Universalidades Cartera Castigada de Vivienda (CCV)

Einstein’s famous formula

E = mc2

tells us that there is an amount of energy E equal to the product of the mass m and the square of the speed of light c stored in every particle at rest.

The speed of light c is a very large number, equal to 300,000 kilometers per second. Because it is so large, the amount of energy contained in any object we are familiar with is simply horrendously large. Take, for example, a kilogram of garbage. The amount of energy computed from this formula is about 30 billion kilowatt-hours, or the total amount of power produced by the Hoover Dam in two years.

Clearly, that is a lot of energy! How nice it would be if we could convert all the garbage in the world into clean energy. It would help the environment, and we would never have to fight for energy again. Many wars might thereby be avoided.

Unfortunately, to extract that energy you have to — literally — get rid of the garbage from this universe. Hiding it in a landfill or burying it at sea does not count. The permanence of matter, or in the language we learned in the last chapter, the conservation of nucleonic and leptonic numbers, tells us that the garbage cannot just vanish — unless you can find a kilogram of anti-garbage to annihilate it.

In other words, although the rest energy is there, there is no

easy way to extract it because of the permanence of matter, or

because of the lack of naturally occurring anti-matter in the world.

Maybe it is just as well that the rest energy cannot be extracted easily. Otherwise, in the wrong hands, cheap energy could be used to make bigger bombs to annihilate mankind.

The natural lack of anti-matter raises a very interesting question. Dirac’s theory is symmetrical between particles and anti-particles, so how come this universe contains so few anti- particles? This is actually a deep question, which will be discussed in Chap. 18.

The problem becomes even more acute when we realize that the universe started with no matter, namely, zero baryonic and leptonic numbers. The symmetry between particles and anti- particles inherent in Dirac’s theory was then obeyed. How come matter is present without an equal amount of anti-matter at the present?

Although anti-particles do not occur naturally on earth, they can be produced in high energy accelerators. To do so we need to supply at least twice the electron rest energy mc2 _{to produce an}

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electron and positron pair. Pair creations of this kind are done all the time in present day high energy accelerators. Note that it is impossible to produce an electron without a positron, because of the conservations of electric charge and leptonic numbers.

Any number of particles can be produced in these accelerators as long as energy is available and conservation laws are not violated. To be able to provide a large amount of energy, these accelerators must be very large. Figure 32 shows the size of the Large Hadron Collider (LHC), which can produce two colliding proton beams of about 7 TeV each. It is the largest machine currently on earth, scheduled to commence operation in 2007 or 2008.

Figure 32: The large circle shows the location of the underground Large Hadron Collider, straddling Switzerland (bottom) and France (top). The dotted line is the national boundary, and the long white object in the foreground is Geneva airport.

Speaking of energy, there are many units that can be used to quantify it. When atoms and nuclei are involved, it is common to use the unit of electronvolt (eV), which is the energy gained when a particle with one unit of electron charge slides down a one volt electrical potential. A thousand eV is known as a keV, a million an MeV, a billion a GeV, and a trillion a TeV. At the other end of the scale, a thousandth of an eV is known as an meV.

One often uses this unit to measure mass as well. By saying a mass is so many electronvolts, what one really means is that the rest energy of that mass is so many electronvolts. In this unit, the mass of an electron is 0.51 MeV, the mass of a proton is 938.3 MeV, and the mass of a neutron is 939.6 MeV.

In kilograms, the mass of a proton is 1.67 × 10−27 _kilograms.

Thus, in this language, one kilogram is equivalent to 938.3 divided by 1.67 × 10−27_{, namely, 5.62 × 10}29 _MeV.

We may sometimes express energy in kilograms as well, according to this conversion relation.

So far we have talked about the rest energy of a massive particle at rest. What if it is moving? Then its energy consists of the sum of rest energy and kinetic energy. Its kinetic energy increases with the velocity of the particle, but it is no longer given by the formula KE = mv2_{/2 when the velocity v approaches}

the speed of light. Instead, its kinetic energy approaches infinity in that limit.[1] _{For that reason it requires an infinite amount of}

energy to push a massive particle to the speed of light, which is an impossible task. This is why no massive particle can travel at or beyond the speed of light.

When the velocity is sufficiently large, the kinetic energy becomes much larger than the rest energy, so in comparison the latter can be neglected. A particle with that kind of velocity is known as a relativistic particle. Otherwise, the particle is non-

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Another form of energy very important both in daily life and in cosmology, associated with a large number of particles, is the heat

energy, or thermal energy. We shall take that up in the next chapter.