The general structure of the Special Theory lies in the concept of converting finite mass to energy. This concept presents unlimited possibilities for the engineering sciences of almost every discipline. Research in scientific areas related to energy, has been gaining momentum for the past hundred years. In general simplified terms, the special theory dictates that mass, accelerated to unimaginable speeds (specifically speed of light), will release immense amounts of energy. Any scientific theory that propagates production of large amounts of energy from small amounts of matter is of great interest to engineers worldwide (Doyle, 2000).

Dr. Einstein’s theory cuts across the universe into the deepest secrets of genesis. It builds on the universal Newtonian laws, and forward into the still dark areas of the "undiscovered countries" of the future research (Asimov, 1991).

The amazing atom

In the ancient past, approximately 300 - 400 BC, Greek philosophers coined the term atom – a for "not" and tom for "divided – it was generally considered that atom was the smallest and indivisible building block of the universe (it is quite fascinating that we are still, in this day and age, learning from the ancient philosophic minds). Since then, in the fairly recent times, physicists have discovered the host of smaller components in the illusive "inner world" of the atom.

Inside of every atom lies an inner core – the nucleus, which is made up of positively charged protons and neutrally charged neutrons, surrounded by negatively charged electrons, which encircle the inner core at tremendous speeds. It is a fascinating fact that each atom is a sort of a "perpetual motion machine" because each revolution of the electrons around the nucleus is performed at exactly the same speed, without any loss of energy. If any such loss had occurred, the circular motion of the electrons would have become "spiral" and eventually come to the complete rest. Luckily this is not the case, because it would cause the complete atomic collapse and the end of the universe, as we know it.

Inside the protons and neutrons lie even smaller sub-atomic particles – quarks. These particles are approximately 1000 times smaller than proton and have an electrical charge that is a fraction (» 1/3) of the strength of the proton.

Simply put, atoms are extremely small. For example, a 1-gram sample of Zinc, weighing .034 ounces, holds an immense amount of atoms – 2 x 10²³ (2 followed by 23 zeros). Atoms vary in size. From the smallest atom, Hydrogen to largest atom, Francium, the number of electron levels in the outer shell determines the actual size. One interesting comparative example, regarding the size of the atom, was published by Time-Life magazine:

"One way of envisioning the size of atoms is to imagine the relationship between the hydrogen atom, a golf ball, and the Earth. A golf ball is as many times larger than an atom as the Earth is larger than a golf ball" (Time-Life, 1992).

 

The Equation Simplified

Let us break down the equation E= mc² into its basic components.
E stands for Energy measured in joules
m represents mass and is measured in kilograms
c represents the speed of light (300,000 km/sec or 186,000 miles/sec, or presented
in mathematical terms 3 ´ 10⁸ ms^-1

Energy

Energy is measured in Joules (J). To better visualize the representation of energy in joules, imagine an everyday light bulb. One watt represents one joule per second. So a 60W light bulb is using 60 joules every second, or 3,600 J / per hr.

Mass

Encyclopedia Britannica defines mass as the following: "In physics, quantitative measure of inertia, a fundamental property of all matter. It is, in effect, the resistance that a body of matter offers to a change in its speed or position upon the application of a force. The greater the mass of a body, the smaller the change produced by an applied force. Although mass is defined in terms of inertia, it is conventionally expressed as weight. By international agreement the standard unit of mass, with which the masses of all other objects are compared, is a platinum-iridium cylinder of one kilogram. This unit is commonly called the International Prototype Kilogram and is kept at the International Bureau of Weights and Measures in Sèvres, France. In countries that continue to favor the English system of measurement over the International System of Units (SI), the current version of the metric system, the avoirdupois pound is used instead. Another unit of mass, one that is widely employed by engineers, is the slug, which equals 32.17 pounds" (Encyclopedia Britannica, 2001).

Dr. Einstein’s formula does not really take into consideration what material is used for calculations. It assumes any and all materials. It is a different story, however, when it comes to practicality, which material is to be used. In the special theory of relativity, the traditional understanding of mass underwent a radical revision. It is now seen as being equivalent and inter-convertible with energy (Doyle, 2000).

The speed of light

The speed of light is measured in miles or kilometers per second and is traditionally believed to be 300,000 km/sec. Even though actual measurements of the speed of light have shown slightly lower values, the figure above is traditionally assumed to be true and therefore used in most physics calculations. Furthermore, to make mathematical calculations a little easier in the long run, it is sometimes represented as 3 ´ 10⁸ ms^-1 in scientific notation:

E= mc²

= 1kg ´ (3 ´ 10⁸ ms^-1 ) ²

= 1kg ´ (9 ´ 10¹⁶ m² s^{- 2} )

= 9 ´ 10¹⁶ m² s^{- 2}

Even though a more detailed explanation of how the units (kg m² s^{- 2} ) could have the same representation as joules may be outside the limited scope of this paper, the result above may be interpreted as 9 ´ 10¹⁶ joules.

This means that from 1 kilogram of matter one may obtain (at least mathematically) 90,000,000,000,000,000 joules of energy.

Professor James Doyle from Napier University expands this further:
"If we converted 1 kg of mass into energy and used it all to power a 100 watt light bulb how long could we keep it lit for?

How long is that in years? A year (365.25 days) is 31,557,600 seconds, so we get:

That is a very, very long time!

Of course, converting mass into energy is not quite that simple, and apart from with some tiny particles in experimental situations, has never been carried out with 100% efficiency. Perhaps that’s just as well!" (Doyle, 2000).

Nuclear Fission

Fission in Latin means, "to split". This is the process, which causes the atomic nucleus to split in two. In nature, fission occurs naturally in radioactive metals, such as Uranium and Plutonium. Their large, unstable nuclei, decay over periods of time. When the force, called in Physics "strong force", that holds the nucleus together, dissolves, the protons and neutrons change their original formation to form two new atoms, producing large amounts of energy and neutrons in the process.

The emission of neutrons causes adjacent atoms to decay, leading to a chain reaction that begins to split neighboring atoms. When the chain reaction reaches its critical state, the immense amount of energy is released, leading to truly catastrophic effects. One of such reactions was observed during the blast of the atomic bomb.

However, when the nuclear reaction is properly controlled, the heat energy released in the fission process is used to drive the steam generators of power plants. The resulting steam spins the turbines that generate electricity.

A look in the distant past

The process of nuclear fission is based on Dr. Einstein’s special relativity principles. When the atoms of the radioactive metals are accelerated to the speed of light (300,000 km/sec), they release energy. The mass-energy equivalency formula in the special relativity states that E= mc² . Theoretically speaking, when viewed in light of mathematics, the opposite effect may also be true – mass may be derived "solidified" from the resulting energy: m=E ¸ c². This formula would mean that the energy "slowed down" at the speed of light might generate various forms of mass. It is not yet exactly known in modern science, but if at the beginning of the universal time, energy was in existence prior to the existence of matter, then the above formula may have played a vital role in the genesis of all existing elements, or at least in the original generation of primary elements such as Hydrogen.

It is not easy for most people to fully comprehend the effects of this formula. It implies, at least in theory, that slowing the energy, which could have initially existed in any state of electro-magnetic spectrum (i.e. heat, magnetic waves, visible light etc.), at the certain speed (c²⁾ makes the difference. If it really does make the difference, and it is yet remains to be proven by future research, a tremendous variety of materials could have been generated by "slowing" the motion of the atomic energy at different speeds.

An energy-mass and mass-energy theory

The formulated effect above is still a strictly theoretical concept, but for educational purposes, to visualize the above effect in much simpler terms, we can use the example from the science of metallurgy. In a very common engineering practice of heat treatment of metals (as one of the most commonly used materials, we will use steel as an example), the material is heated, depending on the engineering application criteria, to a variety of high temperatures. During the heating process, oscillation of the atoms, in the metal, increases. This is because of the accelerated motion of the electrons (Benham, Crawford

& Armstrong, 1996). Even though the forces involved here are a small fraction of the forces applicable in a typical nuclear reaction, this process may to some extent be equated, to Einstein’s formula - E= mc². Of course in this case, m · c² would appear as m · t° (where t° represents any given temperature, because heat is used here as a particle accelerator). After the heating process is completed, the metal is then cooled. Here comes an interesting point – it is cooled at different speeds. The effect of cooling the metal slow or fast (using a variety of methods such as air, oil, and water cooling) makes the material "harder" or "softer" by slightly re-arranging its crystalline structure. Even though the resulting material is still essentially the same – steel, one may view the variety of different hardness steel as somewhat different materials, because at this point each material in the selection has a different variety of engineering properties (i.e. brittleness, ductility, etc.). The cooling process, because the motion of the electrons in the atoms are slowed down, could then be theoretically equated to m=E ¸ c² where m is a resulting material.

Special Relativity applied to exploration of space

One of the most intriguing and almost fantastic aspects of special relativity is time dilation. Albert Einstein’s time dilation theory, even though at first glance seemingly contradicting one of its own postulates, namely the relativity of uniform motion, points out an amazing fact that the time as we know it actually slows down for the objects moving at speeds close to the speed of light. A number of experiments have been conducted using precise atomic clocks installed on a spacecraft orbiting the Earth, which have shown slight difference in time when returned back to Earth. The clocks that went into orbit were slower, confirming the predictions of Special Relativity.

Theoretically, it would mean that cosmonauts, moving at speeds approximating the speed of light, would age at a much slower rate than people remaining on Earth. Imagine going into space for only one year, and when you come back everybody else around you have aged 64 years. This can really put you "back to the future", because theoretically you can see your grandchildren older that yourself. Even though the above theory had been proven to be true, it is still a long way from being achieved. Living organisms cannot travel at such tremendous speeds.

It is obvious that the time dilation theory is still very far from being of any practical use to modern engineers, however, research related to the exploration of space is still on the top of the "scientific list". One of the largest obstacles in space travel is the tremendous distances to even so-called "nearby" stars. When scientists finally develop the ability for humans to move at speeds nearing the speed of light, only then the time dilation principles may be the only hope of human kind to be able to approach some distant stars without getting "too old" in the process.

Nuclear Fusion

In nuclear fusion, two light atomic nuclei join to create one heavy nucleus. This happens naturally within the cores of most stars, where temperatures and immense pressures are high enough to overcome the force that causes nuclei to repel each other, as well as break the strong force that binds protons and neutrons together. In such conditions, hurtling nuclei fuse when they collide. At that time, a new nucleus forms, releasing neutrons, protons, and other sub-atomic particles – neutrinos and positrons, as well as large amounts of energy. In today’s scientific laboratories, scientists hope to generate large quantities of energy, by applying these principles. Their major goal is to create nuclear reactors that will, to some extent, reproduce stellar conditions.

Nuclear fusion produces tremendous amounts of energy. For example one pound of hydrogen yields as much energy as the burning of 9,000 tons of commercial coal (Galan, 1992). The nuclear reaction that can generate such tremendous amounts of energy, even though still in the experimental stage and limited much by economic factors, may be used to power aircraft, trains and automobiles.

Three common types of nuclear fusion reactions are currently experimented with in laboratories:

1. Two deuterium (also known as heavy hydrogen, used in heavy water D₂O) nuclei, consisting of one proton and one neutron are fused together to form helium3 (2protons and 1 neutron). When this reaction is complete, the remaining neutron is released, together with a significant amount of energy.
   
2. Sometimes, for reasons still unknown to modern science, when the above reaction takes place, tritium is produced instead of helium3 (1 proton and 2 neutrons). In this reaction, the remaining proton is released, in addition to even larger amount of energy.
   
   
   
   
   
   
   
3. In the third type of fusion reaction, a one-deuterium nucleus is fused with tritium, producing helium4 (2 protons and 2 neutrons). This reaction, in addition to
   releasing remaining neutron, releases the largest amount of energy – approximately five times more energy than the two preceding reactions.

The nuclear fusion reactions are conducted in special laboratories employing a circular cross-section, torus shaped chamber. Inside the chamber circulates plasma, a highly charged gas heated to a minimum of 100 million degrees ° C (180 million ° F). A powerful magnetic field surrounds the plasma. The magnetic field is needed to keep the plasma away from the chamber walls to prevent melting.

The released energy, produced as a "by-product" of the fusion reaction, is many times greater than the energy required to induce the reaction (i.e. production of plasma, generation of the magnetic field, etc.). This release of energy, when properly controlled, poses great interest to engineers, metallurgists, and scientists of almost every technology-related discipline.

Universities, together with scientific centers, worldwide, need to continue their research endeavors in this field. Nuclear fusion, in time, may prove to be one of the most effective sources of power production known to humankind.

General Applications of Theory of Relativity

For the purpose of this study, general application of the theory of relativity, as well as the general application of nuclear physics, will refer to both, applications as a result of nuclear physics, and applications, employing nuclear physics. An example of the former would be medical imaging. Had there never been any sort of thing known as nuclear physics, we wouldn't need imaging techniques to scan the body for radiation. An example of an application employing nuclear physics would be radioactive dating. The radioactive properties of certain elements are used in order to determine the age of something.

"By re-creating extreme conditions like those in Jupiter’s core, physicists at long last turned hydrogen into a metal. Future work on metallic hydrogen might bring revolutions in electronics, energy and materials" (Nellis, 2000).

One of the most amazing scientific achievements of modern times is the series of experiments leading to the creation of metallic hydrogen. Being the most abundant element in the universe, and having seemingly the simplest atomic structure (i.e. having only one proton and one electron), hydrogen is now considered one of the most complex elements that were ever discovered.

Normally, hydrogen can be cooled to a liquid state at temperatures nearing 18 kelvins
(- 255.15° C), and solidified at approximately 13 kelvins. In both states, hydrogen

normally acts as an insulator. However, when exposed to super high temperatures (» 2,600 kelvins) and tremendous pressures, applied in a form of a "sudden impact" shock wave, the hydrogen increases in density and forms into a special-structured lattice, inhibiting distinctly metallic, semi-conducting, and possibly super-conducting properties (McClintock, 2000).

Unfortunately, a more detailed description of this remarkable research is beyond the scope of this paper. It should be of great interest, however, to students of almost every branch of engineering and technology. An entire historical overview, as well as recent scope of work done in this field can be obtained online from NASA at: (http://www.hq.nasa.gov/office/pao/History/SP-4404/contents.htm)

How it works

Liquid hydrogen, placed between two super hard plates (sapphire is used in current experiments), is subjected to a sudden impact shock wave. Scientific American magazine defines a "shock wave" as the following: "A sudden change in pressure that forces molecules together very rapidly, thus raising their temperature" (Scientific American, May 2000).

"Shooting" a special projectile at approximately 16,000 miles per hour performs the impacting shock. The resulting force exerted onto the sapphire plates produces an immense pressure - approximately 390 gigapascals (» 4 million times the atmospheric pressure at sea level), as well as raise the temperatures to 2,600 kelvins (Holmes, 2000). At that point, solid molecular hydrogen might become metallic.

Properly controlled nuclear reaction may yet prove to be the most able mechanism available to achieve such immense pressures. Scientists estimate that the aforementioned pressure naturally exists only in the center of the Earth, or perhaps inside of many other planets. Creating such conditions inside of the laboratory may definitely be considered among the highest achievements of humankind to date (Holms, 2000).

Engineering applications of metallic hydrogen

Some scientists predict that metallic hydrogen, in its solid form, may conduct electricity without resistance, at normal ambient temperatures. To be able to use such a superconductor has been an illusive dream of electronic engineers worldwide. Dr. William J. Nellis explains this further: " A metallic hydrogen superconductor could revolutionize most aspects of modern life: transmission lines would not loose energy, computers would run faster, trains could be levitated on magnetic cushions, and vast amounts of energy could be stored in magnetic fields without appreciable loss"

(Nellis, 2000).

Fuel Engineering

Solid metallic hydrogen, possessing a very high density (» 0.32 mole), could store large amounts of energy. This energy could be released and used as fuel when converted back to a gaseous state. Replacing current transportation fuels is a subject in tremendous amounts of worldwide research. Solid metallic hydrogen could produce about five times as much thrust per kg. as the liquid fuel currently used as a rocket propellant (Hardy & Whalen 1992). Scientists are constantly searching for environmentally cleaner fuels, not to mention more economic ones. Even though hydrogen, in a slightly different capacity, has been used as fuel (water electrolysis research at SAAB factory), converting metallic hydrogen to fuel energy, which may eventually become the most revolutionary fuel ever invented (Webb, 1996).

Nuclear engineering

One of the possible applications of metallic hydrogen is a fusion pellet in inertial-confinement fusion reactions. Heavy hydrogen, in the form of deuterium and tritium may be used as a fuel. As we have discussed earlier, due to its high density, a solid hydrogen fuel pellet would produce much higher fusion energy yields than any other form of DT (deuterium/tritium) (McClintock, 2000).

Structural engineering

Although this is still in a very experimental stage, some scientists believe that by adding special bonding material to the metallic hydrogen may make it structurally stable as well as strong enough to be used as lightweight structural material. According to Scientific American magazine, the resulting structural material would be three times lighter than aluminum (about 10 times lighter than iron). Even though at this point it is hard to predict its strength or other structural properties, scientists are determined to produce structurally sound metallic hydrogen by the end of the decade.

Applications in manufacturing technology

One of the most amazing and revolutionary processes in modern engineering and manufacturing technology is a process called Rapid Prototyping. This process enables engineers to simply "print" the actual part model in three dimensions. Typically, the solid model is initially designed using any commercially available CAD (Computer Aided Design) system such as Autocadâ or Pro-Engineerâ (Graham, 2001). After the solid geometry is complete, it may be electronically downloaded to a variety of rapid prototyping machines.

One variation of rapid prototyping process equipment is called Stereo Lithography, which means 3-dimensional printing. During this process, the computer divides the entire solid CAD model into very thin layers or "slices"(Wright, 2001). Then, the stereo lithography machine, which contains a basin of liquid polymer, by using a special state-of-the-art laser technology, fuses molecules of the polymer in each slice into solid form. After a relatively short period of time, the entire model is solid, thus recreating the initial part geometry designed on the computer.

Even though this process is very useful in modern engineering design, it is somewhat limited to visual and tactile prototypes only. The available variety of rapid prototyping polymer resins and paraffin-based compounds simply can not withstand the stresses of real-world applications, and therefore, in most cases, limited only for the aesthetic and marketing applications in the product development process. It may look and feel like the real product, but it cannot replace these products in the physical testing process.

The ideal situation, of course, would be to use such technology for a vast variety of available engineering materials, or a least limiting to ferrite metals, such as cast iron and steel. Fusing molecules of steel, however is a much more complicated process than fusing molecules of paraffin wax or polyurethane resin. We would need to generate very high temperatures, very quickly, and focused very locally, so that small portion of steel powder particles are fused without fusing the neighboring particles.

Two currently possible options are available to accomplish such a revolutionary process. Both are, to some extent, related to the special theory of relativity. One is a high frequency laser technology. Laser technology has advanced much in the past twenty years. Among its many applications, it is used very often in the medical industry to perform complex surgery in such delicate areas as the human eye. Most laser surgery procedures are focused on very small areas, so that neighboring tissue is not affected.

This technology may be geared towards fusing the molecules of steel, one at a time, and in a very short period of time. The second is a finely controlled nuclear reaction. Even though this is not yet practiced due to economic, ecological, and safety limitations, the process may become available in the not too distant future. After all, we use nuclear power to generate electricity and propel submarines, why not apply it to solidify metal powder into engineered components? When this process is finally implemented, it would certainly revolutionize manufacturing technology worldwide.

Although the special theory of relativity was introduced almost a century ago, it is still a fairly new concept. The world had seen some of its positive as well as negative results. Worldwide research, related to relativity, as well as nuclear physics in general, is one of the main topics in modern science. Much research is being done in such areas as Medical Imaging, including CAT scans, MRI and NMR technologies, Radioactive/ Radiometric Dating, and Radiation Detection, just to mention a few. Perhaps the greatest potential of all lies in Nuclear Physic’s contribution to saving lives and providing a better and a more secure world. Perhaps, this is the most important goal of all science and engineering.

References and Bibliography

Asimov, Isaac, (1991) Atom: Journey Across the Subatomic Cosmos. Truman Talley Books: Dutton Publications

Benham, P. P.; R. J. Crawford, R.; Armstrong, C.G. (1996). Mechanics of Engineering Materials. Upper Saddle River, New Jersey: Prentice Hall Publishers.

Bodanis, David (2000). E = mc²: A Biography of the World's Most Famous Equation.

New York, NY: Walker & Co Publishers

Doyle, Jim (2000). The Special Theory of Relativity. Edinburgh, UK: Napier University

Einstein, Albert (Reprint 1995). Relativity: The Special and the General Theory. New York, NY: Crown Publishing Co.

Einstein, Albert (Reprint 1994). Ideas and Opinions. New York, NY: Random House & Crown Publishing Co.

Encyclopedia Britannica (2001). [Online]. http://www.britannica.com.

[Accessed September 2, 2001].

Galan, Mark (1992). Structure of Matter. Time Life Books: Time Warner Inc. USA

Graham, G. & Steffen D. (2001). Inside Pro/ENGINEER Solutions 2000i2.

Florence, KY: OnWord Press

Hardy, T., & Whalen, M. (1992). Technology Issues Associated with Using Densified Hydrogen for Space Vehicles. Nashville, TN: AIAA 92-3079, AIAA 28th Joint Propulsion Conference.

Holmes, Neil (2000). "Shocking" Gas Gun Experiments. Science and Technology

Review, September 2000.

McClintock, Peter (2000). Liquid Hydrogen Turns Superfluid.
Physics World. Vol.13 Issue 11.

Nellis, William (2000). Making Metallic Hydrogen. Scientific American. (5), 60-63

National Council of Radiation Protection and Measurements (NCRP), A Handbook of Radioactivity Measurements and Procedures 2nd ed. NCRP: Bethesda, MD: 1989.

Tlusty, George (2000). Manufacturing Process and Equipment. Upper Saddle River, New Jersey: Prentice Hall Publishers.

Webb, Jeremy (1996). Fuel from Water. New Scientist. October 1996

Wright, Paul K. (2001). 21st Century Manufacturing. Upper Saddle River, New Jersey: Prentice Hall Publishers.

Autocad is a registered trademark of Autodesk Corporation, Sausalito, CA.

Pro-Engineer is a registered trademark of Parametric Technologies Corp, Waltham MA.