mass and Energy ------------- Einstein and others showed that mass and energy are equivalent and can be exchanged with each other in physics calculations. We can see how this is possible by examining an electromagnetic wave flowing past an observer. The wave imparts to the observer a momentum and energy, which can be converted to useful work. EMR travels at lightspeed c. The wave conveys energy E, according as its frequency or wavelength. The momentum imparted to the observer is p = E / c From all experiments, this momentum is entirely equivalent to that delivered by a material particle, of mass m, travelling at speed c. Thus p = E / c = m * c E / c = m * c E = m * c^2 This is Einstein's most famous of all his equations, but it is also one of the more misunderstood principles of his physics. For one point, we did NOT demonstrate that EMR has mass. EMR is identicly massless. There are two interpretations of this equation. The first is that we can express mass as an equivalent amount of energy or vice versa. In a formula calling for a quantity in mass units, we can freely replace it with the equal amount energy. Or the other way round. You may think of this equivalence like the way we use the identities (in(a)^2 = 1-(cos(a))^2and meter/second^2 = newton/kilogram. The other way is that mass and energy are convertible from a one into the other. This is by far the most popular way to see the E = m*c^2 relation. By various processes we can indeed extract energy from a material body and its mass will decrease. Or we can add energy to a material and increase its mass. Altho we used electromagnetic waves to show this equivalence, it is general for all forms of energy and mass. +---------------------------+ | MASS-ENERGY EQUIVALENCE | | | | E = m * c^2 | | m = E / c^2 | +---------------------------+ dePretto's Ideas -------------- dePretto in 1903 developed an equivalence of energy and mass in a crude manner, based on the aether theory. In it he figured that matter, in order to conduct light and EMR, had to contain energy, which was dependent on the speed of light in that material. For aether, lightspeed was the maximum value, c, and its material (of thoroly unknown substance) had an equivalent energy content of E = m*c^2. He was not a mainstream physicist, altho he published his findings in science journals. He could not see a way to progress farther in his inquiries. He did speculate about the enormous leverage the square of lightspeed had for a given quantity of mass. Perhaps, he wondered, this energy could be the source of geothermal heat and the light and heat of the Sun? Rest Mass ------- An early common feature of Einstein physics is that of the rest mass of a particle. This is merely the regular mass, as we understand it in Newton physics, when the particle is at rest in our own frame of reference. It's what we measure thru experiments of inertia in a laboratory. However, in the case of a photon, the term 'rest mass' is misleading. The 'mass' we found above applies to a particle which is absolutely without mass and can only travel at speed c in any platform. Yet it is the mass of a fictitious particle, moving at speed c, that carries the same momentum as the photon. Note well that since the energy, and therefore momentum, of a photon is a function of its wavelength, the mass equivalent is also a function of wavelength. Shorter wavelength, higher frequency, photons carry more energy than those with longer wavelength, lower frequency. The more addiurnate concept of rest mass is to avoid the term 'rest mass' completely but to recognize that there is associated with a real body or a photon a mass that is invariant against motion. The 'mass' of the photon, because a photon's speed is always c, is the same for any observer. Likewise, the mass of a material thing at rest in an observer's platform, is the same for all such platforms. Therefore, there is really only one parameter of mass, now called just 'mass' without 'rest' or other qualifier, for each body or quantum. Conservation Law -------------- The establishment of equivalence between mass and energy leads to a unification of the two separate conservation laws. In place of one for mass and one for energy, we now have a single one for the combination of mass-energy. Altho it is now possible to change from mass to energy and vice versa, the sum of the two as ingredients to a reaction must equal the sum of the two as egredients. mi + Ei = mo + Eo The first to demonstrate this were Cockcroft and Walton in 1932. They measured the mass and kinetic energy of a lithium-7 nucleus and a proton. When the proton interacted with the lithium it was absorbed and the combined nucleus, boron-8, decayed into two helium nuclei, or alpha particles. They measured the mass and kinetic energy of these heliums. The mass of the heliums was a trifle less than that of the lithium and proton; the kinetic energy of the heliums was a trifle more than those of the proton and lithium. The decrease of mass was exactly equal, by E = m*c^2, to the increase of energy Mass into Energy -------------- Under Einstein physics, energy is produced by converting mass into energy thru the E=m*c^2 relation. When a fire burns fuel, some of the mass of the fuel is indeed lost and is replaced by the heat, light, and kinetic motion of gases in the fire. The loss loss is so small as to be undetectable because the factor c^2 is so large. It takes only the merest bit of mass to yield a substantial amount of energy. One kilogram of mass yields 9e16 joules of energy. This is a stupendous quantity, equal in electricity to about 2.5e10 kilowatt- hours. This is quite the total electrical energy requirements of New York City for one year, estimated from 1990s data! In principle we could weigh all the ingredient fuel at the power plants supplying New York. (This is in fact done by the power companies to insure they are getting the quantity and quality of fuel they pay for.) Then collect and weigh all the exhaust gases, sludge, soot, ash. The two should differ by but one kilogram. In practice, the exhaust material is not actually collected but is calculated for care and control of the environment. An error of many THOUSAND of kilograms is well within acceptable tolerances. So the one kilo of mass converted into energy is utterly beyond detection. In actuality the mass loss is about four kilograms because only some 1/4 of the energy released by burning the fuel ends up in the electricity. The rest is thrown into the environment as waste heat. This is a brutal feature of energy conversion via heat engines, as limited by Carnot's Law andt he second law of thermodynamics. Energy into Mass -------------- There is no way so far to produce bulk amounts of mass from energy. In atomic labs individual nuclear particles can be created from interaction beams of radiation but these have no practical value outside of the experiment. In ordinary life, when ever we add internal energy to a body, like by heating it, the mass of that body does increase ever so slightly. The increment is undiscernible save by the most heroic of effort. In experiments in atomic labs, the concept of mass in itself is of minimal value. The movement of atomic particles is governed by the energy we put into them, like in an accelerator. Hence, it is quite common to speak of the 'mass' of a particle in terms of its equivalent energy. A proton is said to have a 'mass' of 1.494e-12 joule rather than 1.673e-27 kilogram. When the proton is accelerated to high speed, it acquires energy, in joules, which is added to this base energy to get the new total energy equivalent of the proton. Electron-Volt ----------- A very common unit of energy in atomics is the electron-volt. This is the energy acquired by an electron when impelled between a voltage difference of one volt. One electron-volt, abbreved eV, is 1.602e-19 joule. On this scale, the mass of an electron has energy equivalent of 5.110e5eV and a proton has energy of 9.324e8eV. +-----------------------------+ | ENERGY OF ELECTRON-VOLT | | | | 1 eV = 1.602e-19 joule | | | | electron energy = 5.110e5eV | | | | proton energy = 9.324e8eV | +-----------------------------+ In comparison, a neutrino, which is almost massless, has energy no greater than 5eV. Metric prefixes are used to make the kiloelectron-volt, keV, and higher multiples. The electron energy is 0.511MeV; proton, 932MeV. These multiples are prevalently pronounced 'kevv', mevv', 'gevv', 'tevV, and so on. It is rare to hear 'megaelectron-volt' and the like. There is almost no use for the submultiples like microelectron-volt. Critiques ------- As simple and direct as the Einstein mass-energy equation is, it generated over the decades severe criticism and debate. Some modern physicists and philosophers argue that Einstein somehow fudged the original derivation in 1905. Others argue that this derivation was proper and sound. Over the years, right thru the end of the 20th century, new angles of interpreting this formula were offered. Some ideas are that mass and energy are really only one substance with different names. Mass is 'frozen' or 'static' energy. The equation is really based on experiment and can not be formally derived. Mass and energy are two facets of a new other entity as yet understood. The equation is all baloney and mass-energy can not be merged. Exactly from such lack of a definitive and consistent treatment of this Einstein principle, comes the glossing over of a derivation in almost all popularizations of relativity. The trick of the author is to say 'Einstein showed that E = mc2', 'By complex math Einstein derived E = mc2', 'E = mc2 is one of the features of Einstein's theory of relativity', and similar glosses. We did no better here due to this odd history in Einstein physics, but at least there is good sense to it as showed by actual atomic experiments. For home astronomy purposes it's easiest to allow that mass and energy are two entities but they can be commuted from the one to the other. Atomic Bombs ---------- The allure of extracting energy from atoms comes from the vastly greater fraction of an atom's mass that is converted into energy when atoms decay. The mass of the fission or daughter atoms is less by order 1/5 percent of the original atom. This may not seem like much but the factor of c^2 makes for a lot of energy release. In the 1920s there arose the general realization that the atom locked up stupendous reserves of energy which conceivably could substitute for fossil fuels. Fossil fuels -- coal, oil, gas -- were dirty substances, dangerous to mine and purify. They released during combustion noxious and even poisonous byproducts. Besides, there were fewer and fewer easily mined fuels as the coal and oil fields were depleted. In the case of petroleum, the world's supply was controlled by the Middle East, whose stability, politics, and ideology clashed decade after decade with the western nations. There was always the threat of an oil stoppage, throwing the world's industry, commerce, and transport into chaos. By World War II atomic power was under intense study but its first large scale use was for atomic weapons. The atom bomb was a runaway uncontrolled release of energy by the instantaneous decay of, typicly, uranium atoms. Neutrons ejected from the initial set of atoms strike and induce fission in neighboring ones. The reaction concatenates thruout the mass of uranium to create an instantaneous issuance of heat and shock and radiation. However, if the mass is too small, most of the initial neutrons leave it without hitting other atoms and the reaction remains subdued and slow. By assembling a certain critical mass of uranium, the majority of neutrons do hit other atoms and the reaction 'goes critical' or self perpetuates. The atom bomb in essence is two chunks of uranium in separate chambers, each being a little more than half of the critical mass. A chemical bomb and mechanical mechanism at triggering force and hold the two chunks together to make one of a little more than the critical mass and the bomb detonates. Atomic Power ----------qThe atom bomb released the nuclear energy almost instantaneously. if this everhy could be released slowly in a deliberate way its heat could be used to generate electriciry. An atomic, or nulclear, power plant does this. The urnaium totalling amore that the critical mass, is placed in rods set up in a chamber. The rods are close enough for neutrons from one to reach the others and start the chain reaction. To control the strength of the reaction a second set of rods is place among the fuel rods. Thesse, the control rods, are movanle into and out off the fuel rod grid and are filled with a neutron-anosrbing material. Boron and graphite are common materials. When the power plant is ready to start operations the control tods are fully in place. They soak up neutrons, preventing them from triggering the chain reaction. To begin heat production the control rodsa re pulled out. Neutrons can strike other uranium fuel rods and the power plant 'goes critical'. The released heat vboils circulating water around the rods for turbine stram. Mind well that regardless of the degree of steam generationm even noe for the control rods shutting off the reaction, the uranium atoms continue to decay and spit out neutrons. To maximize the use of nuclear heat, a nuclear power plant tupicly runs full output 24/7. it is a 'base load' project supplying electric for all hours of the day. Other fossil fuel or eater, projects run on and off to follow the need for electric above the base amount furnihed by the atomic plant., Recycling of Fuel --------------- After a couple years the uranium in the fuel rods is too 'cold' to make turbine steam. The uranium isotopes are used up, and the rods are laced with stable or weakly radioactive daughter atoms. The rods are removed and replaced with new fuel rods. In some countries, like the United States, the old rods are stored in deep pools of water, for shielding, on the plant premises. They are taken away by an agency or firm to be buried in deep rock caves, probably for many decades. All-new rods are built with fresh uranium for the power plant. a In other countries the firm or agency removes the old uranium and daughter products from the rods. New uranium is loaded and the filled rods are sent back to the power plant. The collects material is packaged for industrial or medical uses. Each country with atomic power plants works out its own program for handling the spent fuel rods. Some built a recycling program with the development of their nuclear power system. Others delayed many years, maybe after the first round of reloading of fuel rods, to start recycling. Others, like the United States, as at end of the 20th century have no recycling program in the works. New York Els ---------- In about 1900 the company running the els in New York (Brooklyn had a separate system) was under severe social and political pressure to do something about its coal-fired locomotives. The company itself was moved to seek alternate power due to the hazards of handling coal. For starts, the supply was interrupted by continual rail and mine labor unrest and was subjected to erratic price swings. One alternative was electricity, then offered by nascent electric utilities, too small and weak to furnish the power for a vast network of els. More over, converting to electric would call for junking the entire fleet of coal-fired engines, wiring a hundred kilometers of road, hiring and training allnew crews, and running onsite electric generating stations. The cost would excede the all-time investment in the existing el system! The Manhattan el company came across a news item about a magic rock found by a lady scientist in France. This rock effused heat without flame or smoke or soot. This heat flux was constant, apparently immune to weather or other circumstances. This heat was so vigorous that a pebble of this material could boil a barrel of water within an hour. Could not this rock, like a hunk of coal, be loaded into a locomotive? A quick calculation, in modern measure, showed that a kilogram of this stuff had the heating equivalent of 5,000 TONS of coal! By placing just a kilo in the engine's boiler, the engine could run without refueling for the rest of its mechanical life! The company wired the discoverer in France to buy a few kilos for testing. The word came back that in all the world there only mere milligrams of this material. The 'rock' was the raw ore. And to get the special substance out in pure form cost thousands of dollars per gram. A kilo, if it could even be accumulated, would coast over a million dollars, a vast sum in the early 1900s. The samples asked would equal in cost the all-time investment in the whole el system! The material was the newly found radium, discovered by Marie Curie. Gritting their teeth, the els converted to electric and the rest is history. Never the less it is incredible that at the start of the 20th century there was serious, if wholly impossible, thought of using atomic power for large-scale civic purposes. Mass Increase ----------- Among the most misunderstood aspects of Einstein physics is that of the increase of a body's mass with increase in speed relative to the observer. This is of particular concern for the home astronomer. In his early days in astronomy he may read popular works on Einstein physics. These almost universally describe this feature of mass and speed. As he moves along in astronomy he starts to read the technical articles and books, intended for within th profession. There he finds that the whole concept of mass increase under relative motion is almost completely absent! As a matter of fact, among physicists the notion that the actual matter of a body enlarges because of motion vanished in the 1950s. Einstein himself in 1948 urged that it not to promulgated anymore for being an outdated and erroneous concept! What happened? Early Ideas --------- To see how the idea that a body materially increases its mass with motion, consider a spaceship with an engine that exerts a constant known thrust. The spaceship is its own motional platform has mass m[m/m]. When the rocket is turned on, the spaceship suffers an acceleration a[m/m] = delV[m/m]/delT[m/m]. Recall the notion that the first subscript, in the 'numerator', is the platform whose parameter is under examination. The second, in the 'demoniator', is the platform where the examination is carried out. 'm' is the motional frame; 's', stational. Thus we have F = m[m/m] * delV[m/m] / delT[m/m]. = m[m/m] * delX[m/m] / (delT[m/m] * delT[m/m]) We now examine this acceleration from the stational frame with the relative speed V[m/s] F = m[m/s] * delX[m/s] / (delT[m/s] * delT[m/s]) But space and time are distorted as perceived from the stational platform by the factor beta = (1-(V[m/m]/c)^2)^(1/2) delT[m/s] = delT[m/m] / beta delX[m/s] = delX[m/m] / beta F = m[m/s] * (delX[m/m] / beta) / ((delT[m/m] / beta) * (delT[m/m] / beta)) = m[m/s] * delX[m/m] / (delT[m/m] * delT[m/m]) * (1 / beta) / ((1 / beta) * (1 / beta)) = (m[m/s] * delX[m/m] / (delT[m/m] * delT[m/m])) * 1 / (1 / beta)) = (m[m/s] * delX[m /m] / (delT[m/m] * delT[m/m])) *beta Which is to say, from the stational frame the rocket undergoes a lesser acceleration for the given force compared to that experienced in the rocket itself. Now, because the force is the same in the both frames, F = m[m/m] * delX[m/m] / (delT[m/m] * delT[m/m]) = (m[m/s] * delX[m/m] / (delT[m/m] * delT[m/m]))*beta m[m/m] * delX[m/m] / (delT[m/m] * delT[m/m]) = (m[m/s] * delX[m/m] / (delT[m/m] * delT[m/m])) * beta m[m/m] = m[m/s] * beta m[m/s] = m[m/m] / beta Hence, at first blush it does indeed seem that the mass of the rocket sensed on the stational frame is greater than that sensed within the rocket. Mass increased with motion. Relativistic Mass --------------- Popular treatises on relativity speak of 'relativistic mass' and 'rest mass'. The rest mass of a body is the material content assayed in that body when it is at rest in the observer's frame of reference. This is m[m/m] or m[s/s]. Rest mass is commonly symboled by m0. The mass of the body when observed from an other frame and augmented by the factor beta is the relativistic mass, synboled by m or M. This is m[m/s] or m[s/m]. m[s/m] = m[s/s]/beta or m[m/s] = m[m/m]/beta. These terms come from the early era of relativity, mainly before experience was accumulated from atomic experiments. The present practice of physics discourages the use of 'mass' in relativity and atomics except to mean the rest mass. In fact, the practice nowayears is to use plain m for this mass, without any distinction with a subscript 0. Any 'increase' in mass, what made the rest mass become the relativistic mass, is now always expressed as energy. Because so much of the experience with changes of mass with velocity comes from atomic experiments, this energy is prevalently stated in electron-volts. That's why when you read litterature within physics or astronomy, rather than that for the general public, the notion of mass increase is just about completely absent. This lapse is a source of great consternation among home astronomers! Mass-Energy Equation ------------------ We can see this by starting with the rocket, where we found m[m/s] = m[m/m] / beta m[m/s] * c^2 = m[m/m] * c^2 / beta m[m/s] * (c^2) * beta = m[m/m]] * c^2 m[m/s] * (c^2) * (1 - (V^^2/c^2)^(1/2) = m[m/m] * c^2 (m[m/s] * (c^2))^2 * (1 - (V^2 / c^2) = (m[m/m] * c^2)^2 (m[m/s] * (c^2))^2 - (m[m/s] * (c^2))^2 * (V^2 / c^2) = (m[m/m] * c^2)^2 (m[m/s] * (c^2))^2 - (m[m/s]^2 * V^2 * c^2) = (m[m/m] * c^2)^2 (m[m/s] * (c^2))^2 = (m[m/m] * c^2)^2 + (m[m/s]^2 * V^2 * c^2) E^2 = (m[m/m] * c^2)^2 + (m[m/s]^2 * V^2 * c^2) The total energy of the body is the sum of the energy equivalent of its rest mass plus the energy equivalent of its momentum. The more usual statement of this relation is E^2 = (m[m/m] * c^2)^2 + p[m/s]^2 * c^2 In simplified notation, E^2 = (m0 * c^2)^2 + (p * c)^2 +--------------------------------+ | MASS-ENERGY EQUATION | | | | E^2 = (m0 * c^2)^2 + (p * c)^2 | +--------------------------------+ No Real Mass Increase ------------------- In the present scheme of relativity, the old rest mass, the current simple mass, is invariant with motion. There is NO actual enlargement of the matter in the body with motion. All the increase is in the form of momentum. In the stead of citing just this increment in energy units, the entire package of the rest mass plus the energy increment is expressed as an energy. The proper way to see this is to note that the total energy of a body in motion is the combination of its rest mass, expressed as energy thru E = m0*c^2, and its momentum, also expressed as energy thru E = p*c. When an object is in motion relative to the stational frame, it acquired energy of motion but its real material content does not change at all. The flub comes from the naive conversion of the entire energy of the body, mass plus momentum, back to a mass by dividing by c^2. We get the original equation based on the rocket experiment m[m/s] = m[m/m] / beta This manipulation can lead to really silly explanations. One is that the observer on the motional frame, the spaceship, will some how actually feel heavier than when he's at rest! This is ridiculous once you realize that relative to some, even unknown, place in the universe we ourselfs are moving at near lightspeed. Do we sense ourselfs to be far more massive than if we are at rest? Of course not. We are in relative motion with many places out there at various large fractions of lightspeed. For which of them do we respond with acquiring more mass? How does -- or can? -- nature choose which place knows about us to trigger the 'correct' mass increase? Invariant Mass ------------ The proper interpretation is that in the mass-energy relation. The 'rest mass' remains the same for all platforms. That's the m[m/m] or m0. The 'increase' of inertia or mass is entirely due to the mistaken mass equivalent of the increase in momentum. That's the p*c part. It's wrong to convert this -- or the sum of it and the rest energy -- back to a 'mass' with 1/(c^2). In fact, leaving the two components separate helps us to see better why a photon, while having energy and momentum, can be massless. The rest mass of a photon is identicly zero,; it is pure radiant energy. In the mass-energy formula, E^2 = (m0 * c^2)^2 + (p * c)^2 = (0 * c^2)^2 + (p * c)^2 = 0^2 + (p * c)^2 = 0 + (p * c)^2 = (p * c)^2 E = p * c which is just what is demonstrated by Maxwell physics.