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Hyperspace connections:

Black holes, white holes, wormholes
by John Gribbin

When astronomer Carl Sagan decided to write a science fiction novel, he needed a fictional device that would allow his characters to travel great distances across the Universe. He knew, of course, that it is impossible to travel faster than light; and he also knew that there was a common convention in science fiction that allowed writers to use the gimmick of a shortcut through "hyperspace" as a means around this problem. But, being a scientist, Sagan wanted something that would seem to be more substantial than a conventional gimmick for his story. Was there any way to dress up the mumbo-jumbo of Sf hyperspace in a cloak of respectable sounding science? Sagan didn’t know. He isn’t an expert on black holes and general relativity -- his background specialty is planetary studies. But he knew just the person to turn to for some advice on how to make the obviously impossible idea of hyperspace connections through spacetime sound a bit more scientifically plausible in his book Contact.

The man Sagan turned to for advice, in the summer of 1985, was Kip Thorne, at CalTech. Thorne was sufficiently intrigued to set two of his PhD students, Michael Morris and Ulvi Yurtsever, the task of working out some details of the physical behaviour of what the relativists know as "wormholes". At that time, in the mid-1980s, relativists had long been aware that the equations of the general theory provided for the possibility of such hyperspace connections. Indeed, Einstein himself, working at Princeton with Nathan Rosen in the 1930s, had discovered that the equations of relativity -- Karl Schwarzschild’s solution to Einstein’s equations -- actually represent a black hole as a bridge between two regions of flat spacetime -- an "Einstein-Rosen bridge". A black hole always has two "ends", a property ignored by everyone except a few mathematicians until the mid-1980s. Before Sagan set the ball rolling again, it had seemed that such hyperspace connections had no physical significance and could never, even in principle, be used as shortcuts to travel from one part of the Universe to another. Morris and Yurtsever found that this widely held belief was wrong. By starting out from the mathematical end of the problem, they constructed a spacetime geometry that matched Sagan’s requirement of a wormhole that could be physically traversed by human beings. Then they investigated the physics, to see if there was any way in which the known laws of physics could conspire to produce the required geometry. To their own surprise, and the delight of Sagan, they found that there is.

To be sure, the physical requirements seem rather contrived and implausible. But that isn’t the point. What matters is that it seems that there is nothing in the laws of physics that forbids travel through wormholes. The science fiction writers were right -- hyperspace connections do, at least in theory, provide a means to travel to far distant regions of the Universe without spending thousands of years pottering along through ordinary space at less than the speed of light. The conclusions reached by the CalTech team duly appeared as the scientifically accurate window dressing in Sagan’s novel when it was published in 1986, although few readers can have appreciated that most of the "mumbo-jumbo" was soundly based on the latest discoveries made by mathematical relativists. Since then, the discovery of equations that describe physically permissible, traversable wormholes has led to a booming cottage industry of mathematicians investigating these strange phenomena. It all starts with the Einstein-Rosen bridge.

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Time Trax

by Adam Schreckenberger

SUMARY:

Time travel:

The mystery of 1,000 years. Technically Time Travel already exists. For instance, take the stars you look at every night. They are a number of light years away, correct? YES! So, take the star Proxima Centuri, 4.5 light years away. Let X equal the number of years you are looking back in time, and let D equal how many light years a star is away. With this, the equation X=D.

I have my own computation for time travel, but first there are two components that make up this theory. In my first two years of research, I read a lot of books on Einstein and Relativity: E=MC2. E=MC2 is a large part of my calculation, as well as Asimov’s theory 2
p times the square root of mass divided by kinetic energy. After spending the third and fourth year of my research I composed the equation:

Y±((M/K>)+((-M*9.8+U)+U)K)=T

(m=mass, and k=speed u=momentum W = force against you Y=present year T=year of arrival)

The point of this equation shows where you will end up in time. Anyway, in the 5th year of my research I found a theory that agrees with the Time Stream, and Big Bang-Big Crash theories. First:

Schreckenberger’s Law:

For every jump through time there is an equal action in the future and an opposite action/reaction sequence in the past. For example, take a quarter. If you go to the future, you’ll find the same quarter from the time you came from (present), and you’ll have the same one you brought to the future. The present will have become the past, causing the coin to disappear from the past to the time in which you are.

If you go to the past, the future from the present remains unchanged, but the past to the present (now future) is effected by the coin’s presence (action sequence).

What is the different between action and reaction sequence: An action sequence is when you add, a reaction is when you subtract or repel.

This is a sum up of 5 years of research on the subject of time travel. I give credit to Einstein and Isaac Asimov for basing my theory. Within the next 30 years I hope to build this portal through time. It may come sooner than you think.

The equation
Y±((M/)+M+U)+U)K)=T also has a discriminant. This is called the Timimetric Discriminant Factor.

It is: ((>M/K)+((-M*9.8+U)+U)K) Suppose M=150, K=5, and U=750; the result is about 169. The number that results would be labeled X cliks or in this case 169 cliks. Cliks are the yearly terms used to measure the time stream velocity of the jump. If the Timimetric Discriminant Factor is positive the jump is possible, if it is negative the jump is impossible, and if it is zero, it is still considered possible, but calculations have to be exact. This rule will be called the Timimetric Property. (The short form of clik is Clx)
 


THESIS:

In the first year of study I used various resources to study Einstein’s famous Relativity. E=MC2 means that the energy output equals the objects mass multiplied by the speed of light squared.

 

This played an important role in my first equation: ((2pk)+(2.44e12*k)+(c^2k))k; of course, this equation soon evolved after I studied Asimov’s 2p Theory. This is (2M/K)/2. This soon changed 2pk to M/K These two scientists’ theories were the foundations for my research. Newton, as well, contributed. His Law of Motion: For every action there is an equal and opposite reaction set the standard for Schreckenberger’s Law: Equal Action in the future, opposite action/reaction sequence in the past. It took me into my third year to come up with the PFP Effect, a rare, and almost unbelievable statement that says our actions are predestined. Even if we came to a decision that involved several choices, those choices are previously mapped out by time itself. The only way you can find this theory to be true is if you step outside from the ‘normal’ boundaries.

The fourth year of my research was definitely focused around one thing, mathematical equations. In the last few months my equation jumped from something like completing the square to the Quadratic Formula. A new effect that I termed, the Grandma Effect is something to be considered. If I were to go back into time and marry your dad’s mom, before his dad did, then theoretically speaking your dad wouldn’t exist and neither would you. Everyone would forget your existence. The choices you made would be eliminated and the time stream would once again give people a destined path.

Jumping into past is more dangerous than jumping into the future. If you go to the past then you can mess a lot of people up. That, however, hasn’t happened because we have no recollection of it. So, until someone warps our memory in the past, we can continue to live on the destined track.

My last theory to be discovered is the FPF Effect: It is sort of like the PFP, except it means that someone from the future altered the past, the time stream compensated by altering everything from that point on. We’d have no idea of this change, because we’d believe the change was already in existence. Then another time traveler finds the mistake of the altering of the past and fixes it, setting the present and the future in its previous track. In other words something in the future alters the past and future, but then it is reversed. Now if the PFP Effect is true, we’ll believe that time was still predestined through all of this chaos because we will be unaware of the changes made.

Out of all of this I find Schreckenberger’s Law and the Grandma Effect to be true PFP and FPF work together, however, I wouldn’t count on a young person understanding what that means. The reason why any alterations made in the past won’t disprove the PFP is because to us the changes made would be the way life was for hundreds or even thousands of years. I shall continue my research and someday I hope to visit many historical areas. The question is not where but when.

Here’s is the first section of my Timimetric Periodic Table. Mass is in kilograms and Speed is measured in Km/h. There are many more velocities that are listed in the full version, but it is 3 pages so I transferred it to a spread sheet. Remember cliks are the units used to measure the yearly velocity of a time stream jump.

I’d like to offer you, the reader, a proposition. Study these theories, try to confirm or disprove them. Email me at USX1@juno.com  with questions or comments. Even if these theories don’t work, a failure still advances science. Thanks, and have a nice day.

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Spacelike versus Timelike

Information theory has a general rule:

Whenever you take a finite bandwidth channel and poke it into an infinite bandwidth channel, you’ll get either aliasing or interference depending on whether you look at the communicated information in a space-like or a time-like manner.

If you look at the information in a space-like manner, you will have to accept the notion of non-locality (and aliasing). If you look at the information in a time-like manner, you will have to accept the notion of wavefunctions and wavefunction collapse (and interference).

Aliasing or interference are manifested under non-locality or wavefunction collapse, respectively. The general notion underlying these phenomena is an overlap of states or non-orthogonality.

It is no wonder then that when we take a space-time-like view of the information that we run into trouble integrating QM with Relativity since in this case we should observe both, something like aliasing and something like interference, together.

This is the next conceptual hurdle. How do we represent this ?
 

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Source of Excess energy

by Alexander V Frolov
St. Petersburg, Russia


Abstract


The author offers for discussion an explanation for the excess energy in cold fusion, an explanation which incorporates the concept of negative time. The mathematical basis relies on the work of Dr. N. Kozyrev (Russia), Dr. Nassikas (Greece), and Thomas Bearden (USA).
 


Introduction


"The Hypothesis and The Equations of The Unified Matter Field" by Dr. A. A. Nassikas [1], is a rare instance of scientific and mathematical publication devoted to fundamental questions that leads to a practical approach to space-time engineering. In some sense it is a new solution for the development of free energy and gravitation technologies. Dr. H. E. Puthoff provided an overview of the topic based on the Casimir-effect [2]. This was quite interesting, but the author’s conclusion was "only in principle, yes," but the engineering (practical applications) is "a long way off." Also that the "warp drive" idea in the papers (1994-1997) of Dr. Miguel Alcubierre, Max-Planck-Institute for Gravitationsphysik, Albert-Einstein-Institute, Germany, is a fine idea, but it does not provide any technological solution. The only author who proposed practical approaches to vacuum engineering is Thomas E. Bearden. Let’s see what analogies there may be between Nassikas’ work and the "Gravitobiology" by T. E. Bearden to indicate the shortest practical way toward the technologies of the future.
 


The
Engine of Space-Time


The vacuum or ’space-time medium" of T. E. Bearden is described as cells of so called "gravitons." Those are "the coupled photon/anti-photon pair." Note, that it is a paired process. To make it more clean physically, we have to introduce the negative time axis for the "anti-photon-" So, the notion for the "virtual particles" that is used in many papers as the unlimited sea of free energy can be physically introduced only with the notion of "negative time," and we must take into account the "surface of time" or the "area of possible time directions." In this chronal area, the pair of photon/anti-photon seems to be a balanced situation of two processes that don’t require any energy input, but it is a situation that produces both photon and anti-photon forms of energy. In other words, it is the "energy creation mechanics" itself. The law of energy conservation seems to be the law for a "direct time" and "reversed time" balanced situation only. Certainly in our reality it is possible to detect by means of some measurements only half of the process, i.e. the positive time process of the photon energy.

According to the hypothesis of Dr. A. A, Nassikas, there is no space-time without energy since "The existence or the non-existence of energy implies the existence or the non-existence of space-time, and consequently of any geometry." On this point his concept is closely connected with Bearden’s "vacuum engine." Next point: by Nassikas, the energy of positive or negative electrical charge of the particle, i.e.. its potential field energy can be presented as "equivalent to its internal time." So, the sign of the charge can be defined by the "time axis direction" and the process of the electron is some opposition to the process of the positron. Bearden’s photon/anti-photon pair is a similarly balanced situation. Note, the mass particle here is considered as some dynamical process [3], that is corresponding to some four-dimensional resonance condition, demonstrated in calculations for the DNA-molecule and for other natural material elements.

A practical solution was proposed by Thomas Bearden to create "the local rate of flow of time" that is "determined by the "local time-stress of vacuum potential" is to apply some non-linear materials for translation of energy between different frequencies and harmonics of electromagnetic waves. Normally, i.e. in the ordinary time-flow situation, the non-linear material produce the harmonics from a fundamental wave. But Bearden says that "in a true time-reversed situation, non-linear materials can exhibit the production of a stronger fundamental from a combination of the fundamental and its harmonics." The principle that is designated by Bearden as "Stokes’ principle of time reversibility" (G.G.Stokes (Camb. DubI, Math. J. 4. 1849, p.l) is interesting, but we have to discuss something beyond this that is connected with the potential form of energy, i.e. with Bearden’s "stress of vacuum."

Dr. A. A. Nassikas and Dr. Miguel Alcubierre independently proposed to use the difference in local rate of the time flow as the source for a propulsion force. According to Nassikas, if "the space under the object attracts the object" more or less than the upper one in strength of the different relative times around the object, gravitational Propulsion can be achieved. So, all we need to take the next step from theory to technology is to find a way to change the rate of time. Is it too difficult? No, it is quite simple if we take into account some points:

a) The notion "time" in any case is connected with some certain material system, for example, with some elementary particle or with some planetary system. The different velocity of light in different materials is a demonstration of this connection.
b) The "space" of some curvature (of some rate of time) is a bi-directional or many-directional energy process. Electricity is one of many possible balanced situations that is described as a bi-directional or two-polarity case. For many-polarity energetic situations there is the possibility of three or more time-flow directions.
c) There is no difference in principle between an atom and the space around that atom, according to Faraday [4]. So, the balanced chronal situation of the vacuum engine corresponds to some real properties of matter and we can work with matter to reach the changes in the balance of the vacuum engine in the area of this material
object.

The vacuum is the medium of some known physical properties, for example, the dielectrical permittivity. Physically, it is connected with the velocity of spreading of the photon, and since we can work with different materials of known properties, it means we have the possibility of changing the parameters of the vacuum engine itself. One quite old example of a practical application is USA Patent number 3,187,206, granted in 1959 to Thomas T. Brown. The gradient of dielectrical permittivity is proposed and experimentally proved as the source of reactionless force. It is necessary to note that the same reactionless force is created at the border between two different dielectrical materials of the electrical capacitor, as it is described in many textbooks on the properties of dielectrical materials. The problem of taking the next step to fundamental conclusions is understanding the physical connection between the permittivity of a material, the velocity of light in the material, and the local rate of time for this area of space.

The patents by Thomas T. Brown include also asymmetrical interaction between electrodes. i.e, the topology of the electrical field. Let’s note the analogy between Nassikas’ idea above on "energy and geometry of space" and the invention by Brown of reactionless propulsion. The gradient of the electrical potential that is created in the natural way with distance from the electrically charged particle is a demonstration of the natural topology of space, i.e. the electrical field is created according to the law of creation of space itself. It is the reason for the analogy between the formulation for electrical and gravitational interaction. We have the possibility of changing the topology of the electrical field, for example by means of the asymmetrical dielectrical member in the capacitor of Brown. So we have the possibility of compensating the natural gradient created by the properties of space. It is the way to space-time engineering.

So, the conception by Dr. Nassikas and idea of Dr. Alcubierre are a fine theoretical basis for the technology that was discovered and proved in practice by Thomas T. Brown. Modern industry, specialized in dielectrical materials, is ready now for cheap mass production of warp drive systems. The same technology may be the basis for self rotating generators. The way is short and all we need is the commercial demand and engineering formulation of a step-by-step program.

The concept of negative time by Dr. Nassikas can be useful also in understanding the over-unity effect that is demonstrated in some cold fusion cells. The well-known Pons-Fleischmann experimental set-up includes a cathode that is over-saturated by protons when the set-up is operating. So, the local concentration of positively charged protons can be considered as a local imbalance in vacuum engine and the local rate of time in this area is different from the normal one. The processes are produced by this local change of the curvature of space are multilevel complex energy exchange, but the source of over-unity is the local concentration of positive electrically charged protons that is due to the lnput power source. Let’s consider this point more carefully.

Any electrically charged particle can be presented as some volume of space i.e. the gravitational space by Nassikas, G-space of energy Eg, that is joined with some imaginary electromagnetic space of energy Eem. Conservation of energy is presented as:

dEem + dEg =O F.1

In my view, it is useful to change equation El to the form:

dEem = - dEg E2

In this case it is obviously that mathematically the space of Eem has an "imaginary" value, since the energy and the velocity are connected by the quadratic root of the negative number.


The over-unity output in cold fusion systems means the production of the excess heat energy. Certainly, some cold fusion systems demonstrate power output as the result of nuclear transmutation processes. But if we are considering the water to be distilled H2O in which fusion does not occur, I have to suppose only one way for excess heat production:

dEem >O if dEg<O E3.

I must note that the idea is not a new one since the famous Russian astrophysicist N.A. Kozyrev created in 1947-1980 the "conception for active properties of the time." There is some natural physical mechanism for production of heat energy that is demonstrated by any star and it is not the thermonuclear reaction but the transformation of energy by the mechanism of Kozyrev. In that concept, the kind of energy that is used by the star for heat energy production is the "time flow." On the other hand, we can take into consideration the gravitational description of space instead of its chronal description, and the production of the heat is the transformation of Eg that we noted above.

N.Kozyrev analyzed the wide experimental astrophysical data to find the answer for the question of the common "special condition of matter" inside any star to provide the transformation of energy Eg into energy Eem. His conclusion [5] is quite simple:

B/n = 6 eV F.4

where "B" is the density of the beam energy of the star and "n" is the density of electrons in the volume of space.

We certainly cannot create the conditions of stellar matter in the laboratory, but for a Pd-cathode in a cold fusion cell, the situation is quite similar to Kozyrev’s equation F.4 and heat production can be detected as result of F.3. The difference is the application of protons instead of electrons. To calculate this we have to use the volume density of protons H+ in the material of the cathode instead of the volumetrical density of electrons "n" in star matter.


References

1.   "The Hypothesis and The Equations of The Unified Matter Field" by Dr A.A.Nassikas, Infinite Energy, March-June 1997, p. 120-124
2.   "Can the vacuum be engineered for space flight applications? Overview of theory and experiments," Dr. H.E. Puthoff. Infinite Energy, July-November, 1997.
3.   "The Concept of Mass Process," Alexander V. Frolov, Proceedings of International Scientific Conference "New Ideas in Natural Sciences," June 1996, St. Petersburg,
Russia, Published by "Pik" Ltd.. 1996.
4.   Letter from M. Faraday to R.Teilor of June 25, 1844, published in Journal of Russian Physical Thought, N2, 1991, p. 81.
5.   N.A. Kozyrev, Selected works, published by Leningrad State University, 1991, p.202, in Russian.

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Closed Timelike Curve (CTC) Construct Scale Model prototype
by Thomas G Skeggs

The main aim of this CTC Construct, scale model prototype is to test a hypothetical design (I discovered by accident), for a device or construct to generate closed timelike curves. The CTC Construct is a scale model prototype for a full-sized manned prototype, known as the Flight Test Article (FTA): Defiance. The FTA: Defiance is an 12ft by 12ft by 6ft, prototype Vertical Take-Off and Landing (VTOL) aerosplace vehicle, which has taken nearly six years to design. The design for the CTC Construct and FTA Defiance, was largely inspired by the work carried by Thomas Townsend Brown and Nikola Tesla. I have combined their work with quantum theory and the principles of electrostatics and tribo-electrification, to product a vehicle, unlike any other, (See figure one).

figure 1
 

I originally planned to begin construction on the FTA in the summer of 2001. But this date maybe put back until the winter of 2001, due to numerous construction problems.

It would be almost impossible for anyone to build a time machine, as it would require an extremely powerful energy source to drive it. But there maybe a more energy efficient way to travel through time, by building a device or construct to use a natural time machine like a quantum or astrological phenomenon, in the form of a worm hole or quantum singularity.

The CTC Construct model consists of two triangular shaped pyramids one placed on top of the other, with a smaller pyramid placed on top to create an apex above the model’s centre of gravity. (see figure 2). The model is 2ft by 2ft by 1ft. The frame is made out of balsa wood, and has 3 coats of polyurethane varnish, plus 3 coats of high temperature heat resistant paint to protect the balsa wood frame from igniting.

figure 2
 

The CTC Construct has a specially designed skin, which acts like a capacitor and it is capable of holding a strong electrostatic charge. The skin consists of a metallic-dielectric sandwich. The inner layer is charged positive and the outer layer charged negative, with the dielectric sandwiched between the two metallic layers. The inner and outer layers consists of several coats of nickel electroconductive paint which has a surface resistivity of 0.7 ohms per sq cm. The dielectric layer consists of polyurethane varnish, with a dielectric constant (k) of 2.5-2.6.

The skin’s unique configuration maybe able to overcome the average weak energy condition, to produce tiny amounts of exotic matter, enough to create a same and observable antigravitic effect. The design for this skin configuration is based on the Casimir effect. And on the work carried out by Thomas Townsend Brown.

I have been working on a hypothesis that if you build a construct with a high electrically charged skin, then the space-time within the CTC Construct will move at a slower speed, than the space-time surrounding it. This hypothesis is explained in a paper I have written called the Tempus Codex. ( This paper is still being written and will be ready at the end of December, or the beginning of January 2001, I have also recently discovered on the Time Travel website, that a Russian scientist, Vadim Chernobrov from the Moscow’s Aviation Institute, has also been conducting tests on a model similar to my design. Mr Chernobrov also believes that a device with an electromagnetic skin can create an time dilation to occur within the device).

The skin is energized by the model’s Main Propulsion System (MPS). The MPS works in unison with the electroconductive skin, and uses the principle of tribo-electrification. This is where friction can generate and electrical charge. The MPS uses a oxygen and/or hydrogen gas mixture, ionised in a small chamber and is blown upwards through a pipe, where ions hit the inner surface of the electroconductive skin. (The MPS uses a 15Kv transformer to ionise the gas mixture). This results in an very high electrostatic charge building up on the electroconductive skin, due to the friction from the flow of millions of ions. Not only does this MPS/electroconductive skin configuration produce a high electrostatic charge. This configuration may also produce thrust. When the ions strike the inner surface of the skin, they produce kinetic energy. This kinetic energy is focused downwards by the pyramid shape, and the kinetic energy radiates along the skin’s surface travelling downwards resulting in a small thrust.

The MPS is positioned inside the CTC Construct, at the centre of gravity. A pipe connects the MPS to the inside of the hollow apex, located in the top of the construct. Located around the apex are 3-1.5mm holes, where ionised gas is allowed to escape. This ionised gas reacts with the surrounding air molecules and gives them an electrical charge. The air molecules are then repelled by the electroconductive skin, and this results in a boundary layer to form around the CTC Construct. This process results in a reduction in drag. This process is known as, "plasma magic", (See New Scientist Magazine. 28th Oct2000).

Due to the small size of the model, not all the necessary systems can fit inside it. So a special jig has been made for the model to sit on during testing. In the centre of the jig, is a small plastic pipe with three inlet pipes. Hydrogen and oxygen gas is produced by a home-made electrolysis cell. The hydrogen/oxygen mixture is blown into the MPS, by using a 12 volt air pump.

Inside the top pyramid forms a hollow apex. Inside the hollow apex are 3 small plastic pipe connectors. These connectors are joined by silicone tubes to the Reaction Control & Stabiliser System (RCSS). Ionised gas from the hollow apex is forced down the silicone tubes by pressure within the apex, into the RCSS. The RCSS consists of 3 round pipe sections, fixed to 3 thrust chambers to create an RCSS assembly. Each RCSS assembly are placed in a triangular pattern with the CTC construct and are located at each tip of the model. Ionised gas is forced under pressure into the round pipe sections, where the gas mixture is given an additional high voltage charge. The ionised gas are accelerated out of the RCSS assemblies to produce thrust. Each RCSS assembly will be powered by a 5Kv Cockcroft-Walton multiplier.

The CTC Construct is simple in design, but complex to manufacture. The CTC Construct, Scale Model Prototype has taken 4 months to build so far. And it may require another month of work before it is ready for testing. Due to a small risk of fire caused by the mixing of hydrogen with oxygen. Numerous safety features, equipment and procedures are being added, and this may delay testing until early next year.

The CTC Construct consists of the following unique design features:

  • The CTC construct has a unique double triangular pyramid shaped aerospace frame.

  • The CTC skin’s configuration maybe able to overcome the average weak energy condition, to produce tiny amounts of exotic matter, enough to create an antigravitic effect. The design for this skin configuration is based on the Casimir effect. And on the work carried out by Thomas Townsend Brown.

  • The CTC Construct skin configuration maybe able to overcome the average weak energy condition. The space-time within the CTC Construct will move at a slower speed, than the space-time surrounding it.

  • The CTC may generate an antigravitic effect, plus drag reduction. This means small ion motors can be used for directional control. Resulting in a massive saving in weight and mass by not having to install large and heavy standard aircraft engines or rocket motors.

  • The Main Propulsion System/skin configuration uses tribo-electrification, to generate a very high electrostatic charge.

  • This MPS/skin configuration acts just like a Van de Graaff generator.

  • The CTC construct has a unique propellantless fuel system. It uses atomspheric air as a propellent when in the earth’s atmosphere and hydrogen when in space. Hydrogen is also used during take-off to generate more thrust.

  • The FTA will have a unique water-based propellant. Water is converted into hydrogen and oxygen, the hydrogen is used as fuel for the ion/plasma generator, and on the full size prototype the oxygen is used to maintain life support.

  • The water-based fuel system does away with large and bulky cryogenic fuel tanks resulting in a greater payload capability and large savings in weight.

  • The CTC construct has a drag reduction skin to reduce friction and wave drag, in a process known as, "Plasma Magic".

  • Due to the lack of ailerons, rudders, and flaps this offers a considerable savings in weight and can dramatically reduce drag.

  • The unique shape of the CTC construct, makes it ideal for taking off and landing vertically.

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Views of Time Travel

by Amitabh P. Tamhane
 


INTRODUCTION

TIME....it has always fascinated the whole world throughout ages. If we think of time as a phenomenon and consider that it always happens then well we are thinking short. We are not looking at the wonders that will happen if we are able to control time. A century or two ago no-one would have imagined that we could defeat Nature anytime but as we all are witness to the technological developments and also the medicines that are being developed have virtually dominated Nature. Here we should be wise enough to know that we are not trying to stop the functioning of Nature, but we are trying to configure the Nature for its optimal use. In the same way, just like Nature if we are able to control Time then it would be just like mending Time for its optimal use. Here we should note that we are in no position to stop Time from working, but we can definitely control Time. Time is relative...and all the terms of Time-Travel are w.r.t. you and the rest of the universe.

Albert Einstein has proved mathematically that speed of light is fundamental. His theory of relativity is partly based on the basic assumption that the only term that is constant throughout the universe is the speed of Light.
And everything including time is relative and not constant. So, he said Time-Travel is quite possible.

He also proved these two formulae :

     

where,

M    = mass of body moving at ’V’ speed.
T     = time for the person moving at ’V’ Velocity.
t, m = time and mass of stationary body.

So, it is quite obvious from the above two formulae that as the speed at which any object is traveling increases its mass also increases and for that body the time slows down. Then what happens when V = C, well when V=C then denominator become zero and Time becomes infinite. The physical conclusion that can be derived is that at the speed of light the time-loops come to a Halt. And so at speed of light we can Time-Travel.
You will understand this better after reading this example:

Imagine yourself traveling at half the speed of light. So, according to the formula of time given above ...the denominator of the above equation changes and so value of time at ’V’ speed increases than the value of time at zero speed. Well, what do I mean by "value" of time.


Value of time means the amount of time. So, when you are traveling at half the speed of light for you, your clock shows correctly ...ie.60sec=1min. But, that one minute of yours may be one or more than one hour for the person who is at zero speed. Well, it means you have traveled through "Time".
 


MY VIEWS

Well, as we know the formulae proved by Einstein it is obvious that the Time loops come to a halt and we can travel through Time if we are traveling at speed of light. But our body’s mass also reaches to infinity at that high speed.

Here the RED ring like structure is time and the rod shown is our world and the Time is moving continuously (neglect the window).

It can be imagined that the time as an infinite cycle of collection of events and these events are PAST, PRESENT & FUTURE. Which events are Past, Present & Future are relative to a particular person and the when this frame of reference changes we can say that we that person has traveled through Time. These events are occurring in cyclic order which can be imagined with the help of figure shown above. And these cycles are moving at particular speed and this speed is equal to the speed of light. When we travel at the speed of light then with respect to these Time-loops, we come to a halt [relative to those red Time rings] and now at speed of light we are free to travel through the Time or through the collection of events. When at speed of light we can surely travel through various events. BUT...nothing would be happening at that time for everything moves with Time and now Time itself has stopped. So, the events would stop happening and it would be a stage where all objects will be in stand-still position!


And when we travel at speed more than that of light we can travel towards past. The cylinder shown above is only for one Dimension and such cylinder are present for various other Dimensions and so we can say there exist more than one universe. This is the basis of the theory of Parallel universe.

Now the question remains is that "What is present between those Cylindrical Time-Dimensions?"
And "What if we (by some means) are able to make ourselves free from the Time-Loop?"


Well, there is nothing present between these Time-Dimensions. And if we are able to make ourselves free from these Time-Loops then we can travel not-only through our Past, Present & Future but also through various other Dimensions. And that would be the beginning of the phase in which we actually be aliens in “Other World”!

But, it is practically impossible for anyone to travel at the speed of light. So, we can definitely draw an obvious conclusion that for traveling through Time or in other words to travel at the speed of light, there should be some kind of process through which we can convert our material body into energy (electromagnetic waves) so that these waves can travel through time.

 

And the reverse process would bring back the person who would have traveled through time. Also, we know that every living organism has its peculiar DNA and that the DNA structure is having its own unique pattern of genes. Now, we know that any two material particles are having some potential difference between them. So, every two genes would be having some potential difference whose value is unique for those two genes. So, a unique pattern of voltages (of very small value) can be developed for each living animal. And when we convert those potential differences into a band of electromagnetic waves.....with the frequencies of each wave corresponds to the particular voltage ...so we can generate a unique pattern (band) of electromagnetic waves which will be unique to each living animal. And these waves can be sent through Time. And replica of Electromagnetic waves pattern can be generated.


So, we can send a person (wave pattern) through Time and that person can exist simultaneously at different places.

This particular way of possibility is solely my idea....and I accept there may be some flaws with this theory but I know this is one of the ways in which a particular living organism’s replica can be sent through Time barrier. I would love to receive feed back from you people on this.

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Tempus Codex
Conjectured Solutions to creating Closed Timelike Curves

by Thomas G Skeggs
 


Introduction


It would be almost impossible for anyone to build or construct a time machine. Dr Michio Kaku, professor of theoretical physics at City University of New York, believes time travel could be achieved, but the energy required would far exceed any energy source on earth. The technology would have to be advanced and powerful enough to manipulate energies on the scale of a star. (1)

So any realistic time travelling design would use a quantum or astrological phenomenon like worm holes or quantum singularities, which would act like natural time machines. For anyone to design a device capable of creating closed timelike curves, (time travel into the past) would need to design and build a practical device which is capable of holding worm holes open long enough, so a device can safely pass through it. The device would be like making a key to fit a lock, or cryptanalysis trying to crack an unbreakable code. This is why I have called this short paper the ’Tempus Codex’.
 


Exotic Material & the Casimir Effect

Contrary to popular believe, exotic material is not a copy of Playboy magazine!. It is a cunning way to hold open a worm hole and this idea was dreamt up by Physicist Kip Thorne and his colleagues at the California Institute of Technology. Thorne was approached by astronomer and writer Carl Sagan, who was writing a novel called "Contact", about a extra-terrestrial species sending the human race a message. (2)

Thorne came up with an idea of using a Schwarzchild wormhole, which exist naturally in the universe, but are extremely small. Even to small for particles to travel through. Schwarzchild wormholes also have a very brief lifespan, opening and closing before anything can enter the worm hole. But Thorne came up with a ingenious way of opening a Schwarzchild wormhole, and he decided to use a form of anti gravity, produced by a substance called exotic material to line the worm hole, and hold it open so someone can pass through a worm hole safely. But can enough exotic material be produced to hold open a worm hole?. (3)

This maybe possible. Dutch Physicist, Hendrik Casimir, carried out some experiments in the 1950s and it later became known as the "Casimir Effect". (4) The Casimir experiment involved placing two metal plates a few millionths of a metre apart, within a vacuum. An electrical charge was then applied to the two plates. The two plates were then pulled together, due to the presence of ’exotic material’ . This strange effect occurs due to the nature of space being made up of vacuum fluctuations, where pairs of matter and anti-matter particles continuously appear and disappear to create a boiling sea of virtual particles. Outside these two plates, particles which move in a wave like motion are allowed to exist in larger numbers, but between these plates, there are fewer vaccum fluctuations and only certain wave particles are aloud to exist, as many particles or waves are just to large to fit within the space between the plates. (5)

So this means there are less particles or waves bouncing around between the plates, than outside them. And so the pressure between the plates is lower than outside. Remembering that the plates are in a vacuum, this means what lies between the plates must have less than zero energy, or has negative energy. This is known as the negative energy density and repels mass instead of attracting it. The main disadvantage with creating exotic material by using the Casimir effect is it would require a great deal of energy.

Under certain conditions, particles may interact with vacuum fluctuations to create exotic material in free space. These certain conditions could be explained by a theory originally designed to explain the evaporation of black holes. (A black hole is created when a star collapses into a singularity, where the density and curvature of space time are infinite). One clue to achieving time travel, may lie within black holes.
 


Black Holes & Relativity

The world famous Cosmologist Stephen Hawking, Lucasian Professor of Mathematics at Cambridge University developed a theory explaining why black holes have entropy and emit radiation. Over several years Stephen Hawking discovered that virtual particles that make up vacuum fluctuations are broken apart by the intense gravitational field presence at the surface of the black hole, known as event horizon. Particles with a negative charge are pulled into the black hole and creates a negative energy density. And the particles with a positive charge are emitted. This emission of virtual particles from black holes has become known as Hawking Radiation. (6) So not only black holes consume the mass of a collapsing star. Black holes destroy the very fabric of space itself, by pulling apart the vacuum fluctuations.

But how can this process be replicated, and the energy needed to produce large worm holes or black holes for a machine would require a very powerful energy source. Not only that it would extremely dangerous, and science has ruled out using black holes as a safe means of transport of travelling through space or time. But instead of producing black holes or trying to hold open a very large worm holes with exotic material, there maybe a more energy efficient way of achieving the same effects without creating black holes, or having to produce enormous amounts of exotic matter.

What’s needed is way to reproduce the effects of a black hole, without having to create one. Another clue to producing a practical time travel may lie within Einstein’s theory of general relativity. l came across some basic descriptions of the Einstein effect. Which stated that the presence of mass can bend space time. The Einstein effect describes how a rotating planetary bodies like our planet or star can drag space time around with it, creating a lensing effect. The mass of an object bends spacetime. Gravity being curved space.
 


Gravity

The key to success in producing a practical method of time travel, may lie within quantum gravity. But the drawback with quantum gravity, is that scientific descriptions of quantum gravity are plagued with infinities. So to fill this void of uncertainty regarding the true nature and function of quantum gravity, I had to improvise, and use Einstein’s theory of relativity as a starting point.

I decided to use electrons in my design, as they are lightless of mass particles and easy to accelerate. If an electron is accelerated towards velocities reaching 99% of the speed of light, the mass of the electron will increase dramatically and the electron will also shrink in size. An electron moving at 99% of the speed of light has 7 times as much mass as when it is at rest (7), and the mass of an electron moving at 99.99% of the speed of light will increase by 70 times its rest mass. (8)

So if an electron were accelerated to

0.9999999999999999999999999999999999999999999999999999999999999999999999

the speed of light, the electron would hit you with the impact of a Mack truck traveling at 60 miles per hour. (9)

General Relativity explains why this happens. The mass of a moving object depends on its speed v. And can be explained with the equation:

m=ym0

y is the Lorentz factor equal to 1/H(1-v2/c2). c is the speed of light. m0 is the rest mass as measured by an observer who is at rest relative to the object. So the energy of an object E, and its mass are related by the equation. E=mc2. (10)

The increase in mass with speed can be calculated with the equation:

m=m0/H(1-v2/c2) (11)

So the mass of an object increases with its speed y in accordance with the equation m=y m0. (12)

So when an electron is accelerated towards the speed of light, its mass will increase and the electron will also shrink in volume. This is known as the Lorentz factor and can be worked out using the equation:

1/H(1-v2/c2)

If you could accelerate the Statue of Liberty to 0.999 times the speed of light. The statue which stands 151 feet tall would appear to shrink down to 6.8 ft. (13)

Also when you accelerate an electron, the gravitational mass increases. This increase in gravitational mass of the electron will cause the spacetime surrounding the electron to curve more. Just like in Einstein’s theory of relativity, which predicted the Einstein or lensing effects. Which states gravity is curved space, caused by the presence of mass.

This gravitational distortion which curves spacetime around the electron maybe explained with the equation:

R=2hM/c2

M is mass. h is Planck’s constant and c is the speed of light. (See Note One)

This gravitational distortion produced by high velocity electrons would generate a gravitational time dilation effect. And like in the Casimir experiment where you have two metal plates and you apply an very high voltage to the plates. Electrons would flow at velocities approaching the speed of light and create a small gravitational effect. And with the plates being a few millionths of a meter apart, this would create a negative energy density, due to the low number of vacuum fluctuations between the plates. This results in gravitational field which is repulsive instead of being attractive.

So if we used a 3-dimensional shape such as a hollow cube or sphere, where the walls of the object was made of a pair of metal plates, then the spacetime within this hollow centre would become more probabilistic, due to an increase in entropy.
 


Through the Looking Glass

Actually making the space within the construct more probabilistic is the key to successful time travel. The answer exists in the complex nature of the vacuum fluctuations, which can exist in a superposition of quantum states. This condition allows for particles both mass and virtual to exist simultaneously in any number of quantum states.

One basic example to explain the super position of quantum states is that all particles can act as particles or as waveforms. But the super position of quantum states means that they can exist as a mixture of the two states. The particles exist as probabilities. When particles are observed this causes the super position of quantum states to collapse into a single state. So in most situations the observed particles act as either as a particle or as wave, or under certain conditions a combination of the two states!.

The complex and mind boggling nature of the super position of quantum states, puzzled Hugh Everett at Princeton University to develop a theory known as the "Many Worlds Interpretation". Everett was puzzled by the collapse of the wave function when a observation is made. So he decided it made sense to treat each outcome of every possible quantum event as existing in a real world. (14) This means if a particle was observed to act as a particle in one world, the same particle would act as a wave function in another. So this means there are a infinite number of probabilities that exist as alternative realities and covers all possible eventualities, past, present and future.

In an article featured in the August 2000 edition of Scientific American. Three researchers have been working on the composition and function of the universe. And they believe the universe may consist of a membrane folded up into a cylinder. And other parallel universes may also exist as membranes or D-branes, folded up into this cylinder, and are less than a millimeter apart. They have also formed the opinion that one of the few forces that can travel from one parallel universe to another, is gravity. (See Figure 1) (15)

Its important to point out here that some D-branes may have reversed symmetry, and this may result in particles in some other parallel D-branes to have reversed parity. This may mean that the dimensions within these D-branes could be upside down or back to front. Such reversed symmetry may also result in the emission of gravitinos. So if a graviton was fired into past, it would arrive in future in another parallel D-brane.

If their idea is correct then the double split experiment has more meaning. As the electrons are fired through the slits, they are travelling at very high speeds. And general relativity tells use when an electron is accelerated towards the speed of light, its mass will increase. As the mass of electron increases so does the gravitational mass increase. This increase in gravitational mass of the electron causes the emission of stronger gravitons which can penetrate into other parallel universes and effect the outcome of the double split experiment in another parallel universe. Or the electrons emitted in another parallel universe can emit gravitons or gravitinos which effect the outcome of the double slit experiment within our universe. Causing more interferance.
 


Constructing a Time Travel Device

To create a device to travel back in time, we require a device where it’s interior becomes more isolated from our universe, or to produce its own locality, and to achieve this requires a construct to have a skin that produces a powerful field which no light or radiation can penetrate with the exception of gravity. The construct may consist of a hollow sphere, or box. I have used the Casimir effect as a starting point to develop a double layed metallic skin for the model construct. The original skin design consisted of two metal skins, separated by very thin cavities. (See Figure 2).

This design loosely based on the Casimir experiment and also tries to mimics the configuration of a black hole, where the skins act as an artificial event horizon. Due to the interior space of the construct being cut-off from the surrounding universe, objects or events within construct can act in strange ways. The gravitons being emitted from the skin of the construct would make non-local connections with other particles making up the construct’s interior in other parallel worlds.

So this effects the probability of where the construct’s interior is within space and time, as the interior generates its own locality and connects to other parallel universes. The minimum result is a time dilation effect. A highly efficient, well engineered construct may have the ability to create Closed Timelike Curves and travel in the past. The 3 dimensions of space may become fuzzy, caused by the emission of gravitons effecting the 4th dimension of time.

The only way I can describe my design, is that its similar to the TARDIS, which appeared in the BBC TV Sci-fi series,"Dr Who". TARDIS is an acronym for Time And Relative Dimension In Space, where it’s interior has infinite size, greater than its exterior. The construct is similar. It’s not like a conventional vehicle. Its power source does not physically propel it through space and time. The negative energy density and quantum gravity present within its skin, breaks the connection by warping space and time with the exterior locality, so the interior can create its own time and generate non-local connections with other parallel universes, or moments in time. Its a crude and basic form of teleportation.

Russian scientist, Vadim Chernobrov from the Moscow’s Aviation Institute, has been working on a prototype design known as the Space Transportation System. Chernobrov’s prototype is based on the experimental work carried out by Professor N.A Kozyrev of also of the Moscow Aviation Institute, who carried out work in to the properties of time. Professor’s Kozyrev conclusion of his experimental work, is if you can create a device that changes the density of space, this will effect the rate or density of time. Causing time within the device to slow down or speed up. Chernobrov constructed a prototype made up of electromagnetic layers which fit inside each other like a Russian doll. The difference in time can be worked using the simple equation:

t/tE

tE is the standard Earth time and t is the local time within the device. (16)

Stephen Hawking’s Chronology Protection Conjecture, provides a major problem in any design for a device capable of time travel. As his conjecture claims that any device would be destroyed by the vacuum fluctuations, where warped space-time would turn the virtual particles into almost real mass particles, increasing the density of the virtual particles, and reducing the probabilities of other histories existing in the device. But it maybe these vacuum fluctuations which provide the extra energy to time travel. As an increase in density within the skin of the device would also cause an increase in the entropy within the interior of the device. So the number of probabilities would be low in the skin, but would be high in the interior of the device.
 


Into the Abyss: Travelling back in time

It’s claimed that its impossible to travel to a time earlier than the worm hole first became a time machine. So if a worm hole was created in August 2001, you could not travel back in time to June 2001. The laws of general relativity are unequivocal. (17) But with a better understanding of the universe, being made up of parallel universes (D-branes) there maybe a way to bend the laws of physics slightly, and thus allowing someone to travel safely back into the past.

For example, if you want to travel back in time to Roswell, New Mexico in July 1947, to investigate the alleged UFO crash that occur there. As the time traveller enters the device, they start to imagine being in Roswell, New Mexico in 1947. As the time traveller thinks of this, a connection has already formed in Roswell, New Mexico in 1947, and connects up to the one the time traveller is about to enter. Its important to point out here, when such connections form, the laws of general relativity and causality begin to breakdown within it. The laws of physics suggest that the connection in our present (2001 AD) was created first, but due to the bizarre twist in the nature of time, its means the other connection in 1947 was opened first, some 54 years ago.

Some may claim, from an observer point of view in 2001AD, this is a violation in casualty, but the connection in 1947 is some 54 years old and it has been expanding into hyperspace ever since, until it meets up and connects to the one created in 2001AD.

So when the time traveller enters the device and its switched on, the time traveller will travel backwards in time. Thus generating a time-like curve. It will be the thoughts of the time traveller that connect up the two time periods of 1947 and 2001.

But what about observers from 1947 onwards to 2001?. Would they see the connection forming. The answer is no, as the connection in 1947 onwards would be invisible to the naked eye. So no observers would report seeing it. The only time an observer may see the connection is during a process I have nick-named called, "Convergence". This is when two points of the connection link up to create a non-local connection between two different time periods, so the time traveller can travel back and forth in time.

There are two major drawbacks with this technique. The first is the connection maybe non-transverable. As the time traveller would require the device to travel from the past into the future and appear back in the year 2001. Only what's in the interior of the device travels through time. The device will remain stationary and fixed to its own universe.

The second drawback is some may claim it would be impossible for a time traveller to simply wish themselves into another time period, using the construct. But it could be possible. As the interior will become sensitive to conscious thoughts. If nothing can penetrate the skin of the construct, such as light, sound and electromagnetic radiation. Then nothing can escape out into the surrounding local spacetime. Not even the conscious thoughts of the time traveller. The thoughts of the traveller would exist in the construct as probabilities and would simply be focused elsewhere, in this case, July 1947, Roswell, New Mexico.

But there will be limits, and according to quantum physicist, David Deutch from Oxford University. Time travellers could find themselves in any number of alternate realities or alternate histories. Time travellers could find themselves in a reality where the Nazis won the Second World War, or in a alternate reality where Elvis lives on. But probability rules over imagination. So time travellers will not encounter realities where pigs can fly, or discover real vampires biting the necks of lusty young virgins.

Albert Einstein once stated that ,"Imagination is more important than knowledge". The hypothetical problems of time travel maybe solved one day by the verification of superstring or M-theory, but the technology needed to make time travel a reality will be developed, by using good old fashioned imagination, ingenuity and inventiveness.
 

For I dipt into the future, far as the eye could see,
saw the Vision of the world, and all the wonder that would be.

by Alfred Lord Tennyson
 

 

Note One

This equation is based on Schwarzchild’s radius, which is used to calculate the critical point when a curvature of space is so strong, no mass could escape its gravity and would be compressed down into a singularity. I have just changed the gravitational constant with Planck’s constant, as the gravitational constant was to large to measure the effect of the gravitational distortion created by a mass particle. This equation can also be used on any other mass particle.
 


Summary

Trying to explain how the construct works, has been difficult, so here is a summary on how it works:

  • The construct l have designed uses a process to generate a negative energy density within the walls of the device. This reduces the direct connection with the surrounding spacetime.

  • The interior of construct it produces it’s own local time.

  • The presence of a negative energy within the walls of the construct makes interior more probabilistic and sensitive to conscious thoughts.

  • Other past or future moments in time will exist as probabilities within the interior of the construct. Thinking of a past moment will cause that probability to become higher than the present time.

This paper is an edited version of the original as it takes me a great deal of effort to produce a paper on such a complex subject such as time travel, as I have no academic qualifications whatsoever. This would explain my poor spelling and grammar.

Recently I have made a grave mistake with the CTC Construct Scale Model Prototype. In a bid to keep costs to an absolute minimum, I tried to combine the ideas of the Tempus Codex into prototype aerospace vehicle l have been also developing. I now realize this idea was to ambitious. But I’m having to abandon all research on time travel until the Spring 2002, due to other commitments.
 


Further Information

  • The Fabric of Reality by David Deutsch. A good book which covers subjects such as time travel, quantum computing, virtual reality, alternate realities.
     

  • Black Holes and Time Warps: Einstein’s Outrageous Legacy by Kip S.Thorne. This book is classic, and anyone with an intrest in black holes, worm holes and time travel, should have a copy of this book.
     

  • Time: A Traveller’s Guide by Clifford A. Pickover. This is a book for anyone with an intrest in time travel. Includes detailed information for the novice time traveller, plus a few computer programs.
     

  • In Search of Schrodinger’s Cat: Quantum Phyics and Reality by John Gribbin. This book is a great introduction into the complex subject of quantum physics. This book also details the history of quantum physics, and the scientists who discovered it.
     

  • Timeline by Michael Crichton. This is a fictional book, but a great story. This book is about a team of archaeologists sent back into 14th century France. This book maybe made into a film one day.
     

  • Contact by Carl Sagan. This is also a fictional book and a film that explores the idea of recieving a message from an extra-terrestrial species. If you want to see a how a CTC Construct may work, then see this film.


Weblinks


Bibliography

01. The Physics of Star Trek. L.M.Krauss. Flamingo Books. 1997.
02. p. Q is For Quantum: Particle Physics From A to Z. John Gribbin. Phoenix. 1998.
03. About Time: Einstein’s Unfinished Revolution. Paul Davis.Penguin Books. 1995.
04. p. Q is For Quantum: Particle Physics From A to Z. John Gribbin. Phoenix. 1998.
05. Public Lectures: Space and Time Warps. S. W. Hawkin.
06. p.136. Introducing Stephen Hawking. J.P.McEvoy & O.Zarate. Icon Books. 1999.
07. p.273 Q is For Quantum: Particle Physics From A to Z. John Gribbin. Phoenix. 1998.
08. p.28. Einstein-A beginner’s Guide. J. Breithaupt. Hodder & Stoughton. 2000.
09. p.32. Time: A Traveller’s Guide. C.A.Pickover. Oxford University Press. 1999.
10. p.28. Einstein-A beginner’s Guide. J. Breithaupt. Hodder & Stoughton. 2000.
11. p.28. Einstein-A beginner’s Guide. J. Breithaupt. Hodder & Stoughton. 2000.
12. p.28. Einstein-A beginner’s Guide. J. Breithaupt. Hodder & Stoughton. 2000.
13. p.17. Time: A Traveller’s Guide. C.A.Pickover. Oxford University Press. 1999.
14. p.271. Q is For Quantum: Particle Physics From A to Z. John Gribbin. Phoenix. 1998.
15. p.48-55. The Universe’s Unseen Dimensions. N.Arkani-Hamed, S. Dimopoulos & G.Dvali. Scientific American. August 2000.
16. Experiments on the change of the direction and rate of time motion. V.A.Chernobrov. 1996.
17. p.504. Black Holes & Time Warps, K.S. Thorne. Papermac. 1995.

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