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Can you explain E= MC2 ?
Answer 1:

This is Einstein's brilliant realization that energy (E) and mass (M) are actually equivalent stuff, but behave differently at different temperatures. It was revolutionary at the time, because he was the first to realize it! Now we take it for granted, but we need it to understand a variety of high energy processes in the Universe!
Let's say we have "stuff". At very high temperatures (like millions and millions of degrees, hotter than you can imagine) all the "stuff" is just pure radiation - pure bright light, and it is very hot. But if you somehow cool this "stuff" then matter will start to condense out of the radiation, like drops of water condense out of cooling steam. So that is a way you can think about what this equation is telling you.
Here's an example of how we use this equation in physics:
The helium atom actually weighs just a tad bit less than the sum of the weights of 2 protons and 2 neutrons. This is because when hydrogen is converted into helium by nuclear fusion (like what happens inside the sun to make it shine) a little bit of mass is actually converted into pure energy. This amount of mass is exactly equal to the amount of energy that is released as heat and light that we measure! It's just a little bit, but there is so much matter in the sun, (2 x 10^30 kg of matter!) that it adds up to a lot of heat and light. (Lucky for us on Earth!)
Here is another example: If you take one particle of matter, say a proton, and combine it with its antiparticle, the anti-proton, what you get is pure radiation, and the amount of radiation is exactly equivalent to what you would calculate from that equation E = Mc^2. By the same reasoning, if you have pure radiation that is hot enough, then equal amounts of matter and antimatter can be spontaneously (all of a sudden, all by themselves) created out of the radiation! In the very early universe - like within the first second after the birth of the universe - the temperature was so hot that matter and antimatter particles were being spontaneously created out of the radiation "field". But as soon as they were created, they would annihilate each other and turn back into pure energy. We can understand this from Einstein's equation.
Fortunately for us, however, there was just a little more matter than antimatter, and so when the universe cooled enough so that this creation process had to stop, there was just matter and radiation left, and the radiation cooled down as the universe expanded, until today, when it is around 3 degrees above absolute zero (about -270 Celsius, or -454 Fahrenheit).

Answer 2:

E = M C^2 relates energy to mass. Specifically it says that if you convert 1 g of mass to energy, you get 9x10^20 ergs of energy -- (To use this just keep consistent units -i.e. Joules, Meters, Seconds, Kilograms, and Ergs, centimeters, grams, seconds. It does not tell you how to do it -- however, you can measure the mass of a deuterium atom and of a helium atom -- and 2 deuterons weigh more than 1 helium atom. So in fusion, if you overcome the repulsion of the protons in the deuterium and fuse them to make helium, the mass difference is made up in energy -- this slight difference powers most of the stars... The revolution was that energy and mass were formerly considered to be fundamentally different commodities. In a sense, this relation forged a new understanding that mass and energy were in many senses the same.

Answer 3:

Let me start by saying that I encourage you to keep up your questions and look into the answers! There are a lot of great books on the special theory of relativity (which includes that equation), so you might try going to a bookstore or library.
First, let's identify the variables in the equation. M is the mass of the object that we are considering. c is the speed of light moving through a vacuum (such as outer space). E is the energy of the object. What is revolutionary about this equation is that it means the mass of an object can be turned into energy. Before Albert Einstein discovered relativity, no one had ever believed that mass and energy could be the same thing.
Before, physicists believed that mass always stayed the same and that energy always stayed the same; now we know that they can be changed into each other. The nuclear reactions in the sun happen precisely because they turn mass into energy.
Those are just the basics. I need to tell you also that E=Mc^2 is often oversimplified. To be more precise, we should write E=Mc^2/(1-v^2/c^2)^(1/2). Now we mean that M is the mass of the object when it is at rest, and v is the speed of the object. This is the correct relativistic formula for energy. It includes both the "mass energy" from the rest mass and the "kinetic energy" (energy of motion: you might have learned about it, since you are in 8th grade). The other thing is that what we mean by "rest mass" is often really energy in disguise. For example, if we look at the mass of a nucleus, it is less than the sum of the masses of the parts. That's because the "potential energy" that holds the parts together is negative, so E=Mc^2 tells us that the mass should decrease by that amount. This is just the start of the story, too, as it turns out that most of the mass of the parts of a nucleus comes from the kinetic and potential energies of their parts!This is such a long and interesting story that I urge you to get out and look into it yourself!

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