Independent Study Project

Juan Carlos Castellanos-Smith

Independent Study, Period 8

5/05/02 � Final Revision

This project deals with theoretical physics in the area of black holes and gravitation. I have chosen to do a project in this area because it has interested me for some time now.

My goal for this project is to achieve a working understanding of current gravity theory so that I may pursue this understanding more in depth during my college studies. Although I don�t have the mathematical apparatus to work with these theories on a concrete level, I am attempting to formulate my own theory through logical reasoning, imagination, and insight. I will begin by learning about Relativity and Quantum Mechanics by means of science journals and books.

My plans for presenting the project will include a model and illustrations to vividly convey the significance as well as the aesthetically intriguing nature of my study. When giving my presentation I will use a chalkboard or marker board as an aid to help convey the meaning of my discoveries.

I will also complete this paper highlighting my most significant findings.

Gravitation, Black Holes, and some Temporal Mechanics

Gravitation is one of the most mysterious forces, if not the most mysterious, known. Isaac Newton first attempted to explain how the effects of gravitation could be predicted with his mathematical equation for finding the total gravitational force between two objects, both terrestrial or celestial, due to the mutual gravitation that causes the attraction between them. This equation called The Universal Law of Gravitation, allowed scientists to calculate the acceleration of Earth�s own gravity, which is about 9.81 m/s2. This value has been confirmed with experimentation over and over again. Newton�s Universal Law even allows us to predict the gravitational interaction between two celestial bodies. As wonderful as Newton�s Universal Law was, it came to be largely inaccurate for predicting behavior on submicroscopic and macroscopic levels. As it has been discovered in particle physics and astrophysics, there are many other forces and materials in the universe that are just now being accounted for. Albert Einstein�s Special and General Theories of Relativity invoke the reason for this concern. First, his special theory is the one most largely recognized which is represented by his mathematically aesthetic equation E=mc^2. This shows the �conversion factor� between energy and mass, or as Einstein put it, �mass-energy.� He argued that mass and energy were really just two forms of the same material. In his Special Theory, he also argued that space and time were actually connected as �space-time.� According to him, time and space were very similar. Space is the collection of three dimensions: length, height, and breadth (which are actually three of the same dimension, but at right angles to one another). Time is considered the fourth dimension because you can have a location in time, just as you have a location in space. Apparently time though is universally represented by the constant change in position. Everything in the universe is moving in one form or another. In fact to exist, it must be undergoing some form of movement that includes subatomic interaction of particles or other interactions. It�s even argued that if something didn�t �move� in one form or another, did it exist ? A further explanation of the �arrow of time� and possible �time travel� will be introduced later during the discussion of the role of thermodynamics.

Einstein�s most undiscovered theory, the General Theory of Relativity, discusses the nature of gravitation and how it affects space-time. It has recently been appearing more frequently as scientists are beginning to imagine how the mysterious force operates. The General Theory can basically be summarized in this image: think of a rubber sheet as a plane that represents space-time (yes, a plane has only 2 dimensions whereas space-time has 4, but this idea works well to convey the basic understanding of General Relativity). This plane, as in all planes in geometry, extends indefinitely in all directions. Now think of two masses: the first being a very small and very light marble. Now place that marble on the rubber sheet and observe the very slight indentation that the marble�s weight makes in the sheet. Now imagine the other mass as being a large and heavy bowling ball and place it on the sheet. Observe the more powerful indentation that it makes. General Theory basically says that every mass undergoes gravitation: that is it transmits it and receives it to some degree however large or small. The larger the mass, the more it bends space-time around it.

Here is a �localized� approach for examining gravity�s acceleration. Imagine you are in a box and floating. You do not feel any effects of gravity acting on you. There is an apple beside you. Suddenly, the box is moving closer and closer to your feet and to the apple as well. You can tell it is accelerating. You don�t know this but the box you are in is being pulled by a supernatural force (I�ll let you decide what that force is). What you see as the �bottom� of the box accelerating towards your feet is also moving towards the apple at the same acceleration because you and the apple are suspended in the same vicinity. You don�t feel the effects of the acceleration until your feet hit the bottom of the box and then you see the apple apparently continuing to accelerate towards the bottom. You don�t continue to accelerate because your legs and feet keep you from doing so. This �thought experiment� is analogous to the way we see gravity on Earth. This is attempting to explain why everything on the surface accelerates towards the center at the exact same acceleration when distance and air resistance between the object and Earth is accounted for. This analogy from General Relativity is called the �equivalence principle.� However beautiful and simple this idea is, it does not explain the presence of a downward force, only that relative to the bottom of the box you and the apple are �falling towards it� at the same acceleration. The fact is that we can physically feel the sensation of being pulled downward by force and in the box analogy, we only feel the downward sensation when we make contact with the bottom of the box.

Gravity may simply be a grand manifestation of hydrogen forces, London forces, Van der Waals forces, electromagnetic forces, and etc. All these forces may be smaller manifestations of one great force of attraction; Gravitation.

Now, the discovery and observation of black holes has added another advantage to cosmology and theoretical astrophysics. A black hole is born when a very massive star collapses after it dies. By this I mean, when a massive star dies, it ends it�s life with a supernova; a very large explosion. Since the processes that generate the light and heat flow from the star, have ceased, there is little force to prevent its own gravitation from continuing to pull it in towards the center. When the star has collapsed from the point of a supernova, it becomes a neutron star where the gravitation is so powerful that it forces the atoms to come together and protons and electrons combine to form neutrons. This makes the neutron star an extremely dense object. It has just recently been discovered that when a star continues to collapse it becomes a quark star in which the star is made entirely of quarks . The forces that keep the quarks together are described by Quantum Chromodynamics (QCD). If the star continues pass this stage in which the fermionic repulsion pressure is not powerful enough to counteract the star�s own gravity, it becomes a black hole where all of the matter has been pulled in towards the center to an infinitely dense point called a singularity. The region around the singularity is the black hole. The event horizon of the black hole marks its �sphere of influence� where nothing, not even light can escape. This was the case for some time, and then scientists started detecting very penetrating radiation called gamma rays and X-rays coming from different places in the sky. They were very puzzled about what could be producing such radiation until they all came to the conclusion that the black hole was the best candidate for emitting these types of powerful radiation. It is uncertain why this radiation is being emitted, but scientists are developing very plausible explanations for this phenomenon. First of all, they had to overcome the idea that a black hole could not emit anything. It is suspected that when matter is being pulled into the black hole, the great pressure and friction between the matter particles that is experienced right before it is sucked into the black hole is intense enough to cause this residual �Hawking radiation�. There is much work to be done on the physics of black holes since physics breaks down around such powerful phenomena.

Gravitation is the fourth force that is keeping scientists from developing a Grand Unified Field Theory, �the theory of everything.� However, there is a very promising theory that unifies the physics of the very small and the very large, which are quantum mechanics and gravitation, into what is called �Quantum Gravity.� Quantum Gravity is predicted to emerge from String Theory . String Theory describes the elementary particles of all matter as being produced by different vibrational modes of the truly fundamental objects; strings. These strings can be open like a �hair� or closed like a �loop�. A part of String Theory is Supersymmetry, where every particle of matter called a �fermion� has a respective exchange particle of force called a �boson.� According to Quantum Gravity, the fluctuation of space as caused by gravitational distortion is supposed to be quantized on the Planck Scale . This scale allows General Relativity to be merged with Quantum Mechanics. This Planck Scale is necessary for Quantum Gravity to hold true because gravitation does not operate at a �zero distance� in which particles are �zero� distance apart, yet quantum processes can operate at �zero distance.� This scale is small enough to allow for truth when the two theories are incorporated with one another. However it is too difficult to physically examine this theory on such a small scale. Clever ways of examining Quantum Gravity are currently being devised.

There are other theories that exist to explain the mechanics of gravitation. There is one theory that describes the gravitational signal as being passed through conduits called diallel gravitational lines. These diallels are similar to the magnetic field lines, and for the most part eliminates the need of a �graviton� which is the theoretical exchange particle for gravitation. Another theory that hasn�t been included in mainstream physics because of its rather young development is the �Shift Theory.� The Shift Theory shows the gravitational signal being mediated by the classic exchange particle, the graviton. Basically, a mass is represented by a pair of gravitons. When an incoming graviton hits the pair, the incoming graviton adheres to the one it made contact with and the one on the other end is ejected from the pair. The effect is that the pair has shifted in the direction of the incoming graviton or �source� by one graviton. When trillions upon trillions of these processes occur, they result in the observable movement when two bodies are gravitationally attracted to one another.

I made a conclusion based on this �non-mainstream� theory, but first I must mention another concept. Quantum mechanics predict that light travels as the result of virtual processes. These processes are called �virtual� because two particles are created; yet there is no net gain of mass to the universe when this occurs, so this is consistent with the Law of Conservation of Mass. Anyhow, as light travels, the photon separates into an electron and it�s respective antiparticle, the positron. When they recombine, they annihilate each other and produce radiation as a result. When the �Shift Theory� is applied, this is the result. In the moment that the photon has disassociated into an electron and positron, it is possible for light in this part of the virtual process to experience gravitation under the �Shift Theory� by the interaction of gravitons between the two particles and possibly with other particles outside the vicinity of the pair as well.

As far as time travel goes, first I must mention the �arrow of time� as it is described by thermodynamics. Thermodynamics indicates that the entropy of a system generally increases with time. Since our universe is evidently accelerating its expansion because our universe is theoretically composed of an estimated 65% of dark energy, the entropy of the system is increasing as bodies move away from each other and therefore time travels in this single direction.

When traveling through a wormhole (which might be allowed for under Quantum Gravity) there are three possible outcomes as they pertain to time:

1) An object entering the wormhole would exit the other end simultaneously as it is entered.

2) An object entering the wormhole would exit the other end with a delay.

3) An object will have already begun exiting the other end of the wormhole before it has even entered.

To explain how traveling through a wormhole is actually traveling through (not in) a higher dimension will take some explaining. Consider a surface curved over on self as in a sheet of paper folded over. Following the surface at all locations results in it being two-dimensional relative to the surface. By this I mean if you could not look at the surface from the outside you wouldn�t be able to see that it is three-dimensional. If you were looking for a shortcut through space to the other side of the curve and you discovered physically or by theory the existence of a third dimension, then you would be able to get to the other side by traveling through hyperspace but not actually traveling in it. The resulting tunnel would be a wormhole.

In order for time travel into the past to be possible, every moment of time as it passes must be recorded somewhere. For example, when a motion picture camera records a scene it can later be rewound and viewed. The same would have to be for time. Time is basically the idea that events occur and pass. The idea that �what�s done is done� to explain how time passes would hold true unless every event that occurred was recorded somewhere and then backward time travel would be possible. The real question would then be �what would contain all these events?� A �super-temporal universe� perhaps?

Here are some ideas I have come up with (I think they are original, and if they aren�t then I apologize because it is incredibly difficult to generate original and pragmatic ideas at this elementary level of study).

The extraordinary effect of gravitation that a black hole and its surrounding material experiences could be explained with an �extraordinary� idea as it applies to the singularity. A singularity may actually be the �gate� to a different universe or etc. If this is the case then the �gap� or �tear� in our universe allows material to be pulled in through it to another less dense one. Then what we see as powerful gravitation could actually be explained as the �vacuum effect.�

Another idea to describe how bodies interact gravitationally could be described by �charge waves.� This idea hasn�t developed much, but what if the mediating graviton is actually a relative of the electron; where it�s charge vacillates from being negative to positive. The amount of which it would vacillate would be the frequency of the wave and it would be able to interact with only charge waves of its exact frequency.

In conclusion, I see that there are many avenues I can take to explore in this area. I have also learned that Quantum Gravity is allegedly the most promising theory showing the unification of Quantum mechanics and General Relativity and this will be my primary focus in continuing my study.

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Juan Carlos Castellanos-Smith Independent Study, Period 8 5/05/02 � Final Revision *Abstract* This project deals with theoretical physics in the area of black holes and gravitation. I have chosen to do a project in this area because it has interested me for some time now. My goal for this project is to achieve a working understanding of current gravity theory so that I may pursue this understanding more in depth during my college studies. Although I don�t have the mathematical apparatus to work with these theories on a concrete level, I am attempting to formulate my own theory through logical reasoning, imagination, and insight. I will begin by learning about Relativity and Quantum Mechanics by means of science journals and books. My plans for presenting the project will include a model and illustrations to vividly convey the significance as well as the aesthetically intriguing nature of my study. When giving my presentation I will use a chalkboard or marker board as an aid to help convey the meaning of my discoveries. I will also complete this paper highlighting my most significant findings. *Gravitation, Black Holes, and some Temporal Mechanics* Gravitation is one of the most mysterious forces, if not the most mysterious, known. Isaac Newton first attempted to explain how the effects of gravitation could be predicted with his mathematical equation for finding the total gravitational force between two objects, both terrestrial or celestial, due to the mutual gravitation that causes the attraction between them. This equation called The Universal Law of Gravitation, allowed scientists to calculate the acceleration of Earth�s own gravity, which is about 9.81 m/s2. This value has been confirmed with experimentation over and over again. Newton�s Universal Law even allows us to predict the gravitational interaction between two celestial bodies. As wonderful as Newton�s Universal Law was, it came to be largely inaccurate for predicting behavior on submicroscopic and macroscopic levels. As it has been discovered in particle physics and astrophysics, there are many other forces and materials in the universe that are just now being accounted for. Albert Einstein�s Special and General Theories of Relativity invoke the reason for this concern. First, his special theory is the one most largely recognized which is represented by his mathematically aesthetic equation E=mc^2. This shows the �conversion factor� between energy and mass, or as Einstein put it, �mass-energy.� He argued that mass and energy were really just two forms of the same material. In his Special Theory, he also argued that space and time were actually connected as �space-time.� According to him, time and space were very similar. Space is the collection of three dimensions: length, height, and breadth (which are actually three of the same dimension, but at right angles to one another). Time is considered the fourth dimension because you can have a location in time, just as you have a location in space. Apparently time though is universally represented by the constant change in position. Everything in the universe is moving in one form or another. In fact to exist, it must be undergoing some form of movement that includes subatomic interaction of particles or other interactions. It�s even argued that if something didn�t �move� in one form or another, did it exist ? A further explanation of the �arrow of time� and possible �time travel� will be introduced later during the discussion of the role of thermodynamics. Einstein�s most undiscovered theory, the General Theory of Relativity, discusses the nature of gravitation and how it affects space-time. It has recently been appearing more frequently as scientists are beginning to imagine how the mysterious force operates. The General Theory can basically be summarized in this image: think of a rubber sheet as a plane that represents space-time (yes, a plane has only 2 dimensions whereas space-time has 4, but this idea works well to convey the basic understanding of General Relativity). This plane, as in all planes in geometry, extends indefinitely in all directions. Now think of two masses: the first being a very small and very light marble. Now place that marble on the rubber sheet and observe the very slight indentation that the marble�s weight makes in the sheet. Now imagine the other mass as being a large and heavy bowling ball and place it on the sheet. Observe the more powerful indentation that it makes. General Theory basically says that every mass undergoes gravitation: that is it transmits it and receives it to some degree however large or small. The larger the mass, the more it bends space-time around it.




Here is a �localized� approach for examining gravity�s acceleration. Imagine you are in a box and floating. You do not feel any effects of gravity acting on you. There is an apple beside you. Suddenly, the box is moving closer and closer to your feet and to the apple as well. You can tell it is accelerating. You don�t know this but the box you are in is being pulled by a supernatural force (I�ll let you decide what that force is). What you see as the �bottom� of the box accelerating towards your feet is also moving towards the apple at the same acceleration because you and the apple are suspended in the same vicinity. You don�t feel the effects of the acceleration until your feet hit the bottom of the box and then you see the apple apparently continuing to accelerate towards the bottom. You don�t continue to accelerate because your legs and feet keep you from doing so. This �thought experiment� is analogous to the way we see gravity on Earth. This is attempting to explain why everything on the surface accelerates towards the center at the exact same acceleration when distance and air resistance between the object and Earth is accounted for. This analogy from General Relativity is called the �equivalence principle.� However beautiful and simple this idea is, it does not explain the presence of a downward force, only that relative to the bottom of the box you and the apple are �falling towards it� at the same acceleration. The fact is that we can physically feel the sensation of being pulled downward by force and in the box analogy, we only feel the downward sensation when we make contact with the bottom of the box. Gravity may simply be a grand manifestation of hydrogen forces, London forces, Van der Waals forces, electromagnetic forces, and etc. All these forces may be smaller manifestations of one great force of attraction; Gravitation. Now, the discovery and observation of black holes has added another advantage to cosmology and theoretical astrophysics. A black hole is born when a very massive star collapses after it dies. By this I mean, when a massive star dies, it ends it�s life with a supernova; a very large explosion. Since the processes that generate the light and heat flow from the star, have ceased, there is little force to prevent its own gravitation from continuing to pull it in towards the center. When the star has collapsed from the point of a supernova, it becomes a neutron star where the gravitation is so powerful that it forces the atoms to come together and protons and electrons combine to form neutrons. This makes the neutron star an extremely dense object. It has just recently been discovered that when a star continues to collapse it becomes a quark star in which the star is made entirely of quarks . The forces that keep the quarks together are described by Quantum Chromodynamics (QCD). If the star continues pass this stage in which the fermionic repulsion pressure is not powerful enough to counteract the star�s own gravity, it becomes a black hole where all of the matter has been pulled in towards the center to an infinitely dense point called a singularity. The region around the singularity is the black hole. The event horizon of the black hole marks its �sphere of influence� where nothing, not even light can escape. This was the case for some time, and then scientists started detecting very penetrating radiation called gamma rays and X-rays coming from different places in the sky. They were very puzzled about what could be producing such radiation until they all came to the conclusion that the black hole was the best candidate for emitting these types of powerful radiation. It is uncertain why this radiation is being emitted, but scientists are developing very plausible explanations for this phenomenon. First of all, they had to overcome the idea that a black hole could not emit anything. It is suspected that when matter is being pulled into the black hole, the great pressure and friction between the matter particles that is experienced right before it is sucked into the black hole is intense enough to cause this residual �Hawking radiation�. There is much work to be done on the physics of black holes since physics breaks down around such powerful phenomena. Gravitation is the fourth force that is keeping scientists from developing a Grand Unified Field Theory, �the theory of everything.� However, there is a very promising theory that unifies the physics of the very small and the very large, which are quantum mechanics and gravitation, into what is called �Quantum Gravity.� Quantum Gravity is predicted to emerge from String Theory . String Theory describes the elementary particles of all matter as being produced by different vibrational modes of the truly fundamental objects; strings. These strings can be open like a �hair� or closed like a �loop�. A part of String Theory is Supersymmetry, where every particle of matter called a �fermion� has a respective exchange particle of force called a �boson.� According to Quantum Gravity, the fluctuation of space as caused by gravitational distortion is supposed to be quantized on the Planck Scale . This scale allows General Relativity to be merged with Quantum Mechanics. This Planck Scale is necessary for Quantum Gravity to hold true because gravitation does not operate at a �zero distance� in which particles are �zero� distance apart, yet quantum processes can operate at �zero distance.� This scale is small enough to allow for truth when the two theories are incorporated with one another. However it is too difficult to physically examine this theory on such a small scale. Clever ways of examining Quantum Gravity are currently being devised. There are other theories that exist to explain the mechanics of gravitation. There is one theory that describes the gravitational signal as being passed through conduits called diallel gravitational lines. These diallels are similar to the magnetic field lines, and for the most part eliminates the need of a �graviton� which is the theoretical exchange particle for gravitation. Another theory that hasn�t been included in mainstream physics because of its rather young development is the �Shift Theory.� The Shift Theory shows the gravitational signal being mediated by the classic exchange particle, the graviton. Basically, a mass is represented by a pair of gravitons. When an incoming graviton hits the pair, the incoming graviton adheres to the one it made contact with and the one on the other end is ejected from the pair. The effect is that the pair has shifted in the direction of the incoming graviton or �source� by one graviton. When trillions upon trillions of these processes occur, they result in the observable movement when two bodies are gravitationally attracted to one another. I made a conclusion based on this �non-mainstream� theory, but first I must mention another concept. Quantum mechanics predict that light travels as the result of virtual processes. These processes are called �virtual� because two particles are created; yet there is no net gain of mass to the universe when this occurs, so this is consistent with the Law of Conservation of Mass. Anyhow, as light travels, the photon separates into an electron and it�s respective antiparticle, the positron. When they recombine, they annihilate each other and produce radiation as a result. When the �Shift Theory� is applied, this is the result. In the moment that the photon has disassociated into an electron and positron, it is possible for light in this part of the virtual process to experience gravitation under the �Shift Theory� by the interaction of gravitons between the two particles and possibly with other particles outside the vicinity of the pair as well. As far as time travel goes, first I must mention the �arrow of time� as it is described by thermodynamics. Thermodynamics indicates that the entropy of a system generally increases with time. Since our universe is evidently accelerating its expansion because our universe is theoretically composed of an estimated 65% of dark energy, the entropy of the system is increasing as bodies move away from each other and therefore time travels in this single direction. When traveling through a wormhole (which might be allowed for under Quantum Gravity) there are three possible outcomes as they pertain to time: 1) An object entering the wormhole would exit the other end simultaneously as it is entered. 2) An object entering the wormhole would exit the other end with a delay. 3) An object will have already begun exiting the other end of the wormhole before it has even entered. To explain how traveling through a wormhole is actually traveling through (not in) a higher dimension will take some explaining. Consider a surface curved over on self as in a sheet of paper folded over. Following the surface at all locations results in it being two-dimensional relative to the surface. By this I mean if you could not look at the surface from the outside you wouldn�t be able to see that it is three-dimensional. If you were looking for a shortcut through space to the other side of the curve and you discovered physically or by theory the existence of a third dimension, then you would be able to get to the other side by traveling through hyperspace but not actually traveling in it. The resulting tunnel would be a wormhole. In order for time travel into the past to be possible, every moment of time as it passes must be recorded somewhere. For example, when a motion picture camera records a scene it can later be rewound and viewed. The same would have to be for time. Time is basically the idea that events occur and pass. The idea that �what�s done is done� to explain how time passes would hold true unless every event that occurred was recorded somewhere and then backward time travel would be possible. The real question would then be �what would contain all these events?� A �super-temporal universe� perhaps? Here are some ideas I have come up with (I think they are original, and if they aren�t then I apologize because it is incredibly difficult to generate original and pragmatic ideas at this elementary level of study). The extraordinary effect of gravitation that a black hole and its surrounding material experiences could be explained with an �extraordinary� idea as it applies to the singularity. A singularity may actually be the �gate� to a different universe or etc. If this is the case then the �gap� or �tear� in our universe allows material to be pulled in through it to another less dense one. Then what we see as powerful gravitation could actually be explained as the �vacuum effect.� Another idea to describe how bodies interact gravitationally could be described by �charge waves.� This idea hasn�t developed much, but what if the mediating graviton is actually a relative of the electron; where it�s charge vacillates from being negative to positive. The amount of which it would vacillate would be the frequency of the wave and it would be able to interact with only charge waves of its exact frequency. In conclusion, I see that there are many avenues I can take to explore in this area. I have also learned that Quantum Gravity is allegedly the most promising theory showing the unification of Quantum mechanics and General Relativity and this will be my primary focus in continuing my study.