E = mc2
Ah, now there's the most famous equation in all of physics, which is taught in elementary schools, and which is the key to understanding the structure of the universe. So just what does this formula mean?
On closer inspection, we must confess that it actually means nothing. Any equation in 3 variables, where one of them is a constant, is simply a units conversion formula. Essentially, when we decided how to define the units for energy and mass, we goofed, and now we need to apply a conversion factor (in this case, the speed of light squared, which is a fixed number).
But wait, this isn't just a units conversion formula!
Now this here is just a units conversion formula...
°C = (°F - 32) × (5 / 9)
...and nobody thinks that the deepest mysteries of the universe will yield only to those who have mastered the secret art of converting from Fahrenheit to Celsius. But this...
E = mc2
...identifies a relationship among energy, mass, and light that forms the foundation of modern physics, and without understanding this, we can only stand in awe of the genius who could conceive such a thing? Alas, but it is actually just a units conversion formula.
So why does it seem to be so much more than just a way of converting from one system of measurement to another?
"Seems" is the key word there.
In Newtonian physics, kinetic energy equals mass times speed. For example, if a car hits a brick wall, the energy released is a function of the weight of the car, times the speed of the car. The more the car weighs, and the faster that it is going, the more damage it will do to the brick wall. So energy equals mass times speed, and this is intuitively accessible. Swinging a hammer will impart more force if we swing it faster, or if we get a bigger hammer. That's not hard to understand.
Now we come to ponder Einsteinian physics, wherein energy equals mass times the speed of light squared. Instinctively, we think that we understand, since energy always equals mass times speed. But why doesn't it matter how fast the object is moving? And what does the speed of light have to do with it? And why is it the speed of light squared, and not cubed? And wow, that's going to be a big number!
These are extremely puzzling questions, and which, in fact, have no answers. The reason is that such is not the point. When defining a units conversion factor, we just pick whatever number we want. So it's totally arbitrary. It could have been the speed of light — squared or cubed — wouldn't matter. It could have been Einstein's shoe size, or the amount of funding that he hoped to get.
So why, in fact, did Einstein pick the speed of light squared?
Because the speed of light is a really big number. And then we square it, to make it sound even bigger. But we don't cube it, because not a lot of people have an intuitive sense for cubing numbers, and we definitely want to impress a lot of people with this.
In other words, this was Einstein's way of saying, in a pseudo-scientific way, that there is a lot of energy in nuclear reactions. Mass actually doesn't have anything to do with it, and neither does the speed of light. The strong and weak nuclear forces are the issue. But the general public isn't impressed with the relevant formulas from quantum mechanics, which just make them feel stupid because they can't understand any of it, and then they just get pissed off. So scientists just go with pseudo-scientific "formulas" that are intuitively accessible. Then people are proud of themselves because they think that they can almost understand, while at the same time, they're impressed with the genius of the people who can figure out such things, and even more impressed by how big of a number that's going to be!
Bottom line: when studying physics, keep both eyes on the physicist. It might be science, and then again, it might be something that just sounds like science, and that definitely sounds impressive, but actually doesn't mean anything.
Einstein's Pseudo-Science