If there are any physicists in the audience, please offer corrections in the comments. For the rest of us, may this be a mental exercise.
Across the years, I have from time to time come across the idea that matter bends space.
So is gravity only an illusion caused by a probability function? If that question seemed to come out of left field, don’t worry; I’ll illustrate:
Suppose I stand next to a piece of matter consisting of… let’s say sixty atoms. All those atoms vibrate (because we’ll assume a temperature above absolute zero). Let’s imagine a moment when each atom is moving in a random direction, but the average of all their vectors (directions) is zero (i.e. no movement for the piece of matter as a whole). Acknowledging six cardinal directions (up, down, left, right, forward, backward), we can assume that 1/6 of the atoms in our example matter are moving toward me (more or less) at our example moment. (Imagine me on the matter’s right side. If you don’t know what I look like, just look at the picture:)
Now, if matter bends space, then my presence next to our example matter curves space such that four of the cardinal directions get bent (upward is now slightly rightward; so too are downward, forward, backward slightly rightward). Therefore more than just 1/6 of the example atoms are moving in my direction, and the other five cardinal directions are represented less. This imbalance results in a non-zero average vector for the entire example solid, so that example matter actually moves toward me!
This movement of physical bodies toward each other appears like a pull or attraction, but it’s in fact the result of curved space and probability. As the example matter and I near each other, we approach the place where the curves in space are most pronounced, so our atoms have a higher probability of moving toward each other, and the appearance of attraction increases.
I have always disliked the “rubber sheet” model of gravity, which incorrectly explains gravity and does so in terms of gravity… I’ll try to explain it more accurately.
Gravity curves space-time, not space alone. The full geometry is a bit complex (it’s actually modifying the underlying metric of a Minkowski spacetime, a hyperbolic geometry), but we can still give reasonable explanations much better than the “sinking into soft flat surface”. It’s easier with pictures, but I’ll do my best without.
Suppose we draw a graph of a 1D world. Time is the y axis, space is the x axis. If we plot the position of some moving particle it will make some kind of curve, a different x (position) at every y (time). If there are no forces acting on the particle, this curve will be a straight line: a vertical line if it is not moving, a sloped line if it is moving at a constant speed. If we apply a force to the particle it will accelerate and the path it takes through space-time will be curved. The time element is important here: every particle “moves” through space-time, even if it doesn’t move in space.
General relativity says that gravity, unlike other forces, doesn’t curve the path of particles, it curves the space time in which they still move in straight lines. This curved x-y space-time plane is the origin of the “rubber sheet” analogy. But why we draw it warped the way we do is a bit difficult to understand. We first need to consider the definition of “straight.”
Consider a vehicle with two wheels side by side. Such a vehicle is moving in a straight line if both wheels are turning at the same speed. If the left wheel is turning faster than the right wheel than the vehicle is turning to the right, and vice-versa: the vehicle turns toward the wheel that is making less progress. Let’s take the idea of both wheels turning at the same speed to be the definition of “straight.” (With appropriate mathematical generalizations, a straight path under this notion is called a “geodesic.”) Now let’s suppose that the road has a hump (or dip) in it that is higher (lower) on our right side than on our left. Because the hump (dip) adds some length to the path, the left wheel will cross it before the right wheel so the geodesic across this hump (dip) will turn to the right.
In general relativity, the curvature in space-time caused by gravity causes geodesics to turn toward massive objects the same way they turn toward humps in the road. But the hump moves with the particle as time advances, so it might be more accurate to think of ripples emitting from massive particles as they move. Every particle moves through space-time as time advances; and as it does so the wheel nearer a massive object has bigger ripples to climb, meaning the particle’s geodesic (i.e., motion without any force applied) turns towards massive particles. If it also has forces pulling on it, causing one wheel to turn faster than the other, it still has the curvature of space-time working on it too; thus the geodesic curvature of the earth’s gravity is balanced by the electromagnetic forces caused by my feet not wanting to share space with the ground and thus “turning” away from it.
Space is not bent. The four cardinal directions are still the four cardinal directions, and there’s no change in probability nor is temperature needed. What is bent is space-time. I had some difficulty putting this in text alone, so I wrote up a blog post on it where I could add illustrations.