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Question:
What is the significance of Newton's equation E= MC square?



Replies:
Not to be picky, but your subject (Einstein) does not agree with the subject of your question (Newton) - E = m c^2 (squared) is indeed due to Einstein (early years of this century) and not Newton (who lived over 300 years ago). This equation is often taken to symbolize Einstein's relativity in the popular press, but in fact it is not really a consequence but more a separate fact of nature that fits very well into the initial assumptions of relativity (that the speed of light is a universal constant, independent of reference frame). The E refers to energy. Throughout the 18th and 19th centuries discoveries were made about energy - that various forms of energy were really interchangeable, for example mechanical energy (produced by applying a force to an object over a distance) could be converted into thermal energy (associated with heating an object) or electrical energy, and that there was also chemical energy in various reactions that could be measured. The units of energy are mass * acceleration * distance (using the force definition) or mass * velocity^2 (using the thermal definition) - in metric that is kg * m^2/s^2. The m refers to mass. The famous equation (E = m c^2) says that an object with a mass m has an associated total energy E that is proportional to that mass, and the ratio of proportionality (which has to be a velocity squared because of units) is the maximum velocity possible - speed of light. This relation between mass and energy was made most obvious in the case of radioactivity, when one element changes into another - the masses tend to be different, and the energy released can be very large. The same applies to the nuclear fission and fusion reactions, where the energy released can be determined directly from the mass difference of the reactants. Now, this is actually not really much different from the way in which the chemical energy of molecules changes when molecules join and break up - there would be an associated mass change as well. But the mass change for chemical energy changes is so tiny that nobody had ever observed it, while it is relatively easy to measure in the nuclear case. So the consequence of E = mc^2 is that two quantities that were previously thought to be quite different (energy and mass) were shown to be very closely related and interchangeable, just as in previous centuries the various forms of energy itself had been shown to be really the same kind of quantity.

Arthur Smith



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