Sunday, October 02, 2005

Brian and E=mc^2

Brian Greene had an

  • op-ed in the New York Times

on Saturday about Einstein's famous equation E=mc2. You may recall some of the important developments in the history of physics that took place almost exactly 100 years ago, and some interesting examples showing why this equation is important.

For example, Brian calculates - and you can check it - that if you were able to use the New York Times more efficiently - which means that instead of reading it, you would annihilate it - one copy would give you enough energy for the New York City for one month. :-)

The Times have introduced a funny typo in another article about Einstein on Friday that was corrected on Sunday i.e. two days later. The Lorentz factor was originally written not as

  • sqrt (1 - v2/c2)

but with a sign error. That's pretty entertaining. As far as I understand, it was neither Brian's fault nor the fault of the humble correspondents who were supposed to check his article before it got published. ;-)

It reminds me of the elementary school where I had a bizarre theory. I obviously misunderstood special relativity for quite some time. The best thing I could imagine was - using the current language - a Euclidean spacetime whose signature was (++++). An even more bizarre feature of the model was that the worldlines of light were not tilted lines "x=ct" but rather "x=ctP" where tP was the proper time, namely sqrt(t2 + x2/c2). Whatever the general confused rules were, it meant that the light-like rays were actually horizontal.

How did I add up the velocities? Obviously, as angles in the Euclidean space. And because the speed of light was connected with the angle 90 degrees, you got something like "pi/2+v/c" if you combined the speed of light with another velocity "v" whose angle is "v/c". The sin of this combined angle is still equal to one, up to the second order terms, which - I thought - was enough to explain the negative result of Morley-Michelson aether experiments.

Well, it took several weeks of months before I understood that the spacetime actually is a diagram of the actual events that gives you space at time "t" if you slice it. Such an experience with my own silliness gives one a certain understanding for the reason why many people may have problems to understand relatively simple things - although the understanding is not perfect because if someone had told me how the relativistic spacetime really worked, the confusion could have disappeared instantly, instead of disappearing after long weeks of being lost in the darkness. And maybe not. ;-)


  1. on topic: Albert never wrote the famous equation (in his original paper), as I explain on my blog.

    off topic: Diana is now a movie star, as explained also on my blog.

  2. Meine Damen und Herren,

    you should not understand Wolfgang's statement in the most straightforward way - i.e. that Albert actually did not have an equation equivalent to E=mc^2 in his paper.

    It would be like saying that Wolfgang - who claimed that his Prague fans understood him - did not compose don Giovanni. ;-)

    Albert wrote that if a body absorbs the energy L (from "La Energetiqua"), its mass increases by L/c^2. :-)


  3. Actually, Albert wrote that if a body emits electromagnetic energy L , its mass decreases by L/V^2 , where V is the speed of light.
    He never wrote that famous equation (at least not in his 1905 papers).

  4. By the way, there is a serious point to my remark: New physics is usually not clean and easy. Important breakthroughs are sometimes brief remarks in a half sentence, or a correction in a footnote (e.g. the probability interpretation of QM).
    The conventions and units are usually messy, until somebody cleans it up later (in textbooks).
    Physics often is stuck in a swamp (pun intended) before real progress is made.