Sept. 27, 1905, marked the publication date of the world’s most famous equation. The physics journal Annalen der Physik published Albert Einstein’s paper, “Does the Inertia of a Body Depend Upon Its Energy Content?” where E-mc^2 was first introduced. Energy is equal to the mass of a particle times the square of the speed of light. One of the simplest equations to write has some of the most profound meanings. In honor of that publication, I want to point out five lessons we can take from this simple equation.
The first lesson is that “mass is not conserved.” We often make the mistake of thinking that mass never changes. For example, if you take a block of iron and chop it up into a bunch of iron atoms, you fully expect that the mass of all the atoms will be the same as the mass of the block. That assumption is clearly true, but only if mass is conserved. However, according to this equation, mass is not conserved at all. If you take an iron atom, containing 26 protons, 30 neutrons, and 26 electrons, and place it on a scale, you’ll find something disturbing. An iron atom weighs slightly less than an iron nucleus, and the nucleus weighs significantly less than the 26 protons and 30 neutrons that compose it. This is true because mass is just another form of energy, and the energy required to hold the nucleus together reduces the mass of the parts.
The second lesson is the law of the conservation of energy. Energy is conserved, but only if you account for the changing masses. Imagine the Earth orbiting the Sun at 30 kilometers per second. This is the slowest it can go without falling toward the sun. It orbits 150 million kilometers away from the sun. If you were to weigh the Earth and then weigh the Sun, you would find the total weight of the Earth and the Sun measured separately is much greater than the weight of the Earth and Sun weighed together in motion. This is because the gravitational energy holding them in orbit affects the mass. The tighter the orbit, the more energy it takes to maintain stability and the lower the mass of the combined system. Protons and neutrons bind together in the nucleus of an atom in large numbers, producing a much lighter nucleus and emitting a lot of high-energy photons in the process. This nuclear fusion process can create extreme amounts of energy.
Third, Einstein’s E=mc^2 describes why the Sun and stars shine. Inside the core of the Sun, temperatures rise to over four million degrees Kelvin, allowing nuclear reactions that power the sun to take place. Protons are fused together forming a deuteron and emitting a positron and a neutrino to preserve energy. This process eventually creates helium-4 which only weighs in at 99.3 percent of the mass of the four protons used to create it. The process also releases nearly 28 million volts of electrical energy. Over the lifetime of the sun, it has lost approximately the mass of Saturn due to the nuclear bonding in its core.
Fourth, the conversion of mass to energy is the most energy-efficient process in the universe. One hundred percent of the mass is converted directly to energy, making it 100 percent efficient. Looking closely at the equation, you can see that mass is converted directly to energy and this tells you exactly how much energy you will get out of the system. For every kilogram of mass you convert, you get nine million joules of energy, the power of a 21 Megaton bomb.
Lastly, you can create massive particles out of nothing but pure energy. This is probably the most profound discovery and the hardest to explain. If you take two rubber balls and smash them into each other, you expect to get one result, two rubber balls. With particles like electrons, though, things change. If you smash two electrons together, you will still get two electrons, but if you smash them together hard enough, you can get a pair of anti-matter particles, effectively creating new mass from the energy involved in the collision. Mass can be converted to energy and back again.