Surf’s Up!: Gravity Waves

January 3, 2000
By Jim Kruta

What is it that helps to hold the universe together? No, not duck tape. It’s gravity! Gravity is the weakest of all thefundamental forces. Yet, because it operates on such a large scale, and at infinite distances, it is one of the majorinfluences in our universe. But what exactly is gravity? No one knows for sure but there are many theories currentlyrunning around. This paper will examine the effects and properties of gravity as well as some of the new and oldideas about this fundamental “force.”

“What hinders the fix’d Stars from falling upon one another?” This quote by Sir Isaac Newton shows his interest in thenatural world and in the way it functions. Newton was puzzled by why things in the universe, as well as here on Earth,moved the way they did. This curiosity ultimately led him to discover the laws which governed gravity. He believed thatgravity was a force. It acted like other known forces and could be accounted for by simple laws such as those thatgoverned other properties of matter. Newton’s law of gravitation is this: The force of gravity between two bodies isproportional to the product of their masses, and gravity diminishes according to an inverse square of the distance betweenthem. Or, mathematically put, F= (M*m)/R^2. This law had far-reaching scientific consequences. It led to theconclusion by others after Newton that the universe was not infinite and was not static. The reasoning went thus: Ifthere were an infinite number of stars in the universe, they would all pull on each other to a common center of mass andthe universe would be destroyed in the resultant spherical clump of mass. There are three theories as to how the gravityof the entire universe will eventually affect it. This idea that everything will collapse into everything else is one ofthe current theories of how the universe will end affectionately titled, “The Big Crunch.” The reason this hasn’thappened yet, and possibly will never happen, is that the universe is expanding. The gravitational attraction between allthe matter in the universe may simply not be enough to slow this expansion down. This leads to the two other theories.The first being that there is not sufficient gravitational mass in the universe to halt this expansion so that theuniverse will continue expanding forever. The second being that there is just enough gravitational mass in the universeto slow the expansion to a stop but not enough to reverse it. This amount of matter has been termed the “criticaldensity.” According to the Hubble expansion rate and the accuracy to which we know it, the critical density is 5*10^-30 ofa gram per cubic centimeter of space (Smoot 158). If the density is above this value, we have a big crunch. If thedensity is below this value, we have infinite expansion. If the density is exactly this value, the universe grinds to ahalt and stays there.

For three centuries after Newton, gravity was considered a force. Nearly every scientist accepted this definition andgravity was considered to be the fourth fundamental force of the universe. It is fundamental because there is no otherforce that can be used to describe gravity; gravity is the most basic explanation for phenomenon of the inherentattraction between two masses. However, this concept of gravity being a force was contested by a young man named AlbertEinstein. During his lifetime, he proposed many new ideas about what gravity was and what it did.

In 1905 Einstein proposed his special theory of relativity and several years later, his general theory of relativity.Special relativity showed that space and time, and mass and energy, were equal and opposite properties of each other.General relativity showed that gravity could be considered a curvature in space-time rather than, as Einstein put it, a”mysterious force.” This curvature of space, Einstein said, was not due to a force but was the natural effect thatmatter/energy had upon the geometry of space-time. If this curvature of space really existed, then not only would gravitybend the path of an object made up of matter, it would bend the path of light itself. In other words, if light passed bya massive enough object, it would seem to observers that it had been deflected from its straight line path. Einsteinproposed testing this by examining star positions in the absence of the sun and then examining them with the sun. If hishypothesis was correct, some of the stars would appear to be in different locations. Just a few years after he proposedthis, the experiment was conducted. It was during the solar eclipse of 1919 that this was done. Einstein was shown to becorrect: the light was, indeed, deflected. Even so, it is still not known whether gravity is the warpage of space-timeor if it is a force.

Another consequence of Einstein’s theories is relative time. Because space and time and intimately bound together, anywarpage of space results in a warpage of time. Near greater gravitational masses, time appears to run slower. Anobserver far away from the surface of the earth would see everything moving slower than one on the surface of the earth.This means that everything measured in the universe is done so from a relative reference point. The one thing in theuniverse that will be measured the same no matter what frame of reference one is in is the speed of light. But everythingelse, distance, time, mass, etc., depends upon the velocity one is moving and in relation to what. Einstein showed thatthis has the consequence of mass increasing with velocity. The faster an object moves, the more massive it becomes. Notonly does mass change, but the measurement of time as well. Some interesting aspects of these ideas will be examinedlater.

One of the newest ideas as to the nature of gravity is the theory of superstrings. Superstring theory was originallyinvented to explain the strong nuclear force and was later adapted to fit gravity. Invented in the 1960’s, string theorybasically postulated that all the matter in the universe could be thought of as infinitely thin, vibrating strings.Interactions that take place between these strings are mediated by other strings connecting the strings in question. Itis the vibration of these strings, as well as other properties, that brings about the properties we see in fourdimensional space-time. This theory was largely ignored and the quark-gluon theory was adopted instead. It wasn’t until1984 that string theory was seriously considered. This was because scientists had made little progress in trying toresolve gravity in to a Grand Unified Theory. The GUT gravity, or supergravity as it is called, had too many uncancelableinfinities. Scientists could not resolve some of the problems inherent in supergravity so many of them adoptedsuperstrings theory. Though it was not known for certain whether all the infinities involved in superstring theorycanceled or not, there was a bigger problem: superstring theory only works in ten or twenty-six dimensions. So,unfortunately, scientists are not that much closer to creating a way to unify gravity with the other three fundamentalforces.

Quite a few scientists today believe that it is only a matter of time before gravity is united with the other forces toform a Theory of Everything. Many notable physicists such as Leon Lederman believe that this will be done with the helpof particle accelerators. In his book The God Particle, Lederman introduces one of the newest theories in regards togravity and the Grand Unified Theory. It is believed that all four forces unite into one mediator particle, the Higgs’Boson, at a high enough energy, the Higgs’ energy. This boson is mediated through the Higgs’ field; this field issupposedly what gives particles their mass as well as their gravitational affinities and it what is believed to hide theunderlying symmetry behind all of the fundamental particles. The Higgs’ Boson is a particle comprised of the mediators ofall the fundamental forces, i.e. the photon, the W+ and W-, the Z, and the as yet undiscovered graviton. Though the Higgshas never been seen, there are already countless theories about it being flung around the science world. Severaldifferent Higgs particles and their properties have already been theorized as has their effect on mass and gravity. Onereason the Higgs is so highly sought after is that it is believed that if the relationship between the Higgs and mass canbe found, the express Higgs’ mass of a particle can also be found. The amazing thing about the Higgs’ mass of a particleis that it is theorized to be the rest mass of the particle! This has many far-reaching ramifications and could greatlyaffect our understanding of the properties of relativity and space-time. So the quest for the Higgs Boson continues in aneffort to prove the Higgs’ Field’s existence and its subsequent effect upon the mass and gravity of matter and space.

Theories aside, let’s examine some of the important effects gravity has upon our universe. Assuming the Big Bang model iscorrect, it is gravity which helped bring galaxies, stars, and our solar system together. Though the force of gravity isweak, its action at a distance property makes it possible for huge clouds of hydrogen gas to coalesce into protostars.Gravity continues to influence these protostars to the point where their temperature and pressure is so great that fusionbegins. Once fusion begins, gravity is the only thing which has the ability to hold the newborn star together. Thesubsequent gravitational attraction of the new star makes it possible for smaller clouds of dust and gasses to be caughtin an orbit. These smaller clouds can then condense into planets such as the one upon which we live. These planets andstars are held in galaxies by the collective gravity of each galaxy.

However, it has recently been discovered that all the visible mass in most galaxies is not enough to account for theproperties therein. By examining the speed at which different stars are moving, it was able to be determined that therewas a great deal of missing mass. This mass has been dubbed “dark matter” because of our inability to observe itdirectly. Other techniques, such as gravitational lensing, were also used to discover this dark matter. Gravitationallensing is similar to the experiment mentioned earlier where light was bent around a gravity well only it is much strongerand instead of simply bending light, it splits the light into multiple images around the object being studied. It is nowthought that dark matter may make up the majority of our universe. If enough dark matter is “found,” it may mean that theBig Crunch is a serious possibility. As yet, it would seem rather that the amount of matter is close to the range for acomplete halt to the expansion of the universe as was mentioned earlier.

Gravity is also responsible for other unique phenomenon in our universe. Such as neutron stars and black holes. Neutronstars are formed when a red giant or other massive star has run out of fusionable and fissionable material. Without theoutward force of fission or fusion, the overwhelming force of gravity takes over. In mere seconds, the iron core of thestar experiences a shock wave which completely blows the star apart in a glorious spectacle of light and radiation calleda supernova. The resulting fragments of the star are compressed into a sphere about twelve miles across. This resultingsphere will retain the original velocity of the star and it will also retain any angular momentum the star originally had.The force of the explosion and the gravity of the resulting object collapses all the protons and electrons into neutronsmaking one of the densest objections in the universe, a neutron star. A rotating neutron star is called a pulsar. Thisis because it “pulses.” As it spins, if its poles are aligned correctly with respect to Earth, radio telescopes can pickup pulses as its electromagnetic field passes through our line of sight.

Astronomers are currently looking for systems of double neutron stars orbiting around each other. Such a system would beinvaluable as far as the study of gravity is concerned. One such system has been studied for many years now, the systemPSR 1913 + 16. The orbit of these two stars has been narrowing and it is believed to be because gravity waves arecarrying away the stars energy. Astronomers are in the process of looking for these waves or the effects thereof. Ifgravity waves are detected, it may give insight as to some of the more fundamental properties of gravity such as the speedof its propagation through space and the effect it was on the geometry of space-time.

The other even more unusual object is the black hole. Stephen Hawking gets most of the credit in this field as it was hewho made most of the theories and model presently held today. A black hole occurs when a star with tremendous massexplodes. Instead of turning into a neutron star, there is so much mass that even the neutrons are collapsed into a messof quark soup. The resulting star, for it can still be considered a star, will retain three characteristics of theoriginal: mass, charge, and angular momentum. But it will be a black star or, as it is more commonly called, black hole.The reason a black hole is black is because the gravity is so great that even light cannot escape it. Anything enteringinto the event horizon will be sucked inside the black hole never to return again. Or so was previously thought. StephenHawking showed that things can, in fact, escape from a black hole despite its immense gravity thanks to quantum tunneling.The amount of quantum tunneling depends on the size of the black hole but will occur in any black hole. This tunnelingwill create a certain amount of radiation called Hawking radiation. It is theorized that this Hawking radiation couldmake it possible to see a black hole. Unfortunately, we do not yet currently have the technology to measure the extremelysmall discrepancy in radiation this tunneling would cause.

As can be seen, almost everything known about gravity is theoretical. One reason being because we have never seen theparticle responsible for mediating this force, if, in fact, there is one. I do not believe there is such a particle. Ibelieve, rather, that the Einsteinian model of gravity is more accurate. This is mainly because I like to think that allthe scientists who are trying to unify gravity with the three other forces are doomed to fail. I imagine that God hasthrown them sort of a curve-ball if you will. I still think there may be a Theory of Everything out there, it is justthat we need to start thinking along other lines.

One would wonder, though, how matter, mass, and gravity are all related. Is gravity strictly related to matter or does itdepend upon the mass of the object? According to Einstein, most physical properties in the universe are relative basedupon the observer’s frame of reference. This includes mass. So the questions that presents themselves are: Does anincrease in relative mass mean an increase in gravity? And, if it does, what is the resultant increase (is itproportional or dependent on similar factors)?

Mass is dependent on the value tau. Tau= (1-v^2/c^2)^1/2, where v is the objects velocity and c is the velocity of light.You calculate the relative mass of the object by taking its inverse tau value and multiplying by its relative rest mass.So if a 100 kilogram object is moving away from you at 99.5 per cent light speed, it would mass 1000 kilograms. But wouldthis precipitate a subsequent increase in the gravitational attraction of this object? In other words, would this objectbecome 10 times more attractive? Theory indicates that it would but only relative to the “at rest” observer. At first,that may not seem like that big a deal. But when you take Einstein’s idea about the gravity simply being the curvature ofspace-time into account, things start getting sticky.

To illustrate, I’ll use the well-known rubber sheet analogy. Suppose the sun is a bowling ball resting on a rubber sheet.For our purposes, this sheet is frictionless. The earth and other planets are marbles of varying size rolling around thedepression which the sun is making. These planets of course make their own depressions as do their moons, etc. Now,suppose a binary star system comes screaming into our solar system at 99.5 per cent the speed of light. (I know thisseems unlikely but galaxies crash into each other all the time.) These binary stars are nearly at rest with respect toeach other and therefore their space-time sheet has only mild depressions in them just like our solar system. However,relative to our solar system, the mass of star A is ten times what it is relative to B. It is the same with B. Take intoaccount the relative mass of A and the warpage to space-time is now huge. Again, it is the same with B. Relative to oursolar system, A is creating a huge warpage of space while relative to B, nothing has changed. This means that space iswarped by different amounts at the same time! And it works the other way around, too, since relativity states that eitherset of objects could be considered at rest. If all this is true, it would mean that the nature of space-time itself isrelative to the observer. (Which is pretty cool if you ask me, albeit confusing.)

One last issue that must be discussed when talking about gravity is that of anti-gravity. This much sought after forcehas been the subject of countless science-fiction stories and the idea has been thrown around by scientists for manyyears. But does anti-gravity exist? And in what form? It is my believe that anti-gravity, if it does exist, is not theexact opposite of gravity. Or, at least, it doesn’t seem to behave that way.

There are several different possibilities as to what anti-gravity is and they each depend upon which theory of gravity youexamine. If you think of gravity as an attractive force being mediated by the graviton, the logical conclusion is thatanti-gravity is a repulsive force being mediated by the anti-graviton. There are a few scientists who believe thismediator particle exists in normal space-time, it is just that it doesn’t react with normal matter in the same way agraviton does and therefore has less of an effect upon it. Other-wise, the anti-graviton would balance out the effect ofthe graviton and gravity wouldn’t exist. But if you think of gravity as the curvature of space-time as I do, thenanti-gravity would simply be space-time curving into the opposite direction. This does lead to some interesting resultsas one wonders what space-time curving in the opposite direction would do to time as we know it. Until we find a way tomeasure the curvature of space-time, I do not think anyone will know exactly how anti-gravity would behave.

In conclusion, gravity is a strange and wonderful thing. Even though we do not know much about it, we have a fairly goodunderstanding of how it influences the universe. And perhaps in the future, we will develop theories and equipment bettersuited to answering the questions surrounding gravity.

Bibliography

Hawking, Stephen W. A Brief History of Time: From the Big Bang to Black Holes. New York, NY: Bantam Books. 1988.
Lederman, Leon. The God Particle. New York, NY: Dell Publishing. 1993.
Smoot, George and Davidson, Keay. Wrinkles in Time. New York, NY: William Morrow and Company, Inc. 1993.

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