Warped Passages - Lisa Randall [31]
As of now, we do not know which, if any, of the many possibilities is the true description of the universe. I will therefore keep all options open, so as not to omit anything interesting. Whatever scenario turns out to describe our world, the ones I will present introduce new and fascinating ideas that no one would previously have thought possible.
4
Approaches to Theoretical Physics
She’s a model and she’s looking good.
Kraftwerk
“Hey, Athena, is that Casablanca you’re watching?”
“Sure is. Want to join me? This is such a great scene.”
You must remember this,
A kiss is just a kiss.
A sigh is just a sigh.
The fundamental things apply as time goes by.
“Hang on, Ike. Don’t you think that last line’s a little weird? It’s supposed to be so romantic, but it almost sounds as if it’s about physics.”
“Athena, if you think that’s strange, you’ve got to hear the opening verse of the original:”
This day and age we’re living in
Give cause for apprehension,
With speed and new invention.
And things like fourth dimension,
Yet we get a trifle weary
With Mr. Einstein’s theory…
“Ike, you don’t really expect me to believe that, do you? Next thing I know you’ll tell me Rick and Ilsa escape into the seventh dimension! Why don’t we forget I ever said anything and just sit back and watch the movie?”
Einstein introduced general relativity in the early twentieth century, and by 1931 Rudy Vallee had recorded Ike’s (true) version of Herman Hupfeld’s song. However, by the time Sam played the tune in Casablanca, the omitted lyrics—as well as the science of spacetime—were all but forgotten in popular culture. And although Theodor Kaluza introduced the idea of an extra dimension back in 1919,* physicists didn’t take the idea all that seriously until very recently.
Now that we’ve seen what dimensions are and how dimensions could escape our notice, we are almost set to ask what triggered this renewed interest in extra dimensions. Why should physicists believe that they might actually exist in the real physical world? That will require a far longer explanation—one that involves some of the most significant physics developments of the past century. In the next few chapters, before launching into a description of possible extra-dimensional universes, I will review these developments and why they serve as precursors for more recent theories. We will look at the major paradigm shifts that happened in the early twentieth century (quantum mechanics, general relativity), the essence of particle physics today (the Standard Model, symmetry, symmetry breaking, the hierarchy problem), and new ideas for approaching currently unresolved problems (supersymmetry, string theory, extra dimensions, and branes).
However, before we plunge into these subjects, this chapter will take a brief journey inside matter in order to set the physical stage. And because understanding where we’re heading also requires some familiarity with the types of reasoning that today’s theorists employ, we’ll consider the theoretical approaches that are critical to more recent developments.
At first I thought “the fundamental things apply” was a clever choice of song quote. But on further reflection the words sounded so much like physics that I decided to check that my memory wasn’t playing tricks on me, as sometimes happens with song lyrics—even those you think are burnt into your head. I was rather surprised (and amused) when I discovered that the song was more rooted in physics than I had ever imagined. I certainly hadn’t realized that the “time going by” was supposed to be the fourth dimension!
Physical insights can work like this discovery; small clues sometimes reveal unanticipated connections. When you’re lucky, what you find is better than what you were looking for—but you have to be looking in the right place. In physics, once you discover relationships, even by following tenuous leads, you look for meaning in the way you think best. That might involve educated guesses or it might involve trying to deduce the mathematical consequences