About the everyday miracle of the movement of objects
According to Newton’s first law (the law of inertia), a body will always move in a straight line at constant speed if no forces act on it or if the sum of all forces is zero. For example, if I am in open, absolutely empty space and throw a stone, it will keep flying in a straight line forever.
So what happens on Earth? I throw a stone and it traces out a parabola. Most people will say that it is pulled down by gravity, and it is very intuitive and convenient to talk about it that way. But we do not live in Newton’s times anymore, since Einstein published his general theory of relativity (GR) in 1915.
Within this theory, there is not three-dimensional but four-dimensional spacetime, that is, time is added to the three spatial coordinates as a fourth dimension. Massive bodies like planets strongly curve this spacetime. And objects move through it along so-called geodesics.
If you take a globe and connect Moscow and London with a piece of string, that will be the shortest path between them. If you then look at that same path on a flat map projection, it becomes a curved line. So in three-dimensional and two-dimensional space, shortest paths can look different. A geodesic is the analogue of such a shortest path, but now in four-dimensional spacetime.
Now imagine I am an inhabitant of a two-dimensional flat world map. I see on the map that someone has followed a weird trajectory connecting Moscow and London. It looks silly to me: why do that if you could just go straight? And then a resident of three-dimensional space comes to me and says they flew by plane, and for them that weird curve actually was the shortest route. They were flying along their own geodesic, which looks straight to them but appears curved to me, the two‑dimensional being.
We also do not perceive the additional time dimension directly. So when we throw a stone and see it trace a parabola, what is really happening is that it travels along a straight line in curved four-dimensional spacetime. If we could perceive that fourth dimension, we would see a straight line.
You might object that we do perceive time—five minutes have passed, after all. But we do not perceive it in the same way as space: we can feel its flow, but in practice we only directly experience the “now”, while we can take in an extended spatial object “at a glance”, for instance seeing its length.
So from birth, every single day, we are constantly observing spacetime curvature in action. People often say that the laws of relativity only show up at speeds close to the speed of light and have nothing to do with everyday life—well, except for satellites and such. But look: I throw a slipper, and it follows some trajectory precisely because it moves through curved spacetime, and I am literally watching this with my own eyes right now, while the slipper itself is actually flying along a straight line. It is not that Earth pulls it down with some mysterious force; instead, Earth warps the spacetime we live in so that objects move along different straight lines, which happen to look curved to us.
Those “straight” lines are straight only in 4D. And that leads to a surprising result: the stone or slipper is moving through 4D spacetime strictly in accordance with Newton’s first law—uniformly and in a straight line. Wrapping your head around that for real is a genuine brain-exploder.