Imagine two cubes each with the side 1 light year. One of the cubes is empty of any matter. The other cube contains a massive star.

  • Does the cube which contains the massive star have a larger volume than the empty cube? (Because the mass makes space curvy)

  • If the star is replaced by a gas cloud of the same mass but which is evenly distributed inside the cube, does the volume of the cube change?

  • Is it not enough with geometry to calculate volumes? Is knowledge of the mass (and its distribution?) also necessary?

  • Does mass (concentrations) create new space volume, or does it just change the properties of the space around it?

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    $\begingroup$ I believe your question might be answered by here already. $\endgroup$ – Aaron Jul 2 '14 at 6:18
  • $\begingroup$ Your question seems to assume an absolute reference frame, which we know does not exist. $\endgroup$ – adrianmcmenamin Jul 4 '14 at 14:52

This is a tough question to answer because the dimensions of your proverbial cube would be affected by the mass inside (as dimensions can only exist in space, so anything that affects space will also bend your cube), and mass does not bend space, it bends spacetime. You have to keep in mind that when talking about special and general relativity, you are talking about four-dimensional spacetime. This is what is curved by mass. For example, due to the curvature of spacetime due to Earth's gravity, you feel the same effects on its surface that you would if you were accelerating upwards at 9.8 m/s^2 through deep space (where we assume there is no gravity). This doesn't mean the physical space is curved - if you draw a straight line on a piece of paper in space and then travel down to Earth's surface, it will remain straight. Instead, spacetime is curved, which can affect objects' paths of motion, but not the objects themselves. Now to your questions:

  • The volume inside of the cubes would be exactly the same, but two identical objects flying through each cube would follow two different paths, and if either looked at the other, it would see that the other's clock is moving at a different speed than its own due to time dilation (due to the curvature of spacetime towards mass, time moves more slowly closer to massive objects). We can see evidence of the effect of gravity on paths with gravitational lensing. Light travels in a straight line through spacetime, but when looking at the space around a star, you will actually see objects that should be directly behind the star and blocked from sight. This is because light rays that, in the absence of gravity, would pass next to the star and continue off at an angle are pulled towards the star by it's gravitational field (in reality they're just following the curvature of spacetime around the massive star), so they curve around the star, becoming visible to us, even though, in space alone, they should be blocked by the star.
  • The distribution of the mass has no effect on the gravitational field around it (same with electromagnetic fields). If you look at any equation that has to do with gravity (gravitational potential energy, gravitational force, etc.), you will find a term for the total mass of the object, but unless you are within the bounds of the control volume containing the mass, the distribution does not matter. This is one of the reasons why black holes are so hard to study - we can tell how much mass is inside of them, but without the ability to see inside, we have no other way of detecting their properties.
  • Like I said above, the volume is not affected because space is not warped by gravity, only spacetime. If you made a physical box (or we'll say a cube frame) around empty space and then moved it to a space that contained a star, it would remain the same size and shape (assuming that it was strong enough to withstand the force of gravity pulling it towards the massive star).
  • Neither, it simply curves spacetime.

Is it not enough with geometry to calculate volumes? Is knowledge of the mass (and its distribution?) also necessary?

To answer this question. Mass distribution does make a difference. For example, if a star collapses into a black hole, the mass of the black hole is less than the original mass of the star due to some matter lost during the supernova. But now the star is compressed into a more compact space. So, now one can reach much more closer to its center(and experience more gravitational force) than one could have before, So, a BH is a deadlier object than normal stars.

  • $\begingroup$ Why the downvote? Is there anything wrong with the answer? $\endgroup$ – Yashbhatt Jun 30 '14 at 7:49
  • $\begingroup$ I didn't downvote your answer, but I think that the physical removing of mass (by a supernova) is beside what I'm asking about. Maybe my question was unclear. $\endgroup$ – LocalFluff Jul 2 '14 at 6:23
  • $\begingroup$ What I was trying to say is mass distribution shouldn't affect gravity. $\endgroup$ – Yashbhatt Jul 2 '14 at 12:25

In my opinion yes, mass affects volume. Instead of a cube, imagine a pyramid with a 3 sided base. All edges have the same length defined by the time to reflect light back and forth between the apexs. The number of smaller such pyramids that could be fit inside would increase with mass because the path of light would be bent. Bent light means bent space, as well as bent spacetime. They are not independent. Per Einstein, the speed of light is not constant when mass is present and depends on the coordinates. This amounts to more space. I believe that it was Eddington who first tried to quantify how much space is added by a given amount of mass.


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