Anything under the sun.
Mass and Energy
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.
The Idea of Relativity
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.
The Doppler Effect
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 you 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).
Kinetic Energy
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.
Since it’s the same photons, something else must have changed.
According to Einstein, what also changed was the kinetic energy of the rock.
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.
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.
Newton’s Laws
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.
Physics Formulas
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.
A Magnetic Field
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.
A Rock in Space
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).
Mass, Energy and Light
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.
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.
F = ma
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.
