# Does space have mass/weight?

1. May 26, 2004

### techwonder

Does space have mass/weight? Has this been considered in astronomy? I am aware of the huge discrepancies between the zero point energies (ZPE) in QM and GR, but would/could the ZPE have a gravitational impact?

It seems to me that if space have mass (and this has not been taken into account) then we don't really need to resort to dark matter to explain the behaviour of the rotational speed of galaxies.

2. May 26, 2004

### marcus

in GR the idea of a ZPE or uniform constant vacuum energy is sometimes called
dark energy or cosmological constant (in one of its versions)

the thing about this is it does not clump or collect in galaxies but is spread out evenly
so it doesnt work to explain rotation speed of galaxies
it doesnt explain how galaxies hold together and clusters of galaxies, even though they are moving around speedily

the thing about dark matter is it clumps. It can gather and collect in concentrations, just like ordinary matter, and contribute to the mass of galaxies and clusters of galaxies so they can hold together

the usual assumption about dark energy (cosm. const. vacuum energy whatever) is that it is constant at about
0.6 joules per cubic kilometer
constant throughout space and time
0.6 joules/cubic km is just the right amount to explain the observed flatness of the U
and to explain the observed acceleration in the expansion of the U
as measured using supernovas.

the interesting thing about this constant vacuum energy is how it contributes to accelerating expansion. it is classical physics how a constant energy density would do this (1915, not terribly modern or esoteric)

we dont know it is there but if it is it would operate in this classical reasonably familiar way so as to explain both the flatness and the acceleration and this makes it very appealing to many people

(though something else, more clumpy, is needed to explain galaxy rotation curves)

3. May 26, 2004

### techwonder

more space near mass?

I'm OK with the fact that ZPE is spread evenly all through space, but if space is "bent" near mass then it follows (I think?) that there is more space in the vicinity of a (massive) object than elsewhere.

If there is more space near matter and if the ZPE gravitates then this delta could maybe explain dark matter?

I asked for a space bending formula in another thread and a quick, dirty and crude calculation showed that if the extra space contributed by gravitation contributes 1e-10 kg/m3 then the gravitational mass of the galaxy doubles. I don't expect the number to be proven, but it gave me some comfort of being sufficiently small to ask the question about gravitational ZPE here.

4. May 28, 2004

### techwonder

If space volume is mass dependant, i.e. not just a flat constant, wouldn't it solve the problem ?

5. May 28, 2004

### Chronos

space volume is most definitely mass dependent. without gravity there is no other way to explain it. gravity requires mass and spatial dimensions. we dont know why, but, we do know it does.

6. May 28, 2004

### techwonder

But could it not solve the dark matter problem like this? I mean, assigning a gravitational impact from ZPE? Most of space would pull and push equally to whatever mass, but the "extra" space would only pull.

What I'm trying to say is that if we look at the solar system, then we (Earth) would only feel the extra space inside the sphere from the sun out. The rest will cancel. If we look at the galaxy then there is a lot more space within the sphere defined by their orbit for the stars the furthest out than those close to centre.

If the energy of space is 0.6 J/km3 (to explain space expanding) then this same energy could be used to explain increased galaxy mass (rotation speed).

Am I wrong? Then I'd really like to understand why ...

7. Jun 2, 2004

### techwonder

Doesn't anybody want to answer?

8. Jun 2, 2004

### Mike2

Try this: When the universe originally came into being, there was a time where there was no particles inside the universe. It only consisted of the space and time within it. The universe was so small, that it was basically a particle in and of itself. As such it must have had some energy/mass, and that energy would have been of the space and time within it. Thus, spacetime has energy. Can anyone refute this?

9. Jun 2, 2004

### marcus

I dont have an especially cogent answer to your question but i will play around with the ideas

Imagine the solarsystem and suppose the sun and all the other planets were suddenly whisked away so there is just the earth sitting in the midst of a uniform spread of dark energy 0.6 joule per cubic km.

In which direction would the d.e. pull the earth?

In no direction at all. there is no effective force acting on the earth from d.e., there is no force from d.e. gravity acting on anything

because in what direction would the force point?

because d.e. is uniformly spread out it cant explain galaxy rotation curves or the earth's orbit around the sun. It doesnt pull in any direction because it isnt concentrated anywhere.

10. Jun 2, 2004

### techwonder

In no direction at all. there is no effective force acting on the earth from d.e., there is no force from d.e. gravity acting on anything

because in what direction would the force point?

That's true ... When there's nothing else, but leave the sun, the earth and a nearby star. The earth would feel the gravity from Msun plus a small part Mzpe, however, the nearby star would feel the full Msun+Mzpe and Mzpe should/could be quite significant (I think).

We would probably be hard pressed to detect this on planetary motions, because we would calculate Mplanets from GMm/rr and only 3-body interactions (in this case) could show us a hint of discrepancy. On galaxy level however, we use luminosity to determine mass and OUPS ... something is wrong.

11. Jun 2, 2004

### Mike2

There is no center of mass for space-time itself. It is everywhere all at once, and there is no center. So it would not pull/push in any particular direction.

12. Jun 2, 2004

### kurious

Techwonder:

Dark energy might cluster in galaxies if it flows through them and is squeezed to a higher density by the galaxy's magnetic field.But to do this Dark energy must have an electric charge.

13. Jun 2, 2004

### kurious

Techwonder:

Dark energy might cluster in galaxies if it flows through them and is squeezed to a higher density by the galaxy's magnetic field.But to do this Dark energy must be split into particles half with an electric charge of one sign and half with an electric charge of the other sign.

14. Jun 3, 2004

### techwonder

Sorry, but I don't agree. Dark energy or zpe is spread evenly throughout the universe. Its value is 0.6J/km3 (mentioned above - haven't checked though). The issue is that since mass introduce a greater volume of space around it (see analogy above) then it follows that there is an extra mass (if space has mass) to take into account when calculating gravitational impact. Not due to all of the space around the objects, but due to the EXTRA space introduced by mass.

If we look the sun-earth system then the volume to take into account is NOT all of the 4*pi/3*(150,000,000 km)^3 but the difference in distance between that particular point that is sun centre to earth without the sun and earth in place. Assume that that distance is 149,500,000 kms then the volume difference is 1.41e23km3 giving an extra mass of 940000kg. We wouldn't be in a position to notice such a value - on solar system scale, but on a galactical scale I can guarantee you we would - we do!

As I mentioned above, I used the light bending formula to calculate the angle the mass of the galaxy would bend light, i.e. light follows a path that is longer due to mass than without mass. I calculated the extra volume from that and got that a value 0.01J/km3 would double the galaxy mass! Yes the approach is crude, but value is not too far off the value measured for dark energy. particularly considering that there is is 6 to 7 times more dark matter than "normal" matter.

15. Jun 3, 2004

### marcus

techwonder you seem to be having fun so more power to you
I do not agree or disagree or presume to criticize
(if you want to do cosmology you have to get the attention of
a working cosmologist who is willing to vet your ideas)

but I will tell you something you might enjoy working out

the formula for the critical density is
$$\frac{3c^2 H^2}{8\pi G}$$

this is the density needed to make the U spatially flat
and the formula is very easy to derive from the Friedmann equation

why dont you evaluate this formula and see if it really does give
0.83 joules per cubic km?

you say you have not checked this

it is the same as checking that dark energy is 0.61, because dark energy is about 73 percent of the total and IIRC 0.61 is about 73 percent of 0.83
(I may be off in second decimal place, but approx)

16. Jun 7, 2004

### techwonder

As my question hinges on the extra volume of space, can anybody give me a formula for that? Assuming a central mass ... Normally one should integrate over the metric (if that makes any sense at all) ..., but well, I don't know how to do that, so ...

Or is my length from A to B based on the space bending formula good enough? It does leave open the question on how to chose A and B ...