By Sebastian Ritter

On November 21, 1905, exactly 114 year ago, Albert Einstein first published the well-known equation E=mc². You might think of nuclear power when seeing E=mc², but here’s something to think about. What does E=mc² really mean and how does it relate to your cup of coffee?

It was June 1905 when the 26-year-old patent commissioner Albert Einstein in Bern, Switzerland, described the basis for the famous equation E=mc² in a publication named “On the electrodynamics of moving bodies.” In it, Einstein developed the “Principle of Relativity”: the laws of physics are “invariant” or “the same” in all inertial systems. Inertia means that a body remains at rest or in unchanging motion unless a force disturbs it. Inertial systems can be described as scenarios where bodies are at rest or move at an unchanging speed. Einstein also introduced a second major principle: the speed of light is unchanging and invariant. Building on these two principles, Einstein published another paper to describe the equivalence of mass and energy. This paper was published in 1905 and was titled “Does the Inertia of an object Depend Upon Its Energy Content?”

What exactly does E=mc^2 mean?

It describes the equivalence of mass and energy in a scenario in which all bodies are at rest or in which the momenta of all bodies sum to zero. The mass m in E=mc^2 is known as the “rest mass” of an object, simply because it is the mass of an object when it is at rest. c is the speed of light. Multiplying the rest mass by the speed of light twice gives the “rest energy” E.

What does equivalence of mass and energy mean?

It means that rest mass and rest energy are simply two names for the same property of a physical body. The only difference is the mathematical factor c^2. But if rest mass and rest energy are the same, why do we only see either mass or energy in our daily life? This is because we typically encounter only tiny amounts of energy. For example, a hot coffee has a larger rest mass than that of a cold one: it is heavier by the amount of energy added to heat it up. For a Starbucks Grande Caffè Americano that’s around one billionth of a gram!

E=mc^2 is only nuclear, right?

Some of us think about nuclear energy when we see E=mc². However, it directly applies to all resting objects around us. Burning wood releases molecular energies in the form of heat following Einstein’s law E=mc^2. Nuclear bombs instantly release about 1 gram of mass as energy. This is much more than the one billionth of a gram a cup of hot coffee releases as energy when it slowly cools off.

So, whether it’s your cup of coffee, wood-fired oven, or phone battery, just remember that E=mc^2 applies. Here is something to think about. How does E=mc^2 relate to your life?

Sebastian Ritter is a nuclear engineering graduate student at the Pennsylvania State University where he is a member of a nuclear fusion research group. He received an undergraduate degree in physics at the TU Wien in Vienna, Austria. He is also an ANS member and part of the ANS Social Media Team.

Ken BockmanIn relativistic dynamics, the kinetic energy of a moving body is (M – M sub 0) C^2, where M sub 0 is the rest mass, and the two mass values are related by the square root of

[1 – (V/C)^2].

PierreVery nice article – it gives a good introduction into this matter with a daily-life comparison. One thing I still don’t get completely (as a layman) is: what does it EXACTLY mean that energy equals mass multiplied by c-SQUARED… Does it – to put it simple – mean that there’s much much more energy in some object than one might think of? I mean, it’s c-squared, not just c, right?

How can you explain that to someone without specific knowledge (like me)?

Thanks.

Pierre

Larry KenworthyNice article. Whenever I see something like this,I am compelled to check the math. It checks out good. I have always thought of the mass in E = mc^2 as the relativistic mass. But I guess if we don’t stir the coffee it is the rest mass.

Neil TodreasSebastien– you start your article with what I assume you feel is an innocent statement ” You might think of nuclear power and nuclear bombs when seeing E=mc², but here’s something to think about.”. Not so innocent since you add to the public concern that nuclear power utilization is directly related to nuclear weapons. Im sure you likely recognize the great differences which can be stated between these two applications of nuclear energy. I urge you in any future statements you make directed at public reading to clearly and purposely separate the development and usage of nuclear power from nuclear weapons. Neil E. Todreas , Prof Emeritus, Department of Nuclear Science and Engineering, MIT