# I Could it be meaningful to speak of the "density of space"?

1. Nov 16, 2015

### Gerinski

GR tells us that space is in a sense malleable. It can be stretched and compressed, bent, or it can ripple.

Intuitively one might think that if we take a certain region in space, say a region defined by the relative distances between a series of celestial objects, if the space in that region was "stretched" (say for example due to the pull of hugely massive external structures pulling outwards) the "density of space" in that region would be smaller than normal, than if the stretching by those massive external structures was not present.

Conversely, if that same region was "compressed" or "squeezed" due to a huge presence of matter inside it (without any alteration of the volume of that region, the objects which define it remain at exactly the same distances from each other), the "density of space" in that region would be high, it would contain "squeezed space".

In other words, a certain region of space might consist of highly stretched space or of highly squeezed space. The "space density" in that region would be different in both examples. Perhaps if we consider dark energy to be an intrinsic property of space, we might measure that that same region displays a different amount or rate of tendency to expand. The highly squeezed, "high space density" scenario would display more tendency to expansion than the "low space density, stretched space" scenario?

Or if we consider virtual particles to be a property of space (I know most will say they are not) we might notice that the "squeezed space" region produces a higher number of them than when the same region is being "stretched space".

Does this make any sense? That would seem to regard space as some physical medium, a sort of aether in a sense, a sort of "cosmic chewing gum medium".

I know this is not the way modern science regards space, the aether view was discarded long ago, but I would like some comments on the subject, why the view I described is wrong.

Thanks!

2. Nov 16, 2015

### Orodruin

Staff Emeritus
No, it does not. Generally when you talk about a density, it is defined as an amount of something per volume. If you want to talk about the amount of space, that is in itself a volume and so you get volume per volume which is one.

3. Nov 16, 2015

### Gerinski

Thanks but what if we talk about supposed properties of space such as amount of dark energy or amount of "potential energy" in the form of virtual particles? (sorry I can not come with a better expression for what I have in mind).
Then we could talk about "amount of dark energy per volume", or "amount of potential energy provided by virtual particles" per volume.

4. Nov 16, 2015

### Demystifier

In GR, the energy-density of empty space (vacuum) is
$$T_{\mu\nu}(x)=\lambda g_{\mu\nu}(x)$$
where $\lambda$ is a constant, called the cosmological constant. It can be interpreted as the energy-density of empty space. No matter how space stretches or shrinks, it remains constant.

However, in some alternative theories of gravity (slightly different from GR) $\lambda$ is not a constant, but a scalar function $\lambda(x)$. This $\lambda(x)$ has some similarities with the idea of the thread starter.

Last edited: Nov 16, 2015
5. Nov 17, 2015

### bcrowell

Staff Emeritus
The following is the closest thing I can think of to what the OP is asking about, in standard GR. We introduce a timelike congruence, which means a set of smooth, timelike curves such that their union completely covers some region of spacetime. Then we can define a scalar $\Theta$ called the expansion, and you could say that $\Theta$ is a measure of how the "density of space" is changing. However, it measures a rate of change, not the "density" itself, and it also depends on what congruence you pick (although for many spacetimes there is a particularly natural congruence based on the symmetry).

6. Jun 8, 2016

### Kryten

I completely understand where the OP is going with this notion. I found this post googling to see who else has had similar ideas and was wondering if this idea had any credence. I am coming from an uneducated background. All my knowledge comes from popular science books.

I was trying to visualise how space causes gravity. In my head I visualized a ship traveling past a planet. What caused it to change course/orbit was that there was a "higher density of space" ie: more space nearer the planet. So the side of the ship nearer the planet had to traverse a longer path.

This idea can then get translated to an object in freefall as well. The side of the object nearer the planet exists in a higher density (ie: more) space. So that side of the object is "diluted" more. So in an effort to equalize the pressure the object moves closer to the planet. The same issue still exists so it keeps moving closer to the planet.

This is not meant to be an accurate Description of space, rather an easier way to explain to a class of year 10s how it can be that space causes objects to orbit.

I'm more interested in finding out from those more educated that I where this analogy starts to fall apart.

7. Jun 8, 2016

### Staff: Mentor

This is a bad sign. You should not be trying to learn actual science from pop science books.

Right at the start.

8. Jun 8, 2016

### Ibix

Density is "something per unit volume". What would that mean for space? The amount of space per unit volume is the volume per unit volume, which is one by definition. To get an interesting number out of it you would need to embed spacetime in something, and measure the amount of spacetime in a unit volume of the embedding structure. But we've no evidence of any structure external to spacetime and GR works fine without it. So it's unlikely that a density of spacetime could be defined in a meaningful way, I'm afraid. Certainly not in a simple way, taking bcrowell's last post into account.

9. Jun 8, 2016

### phinds

These are the kind of utter nonsense ideas that you get from pop-science. I love pop-science shows myself because I'm simple minded and they have pretty pictures and nice graphics and so forth, but I have come to understand that even reputable scientists cannot be trusted when they are pontificating on such shows. It seems to be part of their contracts that they have to dumb things down to the point where much of what they they say is actually wrong.

And of course many of the people on such shows are not even scientists at all (Morgan Freeman comes to mind) and just read whatever total crap is handed to them. Some such shows clearly spend their money on celebrity talking heads and graphics artists and zero on science editors.

10. Jun 8, 2016

### Hornbein

They have these metaphors about space being bent and so forth. What they really mean is that a bit of matter will move in a curved path in that space.

11. Jun 8, 2016

### pervect

Staff Emeritus
In the special case of a space-time with a timelike Killing vector field, I think one can somewhat imaginatively interpret the length of the Killing vector field as a density, if one takes the Hodges dual of the Killing vector field.

I.e. $\xi^a$ is a Killing vector and $\xi_a$ is a Killing co-vector, $L = \sqrt{ |\xi^a \xi_a|}$ is the length of the Killing vector field, $V = *\xi_a$ is a three-form, the Hodges dual of the Killing co-vector field. The three-form V will have some volume, I believe that the definition of the Hodges dual requires that the wedge product $\xi_a \wedge V$ be a unit 4-form, making the ratio of $\xi^a$ to a unit timelike vector be related to the ratio of V to a unit volume.

It remains to be shown that the length of the Killing vector field, is actually something that's useful. Rather than address this point, my immediate concern is to mull over (and get comments on) the notion that interpreting the length of a Killing vector field as a sort of "density" is reasonable, or if it's too far afield.

12. Jun 8, 2016

### phinds

And of course it truly is too complicated to explain that it isn't actually curved at all when looked at with the geometry (Riemann) that describes space-time instead of inappropriately applying Euclidean terms where they actually do not apply.

13. Jun 8, 2016

### Orodruin

Staff Emeritus
No it will not, not unless it is acted upon by an external force. If not it will follow a space-time geodesic. The space-time is what is curved and there is a precise mathematical definition of what is meant by this. Of course all of the rubber sheet analogies and similar are just that, analogies.

14. Jun 8, 2016

### Staff: Mentor

I would not attempt this at all. I would stick to Newtonian gravity in teaching that age range. At most I would say that there is another theory of gravity, General Relativity, which gives more accurate predictions in certain circumstances, but that the theory is beyond the scope of the class.

15. Jun 9, 2016

### Kryten

Whether the upper echelons of the physics community likes it or not, lay people will always attempt to make easier to understand approximations of how humanity understands the universe to work. I don't particularly like the ball and rubber sheet explanation, I think this is an easier approximation to grasp without questions like "but what's pulling the sheet down?"

I would never attempt to teach this in a class of year 10, 11 or 12, however if one asks you after class, I would feel a duty to explain as best I could and offer thoughts on further reading.

16. Jun 9, 2016

### Ibix

The rubber sheet analogy is, indeed, rubbish. Unfortunately, density of space doesn't make any more sense. If you want to explain it to the odd interested kid, how about the truth minus the maths:

Mass and energy alter the rules of geometry near them by a mechanism we don't yet understand. This means that objects moving freely don't move in straight lines, they move in curves. Because we are talking about the geometry of spacetime, not just space, even objects that are at rest with respect to another mass will start to move towards it because "just moving forward in time" curves slightly into "moving through space".

You could also consider bookmarking this video:
which has a nice (and correct!) visual comparison of gravity as understood by Newton and gravity as understood by Einstein.

17. Jun 9, 2016

### Staff: Mentor

I feel quite differently about teaching. I believe that you should not teach something that the student is not prepared to learn, and you should minimize the stuff that they will have to unlearn later. Simply asking the question does not imply that the student is ready for the answer. And simply answering the question without the foundation is counter to the purpose of a teacher.

A student asking about GR needs to understand differential geometry including Riemannian manifolds, tangent spaces, tensor fields, curvature, and coordinate charts first.

If a year 10 student came to me and asked about GR, I would start by teaching them about Riemannian geometry. Laying the groundwork for understanding. In particular I would focus on the geometry of a sphere. Most of the key concepts in differential geometry can be understood on a sphere. That is where I would start with such a question.

Frankly, if you teach them the density concept then you are lying to them. You are abusing your position of authority to trick them into believing that you are teaching them accepted science when in fact you are simply pushing an unaccepted personal speculation. They will have to unlearn your concept later in order to progress. You will have set them back while giving them the impression that you have pushed them ahead.

Last edited: Jun 9, 2016
18. Jun 9, 2016

Staff Emeritus
Why are we discussing a personal theory here?

19. Jun 9, 2016