Spacetime

Over the years, I’ve read a number of “popular” physics books aimed at a general audience who are not physicists. I usually learn something new from the book I’m reading, or at least I think I do. Several years later, I read another book that discusses the same topic and sometimes I skim because it just sounds the same. But on occasion, I start to realize that what I thought I learned is now superceded by a better explanation. This is the case with why does E=mc²?by Brian Cox and Jeff Forshaw. 

 

The crux of the story is why mass exists and the equivalence of mass and energy via Einstein’s famous formula. While that’s not new to me, how they narrate the story is enlightening. Instead of a historical derivation, they begin with the conversation of momentum augmented by the need to use special relativity so that all observers agree on the reference frame. This frame is done by combining space and time into four-dimensional spacetime, a blocky and seemingly static Parmenidean picture – but with the advantage of allowing for conservation or un-changing-ness. Beautifully, the law of conservation of energy pops out from this story. This was my Ionian Enchantment moment. The authors promised me that it would come, and they delivered!

 

Unlike other pop physics texts, there is some math in this one. Not too much to turn you off, but enough for me to appreciate the power of their approach. There are a number of figures in their book (mostly two-dimensional graphs) and I found them particularly helpful in appreciating the difference between Pythagoras and Minkowski, and why spacetime diagrams are often pictured as two cones with pointy ends touching each other. The authors also clarified for me why being at rest means roaring forward at the cosmic speed limit of c, and that this definition of c is more general than thinking of it as the speed of light. They also shed light on why massless photons speed off at c from any observer’s reference.

 

In my quantum chemistry class, I briefly make reference to E=mc² and distinguish rest mass from relativistic mass by its “enhancement factor”. Cox and Forshaw derive this same factor in more than one way, thus highlighting its significance. They also make a useful approximation that combines Einstein’s formula with the standard expression for kinetic energy of ½mv², which was very useful in thinking about the whole baffling problem of clocks running differently for observers traveling at different speeds relative to each other. So although this book was aimed at the story of the origin of mass, what I learned from it was how to think about spacetime.

 

The origin of mass story is interesting in its own right. I learned a little more about interpreting Feynman diagrams, and now I have some appreciation for the parts of the equation in the standard model that describe the Higgs field. I still have trouble thinking in terms of fields – perhaps that’s why I’m a particulate-thinking chemist rather than a physicist – but I now know a tiny bit more why gauge symmetry is important. If much of what I’ve written in the last few paragraphs sound like science gobbledygook to you, I recommend Cox and Forshaw’s book. It takes a little more work to digest (at least for me it did), but I got more out of it. Perhaps the moral of the story is that I need to put in the work to reap the reward. And yet, there is so much more to learn. The authors couch their story with a sense of wonder, and it leaps off the pages in their book. It’s motivated to do better in my teaching – to improve the clarity of a complex topic while maintaining its enchantment!