• Question: What is the equation E=mc^2 used for?

    Asked by michellerana to Cesar, Emily, Jamie, Kate, Philippa on 14 Jun 2011.
    • Photo: Jamie Gallagher

      Jamie Gallagher answered on 14 Jun 2011:

      Oh I think this may be up Cesars street.

      E=mc^2 is used when convering mass to energy. Particles can be though off as being a way of containing vast amounts of energy. This tells us that for every little bit of mass we convert directly into energy we must mulitply it by 9 x10^16 a huge huge number.

      There is still more to this equation though the full equation is:
      E^2=(mc^2)^2+(pc)^2

      but normally p (the momentum = 0) so it all cancels

    • Photo: Cesar Lopez-Monsalvo

      Cesar Lopez-Monsalvo answered on 14 Jun 2011:

      You were right Jamie, I really like these questions!

      This equation is certainly the most famous result derived by Einstein. But what does it tell us? I will guide you through it very slowly so you can get to appreciate its power.

      E means energy. Now you may think you know what energy is. Try to explain someone what is it. I have done it myself and is something that puzzles me even today. I do have a feeling for what it is, but that does not matter for the answer. What matters is that everything, absolutely everything in the universe has some energy associated with it, even the vacuum itself!

      = means the same as

      m stands for mass. Now, mass is easier to understand than energy. Mass is a property of things. If you want a “dictionary like” definition of mass, you can say that it is the opposition of things to changes in their state of motion.

      c^2 is simple c squared, where c represents the speed of light. The reason the speed of light sits there has to do with my explanation about what spacetime is (see http://ias.im/47.305 ), but you can think of it just as a number. In fact, to make calculations easier, it is quite common that physicists just use units in which that number is simply equal to one. So, you can actually write E=mc^2 simply as

      E = m

      Now here is the catch. I told you that everything in the universe has energy, but that is not true for mass. There are things in the universe which are mass-less, for example light. So one way to read the equation is E equals m, that is, if something has energy, then we can find out what its mass is (or would be if it were massless). But also you can read it the other way around: m equals E, that means that every massive object has an energy associated with it just because of its mass. So you use this equation to convert one into the other because they are basically the same thing!!

      One last thing, remember that I am using “funny” units in which c=1, but in this units we measure time with rulers instead of clocks! That was just to make calculations a bit easier. In order to obtain the right results we need to restore the speed of light to its original value of c = 3 x 10^8 m/s or whichever unist are useful for an experiment.

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