Do objects really take up space?

[taurusaud]

Do objects really take up space, or does space bend around objects (like when you put a heavy object in water, and the water bends around the object to make room for it)?

In other words, does matter effect the size of space? Like if you removed all physical matter from the universe, would the amount of space also decrease, or would it remain the same?

 

[phinds]

Given that the removal of an object in one place cannot possibly affect the existence of space that is outside its light cone, I can't see how it would be possible to say that it has any affect on space.

 

[taurusaud]

Given that the removal of an object in one place cannot possibly affect the existence of space that is outside its light cone, I can't see how it would be possible to say that it has any affect on space.

So do objects not affect the shape of space then? Because I read that gravity was caused by space "curving" around an object? Michiu Kaku says this much:

"Stretch out a bedsheet and place a rock at its center. The rock will curve the sheet in its direction. Then imagine rolling marbles around the bed sheet in a circular fashion. This circular movement is caused by the curvature of the bedsheet around the rock.

This is the Einsteinian definition of gravity - curved space-time causes acceleration or motion. The reason why planets orbit around the sun is because they are moving in the space curved by the density of the sun. The reason we can stand on the Earth is because the Earth warps the space around us."

Now obviously this is just a simple extrapolation for visualization purposes, but one could say here that the sheet does move to make way for the rock (the rock indents the bedsheet). So I'm wondering if this is also true given a 3-d (or 4-d) model of space?

 

[phinds]

So do objects not affect the shape of space then?

That is not even remotely what I said. You are now asking a different question. Objects affect the geodesic along which light travels so the removal of a massive body would change the geodesic, but that has nothing to do with the SIZE of space, which is what you asked about in your first post.

 

[taurusaud]

That is not even remotely what I said. You are now asking a different question. Objects affect the geodesic along which light travels so the removal of a massive body would change the geodesic, but that has nothing to do with the SIZE of space, which is what you asked about in your first post.

... I'm sorry, I guess I meant shape, not size...

If you have a bathtub full of water and you throw rocks inside, the water level will rise, because the shape of the water curves around the rocks...

So is it fair to say that if you (for visualization purposes) had the whole universe in a bathtub, and you removed all the planets, stars and particle matter, would the level of space inside the bathtub decrease? That's what I'm wondering. Do objects really take up space (i.e. drawing lines on a sheet of paper - those lines now take up space on the paper), or does space curve to accommodate objects (i.e. water curves to make room for rocks and other objects)?



In other words - if it's the latter (which sounds like what Michiu is saying and, I believe you, are saying)... then I have a hard time accepting that... because as space expands (under universal expansion), wouldn't matter be constantly expanding as well since atoms are mostly empty space? Wouldn't we all be torn apart as space expands? Wouldn't the fact that we're all still here point more toward objects indeed taking up space rather than space curving to accommodate them... ?

 

[phinds]

... I'm sorry, I guess I meant shape, not size...

If you have a bathtub full of water and you throw rocks inside, the water level will rise, because the shape of the water curves around the rocks...

So is it fair to say that if you (for visualization purposes) had the whole universe in a bathtub, and you removed all the planets, stars and particle matter, would the level of space inside the bathtub decrease? That's what I'm wondering. Do objects really take up space (i.e. drawing lines on a sheet of paper - those lines now take up space on the paper), or does space curve to accommodate objects (i.e. water curves to make room for rocks and other objects)?

I have already answered that question. Read post #2.

In other words - if it's the latter (which sounds like what Michiu is saying and, I believe you, are saying)... then I have a hard time accepting that... because as space expands (under universal expansion), wouldn't matter be constantly expanding as well since atoms are mostly empty space? Wouldn't we all be torn apart as space expands? The fact that we're not would point more toward objects indeed taking up space rather than space curving to accomadate them... ?

Matter does not expand. No gravitationally bound systems expand. Space expands.

 

[taurusaud]

I have already answered that question. Read post #2.



Matter does not expand. No gravitationally bound systems expand. Space expands.

I don't understand your answer. Are you saying that

1) objects take up space
-or -
2) space curves to accommodate objects

 

[Fredrik]

If space was really deformed in the way you imagine by the presence of an object, then things would be really weird. For example, suppose that you and I are standing 10 m from each other, and that a third person puts a 1 m × 1 m × 1 m metal cube at the midpoint of the straight line from you to me. If space is pushed away the way you imagine, then you and I would both measure the distance to the closest face of the cube to be 5 m, not 4.5 m.

The geometry of spacetime (and therefore "space") is affected by matter, but not in that way. The relationship between geometry and matter is much more complicated. It's described by Einstein's equation.

 

[taurusaud]

If space was really deformed in the way you imagine by the presence of an object, then things would be really weird. For example, suppose that you and I are standing 10 m from each other, and that a third person puts a 1 m × 1 m × 1 m metal cube at the midpoint of the straight line from you to me. If space is pushed away the way you imagine, then you and I would both measure the distance to the closest face of the cube to be 5 m, not 4.5 m.

The geometry of spacetime (and therefore "space") is affected by matter, but not in that way. The relationship between geometry and matter is much more complicated. It's described by Einstein's equation.

I'm not sure why you say the difference would be .5m? Where did you get that number from?

Because if the "space curves" conclusion is correct then placing the metal cube would indeed bend the space around it, but surely it wouldn't bend by a whole .5m in every direction? Much like gravity, the space-curvature should only be measurable on objects of astronomical scales (like planets, stars, etc), right? Since the actual curving is taking place on an atomic scale (i.e. space is basically wedging itself in between all the atoms of the object), therefor you'd need something either really large or really dense to measure a discernible curve in the outerlying space..

The metal box would effectively bend space, but the resulting curve would be so tiny that it's barely detectable by our current measurements. So unless you can explain how you got the .5m, I think your example doesn't really apply here. And note that I'm not saying that space does or doesn't curve to accommodate objects - I'm here asking because I don't know...

 

[Fredrik]

OK, I misunderstood you then. I don't see anything wrong with what you're saying now (in post #9).

 

[Drakkith]

So is it fair to say that if you (for visualization purposes) had the whole universe in a bathtub, and you removed all the planets, stars and particle matter, would the level of space inside the bathtub decrease? That's what I'm wondering. Do objects really take up space (i.e. drawing lines on a sheet of paper - those lines now take up space on the paper), or does space curve to accommodate objects (i.e. water curves to make room for rocks and other objects)?

The following is my understanding of how it all works. I could be wrong.

Spacetime is curved by mass in such a way that it alters the geometry associated with spacetime. However this is not the same thing as matter taking up space.

For example let's consider an empty stretch of space with 10 points in a line equally spaced apart to represent the shortest distance from the 1st point to the last point. This is called a geodesic. Now, if we add a massive object nearby the 10 points are no longer in a straight line through space. The line from point to point is now curved. The points still represent the geodesic, the shortest distance from the first to the last point. Realize that the points do NOT represent space itself, only locations within space. This is the key thing to understand. Spacetime is not a "physical thing" in the sense that you can touch it, meaure it, etc. Our understanding of spacetime, as given by General Relativity, only describes how matter and light acts within spacetime, not what spacetime is itself. When we say that it is curved what we mean is that the movement of light and matter within spacetime behaves as if the underlying "surface" it were on were being curved. This is analogous to how things move around on the surface of the Earth, as the surface is noticebly curved at a large enough scale. However, this is only an analogy! This in no way says that spacetime *IS* a physical surface like the surface of the Earth is.

So, is space getting bigger or smaller? Not to our understanding.

In other words - if it's the latter (which sounds like what Michiu is saying and, I believe you, are saying)... then I have a hard time accepting that... because as space expands (under universal expansion), wouldn't matter be constantly expanding as well since atoms are mostly empty space? Wouldn't we all be torn apart as space expands? Wouldn't the fact that we're all still here point more toward objects indeed taking up space rather than space curving to accommodate them... ?

The expansion of space can be thought of as a small force that adds up over vast distances. On the scale of atoms this expansive force is unimanginably small. Many many orders of magnitude smaller than the forces holding them together. It's similar to an ant trying to pull apart two giant magnets. It isn't going to do anything.

Now, as I explained above GR explains the way that spacetime is "shaped" only in the sense of how matter and light works within it. GR simply says that the geometry of space causes objects within it to get further away from each other. But only once the forces holding them together have dropped off to a point that the expansion can "overpower" them. This is commonly interpreted as "creating space" or "space expanding", however the math simply says that things get further apart.

I hope that answers your question.

 

[taurusaud]

Fantastic answer! Thanks for putting it into words I can understand! Take care now.