happenings’ take place within the reference frame of time and space. The presence of a single particle in this nothingness would have instantaneously broken the perfect symmetry of this era because there would then have been a favored point in space different from all others; the point occupied by the particle. This nothingness didn’t evolve either, because evolution is a time-ordered process. The introduction of time as a favored coordinate would have broken the symmetry too. It would seem that the ‘Trans-Creation’ state is beyond conventional description because any words we may choose to describe it are inherently laced with the conceptual baggage of time and space. Heinz Pagels reflects on this ‘earliest’ stage by saying, “The nothingness ‘before’ the creation of the universe is the most complete void we can imagine. No space, time or matter existed. It is a world without place, without duration or eternity…”

A perusal of the scientific literature during the last 20 years suggests that we may be rapidly approaching a major crossroad in physics. One road seems to be leading to a single unification theory that is so unique among all others that it is the only one consistent with all the major laws we know about. It is internally consistent; satisfies the principles of relativity and quantum mechanics and requires no outside information to describe the particles and forces it contains . A prototype of this may be superstring theory with its single adjustable parameter, namely, the string tension. The other road is much more bleak. It may also turn out that we will create several theoretical systems that seem to explain everything but have within them hard to detect flaws. These flaws may stand as barracades to further logical inquiry; to be uncovered only through experiments that may be beyond our technological reach. It is possible that we are seeing the beginning of this latter process even now, with the multiplicity of theories whose significant deviations only occur at energies near 10^19 GeV.

I find it very hard to resist the analogy between our current situation and that of the Grecian geometers. For 2000 years the basic postulates of Eulidean geometry and the consequences of this logical system, remained fixed. It became a closed book with only a few people in the world struggling to find exceptions to it such as refutations of the parallel line postulate. Finally during the 19th century, non-euclidean geometry was discovered and a renaissance in geometry occurred. Are physicists on the verge of a similar great age, finding themselves hamstrung by not being able to devise new ways of thinking about old problems? Egyptian cosmology was based on motifs that the people of that age could see in the world around them; water, sky, land, biological reproduction. Today we still use motifs that we find in Nature in order to explain the origin of the universe; the geometry of space, virtual particles and vacuum fluctuations. We can probably expect that in the centuries to follow, our descendents will find still other motifs and from them, fashion cosmologies that will satisfy the demands of that future age with, possibly, much greater accuracy and efficiency than ours do today. Perhaps, too, in those future ages, scientists will marvel at the ingenuity of modern physicists and astronomers, and how in the space of only 300 years, we had managed to create our own quaint theory as the Egyptians had before us.

In the meantime, physicists and astronomers do the best they can to fashion a cosmology that will satisfy the intellectual needs of our age. Today, as we contemplate the origin of the universe we find ourselves looking out over a dark, empty void not unlike the one that our Egyptian predecessors might have imagined. This void is a state of exquisite perfection and symmetry that seems to defy description in any linguistic terms we can imagine. Through our theories we launch mathematical voyages of exploration, and watch the void as it trembles with the quantum possibilities of universes unimaginable.

Decay of the False Vacuum

The Decay of the False Vacuum

Written by Sten Odenwald. Copyright (C) 1983 Kalmbach Publishing. Reprinted by permission

In the recently developed theory by Steven Weinberg and Abdus Salam, that unifies the electromagnetic and weak forces, the vacuum is not empty. This peculiar situation comes about because of the existence of a new type of field, called the Higgs field. The Higgs field has an important physical consequence since its interaction with the W, W and Z particles (the carriers of the weak force) causes them to gain mass at energies below 100 billion electron volts (100 Gev). Above this energy they are quite massless just like the photon and it is this characteristic that makes the weak and electromagnetic forces so similar at high energy.

On a somewhat more abstract level, consider Figures 1 and 2 representing the average energy of the vacuum state. If the universe were based on the vacuum state in Figure 1, it is predicted that the symmetry between the electromagnetic and weak interactions would be quite obvious. The particles mediating the forces would all be massless and behave in the same way. The corresponding forces would be indistinguishable. This would be the situation if the universe had an average temperature of 1 trillion degrees so that the existing particles collided at energies of 100 Gev. In Figure 2, representing the vacuum state energy for collision energies below 100 Gev, the vacuum state now contains the Higgs field and the symmetry between the forces is suddenly lost or ‘broken’. Although at low energy the way in which the forces behave is asymmetric, the fundamental laws governing the electromagnetic and weak interactions remain inherently symmetric. This is a very remarkable and profound prediction since it implies that certain symmetries in Nature can be hidden from us but are there nonetheless.

During the last 10 years physicists have developed even more powerful theories that attempt to unify not only the electromagnetic and weak forces but the strong nuclear force as well. These are called the Grand Unification Theories (GUTs) and the simplist one known was developed by Howard Georgi, Helen Quinn,and Steven Weinberg and is called SU(5), (pronounced ‘ess you five’). This theory predicts that the nuclear and ‘electroweak’ forces will eventually have the same strength but only when particles collide at energies above 1 thousand trillion GeV corresponding to the unimaginable temperature of 10 thousand trillion trillion degrees! SU(5) requires exactly 24 particles to mediate forces of which the 8 massless gluons of the nuclear force, the 3 massless intermediate vector bosons of the weak force and the single massless photon of the electromagnetic force are 12. The remaining 12 represent a totally new class of particles called Leptoquark bosons that have the remarkable property that they can transform quarks into electrons. SU(5) therefore predicts the existence of a ‘hyperweak’ interaction; a new fifth force in the universe! Currently, this force is 10 thousand trillion trillion times weaker than the weak force but is nevertheless 100 million times stronger than gravity. What would this new force do? Since protons are constructed from 3 quarks and since quarks can now decay into electrons, through the Hyperweak interaction, SU(5) predicts that protons are no longer the stable particles we have always imagined them to be. Crude calculations suggest that they may have half-lives between 10^29 to 10^33 years. An immediate consequence of this is that even if the universe were destined to expand for all eternity, after ‘only’ 10^32 years or so, all of the matter present would catastrophically decay into electrons, neutrinos and photons. The Era of Matter, with its living organisms, stars and galaxies, would be swept away forever, having represented but a fleeting episode in the history of the universe. In addition to proton decay, SU(5) predicts that at the energy characteristic of the GUT transition, we will see the affects of a new family of particles called supermassive Higgs bosons whose masses are expected to be approximately 1 thousand trillion GeV! These particles interact with the 12 Leptoquarks and make them massive just as the Higgs bosons at 100 GeV made the W, W and Z particles heavy. Armed with this knowledge, let’s explore some of the remarkable cosmological consequences of these exciting theories.

The GUT Era

To see how these theories relate to the history of the universe, imagine if you can a time when the average temperature of the universe was not the frigid 3 K that it is today but an incredable 10 thousand trillion trillion degrees (10^15 GeV). The ‘Standard Model’ of the Big Bang, tells us this happened about 10^-37 seconds after Creation. The protons and neutrons that we are familiar with today hadn’t yet formed since their constituent quarks interacted much too weakly to permit them to bind together into ‘packages’ like neutrons and protons. The remaining constituents of matter, electrons, muons and tau leptons, were also massless and traveled about at essentially light-speed; They were literally a new form of radiation, much like light is today! The 12 supermassive Leptoquarks as well as the supermassivs Higgs bosons existed side-by-side with their anti-particles. Every particle-anti particle pair that was annihilated was balanced by the resurrection of a new pair somewhere else in the universe. During this period, the particles that mediated the strong, weak and electromagnetic forces were completely massless so that these forces were no longer distinguishable. An inhabitant of that age would not have had to theorize about the existence of a symmetry between the strong, weak and electromagnetic interactions, this symmetry would have been directly observable and furthermore, fewer types of particles would exist for the inhabitants to keep track of. The universe would actually have beed much simpler then!

As the universe continued to expand, the temperature continued to plummet. It has been suggested by Demetres Nanopoulis and Steven Weinberg in 1979 that one of the supermassive Higgs particles may have decayed in such a way that slightly more matter was produced than anti-matter. The remaining evenly matched pairs of particles and anti-particles then annihilated to produce the radiation that we now see as the ‘cosmic fireball’.

Exactly what happened to the universe as it underwent the transitions at 10^15 and 100 GeV when the forces of Nature suddenly became distinguishable is still under investigation, but certain tantalizing descriptions have recently been offered by various groups of theoriticians working on this problem. According to studies by Alan Guth, Steven Weinberg and Frank Wilczyk between 1979 and 1981, when the GUT transition occured, it occured in a way not unlike the formation of vapor bubbles in a pot of boiling water. In this analogy, the interior of the bubbles represent the vacuum state in the new phase, where the forces are distinguishable, embedded in the old symmetric phase where the nuclear, weak and electromagnetic forces are indistinguishable. Inside these bubbles, the vacuum energy is of the type illustrated by Figure 2 while outside it is represented by Figure 1. Since we are living within the new phase with its four distinguishable forces, this has been called the ‘true’ vacuum state. In the false vacuum state, the forces remain indistinguishable which is certainly not the situation that we find ourselves in today!

Cosmic Inflation

An exciting prediction of Guth’s model is that the universe may have gone through at least one period in its history when the expansion was far more rapid than predicted by the ‘standard’ Big Bang model. The reason for this is that the vacuum itself also contributes to the energy content of the universe just as matter and radiation do however, the contribution is in the opposite sense. Although gravity is an attractive force, the vacuum of space produces a force that is repulsive. As Figures 1 and 2 show, the minimum energy state of the false vacuum at ‘A’ before the GUT transition is at a higher energy than in the true vacuum state in ‘B’ after the transition. This energy difference is what contributes to the vacuum energy. During the GUT transition period, the positive pressure due to the vacuum energy would have been enormously greater than the restraining pressure produced by the gravitational influence of matter and radiation. The universe would have inflated at a tremendous rate, the inflation driven by the pressure of the vacuum! In this picture of the universe, Einstein’s cosmological constant takes on a whole new meaning since it now represents a definite physical concept ; It is simply a measure of the energy difference between the true and false vacuum states (‘B’ and ‘A’ in Figures 1 and 2.) at a particular time in the history of the universe. It also tells us that, just as in de Sitter’s model, a universe where the vacuum contributes in this way must expand exponentially in time and not linearly as predicted by the Big Bang model. Guth’s scenario for the expansion of the universe is generally called the ‘inflationary universe’ due to the rapidity of the expansion and represents a phase that will end only after the true vacuum has supplanted the false vacuum of the old, symmetric phase.

A major problem with Guth’s original model was that the inflationary phase would have lasted for a very long time because the false vacuum state is such a stable one. The universe becomes trapped in the cul-de-sac of the false vacuum state and the exponential expansion never ceases. This would be somewhat analogous to water refusing to freeze even though its temperature has dropped well below 0 Centigrade. Recent modifications to the original ‘inflationary universe’ model have resulted in what is now called the ‘new’ inflationary universe model. In this model, the universe does manage to escape from the false vacuum state and evolves in a short time to the familiar true vacuum state.

We don’t really know how exactly long the inflationary phase may have lasted but the time required for the universe to double its size may have been only 10^-34 seconds. Conceivably, this inflationary period could have continued for as ‘long’ as 10^-24 seconds during which time the universe would have undergone 10 billion doublings of its size! This is a number that is truely beyond comprehension. As a comparison, only 120 doublings are required to inflate a hydrogen atom to the size of the entire visible universe! According to the inflationary model, the bubbles of the true vacuum phase expanded at the speed of light. Many of these had to collide when the universe was very young in order that the visible universe appear so uniform today. A single bubble would not have grown large enough to encompass our entire visible universe at this time; A radius of some 15-20 billion light years. On the other hand, the new inflationary model states that even the bubbles expanded in size exponentially just as their separations did. The bubbles themselves grew to enormous sizes much greater than the size of our observable universe. According to Albrecht and Steinhardt of the University of Pennsylvania, each bubble may now be 10^3000 cm in size. We should not be too concerned about these bubbles expanding at many times the speed of light since their boundaries do not represent a physical entity. There are no electrons or quarks riding some expandind shock wave. Instead, it is the non-material vacuum of space that is expanding. The expansion velocity of the bubbles is not limited by any physical speed limit like the velocity of light.

GUMs in GUTs

A potential problem for cosmologies that have phase transitions during the GUT Era is that a curious zoo of objects could be spawned if frequent bubble mergers occured as required by Guth’s inflationary model. First of all, each bubble of the true vacuum phase contains its own Higgs field having a unique orientation in space. It seems likely that no two bubbles will have their Higgs fields oriented in quite the same way so that when bubbles merge, knots will form. According to Gerhard t’Hooft and Alexander Polyakov, these knots in the Higgs field are the magnetic monopoles originally proposed 40 years ago by Paul Dirac and there ought to be about as many of these as there were bubble mergers during the transition period. Upper limits to their abundance can be set by requiring that they do not contribute to ‘closing’ the universe which means that for particles of their predicted mass (about 10^16 GeV), they must be 1 trillion trillion times less abundant than the photons in the 3 K cosmic background. Calculations based on the old inflationary model suggest that the these GUMs (Grand Unification Monopoles) may easily have been as much as 100 trillion times more abundant than the upper limit! Such a universe would definitly be ‘closed’ and moreover would have run through its entire history between expansion and recollapse within a few thousand years. The new inflationary universe model solves this ‘GUM’ overproduction problem since we are living within only one of these bubbles, now almost infinitly larger than our visible universe. Since bubble collisions are no longer required to homogenize the matter and radiation in the universe, very few, if any, monopoles would exist within our visible universe.

Horizons

A prolonged period of inflation would have had an important influence on the cosmic fireball radiation. One long-standing problem in modern cosmology has been that all directions in the sky have the same temperature to an astonishing 1 part in 10,000. When we consider that regions separated by only a few degrees in the sky have only recently been in communication with one another, it is hard to understand how regions farther apart than this could be so similar in temperature. The radiation from one of these regions, traveling at the velocity of light, has not yet made it across the intervening distance to the other, even though the radiation may have started on its way since the universe first came into existence. This ‘communication gap’ would prevent these regions from ironing-out their temperature differences.

With the standard, Big Bang model, as we look back to earlier epochs from the present time, the separations between particles decrease more slowly than their horizons are shrinking. Neighboring regions of space at the present time, become disconnected so temperature differences are free to develope. Eventually, as we look back to very ancient times, the horizons are so small that every particle existing then literally fills the entire volume of its own, observable universe. Imagine a universe where you occupy all of the available space! Prior to the development of the inflationary models, cosmologists were forced to imagine an incredably well-ordered initial state where each of these disconnected domains (some 10^86 in number) had nearly identical properties such as temperature. Any departure from this situation at that time would have grown to sizable temperature differences in widely separated parts of the sky at the present time. Unfortunately, some agency would have to set-up these finely-tuned initial conditions by violating causality. The contradiction is that no force may operate by transmitting its influence faster than the speed of light. In the inflationary models, this contradiction is eliminated because the separation between widely scattered points in space becomes almost infinitly small compared to the size of the horizons as we look back to the epoc of inflation. Since these points are now within each others light horizons, any temperature difference would have been eliminated immediatly since hotter regions would now be in radiative contact with colder ones. With this exponentially-growing, de Sitter phase in the universe’s early history we now have a means for resolving the horizon problem.

Instant Flat Space

Because of the exponential growth of the universe during the GUT Era, its size may well be essentially infinite for all ‘practical’ purposes . Estimates by Albrecht and Steinhardt suggest that each bubble region may have grown to a size of 10^3000 cm by the end of the inflationary period. Consequently, the new inflationary model predicts that the content of the universe must be almost exactly the ‘critical mass’ since the sizes of each of these bubble regions are almost infinite in extent. The universe is, for all conceivable observations, exactly Euclidean (infinite and flat in geometry) and destined to expand for all eternity to come. Since we have only detected at most 10 percent of the critical mass in the form of luminous matter, this suggests that 10 times as much matter exists in our universe than is currently detectable. Of course, if the universe is essentially infinite this raises the ghastly spectre of the eventual annihilation of all organic and inorganic matter some 10^32 years from now because of proton decay.

In spite of its many apparent successes, even the new inflationary universe model is not without its problems. Although it does seem to provide explainations for several cosmological enigmas, it does not provide a convincing way to create galaxies. Those fluctuations in the density of matter that do survive the inflationary period are so dense that they eventually collapse into galaxy-sized blackholes! Neither the precise way in which the transition to ordinary Hubbel expansion occurs nor the duration of the inflationary period are well determined.

If the inflationary cosmologies can be made to answer each of these issues satisfactorily we may have, as J. Richard Gott III has suggested, a most remarkable model of the universe where an almost infinite number of ‘bubble universes’ each having nearly infinite size, coexist in the same 4-dimensional spacetime; all of these bubble universes having been brought into existence at the same instant of creation. This is less troublesome than one might suspect since, if our universe is actually infinite as the available data suggests, so too was it infinite even at its moment of birth! It is even conceivable that the universe is ‘percolating’ with new bubble universes continually coming into existence. Our entire visible universe, out to the most distant quasar, would be but one infinitessimal patch within one of these bubble regions. Do these other universes have galaxies, stars, planets and living creatures statistically similar to those in our universe? We may never know. These other universes, born of the same paroxicism of Creation as our own, are forever beyond our scrutiny but obviously not our imaginations!

Beyond The Beginning…

Finally, what of the period before Grand Unification? We may surmise that at higher temperatures than the GUT Era, even the supermassive Higgs and Leptoquark bosons become massless and at long last we arrive at a time when the gravitational interaction is united with the weak, electromagnetic and strong forces. Yet, our quest for an understanding of the origins of the universe remains incomplete since gravity has yet to be brought into unity with the remaining forces on a theoretical basis. This last step promises to be not only the most difficult one to take on the long road to unification but also appears to hold the greatest promise for shedding light on some of the most profound mysteries of the physical world. Even now, a handful of theorists around the world are hard at work on a theory called Supergravity which unites the force carriers (photons, gluons, gravitons and the weak interaction bosons) with the particles that they act on (quarks, electrons etc). Supergravity theory also predicts the existence of new particles called photinos and gravitinos. There is even some speculation that the photinos may fill the entire universe and account for the unseen ‘missing’ matter that is necessary to give the universe the critical mass required to make it exactly Euclidean. The gravitinos, on the other hand, prevent calculations involving the exchange of gravitons from giving infinite answers for problems where the answers are known to be perfectly finite. Hitherto, these calculations did not include the affects of the gravitinos.

Perhaps during the next decade, more of the details of the last stage of Unification will be hammered out at which time the entire story of the birth of our universe can be told. This is, indeed, an exciting time to be living through in human history. Will future generations forever envy us our good fortune, to have witnessed in our lifetimes the unfolding of the first comprehensive theory of Existence?

What is Space? Part I

Does Space Have More Than 3 Dimensions?
Written by Sten Odenwald
Copyright (C) 1984 Kalmbach Publishing. Reprinted by permission

The intuitive notion that the universe has three dimensions seems to be an irrefutable fact. After all, we can only move up or down, left or right, in or out. But are these three dimensions all we need to describe nature? What if there aree, more dimensions ? Would they necessarily affect us? And if they didn’t, how could we possibly know about them? Some physicists and mathematicians investigating the beginning of the universe think they have some of the answers to these questions. The universe, they argue, has far more than three, four, or five dimensions. They believe it has eleven! But let’s step back a moment. How do we know that our universe consists of only three spatial dimensions? Let’s take a look at some “proofs.”

On a 2-dimensional piece of paper you can draw an infinite number of polygons.  But when you try this same trick in 3-dimensions you run up against a problem.There are five and only five regular polyhedra. A regular polyhedron is defined as a solid figure whose faces are identical polygons – triangles, squares, and pentagons – and which is constructed so that only two faces meet at each edge. If you were to move from one face to another, you would cross over only one edge. Shortcuts through the inside of the polyhedron that could get you from one face to another are forbidden. Long ago, the mathematician Leonhard Euler demonstrated an important relation between the number of faces (F), edges (E), and corners (C) for every regular polyhedron: C – E + F = 2. For example, a cube has 6 faces, 12 edges, and 8 corners while a dodecahedron has 12 faces, 30 edges, and 20 corners. Run these numbers through Euler’s equation and the resulting answer is always two, the same as with the remaining three polyhedra. Only five solids satisfy this relationship – no more, no less.

Not content to restrict themselves to only three dimensions, mathematicians have generalized Euler’s relationship to higher dimensional spaces and, as you might expect, they’ve come up with some interesting results. In a world with four spatial dimensions, for example, we can construct only six regular solids. One of them – the “hypercube” – is a solid figure in 4-D space bounded by eight cubes, just as a cube is bounded by six square faces. What happens if we add yet another dimension to space? Even the most ambitious geometer living in a 5-D world would only be able to assemble thee regular solids. This means that two of the regular solids we know of – the icosahedron and the dodecahedron – have no partners in a 5-D universe.
For those of you who successfully mastered visualizing a hypercube, try imagining what an “ultracube” looks like. It’s the five- dimensional analog of the cube, but this time it is bounded by one hypercube on each of its 10 faces! In the end, if our familiar world were not three-dimensional, geometers would not have found only five regular polyhedra after 2,500 years of searching. They would have found six (with four spatial dimension,) or perhaps only three (if we lived in a 5-D universe). Instead, we know of only five regular solids. And this suggests that we live in a universe with, at most, three spatial dimensions.

All right, let’s suppose our universe actually consists of four spatial dimensions. What happens? Since relativity tells us that we must also consider time as a dimension, we now have a space-time consisting of five dimensions. A consequence of 5-D space-time is that gravity has freedom to act in ways we may not want it to.

To the best available measurements, gravity follows an inverse square law; that is, the gravitational attraction between two objects rapidly diminishes with increasing distance. For example, if we double the distance between two objects, the force of gravity between them becomes 1/4 as strong; if we triple the distance, the force becomes 1/9 as strong, and so on. A five- dimensional theory of gravity introduces additional mathematical terms to specify how gravity behaves. These terms can have a variety of values, including zero. If they were zero, however, this would be the same as saying that gravity requires only three space dimensions and one time dimension to “give it life.” The fact that the Voyager space- craft could cross billions of miles of space over several years and arrive vithin a few seconds of their predicted times is a beautiful demonstration that we do not need extra-spatial dimensions to describe motions in the Sun’s gravitational field.

From the above geometric and physical arguments, we can conclude (not surprisingly) that space is three-dimensional – on scales ranging from that of everyday objects to at least that of the solar system. If this were not the case, then geometers would have found more than five regular polyhedra and gravity would function very differently than it does – Voyager would not have arrived on time. Okay, so we’ve determined that our physical laws require no more than the three spatial dimensions to describe how the universe works. Or do they? Is there perhaps some other arena in the physical world where multidimensional space would be an asset rather than a liability?

Since the 1920s, physicists have tried numerous approaches to unifying the principal natural interactions: gravity, electromagnetism, and the strong and weak forces in atomic nuclei. Unfortunately, physicists soon realized that general relativity in a four-dimensional space-time does not have enough mathematical “handles” on which to hang the frameworks for the other three forces. Between 1921 and 1927, Theodor Kaluza and Oskar Klein developed the first promising theory combining gravity and electromagnetism. They did this by extending general relativity to five dimensions. For most of us, general relativity is mysterious enough in ordinary four-dimensional space-time. What wonders could lie in store for us with this extended universe?

General relativity in five dimensions gave theoreticians five additional quantities to manipulate beyond the 10 needed to adequately define the gravitational field. Kaluza and Klein noticed that four of the five extra quantities could be identified with the four components needed to define the electromagnetic field. In fact, to the delight of Kaluza and Klein, these four quantities obeyed the same types of equations as those derived by Maxwell in the late 1800s for electromagnetic radiationl Although this was a promising start, the approach never really caught on and was soon buried by the onrush of theoretical work on the quantum theory of electromagnetic force. It was not until work on supergravity theory began in 1975 that Kaluza and Klein’s method drew renewed interest. Its time had finally come.

What do theoreticians hope to gain by stretching general relativity beyond the normal four dimensions of space-time? Perhaps by studying general relativity in a higher-dimensional formulation, we can explain some of the constants needed to describe the natural forces. For instance, why is the proton 1836 times more massive than the electron? Why are there only six types of quarks and leptons? Why are neutrinos massless? Maybe such a theory can give us new rules for calculating the masses of fundamental particles and the ways in which they affect one another. These higher-dimensional relativity theories may also tell us something about the numbers and properties of a mysterious new family of particles – the Higgs bosons – whose existence is predicted by various cosmic unification schemes. (See “The Decay of the False Vacuum,” ASTRONOMY, November 1983.)

These expectations are not just the pipedreams of physicists – they actually seem to develop as natural consequences of certain types of theories studied over the last few years. In 1979, John Taylor at Kings College in London found that some higher- dimensional formalisms can give predictions for the maximum mass of the Higgs bosons (around 76 times that of the proton.) As they now stand, unification theories can do no more than predict the existence of these particles – they cannot provide specific details about their physical characteristics. But theoreticians may be able to pin down some of these details by using extended theories of general relativity. Experimentally, we know of six leptons: the electron, the muon, the tauon, and their three associated neutrinos. The most remarkable prediction of these extended relativity schemes, however, holds that the number of leptons able to exist in a universe is related to the number of dimensions of space-time. In a 6-D space-time, for example, only one lepton – presumably the electron – can exist. In a 10-D space-time, four leptons can exist – still not enough to accommodate the six we observe. In a 12-D space- time, we can account for all six known leptons – but we also acquire two additional leptons that have not yet been detected. Clearly, we would gain much on a fundamental level if we could increase the number of dimensions in our theories just a little bit.

How many additional dimensions do we need to consider in order to account for the elementary particles and forces that we know of today? Apparently we require at least one additional spatial dimension for every distinct “charge” that characterizes how each force couples to matter. For the electromagnetic force, we need two electric charges: positive and negative. For the strong force that binds quarks together to form, among other things, protons and neutrons, we need three “color” charges – red, blue, and green. Finally, we need two “weak” charges to account for the weak nuclear force. if we add a spatial dimension for each of these charges, we end up with a total of seven extra dimensions. The properly extended theory of general relativity we seek is one with an 11 -dimensional space-time, at the very least. Think of it – space alone must have at least 10 dimensions to accomodate all the fields known today.

Of course, these additional dimensions don’t have to be anything like those we already know about. In the context of modern unified field theory, these extra dimensions are, in a sense, internal to the particles themselves – a “private secret,” shared only by particles and the fields that act on them! These dimensions are not physically observable in the same sense as the three spatial dimensions we experience; they’stand in relation to the normal three dimensions of space much like space stands in relation to time.

With today’s veritable renaissance in finding unity among the forces and particles that compose the cosmos, some by methods other than those we have discussed, these new approaches lead us to remarkably similar conclusions. It appears that a four-dimensional space-time is simply not complex enough for physics to operate as it does.

We know that particles called bosons mediate the natural forces. We also know that particles called fermions are affected by these forces. Members of the fermion family go by the familiar names of electron, muon, neutrino, and quark; bosons are the less well known graviton, photon, gluon, and intermediate vector bosons. Grand unification theories developed since 1975 now show these particles to be “flavors” of a more abstract family of superparticies – just as the muon is another type of electron. This is an expression of a new kind of cosmic symmetry – dubbed supersymmetry, because it is all-encompassing. Not only does it include the force-carrying bosons, but it also includes the particles on which these forces act. There also exists a corresponding force to help nature maintain supersymmetry during the various interactions. It’s called supergravity. Supersymmetry theory introduces two new types of fundamental particles – gravitinos and photinos. The gravitino has the remarkable property of mathematically moderating the strength, of various kinds of interactions involving the exchange of gravitons. The photino, cousin of the photon, may help account for the “missing mass” in the universe.

Supersymmetry theory is actually a complex of eight different theories, stacked atop one another like the rungs of a ladder. The higher the rung, the larger is its complement of allowed fermion and boson particle states. The “roomiest” theory of all seems to be SO(8), (pronounced ess-oh-eight), which can hold 99 different kinds of bosons and 64 different kinds of fermions. But SO(8) outdoes its subordinate, SO(7), by only one extra dimension and one additional particle state. Since SO(8) is identical to SO(7) in all its essential features, we’ll discuss SO(7) instead. However, we know of far more than the 162 types of particles that SO(7) can accommodate, and many of the predicted types have never been observed (like the massless gravitino). SO(7) requires seven internal dimensions in addition to the four we recognize – time and the three “every day” spatial dimensions. If SO(7) at all mirrors reality, then our universe must have at least 11 dimensions! Unfortunately, it has been demonstrated by W. Nahm at the European Center for Nuclear Research in Geneva, Switzerland that supersymmetry theories for space-times with more than 11 dimensions are theoretically impossible. SO(7) evidently has the largest number of spatial dimensions possible, but it still doesn’t have enough room to accommodate all known types of particles.

It is unclear where these various avenues of research lead. Perhaps nowhere. There is certainly ample historical precedent for ideas that were later abandoned because they turned out to be conceptual dead-ends. Yet what if they turn out to be correct at some level? Did our universe begin its life as some kind of 11-dimensional “object” which then crystallized into our four- dimensional cosmos?

Although these internal dimensions may not have much to do with the real world at the present time, this may not always have been the case. E. Cremmer and J. Scherk of I’Ecole Normale Superieure in Paris have shown that just as the universe went through phase transitions in its early history when the forces of nature became distinguishable, the universe may also have gone through a phase transition when mensionality changed. Presumably matter has something like four external dimensions (the ones we encounter every day) and something like seven internal dimensions. Fortunately for us, these seven extra dimensions don’t reach out into the larger 4-D realm where we live. If they did, a simple walk through the park might become a veritable obstacle course, littered with wormholes in space and who knows what else!

Alan Chocos and Steven Detweiler of Yale University have considered the evolution of a universe that starts out being five- dimensional. They discovered that while the universe eventually does evolve to a state where three of the four spatial dimensions expand to become our world at large, the extra fourth spatial dimension shrinks to a size of 10^-31 centimeter by the present time. The fifth dimension to the universe has all but vanished and is 20 powers of 10 – 100 billion billion times – smaller than the size of a proton. Although the universe appears four- dimensional in space-time, this perception is accidental due to our large size compared to the scale of the other dimensions. Most of us think of a dimension as extending all the way to infinity, but this isn’t the full story. For example, if our universe is really destined to re-collapse in the distant future, the three- dimensional space we know today is actually limited itself – it will eventually possess a maximum, finite size. It just so happens that the physical size of human beings forces us to view these three spatial dimensions as infinitely large.

It is not too hard to reconcile ourselves to the notion that the fifth (or sixth, or eleventh) dimension could be smaller than an atomic nucleus – indeed, we can probably be thankful that this is the case.

Einstein’s Fudge

Einstein’s Cosmic Fudge Factor

Written by Sten Odenwald
Copyright (C) 1991. Sky Publishing Corporation. Reprinted by permission. See April, 1991 issue

Black holes…quarks…dark matter. It seems like the cosmos gets a little stranger every year. Until recently, the astronomical universe known to humans was populated by planets, stars, galaxies, and scattered nebulae of dust and gas. Now, theoretists tell us it may also be inhabited by objects such as superstrings, dark matter and massive neutrinos — objects that have yet to be discovered if they exist at all!
As bizarre as these new constituents may sound, you don’t have to be a rocket scientist to appreciate the most mysterious ingredient of them all. It is the inky blackness of space itself that commands our attention as we look at the night sky; not the sparse points of light that signal the presence of widely scattered matter.

During the last few decades, physicists and astronomers have begun to recognize that the notion of empty space presents greater subtleties than had ever before been considered. Space is not merely a passive vessel to be filled by matter and radiation, but is a dynamic, physical entity in its own right.

One chapter in the story of our new conception of space begins with a famous theoretical mistake made nearly 75 years ago that now seems to have taken on a life of its own.

In 1917, Albert Einstein tried to use his newly developed theory of general relativity to describe the shape and evolution of the universe. The prevailing idea at the time was that the universe was static and unchanging. Einstein had fully expected general relativity to support this view, but, surprisingly, it did not. The inexorable force of gravity pulling on every speck of matter demanded that the universe collapse under its own weight.

His remedy for this dilemma was to add a new ‘antigravity’ term to his original equations. It enabled his mathematical universe to appear as permanent and invariable as the real one. This term, usually written as an uppercase Greek lambda, is called the ‘cosmological constant’. It has exactly the same value everywhere in the universe, delicately chosen to offset the tendency toward gravitational collapse at every point in space.

A simple thought experiment may help illustrate the nature of Lambda. Take a cubic meter of space and remove all matter and radiation from it. Most of us would agree that this is a perfect vacuum. But, like a ghost in the night, the cosmological constant would still be there. So, empty space is not really empty at all — Lambda gives it a peculiar ‘latent energy’. In other words, even Nothing is Something!

Einstein’s fudged solution remained unchallenged until 1922 when the Russian mathematician Alexander Friedmann began producing compelling cosmological models based on Einstein’s equations but without the extra quantity. Soon thereafter, theorists closely examining Einstein’s model discovered that, like a pencil balanced on its point, it was unstable to collapse or expansion. Later the same decade, Mount Wilson astronomer Edwin P. Hubble found direct observational evidence that the universe is not static, but expanding.

All this ment that the motivation for introducing the cosmological constant seemed contrived. Admitting his blunder, Einstein retracted Lambda in 1932. At first this seemed to end the debate about its existence. Yet decades later, despite the great physicist’s disavowal, Lambda keeps turning up in cosmologists’ discussions about the origin, evolution, and fate of the universe.

THEORY MEETS OBSERVATION

Friedmann’s standard ‘Big Bang’ model without a cosmological constant predicts that the age of the universe, t0, and its expansion rate (represented by the Hubble parameter, H0) are related by the equation t0 = 2/3H0. Some astronomers favor a value of H0 near 50 kilometers per second per megaparsec (one megaparsec equals 3.26 million light years). But the weight of the observational evidence seems to be tipping the balance towards a value near 100. In the Friedmann model, this implies that the cosmos can be no more than 7 billion years old. Yet some of our galaxy’s globular clusters have ages estimated by independent methods of between 12 and 18 billion years!

In what’s called the Einstein-DeSitter cosmology, the Lambda term helps to resolve this discrepancy. Now a large value for the Hubble parameter can be attributed in part to “cosmic repulsion”. This changes the relationship between t0 and H0, so that for a given size, the universe is older than predicted by the Friedmann model.

In one formulation of Einstein’s equation, Lambda is expressed in units of matter density. This means we can ask how the cosmological constant, if it exists at all, compares with the density of the universe in the forms of stars and galaxies.

So far, a careful look at the available astronomical data has produced only upper limits to the magnitude of Lambda. These vary over a considerable range – from about 10 percent of ordinary matter density to several times that density.

The cosmological constant can also leave its mark on the properties of gravitational lenses and faint galaxies. One of the remarkable features of Einstein’s theory of general relativity is its prediction that space and time become deformed or ‘warped’ in the vicinity of a massive body such as a planet, star or even a galaxy. Light rays passing through such regions of warped “space-time” have their paths altered. In the cosmological arena, nearby galaxies can deflect and distort the images of more distant galaxies behind them. Sometimes, the images of these distant galaxies can appear as multiple images surrounding the nearby ‘lensing’ galaxy.

At Kyoto University M. Fukugita and his coworkers predicted that more faint galaxies and gravitational lenses will be detected than in a Friedmann universe if Lambda is more than a few times the matter density. Edwin Turner, an astrophysicist at Princeton University also reviewed the existing, scant, data on gravitational lenses and found that they were as numerous as expected for Lambda less that a few times the matter density. By the best astronomical reconning, Lambda is probably not larger than the observed average matter density of the universe. For that matter, no convincing evidence is available to suggest that Lambda is not exactly equal to zero. So why not just dismiss it as an unnecessary complication? Because the cosmological constant is no longer, strictly, a construct of theoretical cosmology.

NOTHING AND EVERYTHING

To understand how our universe came into existence, and how its various ingredients have evolved, we must delve deeply into the fundamental constituents of matter and the forces that dictate how it will interact. This means that the questions we will have to ask will have more to do with physics than astronomy. Soon after the big bang, the universe was at such a high temperature and density that only the details of matter’s composition (quarks, electrons etc) and how they interact via the four fundamental forces of nature were important. They represented the most complex collections of matter in existence, long before atoms, planets, stars and galaxies had arrived on the scene.

For two decades now, physicists have been attempting to unify the forces and particles that make up our world – to find a common mathematical description that encompasses them all. Some think that such a Theory of Everything is just within reach. It would account not only for the known forms of matter, but also for the fundamental interactions among them: gravity, electromagnetism, and the strong and weak nuclear forces.

These unification theories are known by a variety of names: grand unification theory, supersymmetry theory and superstring theory. Their basic claim is that Nature operates according to a small set of simple rules called symmetries.

The concept of symmetry is at least as old as the civilization of ancient Greece, whos art and archetecture are masterworks of simplicity and balance. Geometers have known for a long time that a simple cube can be rotated 90 degrees without changing its outward appearance. In two dimensions, equalateral triangles look the same when they are rotated by 120 degrees. These are examples of the geometric concept of Rotation Symmetry.

There are parallels to geometric symmetry in the way that various physical phenomena and qualities of matter express themselves as well. For example, the well-known principle of the Conservation of Energy is a consequence of the fact that when some collections of matter and energy are examined at different times, they each have precisely the same total energy, just as a cube looks the same when it is rotated in space by a prescribed amount. Symmetry under a ‘shift in time’ is as closely related to the Conservation of Energy as is the symmetry of a cube when rotated by 90 degrees.

Among other things, symmetries of Nature dictate the strengths and ranges of the natural forces and the properties of the particles they act upon. Although Nature’s symmetries are hidden in today’s cold world, they reveal themselves at very high temperatures and can be studied in modern particle accelerators.

The real goal in unification theory is actually two-fold: not only to uncover and describe the underlying symmetries of the world, but to find physical mechanisms for ‘breaking’ them at low energy. After all, we live in a complex world filled with a diversity of particles and forces, not a bland world with one kind of force and one kind of particle!

Theoreticians working on this problem are often forced to add terms to their equations that represent entirely new fields in Nature. The concept of a field was invented by mathematicians to express how a particular quantity may vary from point to point in space. Physicists since the 18th century have adopted this idea to describe quantitatively how forces such as gravity and magnetism change at different distances from a body.

The interactions of these fields with quarks, electrons and other particles cause symmetries to break down. These fields are usually very different than those we already know about. The much sought after Higgs boson field, for example, was introduced by Sheldon Glashow, Abdus Salam and Steven Weinberg in their unified theory of the electromagnetic and weak nuclear forces.

Prior to their work, the weak force causing certain particles to decay, and the electromagnetic force responsible for the attraction between charged particles and the motion of compass needles, were both considered to be distinct forces in nature. By combining their mathematical descriptions into a common language, they showed that this distinction was not fundamental to the forces at all! A new field in nature called the Higgs field makes these two forces act differently at low temperature. But at temperatures above 1000 trillion degrees, the weak and electromagnetic forces become virtually identical in the way that they affect matter. The corresponding particles called the Higgs Boson not only cause the symmetry between the electromagnetic and weak forces to be broken at low temperature, but they are also responsible for confiring the property of mass on particles such as the electrons and the quarks!

There is, however a price that must be paid for introducing new fields into the mathematical machinery. Not only do they break symmetries, but they can also give the vacuum state an enormous latent energy that, curiously, behaves just like Lambda in cosmological models.

The embarrassment of having to resurrect the obsolete quantity Lambda is compounded when unification theories are used to predict its value. Instead of being at best a vanishingly minor ingredient to the universe, the predicted values are in some instances 10 to the power of 120 times greater than even the most generous astronomical upper limits!

It is an unpleasant fact of life for physicists that the best candidates for the Theory of Everything always have to be fine-tuned to get rid of their undesirable cosmological consequences. Without proper adjustment, these candidates may give correct predictions in the microscopic world of particle physics, but predict a universe which on its largest scales looks very different from the one we inhabit.

Like a messenger from the depths of time, the smallness – or absence – of the cosmological constant today is telling us something important about how to craft a correct Theory of Everything. It is a signpost of the way Nature’s symmetries are broken at low energy, and a nagging reminder that our understanding of the physical world is still incomplete in some fundamental way.

A LIKELY STORY

Most physicists expect the Theory of Everything will describe gravity the same way we now describe matter and the strong, weak and electromagnetic forces – in the language of quantum mechanics. Gravity is, after all, just another force in Nature. So far this has proven elusive, due in part to the sheer complexity of the equations of general relativity. Scientists since Einstein have described gravity ( as well as space and time) in purely geometric terms. Thus we speak of gravity as the “curvature of space-time”.

To acheive complete unification, the dialects of quantum matter and geometric space have to be combined into a single language. Matter appears to be rather precisely described in terms of the language of quantum mechanics. Quarks and electrons exchange force-carrying particles such as photons and gluons and thereby feel the electromagnetic and strong nuclear forces. But, gravity is described by Einstein’s theory of general relativity as a purely geometric phenomenon. These geometric ideas of curvature and the dimensionality of space have nothing to do with quantum mechanics.

To unify these two great foundations of physics, a common language must be found. This new language will take some getting used to. In it, the distinction between matter and space dissolves away and is lost completely; matter becomes a geometric phenomenon, and at the same time, space becomes an exotic form of matter.

Beginning with work on a quantum theory of gravity by John Wheeler and Bryce DeWitt in the 1960’s, and continuing with the so-called superstring theory of John Schwartz and Michael Green in the 1980’s, a primitive version of such a ‘quantum-geometric’ language is emerging. Not surprisingly, it borrows many ideas from ordinary quantum mechanics.

A basic concept in quantum mechanics is that every system of elementary particles is defined by a mathematical quantity called a wave function. This function can be used, for example, to predict the probability of finding an electron at a particular place and time within an atom. Rather than a single quantity, the wave function is actually a sum over an infinite number of factors or ‘states’, each representing a possible measurement outcome. Only one of these states can be observed at a time.

By direct analogy, in quantum gravitation, the geometry of space-time, whether flat or curved, is only one of an infinite variety of geometric shapes for space-time, and therefore the universe. All of these possibilities are described as separate states in the wave function for the universe.

But what determines the probability that the universe will have the particular geometry we now observe out of the infinitude of others? In quantum mechanics, the likelihood that an electron is located somewhere within an atom is determined by the external electric field acting on it. That field is usually provided by the protons in the atomic nucleus. Could there be some mysterious field ‘outside’ our universe that determines its probability?

According to Cambridge University theorist Stephen Hawking, this is the wrong way to look at the problem. Unlike the electron acted upon by protons, our universe is completely self-contained. It requires no outside conditions or fields to help define its probability. The likelihood that our universe looks the way it does depends only on the strengths of the fields within it.

Among these internal fields, there may even be ones that we haven’t yet discovered. Could the cosmological constant be the fingerprint in our universe of a new ‘hidden’ field in Nature? This new field could affect the likelihood of our universe just as a kettle of soup may contain unknown ingredients although we can still precisely determine the kettle’s mass.

A series of mathematical considerations led Hawking to deduce that the weaker the hidden field becomes, the smaller will be the value we observe for the cosmological constant, and surprisingly, the more likely will be the current geometry of the universe.

This, in turn, implies that if Lambda were big enough to measure by astronomers in the first place, our universe would be an improbable one. Philosophically, this may not trouble those who see our cosmos as absolutely unique, but in a world seemingly ruled by probability, a counter view is also possible. There may, in fact, exist an infinite number of universes, but only a minority of them have the correct blend of physical laws and physical conditions resembling our life-nurturing one.

Hawking continued his line of speculation by suggesting that, if at the so-called Planck scale of 10 to the power of -33 centimeters the cosmos could be thought of as an effervescent landscape, or “space-time foam”, then perhaps a natural mechanism could exist for eliminating the cosmological constant for good.

One of the curiosities of combining the speed of light and Newton’s constant of gravitation from general relativity, with Planck’s constant from quantum mechanics, is that they can be made to define unique values for length, time and energy. Physicists believe that at these Planck scales represented by 10 to the power of -33 centimeters and 10 to the power of -43 seconds, general relativity and quantum mechanics blend together to become a single, comprehensive theory of the physical world: The Theory Of Everything. The energy associated with this unification, 10 to the power of 19 billion electron volts, is almost unimaginably big by the standards of modern technology.

The universe itself, soon after the Big Bang, must also have passed through such scales of space, time and energy during its first instants of existence. Cosmologists refer to this period as the Planck Era. It marks the earliest times that physicists are able to explore the universe’s physical state without having a complete Theory of Everything to guide them.

WORMHOLES

Harvard University physicist Sidney Coleman has recently pursued this thought to a possible conclusion. Instead of some mysterious new field in Nature, maybe the Lambda term appears in our theories because we are using the wrong starting model for the geometry of space at the Planck scale.

Previous thinking on the structure of space-time had assumed that it behaved in some sense like a smooth rubber sheet. Under the action of matter and energy, space-time could be deformed into a variety of shapes, each a possible geometric state for the universe. Nearly all candidates for the Theory of Everything’s embed their fields and symmetries in such a smooth geometrical arena.

But what if space-time were far more complicated? One possibility is that ‘wormholes’ exist, filling space-time with a network of tunnels. The fabric of space-time may have more in common with a piece of Swiss cheese than with a smooth rubber sheet.

According to Coleman, the addition of wormholes to space-time means that, like the ripples from many stones tossed into a pond, one geometric state for the universe could interfere with another. The most likely states ( or the biggest ripples) would win out. The mathematics suggest that quantum wormhole interference at the Planck scale makes universes with cosmological constants other than zero exceedingly unlikely.

How big would wormholes have to be to have such dramatic repurcussions? Surprisingly, the calculations suggest that small is beautiful. Wormholes the size of dogs and planets would be very rare. Universes containing even a few of them would exist with a vanishingly low probability. But wormholes smaller than 10 to the power of -33 centimeters could be everywhere. A volume the size of a sugar cube might be teeming with uncounted trillions of them flashing in and out of existence!

Coleman proposes that the action of these previously ignored mini- wormholes upon the geometric fabric of the universe that forces Lambda to be almost exactly zero. Like quantum ‘Pac Men’, they gobble up all the latent energy of space-time that would otherwise have appeared to us in the form of a measureable cosmological constant!

The addition of wormholes to the description of space-time admits the possibility that our universe did not spring into being aloof and independent, but was influenced by how other space-times had already evolved – ghostly mathematical universes with which we can never communicate directly.

The most likely of these universes had Lambda near zero, and it is these states that beat out all other contenders. In a bizarre form of quantum democracy, our universe may have been forced to follow the majority, evolving into the high probability state we now observe, without a detectable cosmological constant.

EPILOG

Wormholes? Wave functions? Hidden fields? The answer to the cosmological constant’s smallness, or absence, seems to recede into the farthest reaches of abstract thinking, faster than most of us can catch up.

As ingenious as these new ideas may seem, the final pages in this unusual story have probably not been written, especially since we can’t put any of these ideas to a direct test. It is a tribute to Einstein’s genius that even his ‘biggest blunder’ made near the beginning of this century still plagues physicists and astronomers as we prepare to enter the 21st century. Who would ever have thought that something that may not even exist would lead to such enormous problems!

The Planck Era

The Big Bang theory says that the entire universe was created in a tremendous explosion about 14 billion years ago. The enormity of this event is hard to grasp and it seems natural to ask ourselves ‘What was it like then?’ and ‘What happened before the Big Bang?’.

Thanks to what physicists call the Standard Model, we have a detailed understanding of quantum physics, matter, energy and force that let us reproduce what the universe looked like as early as a billionth of a second after the Big Bang.  The results of high-precision observational cosmology also let us verify that the Standard Model predictions match what we see as the general properties of the matter and energy in our universe up until this unimaginable time.  We can actually go a bit farther back towards the beginning thanks to detailed studies of the cosmic background radiation!

At a time 10(-36) second ( that is  a trillionth of a trillionth of a trillionth of a second!) after the Big Bang, a spectacular change in the size of the universe occurs. This is the Inflationary Era when the strong nuclear force becomes distinguishable from the weak and electromagnetic forces. The temperature is an incredable 10 thousand trillion trillion degrees and the density of matter has sored to nearly 10(75) gm/cm3. This number is so enormous  even our analogies are almost beyond comprehension. At these densities, the entire Milky Way galaxy could easily be stuffed into a volume no larger than a single hydrogen atom!

Between a billionth of a second and 10(-35) seconds is a No Man’s Land currently in accessible to our technology and requires instruments such as the CERN Large Hadron Collider scaled up to the size of our solar system or even larger!  This is also the domain of the so-called Particle Desert that I previously wrote about, and the landscape of the predictions made by supersymmetric string theory, for which there is as yet no evidence of their correctness despite decades of intense theoretical research.

THROUGH A LOOKING GLASS, DARKLEY

Since our technology will not allow us to physically reproduce the conditions during these ancient times, we must use our mathematical theories of how matter behaves to mentally explore what the universe was like then. We know that the appearence of the universe before 10(-43) second can only be adequatly described by modifying the Big Bang theory because this theory is, in turn, based on the General Theory of Relativity.  At the Planck Scale, we need to extend General Relativity so that it includes not only the macroscopic properties of gravity but also is microscopic characteristics as well. The theory of ‘Quantum Gravity’ is still far from completion but physicists tend to agree that there are some important quide-posts to help us understand how it applies to Big Bang theory.

QUANTUM COSMOLOGY

In the language of General Relativity, gravity is a consequence of the deformati on of space caused by the presence of matter and energy.  In Quantum Gravity theory, gravity is produced by massless gravitons, or strings (in what is called string theory), or loops of energy (in what is called loop quantum gravity), so that gravitons now represent individual packages of curved space.

The appearence and dissappearence of innumerable gravitons gives the geometry of space a very lumpy and dynamic appearance. The geometry of space twists and contorts so that far flung regions of space may suddenly find themselves connected by ‘wormholes’ and quantum black holes, which constantly appear and dissappear within 10(-43) seconds. The geometry of space at a given moment will have to be thought of as an average over all 3-dimensional space geometries that are possible.

What this means is that we may never be able to calculate with any certainty exactly what the history of the universe was like before 10(-43) seconds.  To probe the history of the universe then would be like trying to trace your ancestral roots if every human being on earth had a possibility of being one of your parents. Now try to trace your family tree back a few generations! An entirely new conception of what we mean by ‘a history for the universe’ will have to be developed. Even the concepts of space and time will have to be completely re-evaluated in the face of the quantum fluctuations of spacetime at the Planck Era!

Now we get to a major problem in investigating the Planck Era.

BUT WAIT…THERE’S MORE!

Typically we make observations in nuclear physics by colliding particles and studying the information created in the collision, such as the kinds of particles created, their energy, momentum, spin and other ‘quantum numbers’.  The whole process of testing our theories relies on studying the information generated in these collisions, searching for patterns, and comparing them to the predictions. The problem is that this investigative process breaks down as we explore the Planck Era.  When the quantum particles of space (gravitons, strings or loops)collide at these enormous energies and small scales, they create quantum black holes that immediately evaporate. You cannot probe even smaller scales of space and time because all you do is to create more quantum black holes and wormholes.  Because the black holes evaporate into a randomized hailstorm of new gravitons you cannot actually make observations of what is going on to search for non-random patterns the way you do in normal collisions!

Quantum Gravity, if it actually exists as a theory, tells us that we have finally reached a theoretical limit to how much information we can glean about the Planck Era. Our only viable options involve exploring the Inflationary Era and how this process left its fingerprints on the cosmic background radiation through the influence of gravitational waves.

Fortunately, we now know that gravity waves exist thanks to the discoveries by the LIGO instrument in 2016. We also have indications of what cosmologists call the cosmological B-Modes which are the fingerprints of primordial gravity waves interacting with the cosmic background radiation during the Inflationary Era.

We may not be able to ever study the Planck Era conditions directly when the universe was only 10(-43) seconds old, but then again, knowing what the universe was doing  10(-35) seconds after the Big Bang all the way up to the present time is certainly an impressive human intellectual and technological success!

 

Check back here on May 3 for the next blog!

The Mystery of Gravity

In grade school we learned that gravity is an always-attractive force that acts between particles of matter. Later on, we learn that it has an infinite range through space, weakens as the inverse-square of the distance between bodies, and travels exactly at the speed of light.

But wait….there’s more!

 

It doesn’t take a rocket scientist to remind you that humans have always known about gravity! Its first mathematical description as a ‘universal’ force was by Sir Isaac Newton in 1666. Newton’s description remained unchanged until Albert Einstein published his General Theory of Relativity in 1915. Ninety years later, physicists, such as Edward Witten, Steven Hawkings, Brian Greene and Lee Smolin among others, are finding ways to improve our description of ‘GR’ to accommodate the strange rules of quantum mechanics. Ironically, although gravity is produced by matter, General Relativity does not really describe matter in any detail – certainly not with the detail of the modern quantum theory of atomic structure. In the mathematics, all of the details of a planet or a star are hidden in a single variable, m, representing its total mass.

 

The most amazing thing about gravity is that is a force like no other known in Nature. It is a property of the curvature of space-time and how particles react to this distorted space. Even more bizarrely, space and time are described by the mathematics of  GR as qualities of the gravitational field of the cosmos that have no independent existence. Gravity does not exist like the frosting on a cake, embedded in some larger arena of space and time. Instead, the ‘frosting’ is everything, and matter is embedded and intimately and indivisibly connected to it. If you could turn off gravity, it is mathematically predicted that space and time would also vanish! You can turn off electromagnetic forces by neutralizing the charges on material particles, but you cannot neutralize gravity without eliminating spacetime itself.  Its geometric relationship to space and time is the single most challenging aspect of gravity that has prevented generations of physicists from mathematically describing it in the same way we do the other three forces in the Standard Model.

Einstein’s General Relativity, published in 1915, is our most detailed mathematical theory for how gravity works. With it, astronomers and physicists have explored the origin and evolution of the universe, its future destiny, and the mysterious landscape of black holes and neutron stars. General Relativity has survived many different tests, and it has made many predictions that have been confirmed. So far, after 90 years of detailed study, no error has yet been discovered in Einstein’s original, simple theory.

Currently, physicists have explored two of its most fundamental and exotic predictions: The first is that gravity waves exist and behave as the theory predicts. The second is that a phenomenon called ‘frame-dragging’ exists around rotating massive objects.

Theoretically, gravity waves must exist in order for Einstein’s theory to be correct. They are distortions in the curvature of spacetime caused by accelerating matter, just as electromagnetic waves are distortions in the electromagnetic field of a charged particle produced by its acceleration. Gravity waves carry energy and travel at light-speed. At first they were detected indirectly. By 2004, astronomical bodies such as the  Hulse-Taylor orbiting pulsars were found to be losing energy by gravity waves emission at exactly the predicted rates. Then  in 2016, the  twin  LIGO gravity wave detectors detected the unmistakable and nearly simultaneous pulses of geometry distortion created by colliding black holes billions of light years away.

Astronomers also detected by 1997 the ‘frame-dragging’ phenomenon in  X-ray studies of distant black holes. As a black hole (or any other body) rotates, it actually ‘drags’ space around with it. This means that you cannot have stable orbits around a rotating body, which is something totally unexpected in Newton’s theory of gravity. The  Gravity Probe-B satellite orbiting Earth also confirmed in 2011 this exotic spacetime effect at precisely the magnitude expected by the theory for the rotating Earth.

Gravity also doesn’t care if you have matter or anti-matter; both will behave identically as they fall and move under gravity’s influence. This quantum-scale phenomenon was searched for at the Large Hadron Collider ALPHA experiment, and in 2013 researchers placed the first limits on how matter and antimatter ‘fall’ in Earth’s gravity. Future experiments will place even more stringent limits on just how gravitationally similar matter and antimatter are. Well, at least we know that antimatter doesn’t ‘fall up’!

There is only one possible problem with our understanding of gravity known at this time.

Applying general relativity, and even Newton’s Universal Gravitation, to large systems like galaxies and the universe leads to the discovery of a new ingredient called Dark Matter. There do not seem to be any verifiable elementary particles that account for this gravitating substance. Lacking a particle, some physicists have proposed modifying Newtonian gravity and general relativity themselves to account for this phenomenon without introducing a new form of matter. But none of the proposed theories leave the other verified predictions of general relativity experimentally intact. So is Dark Matter a figment of an incomplete theory of gravity, or is it a here-to-fore undiscovered fundamental particle of nature? It took 50 years for physicists to discover the lynchpin particle called the Higgs boson. This is definitely a story we will hear more about in the decades to come!

There is much that we now know about gravity, yet as we strive to unify it with the other elementary forces and particles in nature, it still remains an enigma. But then, even the briefest glance across the landscape of the quantum world fills you with a sense of awe and wonderment at the improbability of it all. At its root, our physical world is filled with improbable and logic-twisting phenomena and it simply amazing that they have lent themselves to human logic to the extent that they have!

 

Return here on Monday, March 13 for my next blog!