E = mc2 -- 5/18/22

Today's selection -- from Frequently Asked Questions about the Universe by Jorge Cham & Daniel Whiteson. Einstein teaches us that mass and energy are different forms of the same thing:

"If there's one physics equation most people know, it's probably E  = mc2. It's the most famous equation in physics, likely because it's easy to remember. Its form is simple and elegant, almost like the Nike 'swoosh' logo. Compared to other physics formulas that look more like Egyptian hieroglyphics, this one definitely has brand appeal. Of course, it doesn't hurt that it came from Einstein, whose brilliance (and famous hairdo) have been a part of popular culture since the last century.

"But physics formulas are not just math; they're supposed to de­scribe something about the physical universe. And this is another reason why E = mc2 sticks in people's minds. Here E stands for energy, m means mass, and c is the speed of light in a vacuum, or 299,792,458 meters per second. To have them all in a simple, easy­-to-remember formula implies that they're connected to one another in a deep and profound way.

"But what exactly does that mean? How are mass and energy and light actually related to one another? And what does this relationship say about the fundamental nature of ourselves and the universe?

"For most of us, mass is the stuff we're made out of. If something has mass, it generally means that it's heavy, hefty, substantial. We tend to think of things with less mass as lighter, ethereal, or barely there.

The equation in Albert Einstein's own handwriting from 1912

"This is something we develop in our intuition at an early age, and it's something that was captured by Newton's laws of motion. For centuries, F = ma held the top spot as the most important physics equation in the world. In this formula, F is the force that you apply to an object, m is the object's mass, and a is the acceleration, or how quickly the object starts to move. If the object has a lot of mass, then it takes a really big F to get the object moving. And if m is small, then a gentle push is enough to make it go.

"To us, mass is a measure of the substance of something. Things with more mass, like mountains and planets, feel more real and solid.

"On the other hand, we tend to think of energy as something com­pletely different. We associate energy with heat, light, fire, or motion. It seems like something ephemeral that can flow or be transmitted. It gives you the power to do things and burn things. Like a magical quantity, it's something you can store and release when needed.

"For a long time, this intuition about mass and energy fit quite neatly with Newton's laws and our basic understanding of the uni­verse. Mass and energy were two different things, although it was clear they could interact with each other.

"For example, if you added energy to something, like a cup of water, you could think about it speeding up the little water mole­cules in the cup, but not changing the mass of the water. After all, adding heat didn't change how many H20 molecules there were; it just made them wiggle faster. At least, that's what we thought.

"In the late 1880s, physicists started asking pesky questions, like 'Where does mass actually come from?' and 'What is it anyway?' Initially, they looked at the electron, which had just been discovered. Physicists noticed that when a charged particle (like the electron) moves, it makes a magnetic field. This magnetic field then pushes back on the particle, making it harder to get the particle moving faster. It's the same effect as if the electron had some kind of hard-to-push mass stuff to it, which gave physicists the first idea that mass and energy (in this case, the energy of the magnetic field) could be more than just two different things.

"Then, Einstein stepped in with a clever argument that settled the debate.

"At the time, Einstein had been preoccupied with the idea of rela­tivity, the study of how the laws of physics apply to things that are moving relative to one another. It was known back then that nothing can move faster than the speed of light, and that this speed limit worked no matter how fast you were moving. If you were moving really fast, you would still see light moving at the speed of light. This fundamental limitation makes for some really strange effects when you consider how things look to someone standing on Earth and someone going really fast on a rocket ship.

"For example, Einstein considered the case of a rock in space giv­ing off heat. That heat will come off the rock in the form of infra­red photons. If you are floating in space next to the rock, you might not notice anything strange. You would see photons coming off the rock and you would measure that the photons had a certain energy (as all photons do).

"But if you were traveling past Earth on a speeding rocket ship, you would see something different. Einstein used the formulas of relativ­ity to figure out that you would see the photons coming off the rock at a different frequency of light. This is an effect called the relativis­tic Doppler effect, which is similar to how, for example, a police si­ren sounds different if the police car is coming toward or away from you. In this case, though, the shift is a little stranger because of rel­ativity rules (since you can't see the photon going faster or slower than the speed of light). The net effect is that you, in the spaceship, would measure the energy of the photons to be different than if you measured it when you're floating next to the rock. But since it's the same photons, something else must have changed.

"According to Einstein, what also changed was the kinetic energy of the rock. But kinetic energy comes from the mass and the veloc­ity of an object, and since the rock's velocity didn't change when it gave off photons, Einstein concluded that its mass must have changed. In fact, he found that the mass of the rock changed by an amount equal to the energy of the photons, if you multiplied it by the speed of light squared. In other words, he found the following:
"Energy of the photon = (Change in mass of the rock) x (speed of light)2
"What this means is that when a photon leaves the rock, it actu­ally changes the mass of the rock. This change in mass is the same (if you multiply it by the speed of light squared) as the energy of the photon emitted. It seems that a little bit of the mass of the rock was transformed into energy, which then went off in the form of a pho­ton (remember that photons don't have any mass; they are pure energy).

"This was a pretty groundbreaking result, to say the least. It threw out thousands of years of human intuition that told us that mass and energy were totally different things. Instead, Einstein's equation says that the two things are related to each other and that you can somehow transform one to the other in the same way that you can walk into a currency store and trade dollars for euros."

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Jorge Cham & Daniel Whiteson


Frequently Asked Questions about the Universe


Riverhead Books


Copyright 2021 by Jorge Cham and Daniel Whiteson


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