Last time, I answered some questions from readers Ms. C and Mr. A on special and general relativity. Mr. A asked some very deep follow-up questions, so I thought I’d share them.

Mr. A asks:

I believe you already answered what I had intended to be my follow-up question: spacetime curvature accounts for the acceleration of an object already in motion; but why does a body at rest being to move (e.g. why doesn’t a stationary object hover in the air until someone touches it)?   If I understand you’re post correctly, Einstein would say that there is no such thing as being at absolute rest — all objects are always in motion.  Is that right?

So here’s a different, tangential follow-up:

Quantum mechanics says there is a gravitational force that’s propagated between masses via a particle called a graviton.  Is there a way to reconcile that specific quantum idea with General Relativity, or is this one of the many areas of quantum mechanics that simply diverges from Relativity?  Moreover, what made quantum mechanics physicist decide that Einstein was mistaken and a gravitation force actually does exist?

Yes, you’re right that there is no such thing as absolute rest. Einstein argued that we can only define relative motion. So we can say that two objects are moving (or not moving) relative to each other, but we can’t say that one of them is stopped relative to the entire universe.

There’s another piece to this puzzle, though. Every object is constantly moving forwards in time, so the path through spacetime (as opposed to just space) can be influenced by gravity. Someone’s path through spacetime is called their worldline. In the absence of gravity or an applied force, your worldline will be a straight line pointing mostly in the time direction. However, if spacetime is curved (i.e., there’s gravity), the straightest possible worldline may still be curved. And, as I showed with my Narita to San Francisco example, the straightest possible path may appear more curved than the obvious path. We also talk about worldlines in special relativity (which is the context in which we discovered them), and they’re related to the mathematical description of causality.

Regarding the graviton: I’d say that whether or not gravity is a true “force” is up in the air. General relativity is an incredibly successful theory, as is quantum mechanics, and it’s not at all clear how to reconcile the two. I’d actually say that this is the biggest open problem in theoretical physics. (I’m biased—it’s my research area!) The field is called “Quantum Gravity” and string theory is one possible candidate for a solution. (String theory is by no means the only candidate, by the way. “Loop quantum gravity” is also very popular, and there are plenty of less popular theories too. I work on something called “causal dynamical triangulations,” another candidate theory.) Unfortunately, all potential theories are incomplete, and we’re a long way off from being able to make testable predictions.

In either case, we should expect a graviton, even if it isn’t a force carrier. You’ve probably heard of particle-wave duality, which is the idea that every particle is also a wave. This is one of the foundational ideas of quantum mechanics.

General relativity predicts something called a “gravitational wave,” which is a ripple in the space-time continuum. Essentially, distance alternatively shrinks and grows in time, making a wave of curvature in spacetime. We haven’t observed gravitational waves yet, but we’re trying very hard. The biggest project dealing with this is LIGO:
http://en.wikipedia.org/wiki/Ligo
http://ligo.org/

It’s important not to get confused here. Spacetime is static and unchanging. After all, for something to change, you have to wait, and spacetime encompasses time itself. What can change is the spatial part of spacetime. As the spatial part changes in time, we can get a gravitational wave. This is what the header image shows.

In the late 1800s, James Clerk Maxwell discovered that light can be described as a wave in electric and magnetic fields. Later, scientists discovered that there’s a particle associated with this wave, the photon, which is both a detectable particle and a wave in Maxwell’s electric and magnetic fields. We think that any combination of quantum mechanics and gravity will result in gravitational waves being both waves and particles. The associated particle, the graviton, doesn’t need to be a force carrier. Although most theoretical physicists believe the graviton should exist and carries force, neither condition is guaranteed.

That said, there are physicists who think of gravity as a quantum-mechanical force. Don’t get me wrong—they don’t go back to talking about Newton’s gravity. Instead, they build off of Einstein’s mathematics while abandoning his basic premise. In the article that prompted you to email me (General Relativity Lets us Take Shortcuts), I said that we can define curvature by how we measure distance. It turns out that you can write down how you measure distance at each point in spacetime. At each point in space and at each time, you write down eight numbers. (They can be different at each point.) The numbers tell you how hard it is to travel in a given direction—e.g., if you go north, it’ll take you twice as much work than if you travel east. This is called a “metric,” and the way it changes as you move around is one way to define curvature.

You can turn the metric into a quantum-mechanical wave function, and if you do this, you’ll get a graviton that carries gravitational force. Doing this is paramount to saying that you believe quantum mechanics more than you believe general relativity, since you’re giving up Einstein’s beautiful geometric interpretation of gravity. Doing this is also controversial. As I said, no one really knows how to combine quantum mechanics and general relativity, and it’s not clear which one to trust more.

I should also say that all attempts to make a quantum-mechanical wave function out of the metric have failed. We really don’t know how to make the math work.

Personally, I am very reluctant to give up general relativity’s geometric interpretation. But this is just my opinion and there’s no evidence that I’m more correct than the physicists who believe gravitons to be force carriers.