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"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).
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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 ...
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"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 w...
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"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 t...
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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 o...
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"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 quan...
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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...
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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, alm...
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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 partic...
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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 a...
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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 hav...
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"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 t...
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"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...
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"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 g...
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For example, would you rather have (A) $3 million upfront or (B) one penny that doubles in value ev...
A good way to see the butterfly effect is with a game of billiards. No matter how consistent you are with the first shot, the smallest of differences in the speed and angle with which you strike the white ball will cause the balls to scatter in different directions every time.
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When you catch yourself thinking "that's crazy," try to figure out why someone would believe that idea.
People are mostly logical, their starting point is just different. When you try to see if you can find the premises for someone's beliefs and ideas, their conclusions wi...
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