# Does spacetime have mass?

1. Jul 4, 2012

### kcrck

We talk about space time as a fabric. Does it have mass?

2. Jul 4, 2012

### phinds

I'm not sure who "we" is, but there IS a lot of sloppy talk that uses the expression "fabric" to discuss space-time. This is very unfortunate since it leads to misconceptions about the "space" part of spacetime, such as that it stretches.

That it might have mass is not a misconception I have heard before. Bascially, the "space" part of spacetime is just geometry, which has no mass, and I assume you would agree that the "time" part does not not mass.

The GEOMETRY of spacetime does "stretch", as an analogy to what it actually does, which, if I understand it correctly, can really only be described with math since our senses are not equiped to experience all of it directly.

I don't find it hard to accept that the distortion of the geometry of spacetime in the solar system caused by the mass of the sun causes the planets to follow their orbits, but I can't imagine how I could ever experience that directly (that is, "see" the distortion of spacetime).

3. Jul 4, 2012

### kcrck

"We" being myself and those trying to conceptualize the math. Here is some more misunderstanding I am sure, but if mass is the resistance to movement, wouldn't time be the ultimate resistance? In other words, is it really reasonable to assume time has no mass?

4. Jul 4, 2012

### marcus

That's an interesting question. There is RECENT thought and discussion about that.

The biggest international conference on gravity and spacetime geometry related stuff is the Marcel Grossmann triennial. It's going on this week in Stockholm. There are 1035 participants from all over the world. Here's one talk relevant to this issue:

http://ntsrvg9-5.icra.it/mg13/FMPro...s&talk_accept=yes&-max=50&-recid=41805&-find=

Tony Padilla says NO, vacuum energy does not gravitate. He and Kimpton have a paper about that. The talk is in session AT2 - Extended Theories of Gravity

Here's the brief summary of the talk:
Co-authors: Ian Kimpton
Cleaning up the cosmological constant
Abstract: We present a novel idea for screening the vacuum energy contribution to the overall value of the cosmological constant, thereby enabling us to choose the bare value of the vacuum curvature empirically, without any need to worry about the zero-point energy contributions of each particle. The trick is to couple matter to a metric that is really a composite of other fields, with the property that the square-root of its determinant is the integrand of a topological invariant, and/or a total derivative. This ensures that the vacuum energy contribution to the Lagrangian is non-dynamical. We then give an explicit example of a theory with this property that is free from Ostrogradski ghosts, and is consistent with solar system physics and cosmological tests.

=======================
A clean cosmological constant (unrelated to any matter fields, just a constant in the Einstein equation) is the simplest way to get a good fit to the observational data of all sorts---including the observed slight acceleration of distance expansion.
=========================

But there are alternative ideas! Not that space is a substance with INERTIA (the conventional measure of mass) but that it is filled with a mysterious "dark energy" which GRAVITATES, so has some aspects associated with mass, and yet paradoxically causes expansion to accelerate. This would replace having a simple constant in the Einstein equation. I think so far this is at the level of FANTASY but people play around with the idea. It gets hyped up.
But anyway there are alternative speculations.

You can probably find some discussion of different "dark energy" if you look thru the program of the Stockholm conference that's happening this week:
http://www.icra.it/mg/mg13/parallel_sessions.htm
===============================

http://arxiv.org/abs/1203.1040
Cleaning up the cosmological constant
(Submitted on 5 Mar 2012)

Last edited: Jul 4, 2012
5. Jul 4, 2012

### kcrck

@Marcus, @PHinds,

6. Jul 4, 2012

### marcus

You are welcome! But you aren't the only one interested in this, and it does not have a consensus mainstream answer. So we could say thank you to you for bringing it up.

In my view the best perspective on the "vacuum energy" versus "vacuum curvature" issue is this paper by Bianchi and Rovelli.
Why all these prejudices against a constant?

They summarize the various arguments made that there is some mysterious "dark energy" field instead of a simple curvature constant in the Einstein equation. And they counter each argument with a rebuttal. Their conclusion is that the slight acceleration is not due to an energy.

So in that case the vacuum would not gravitate---empty space would not have mass in the gravitational sense.

Here's the link in case anyone wants to read the PDF. It's easy reading in parts, written for non-specialist audience. But also has some technical parts:
http://arxiv.org/abs/1002.3966/
You can also get it by googling "rovelli prejudices"

Last edited: Jul 4, 2012
7. Jul 4, 2012

### Naty1

How about gravitational lensing...and less directly, Shapiro delay..?? or GPS time dilation??

It's not part of Einstein's Relativity....and its not in the standard model of particle physics. But that does not make it impossible. I'm glad Marcus did not offer a conventional 'no that's not right' answer....

One thought that comes to mind: ADS/CFT correspondence....a version of the 'Holographic Principle'

There is a mathematical equivalence between a string theory with gravity defined in some dimensional space and a quantum field theory without gravity defined on the boundary of this space with one less dimension. Juan Maldacena found this hypothetical realization [of holography] within string theory: [saying the same thing another way] He showed a particular quantum theory without gravity is indistinguishable from another quantum theory that includes gravity but is formulated with one more space dimension. This implies gravity is somehow linked to the dimensions of space and it's boundaries.....and if that is so, can 'mass' be far away??

We see a version of this 'holographic principle' via the information stored on the horizon of a black hole. All the information hidden inside the black hole, mass,charge, angular momentum, appears on the surface!!!

Another link may be string theories in which the number of dimensions and their shapes and sizes determine the 'mass' of strings...in string theory the energy of the string vibrations determines mass ...more energetic vibrations corresponds to more mass' and those vibrations are governed by the background geometry....the spacetime.....So maybe even if 'mass' isn't there itself in space the 'necessary' building blocks [conditions] are.

8. Jul 4, 2012

### phinds

Gravitation lensing at least is identical, to my mind, to the orbit of the planets. All I can see is the EFFECT of the distortion. I can't see the distortion itself. I may be just getting off into semantics here, but that's the way it feels to me.

9. Jul 9, 2012

### audioloop

very interesting marcus, can you summarize, i mean schematize and systematize.
and what if there is no space, i mean a relational space.

10. Jul 9, 2012

### marcus

Actually I rather incline towards the idea of relational space. That there is substantially no space at all but GEOMETRY instead: a web of relations among events/measurements.

Admittedly my personal bias doesn't matter. I have to say that I CAN'T summarize or schematize as you wish. Tony Padilla's idea is too new. You'd be better off just reading the article. I won't invest time trying to understand and evaluate until I see (enough) signs that it "has legs".

The fact that he got to present it at the MG13 meeting in Stockholm last week is a good sign.
I'm a herd or flock animal, in part (noticing cues from others). I was really intrigued when I encountered it a few months ago, but I want to see how more expert people receive it.

Last edited: Jul 9, 2012
11. Jul 9, 2012

### atyy

In classical general relativity, with spacetime conceived as a "fabric", there are two sorts of things - spacetime and matter. Matter is that which has localized mass-energy, while spacetime does not.

12. Jul 9, 2012

### jcsd

If anything has mass it's the curvature of spacetime. An asympotically flat spacetime that is not Minkowski space, will always have positive, non-zero ADM and Bondi masses

13. Jul 9, 2012

### Blackforest

Indeed and this semi-esoteric remark may be very important (at least in my mind). Although the notion of localization of a particle may also not always be something very clear within a QT approach. Staying in the boat of a semi-classical approach, the remark is pertinent because it relates empty spaces (no matter) to not empty spaces (matter under the form of known particles). The frontier between the two regions may thus be a key componant of a theory trying to explain how an empty region "creates" a non-empty one, or at least a region where our instruments detect something like a particle. Sorry for this semi speculative intervention.

14. Jul 10, 2012

### Naty1

wah wah wah [LOL]...

as if we can ever 'see' stuff!!!!...like vacuum fluctuations, electromagnetic or magnetic fields or the strong force...or radioactive decay or....well, you get the idea.....and besides what you 'see' is usually misleading anyway, like how 'solid' is mass like wood or metal....who would ever think it's 99.99% 'vacuum spacetime'....
and now I think about it, not seeing all that stuff : a good thing because all those fields and stuff would sure make it hard to 'see' important things, like girls on the beach.

15. Jul 10, 2012

### Naty1

atyy:
I like it: a neat concise way to express a fundamental conundrum.

Spacetime sure does have a lot going for it even if it has no mass....gravitational potential and curvature, vacuum fluctuations, thermal, information entopy chacteristics, in addition to setting the 'tone' for string vibrations i described earlier.....and a lot more I can't think of right now...

16. Jul 10, 2012

### cosmik debris

I think that questions like the OPs need teasing out quite a bit before they can be answered. To me there is quite a difference between spacetime and the vacuum. To my way of thinking spacetime is a manifold on which a co-ordinate system is placed. To ask if it has mass is tantamount to asking if 5 inches has mass. The vacuum on the other hand has all sorts of dynamics, it contains energy, dark in the case of GR, and vacuum energy in the case of QFT. In natural units mass and energy are the same and we know that all forms of energy gravitate, so to ask if the vacuum has mass could very well be answered with yes.

17. Jul 10, 2012

### friend

As I understand it, the Higgs boson is what gives particles mass, and the Higgs boson is itself a particle. So the question seems to ask if particles (mass) are made of spacetime? This might be an expected question since one might assume that in the beginning when spacetime began to expand, particles came into existence within that spacetime. So it seems there would be nothing else available with which to make particles except the spacetime that must have come first. Maybe the symmetries responsible for particles can be traced back to the symmetries of spacetime. Any thoughts?

18. Jul 11, 2012

### Blackforest

Cosmik debris said : ..."To me there is quite a difference between spacetime and the vacuum. To my way of thinking spacetime is a manifold on which a co-ordinate system is placed".

Ok in fact you say: the water in the bottle is not the bottle in which the water stays. This is the "classical" well admitted actual way of thinking about that item. But with this, the question of the OP would mean: does the bottle have a mass, whatever is in that bottle?

The Einstein's equations tell us a direct link between the metric tensor (which contains informations concerning the space) and the stress energy tensor. This seems to reveal that yes: the form, the bottle, has an energy, equivalently a mass. (but not the water, the vacuum).

Now, if we change the paradigm and consider the water and the botle as two faces of a Moebius ring... what is inside, what is outside is no more clear. Where does the mass ly?

And we come here to the idea pointed out by friend: "to ask if particles (mass) are made of spacetime?" Particles as (topological) deformations of spacetime, allowing to give mass to vacuum when it deforms... Ouah... very speculative... perhaps is it time to go on the beach as suggested by naty1

19. Jul 11, 2012

### ginga

I believe that the mass is an essential characteristic of the spacetime. You could even say that this is one of the dimensions

20. Jul 11, 2012

### ginga

The water can be poured from one bottle to another. And the original bottle will be empty ( without mass of water). But in the space- time it will not go away. Just this mass moves from one point of space- time to another.