Q:

Why is String theory used when it's not background independent like confirmed general relativity? I know they want to avoid the infinities of a point particle, but still...
Also, why is the effect of gravity additive, when light isn't? *thinking along the lines of photoelectric*...I mean, I could see how it's different exchange bosons, but what makes spin 2 special over spin 1 that it would behave like that?

- Devon (age 24)

USA

- Devon (age 24)

USA

A:

Your first question gave me an excuse to learn a lot from Rob Leigh, a local string theorist. First, I should explain some terms for other readers.

General Relativity is our current theory of spacetime, providing a consistent and very accurate account of gravity. It is "background-free" in the sense that it describes spacetime itself, not some events happening in a spacetime coming from some other theory. The problem is that GR does not fit well with quantum mechanics. A mixed theory, part quantum mechanical and part not, turns out to be logically inconsistent. Simply trying to write a quantum version of GR leads, as Devon says, to calculations coming out infinite, so that doesn't work either.

So that's the motivation to try to find a theory of spacetime which is consistent with quantum mechanics yet looks just like GR on the medium to large distance scales on which GR works so well. String theory is the main candidate for such a theory. However, all current calculations in it start by assuming there's a flat spacetime background, then calculating the ripples and bends around it. Calculations like that can never take the place of a full background-free theory of spacetime. So why would theorists head down a path that couldn't lead to full success?

What Rob tells me is that there's nothing intrinsic in the form of string theory that requires a background. String theory is capable in principle of being a full theory of spacetime. The problem is that the equations are so intractable that one doesn't even know quite how to write their quantum version, unless one makes some major simplifying assumptions. The key assumption is that the spacetime is nearly flat. Someday it should be possible to make a background-free string theory.

Now your second question is easier. "Light", i.e. electromagnetism, is very nearly "additive", in the sense that the fields from different sources just add up, unless they are exceptionally strong. You may have gotten the impression that "light" is not additive because of thinking about its intensity, which goes as the square of the fields. Intensity shows interference effects precisely because it's the fields themselves which are additive, and the sum of two squares is generally not the same as the square of the sum.

Gravity is also "additive" in the same sense. For it too, however, when the fields become very strong (e.g. near a black hole) that additivity breaks down.

Mike W.

General Relativity is our current theory of spacetime, providing a consistent and very accurate account of gravity. It is "background-free" in the sense that it describes spacetime itself, not some events happening in a spacetime coming from some other theory. The problem is that GR does not fit well with quantum mechanics. A mixed theory, part quantum mechanical and part not, turns out to be logically inconsistent. Simply trying to write a quantum version of GR leads, as Devon says, to calculations coming out infinite, so that doesn't work either.

So that's the motivation to try to find a theory of spacetime which is consistent with quantum mechanics yet looks just like GR on the medium to large distance scales on which GR works so well. String theory is the main candidate for such a theory. However, all current calculations in it start by assuming there's a flat spacetime background, then calculating the ripples and bends around it. Calculations like that can never take the place of a full background-free theory of spacetime. So why would theorists head down a path that couldn't lead to full success?

What Rob tells me is that there's nothing intrinsic in the form of string theory that requires a background. String theory is capable in principle of being a full theory of spacetime. The problem is that the equations are so intractable that one doesn't even know quite how to write their quantum version, unless one makes some major simplifying assumptions. The key assumption is that the spacetime is nearly flat. Someday it should be possible to make a background-free string theory.

Now your second question is easier. "Light", i.e. electromagnetism, is very nearly "additive", in the sense that the fields from different sources just add up, unless they are exceptionally strong. You may have gotten the impression that "light" is not additive because of thinking about its intensity, which goes as the square of the fields. Intensity shows interference effects precisely because it's the fields themselves which are additive, and the sum of two squares is generally not the same as the square of the sum.

Gravity is also "additive" in the same sense. For it too, however, when the fields become very strong (e.g. near a black hole) that additivity breaks down.

Mike W.

*(published on 11/30/2010)*