Gravity:

This is an explanation of how gravity pulls on things. As in my blue sky pages, it doesn't provide a completely satisfying picture of why everything is the way it is, but no scientific explanation can do that. It does fill in some of the details of how gravitational pull is modeled by the best known description of particle motion (quantum mechanics) combined with the best known theory of gravity (general relativity).

It is the most intuitive picture I know of how the space-time geometry of general relativity gives rise to a gravitational pull. It's unusual that the addition of quantum mechanics can actually make the description of something more intuitively accessible.

In various places in the following text, I link to the corresponding section of a more mathematical discussion of this same topic (descriptive version | visual version). If you are interested in the equations, you can see them there, but if you're not, you don't have to.

In quantum mechanics, particles are described by wave functions. These waves have a value at every point which is a complex number, a value that can be represented as a little arrow in a two-dimensional plane. The length of the arrow, when squared, has to do with the probability of finding the particle there. The orientation of the arrow is called the phase.

When a particle has a fairly well-defined momentum pointing in some direction, its wave function's phase varies continuously in the direction of motion. If the particle is moving along the z axis and I plot the curve traced out by the tip of the arrow in the x-y plane, the curve is a helix, like a screw. The tighter the helix is, the larger the momentum. The direction of the momentum is related to the handedness of the helix. The wave function in the picture corresponds to an upward-moving particle, so the helix is right-handed.

To the math: Descriptive version | Visual version

If the particle's energy is fairly well-defined, then the phase rotates with time, at a rate determined by the energy of the particle. A wave with a helical phase will appear to slide along in the direction of motion, like the stripes on a barber pole. (The apparent speed of the barber pole is the phase velocity of the wave, which is not the same thing as the group velocity that determines the speed of a localized wave packet. But that is another story.)

Einstein's general theory of relativity is the best working model of gravity as it operates in the world. One thing you may have heard about general relativity is that it predicts gravitational time dilation: clocks run more slowly in regions further down in a gravitational field, according to an observer further up.

To the math: Descriptive version | Visual version

This effect has been seen and measured quite directly, for example, by atomic clocks on airplanes and rockets. The difference is tiny over everyday distance scales. You might regard it, then, as an exotic by-product of general relativity of little relevance to you. Not so! It is, in fact, the cause of gravitational pull under everyday conditions. It's what keeps you pasted to the ground.

Consider, for simplicity, a particle that is traveling vertically upward. It has a moderately well-defined upward momentum and a moderately well-defined energy. The stripes on the barber pole are screwing up into the sky.

How fast is the helix rotating? Well, usually in quantum mechanics, as in classical physics, we are free to set the zero of energy anywhere we want, and consequently redefine the speed of phase rotation. It doesn't make a difference to the calculated results. But all that changes if we are going to study general relativity. General-relativistic effects usually depend on what the absolute, fixed value of the energy, and we can no longer ignore the energy due to the particle's mass, E = mc².

So, okay. The wave function's phase is rotating at a definite fixed speed proportional to mc² plus a tad (for the kinetic energy). With the approximations we're making, we might as well call it mc².

Now consider the effects of variations in time. Time goes a little faster at the top of the helix than at the bottom. The different parts of the helix rotate a bit out of step, and it starts to unwind! Eventually it unwinds completely and starts to wind up again in the opposite direction.

To the math: Descriptive version | Visual version

The helix is now left-handed. The particle's momentum has reversed and is now pointing downward, and increasing. The varying time dilation made it turn around and fall back. The rate of change of momentum is the force. Since the speed of phase rotation is proportional to the mass, the rate at which this whole unwinding and winding process happens is also proportional to the mass. So we've shown that the force on the particle-- its weight-- is proportional to its mass. Looks like gravity, all right.

Romper bomper domper doo. Through my Magic Mirror, I hear some of the brighter of you saying: Wait a minute! We've read that quantum gravity is some elusive chimera of theoretical physics. Did he just produce it for all to see?

Not really. The big problem with quantum gravity is how we make the geometry of spacetime respond to the tug of quantum matter. That seems necessarily to involve a quantum description of the geometry itself, and that is a hard thing to formulate correctly. In this case I just used the classical (that is, non-quantum, but relativistic) notion of the geometry of spacetime near the Earth, and treated that as a static playing field on which quantum particles cavorted. That's not nearly as difficult.