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The equation is about the physical concepts of [[mass (science)|mass]] and [[energy]].
The equation is about the physical concepts of [[mass (science)|mass]] and [[energy]].
Mass refers to what is often called ''inertia'' (though that term is used much less now than it was 100 years ago). It is sometimes called ''inertial mass''. Inertial mass is the resistance of an object to being accelerated when a force is applied. The ''m'' in ''E=mc²'' is the same as the ''m'' in [[Newton]]'s formula of motion ''F=ma''. Gravitational mass is what makes things ''heavy'', that is, what is acted upon by gravity. It is the ''m<sub>1</sub>'' and ''m<sub>2</sub>'' in Newton's formula for gravity <math>F = \frac{Gm_1m_2}{d^2}</math>. The difference between inertial mass and gravitational mass used to be a burning issue among physicists, eventually being tested, and found to be the same, by the famous [[Eotvos experiment]]s. <!--(With the advent of general relativity, we know know why they are the same, but that's not important just now.)-->
Mass refers to what is often called ''inertia'' (though that term is used much less now than it was 100 years ago). It is sometimes called ''inertial mass''. Inertial mass is the resistance of an object to being accelerated when a force is applied. The ''m'' in ''E=mc²'' is the same as the ''m'' in [[Newton]]'s formula of motion ''F=ma''. Gravitational mass is what makes things ''heavy'', that is, what is acted upon by gravity. It is the ''m<sub>1</sub>'' and ''m<sub>2</sub>'' in Newton's formula for gravity <math>F = \frac{Gm_1m_2}{d^2}</math>. The difference between inertial mass and gravitational mass used to be a burning issue among physicists, eventually being tested, and found to be the same, by the famous [[Eotvos experiment]]s. (Note that general relativity does have an explanation for why this should be, but this is not relevant here.)
Energy refers to kinetic energy of motion, or radiated energy.
Energy refers to kinetic energy of motion, or radiated energy.
*''E=mc²'' is not about where the power of the atomic bomb comes from, though the physicists developing atomic power and atomic bombs were completely familiar with it.
*''E=mc²'' is not about where the power of the atomic bomb comes from, though the physicists developing atomic power and atomic bombs were completely familiar with it.
A little calculation will show that ''E=mc²'' is dimensionally correct. So, for example, in [[SI]] units (also called MKS units), E is in [[Joule]]s, m in [[kilogram]]s, and c in [[meter]]s per second. In [[CGS]] units or units of the [[US Customary System of Units|US Customary System]] ([[pound]]s and [[foot|feet]]) it is also dimensionally correct, as long as the units are used consistently. Physicists, when they are really into theory, sometimes like to use "natural units", which are calibrated so that ''c'' is dimensionless and has the value 1. <!-- We won't do that.-->
A little calculation will show that ''E=mc²'' is dimensionally correct. So, for example, in [[SI]] units (also called MKS units), E is in [[Joule]]s, m in [[kilogram]]s, and c in [[meter]]s per second. In [[CGS]] units or units of the [[US Customary System of Units|US Customary System]] ([[pound]]s and [[foot|feet]]) it is also dimensionally correct, as long as the units are used consistently. <ref>Physicists, when they are really into theory, sometimes like to use "natural units", which are calibrated so that ''c'' is dimensionless and has the value 1. That is not the approach taken here, however.</ref>
In any normal units, the value of c, the speed of light, is enormous, its square even more so. This means that ''E=mc²'' equates an extremely tiny amount of mass with an extremely large amount of energy. This gives the equation some of its mystique. <!--We will attempt to dispel that mystique, and explain just what the equation means.-->
In any normal units, the value of c, the speed of light, is enormous, its square even more so. This means that ''E=mc²'' equates an extremely tiny amount of mass with an extremely large amount of energy. This gives the equation some of its mystique. <!--We will attempt to dispel that mystique, and explain just what the equation means.-->