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'''E=mc²''' is perhaps the most famous, most immediately recognizable to the public, most widely quoted by the public, and least understood by the public, of all equations in science.  Most people recognize it instantly, but when asked to explain it, might say something like "It says that matter and energy are the same/equivalent", or "It explains relativity", or "It tells where nuclear power comes from", or "It's about atomic bombs."  In this article, we will attempt to explain what it really is, and what it isn't.

'''E=mc²''' is perhaps the most famous, most immediately recognizable to the public, most widely quoted by the public, and least understood by the public, of all equations in science.  Most people recognize it instantly, but when asked to explain it, might say something like ''"It says that matter and energy are the same/equivalent"'', or ''"It explains relativity"'', or ''"It tells where nuclear power comes from"'', or ''"It's about atomic bombs."'' In this article, we will attempt to explain what it really is, and what it isn't.

The equation is about the physical concepts of 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=mc&sup2; is the same as the "m" in Netwon's formula of motion F=ma.  Gravitational mass is what makes things "heavy", that is, what is acted upon by gravity.  It is the "m₁" and "m₂" 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 experiments.  (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=mc&sup2;'' is the same as the ''m'' in [[Netwon]]'s formula of motion F=ma.  Gravitational mass is what makes things ''heavy'', that is, what is acted upon by gravity.  It is the "m₁" and "m₂" 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.)

Energy refers to kinetic energy of motion, or radiated energy.

Energy refers to kinetic energy of motion, or radiated energy.