Q: Why does “curved space-time” cause gravity?: A better answer.

Physicist: The original post is here.

The curvature of space alone has almost no effect on the movement of objects until they are moving really fast.  With the exception of only the most extreme cases (black holes), space is very, very close to flat.  For example, the total stretching of space due to the Earth amounts to less than 1cm.  The precession of Mercury’s orbit is another example of the tiny effect of the curvature of space (and it is tiny).  Literally, there’s a little more space near the Sun than there “should” be, and as a result the direction in which Mercury’s orbit is elliptical moves.  It takes a little over 3 million years for it to go full circle.

In almost all cases the vast majority of an object’s movement is tied up in its forward movement through time. The curvature of spacetime (not just space) is responsible for gravity. Literally, near heavy objects, the “future direction” points slightly down. So anything that moves forward in time will find its trajectory pointing down slightly.  This takes the form of downward acceleration. This acceleration (time pointing slightly down) is entirely responsible for the motion of the planets, and every other everyday experience of gravity.

In flat space traveling forward in time has no effect on your movement through space. In curved space (e.g., near a large blue mass) parallel lines can come together, and moving through time leads to movement downward.

It may seem a little confusing that, once you’re moving, the explanation doesn’t change and falling is still caused by movement through time.  Well, there is some effect caused by spacial movement and the spacial part of the curvature, but these effects are almost completely overwhelmed by the effects from the time component of the velocity (much, much bigger).

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22 Responses to Q: Why does “curved space-time” cause gravity?: A better answer.

  1. Yoron says:

    This one was a really good definition.
    Pleased to read you.

    Cheers
    Yoron.

  2. Peter Davy says:

    I have been reading a lot about this topic and everybody seems to agree that time is curved. What I don’t understand then is why it doesn’t then become obvious that time MUST be circular. You cannot have a curve, no matter how miniscule, without it eventually becoming a circle. That is a fundamental rule of maths and physics. Therefore time is circular which therefore then becomes the simplest and tidiest explanation of the concept of infinity. Time must eventually come back upon itself and understanding life and the universe is really a matter of understanding how dimensions appear over repetitive circular time rather than linear time.

  3. James says:

    Peter Davy:

    Graph x^2. You will see a curve that never forms a circle. Also, nothing else about what you said makes any sense. Luckily it doesn’t matter so have fun! : )

  4. The Physicist: “In almost all cases the vast majority of an object’s movement is tied up in its forward movement through time.”

    Exactly. Most visualizations don’t show the time dimension. The one below does:

  5. sean farmer says:

    Hi, im digressing slightly as im not sure where to post this question. The explanation of general relativity and the gravitational effects have often been compared to a bowling ball on a trampoline or a footbal on a blanket. Here is my question, if an object with vast density sits in space (like a bowling ball on a trampoline) thus bending spacetime toward it, does that mean if a particle passes this mass BENEATH it, it will NOT be attracted toward the mass?…….Furthermore, can space have an UPSIDE DOWN.

  6. The Physicist The Physicist says:

    In order to be able to picture higher dimensional things, physicists frequently ignore one or two dimensions so that there are no more than three remaining dimensions (which is few enough to be pictured). In the bowling ball metaphor, the sheet is all of space. An object can’t pass above or beneath, because there is no above and beneath. For example, you can go anywhere on Earth, and move in any direction, and gravity will continue to work the same as always, because you’ll always be “on the sheet”.

  7. Ed says:

    Excellent explanation, thanks! I know it’s difficult to explain complex concepts to us non-specialists and I really appreciate when it’s done well.

  8. Joe says:

    In this post the claim is made that space-time is curved, and this is what creates gravity. It also says that the curvature is very tiny. Could the “tininess” of the curvature be an argument as to why gravity is so much weaker than the other forces?

  9. Dylan says:

    Well of course the tininess of the curvature can explain why gravity is so weak! But of course, we have no idea as to why it’s so tiny

  10. Mind2Matter2Reality says:

    Gravity is just an ‘elevator going up’ effect. There is no need for abstract gravity fields and curved spacetimes.

    http://www.themarginal.com/theory_of_everything.html

    Read and think about it. Maybe there is something to be learned from this theory.

  11. Ethan says:

    There are a few things I don’t understand about the curved space theory. First, the theory is represented by a ball on a trampoline, or other flexible surface. Supposedly, the ball causes the flexible surface to form a curve, which you can roll a penny into, and the penny is supposed to rotate. But, if you put a ball on a trampoline and you are in space, no curve will form because there is no gravity from the third dimension to pull the ball downwards into the trampoline. If the curved space theory is true, there must be a force in the fourth dimension to pull our planets, suns, moons, stars, ect ect… against the four dimensional surface our universe is on, which is a surface we cannot see. Why would a curve ever form if there is no “force” to make it form? Also, if the curved space theory is true, why do our planets rotate around the sun? Yes, a ball CAN rotate when it goes into a curve, but it could also just roll straight down into it. Correct me if I’m wrong.

  12. The Physicist The Physicist says:

    @Ethan
    It’s just a metaphor used to explain the idea. However, as you’ve seen, it’s not particularly good. There’s a post about it here and, even better, an xkcd here.

  13. Chad says:

    @Ethan. Not an expert here, but my understanding of the trampoline representation is that the surface of the trampoline represents all dimensions of space time and the mass of the bowling ball is curving it in all directions rather than a single downward force. You could also picture the trampoline surface rotating in all directions around the bowling ball while maintaining the same curvature. In short, mass curves space-time, creating orbital paths for other objects determined by their own mass, trajectory, and speed relative to the first object. Please correct me if I’m wrong.

  14. Barry says:

    In the documentary “Alert Einstein” History Channel,

    http://youtu.be/KcXxHZssCh4

    They said that light from stars moves outward from our expected “straight” path as it passes close to the sun as in the eclipse experiments that confirmed general relativity.
    Why would in move outward from the sun?

  15. Richard says:

    thanks for the post, the better answer, the discussion, and the links… All very fun and informative…

    BTW, penultimate sentence of the first paragraph of the better answer: it’s “than,” not “then.”

  16. The Physicist The Physicist says:

    @Richard
    Thanks kindly!

  17. andrew haworth says:

    I’m curious to understand more, but limited by NOT being a physicist, and having to spend all my time reading medical books instead. The big bang theory vexes me somewhat. I appreciate that we humans are limited by are brains so there are concepts, such as time, which are very hard to get to grips with. I shouldnt therefore be too vexed by the notion that all the mass in the universe originated out of “nowhere”. I’m wondering though if this might be an illusion. If space and time are curved, and perhaps we dont understand the nature and degree of the curve, could this have created the illusion that all the galaxies seem to be expanding away from a single point?
    I am wondering whether the universe might have been created from a series of big bangs. Perhaps, in an infinte universe, there are infinite black holes which can recylce energy. With an infinite number of black holes, all energy lost to space, must eventually be “mopped up”. I’m guessing that a black hole may eventually reach a critical mass when it will explode; could this be the “big bang”.
    I also wonder whether our understanding of the age of the universe can explain the amount of heavy elements found, for example on earth. Given these can only be formed by large supernovas; could there have been enough of these during our perception of the age of the universe, to explain the amount of heavy elements of earth alone?
    Would be grateful if anyone can find the time to put me straight on this; and apologise in advance for the need to have this explained in ways that a non-physicist can understand.

  18. Anders says:

    So does being in free fall count as an inertial reference frame?

  19. The Physicist The Physicist says:

    @Anders
    That’s exactly what an inertial reference frame is!

  20. munna says:

    Time is dimension which we cant visualise. Trampoline example only explains how space-time curvature can be looked at i.e., it gives us best anology to understand the path of a body in spacetime.
    You stand at a place for sometime. Your distance wont change w.r.t earth but still u feel time passing. So, dont understand that just space is curved. In trampoline example only space is curved.

    A real understanding will be as follows.

    Suppose a mass is moving in space with no other mass around it. It follows straight path in space and spacetime. Here you dont observe any difference between space and spacetime. there is change of distance and also time passing but path is linear.

    Now suppose it starts approaching a heavier mass(compare b/w mass of earth and mass of sun for ease). According to general relativity, the path of mass approaching towards larger mass is no more straight line. As time passes it approaches near larger mass but would never travel in straight path but starts to follow a curved path and end up revolving larger mass. There is a chance of smaller mass to spiral around larger mass and take a hit with larger mass and also there is a chance smaller mass to follow a curved path and near larger mass and fly away. Because i comparing with mass of earth and sun i am asuming smaller mass revolving larger mass. So, here as time passes smaller mass takes a path of curve. So we call it as curvature of spacetime: path of smaller mass is curved as time passes.
    But why would it follow a curved path instead of straight line is another explanation and its painstaking to understand.

  21. Greg Marlow says:

    Is it equally correct to say that the gravitational field creates curved spacetime? The potential of a gravitational field at radius R is a diluted speed of light squared ( Ve^2 = 2*G*M/R = (Rs/R)*c^2 ). It is the gravitational potential that bends the speed of light squared of the universe.

  22. VB says:

    The explanation at the top of this page does not answer the question. The question, as I would rephrase it, would be, “Why does the future direction, near massive objects, point slightly downward?” This is the curvature the OP asked about. It does no good to say “it curves”, the question was: “Why does it curve?” Why does the future direction cause a curvature in spacetime near massive objects?

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