Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? Isn’t it gravity that makes the dip in the first place?

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.

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14 Responses to Q: What’s up with that “bowling ball creates a dip in a sheet” analogy of spacetime? Isn’t it gravity that makes the dip in the first place?

  1. Joao Neto says:

    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 🙂

  2. Katrina says:

    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!

  3. The Physicist Physicist says:

    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.

  4. The Physicist Physicist says:

    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).

  5. If this is silly thinking, let me know, but please indulge me for a moment…

    If velocity is distributable in 4 dimensions(x, y, z, t) and particles can only have either positive or negative ‘velocity values’ of any single dimension.

    Isn’t “time” a misnomer in this context? When reading about this, I get a strong sensation that when talking about time, we’re really talking about mass. Time seems like an incredibly subjective effect, while mass seems more interlinked with the other three dimensions. If you take a photon, it has all it’s energy distributed in either x, y or z momentum, and if more energy is added, it goes into simply more mass; time is not affected? So if no particles had energy taken from their x, y, z velocities and put into their ‘mass velocity’, time would not exist?

    As such, does the higgs field create time?

  6. The Physicist The Physicist says:

    When you talk about “4-momentum” the three spacial components are the usual momentum, but the time component (surprisingly) is energy. There’s a beautifully written post that covers this (fairly) well over here: Why does E=MC^2?
    Time and mass are definitely different things. A photon (like everything else) has it’s momentum in the usual spacial components, and it’s energy in the time component. Unlike other things, it’s energy and momentum are strictly tangled up. If you increase its energy, its momentum increases proportionately. This strict proportionality can be derived from the photon’s complete lack of mass, and Einstein’s energy-momentum equation.
    I may not understand your argument entirely, but to the best of my knowledge, aside from the usual (general relativistic) relationships between energy/mass and time there’s nothing special about the Higgs field.

  7. Curious says:

    I have a hypothesis (very ignorant of physics and seeking enlightenment) that gravity is the normalization of mass, and predict that the changes in accelleration due to gravity (relative to distance from a massive object) would correlate (at least roughly) with a normal curve (bell curve). What are your thoughts, anyone!

  8. Curious says:

    Also in reference to “moving through time”. Would this be an example of an infinite string of events, which then could create an analogy between the effects of gravity and regression toward the mean (with large numbers of events).

  9. The Physicist The Physicist says:

    The acceleration due to gravity is proportional to \frac{1}{r^2}. A “normal curve” gravity would be proportional to e^{-r^2}, which decreases much much faster. We know that gravity decreases by \frac{1}{r^2}, in part by direct measurements, and in part because elliptical orbits only exist for “\frac{1}{r^2}” gravity (and orbits are ellipses).

  10. The Physicist The Physicist says:

    If you look at things quantum mechanically, you can sorta describe gravity as a probabilistic thing. Sorta.
    In fact, ignore that.

  11. Paul Barry says:

    I’m wondering how best to describe what is happening to spacetime closer to the surface of a massive object. Let’s take the proverbial apple falling from a tree to the ground as an example. How is spacetime warped here? The apple accelerates in a straight line to the ground (let’s ignore the wind, earth rotation etc.). This doesn’t seem to be a curve so much as a radial acceleration towards a point. What is happening? Is space accelerating into the earth taking the apple with it? Does mass somehow suck up space? What happens to this space? Does it accumulate or vanish in some way or just become mysteriously undefined. Are these stupid questions? Have I missed something?

  12. The Physicist The Physicist says:

    They’re good questions!
    The important part of the curvature is between the radial direction and the time direction (this is very tricky / impossible to picture). The apple starts out traveling entirely in the time direction, and then when it falls its spacetime path (as opposed to just space path) curves more and more into the downward radial direction. There are so old posts that try to cover this, but at the end of the day this is just a difficult thing to wrap your head around.

  13. It gets worse when you consider that the deformation of space-time is not a downward inclination but rather a diminution of the metric of space-timeb all around the centre of gravity. 1 foot = 11 inches. 1 foot = 10 inches, 1 foot = 9 inches, and so on.

    In this case you have to accord a personal speed to an object. So that if the speed is sufficient, the object will be able to pass through de deformation in a curved trajectory, if not sufficient, its speed will stabilise it on an orbit around the centre of gravity of the deformation, and if not speedy enough it will fall to the center of gravity in a curved trajectory.

    As for the apple that falls for a tree, its speed will increase during the fall as Newton formula says. You can take the apple and throw to the ground at great speed and it will still increase as the same formula says. Not because the groud attract the apple but because de déformation of space-time is deformed right to its center of gravity.

    Even the space occupied by the Earth is dĂ©formed. Matter doesn’t dĂ©form space-time; it simply occupies it, without cancelling it. Matter doesn’t replace space; it occupies it. It’s the mass Ă©nergy in matter that dĂ©forms space-time by acting on the centre of gravity of the deformation which is not always the centre of the volume of the object.

    But my way of seing gravity might be wrong; but up untill now, I haven’t found reason to beleive so.

  14. David Martin says:

    What makes the apple start to fall? The shape of space can affect how it moves once its moving, but I can’t see how it gets it moving in the first place. And before it falls, it feels a force pulling it, trying to get it to move. What causes that – again, the shape of space doesn’t seem enough on its own to do that.

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