The original question was: … also brings up the famous Einstein analogy of a bowling ball in a mattress as bending spacetime. What confuses me is that this seems circular- using the analogy, say we put a bowling ball on a mattress and then roll a marble past it. The marble will fall in towards the bowling ball. But what’s causing it to fall in? Gravity!
Physicist: Here’s what this is about. Way back in the day a popular demonstration used to explain how the presence of matter creates gravity was to drop a heavy ball onto a sheet of some kind, and then roll a smaller ball around the inside of the indentation that is made. If you were to try this demonstration while floating around on the space station you’d be wasting time that could be better spent putting on pants two legs at a time (no gravity to pull the bowling ball and make the indentation in the first place).
In Newtonian mechanics gravity is a spooky, unexplained force. In Einstein’s General Relativity gravity is caused by the curvature and stretching of space and time. Objects move in straight lines like always, but the messed up spacetime they move through makes it appear as though they’re changing direction (that is to say: falling). What’s weird as hell is that they really are moving in straight lines locally, but not globally. If you carefully try to draw a straight line on a bowl you’ll find that it may be straight if you look at a tiny piece of it, but if you stand back it’s curved.
The bowling-ball-mattress thing is another example of how messed up geometry can create “force”. It’s just a bad metaphor. In the one case the pull toward the center is a result of the object in question following a straight line through a messed up spacetime, and in the other it’s trying to roll downhill.
Different.
If we place two immobile objects (relative to each other and with no other objects in the near vicinity) they would start approaching due to gravity, right? The shape of space-time must also start this movement, not only change locally the direction of the straight lines. What am I missing?
Thanks for this great blog (and for your patience with silly questions
Related to this – We’ve got a demonstration about gravitational lensing at the museum I’m interning at. One time a visitor asked me how we know that space is bending and not just light itself, and I didn’t know quite how to explain it to him.
On your other post about the bending of space, you mention that the curvature of space can be detected by measuring distance. How exactly is that done? You said that there’s an 18 mm difference in the diameter of the Earth because of the curving of space, but how was that detected, or was that just the result of theoretical calculations?
So do you have a suggestion for a solid, understandable, somewhat brief argument for why we know space gets warped? (And/or, since we all agree that the bowling ball on a sheet is kinda a bad metaphor, any ideas for a better one?)
The question above me is really interesting too. I’m looking forward to an answer for that!
Unfortunately, most tests of general relativity are plagued by noise. The effects are very small, and the best source of mass, and stretched spacetime, we have around (the Sun) is extremely “loud”. There are several, fairly small scale, experiments that verify the effects of curved spacetime and general relativity. They include:
1) Keeping ridiculously accurate clocks on different floors of a building (they go out of sync because the higher floor experiences more time)
2) Observe the progression of Mercury’s orbit (it has a greater distance to travel when its near the Sun, which makes its orbit disagree with Newton’s “flat-space” predictions)
3) Measuring “frame dragging” (the rotation of the Earth does interesting things to spacetime, like twirling a spoon in pudding)
4) Bounce light up and down and show that it experiences red- and blue-shifting.
5) Bounce radar beams off of Venus and Mercury when they’re almost right behind the Sun (the beams are slightly bent, and also delayed because of the spacetime curvature)
#1, #4, and #5 may seem like strictly time experiments, but keep in mind that special relativity gives us a solid understanding of the relationship between space and time, so in these cases and experiment on one is an experiment on both.
#3 is a direct, well known result, that is entirely due to spacetime being curved. None of this “light bouncing around” crap.
The best experiment would be very, very expensive and probably impossible. Build perfectly straight, unimaginably strong, beams that are longer than the Earth is wide. Then build a triangle with them. You’ll find that far away from the solar system (in really, really deep space) the sum of the internal angles is 180°, exactly like you’d expect. But if you build the same triangle near the Earth, the sum of the internal angles will actually add up to a tiny bit more than 180°. This is for exactly the same reason that a triangle drawn on a sphere has more than 180°: it’s on a curved surface.
One of Einstein’s great insights was to consider “movement through time” on a more or less equal footing with “movement through space”. So even if you start with two objects that are perfectly still (with respect to each other), they’ll still be moving through time (your watch still works even when you’re just sitting around). The curvature of spacetime turns this movement through time into movement through space.
In fact, unless you’re moving at nearly the speed of light, most of your velocity is tied up in moving through time.
So there’s no “starting” or “stopping” movement. Everything is always moving, it’s just a question of which direction (and that includes the time direction).