Question about dark matter gravity and the expanding universe.

[bapowell]

Can dark energy be viewed as a fundermental characteristic of space itself which causes space to expand at a certain rate? Perhaps in a similar way to space having certain characteristics which causes light to travel at the speed of light?

I would hesitate to describe it that way. Dark energy, as a source of stress-energy, is no different than radiation or dust, in that it is a density that occupies space, i.e. it occupies the RHS of Einstein's Equations. If the origin of dark energy is indeed quantum vacuum energy, then it is in some sense a fundamental ingredient, but I still wouldn't qualify it as a fundamental characteristic of spacetime itself.

 

[Wim Nobel]

g=-\frac{GM}{r^2} + \frac{\Lambda r}{3}

Thanks for clarifying this. I knew the cosmological constant had something to do with it, but had no idea the formula was as simpe as that. I guess those papers are so full of formulas that I couldn't grasp the essence.

However, two questions remain unsolved for me.

1. Why do we regard the gravitational attraction and the cosmological repulsion as aspects of one and the same force (field)? Or, to put it otherwise, would it be alright if I would say that there is a fundamental force called gravitation that is always attracting, proportional to mass and inversely proportional to distance squared, and that there is another fundamental force called the cosmological force that is always repulsive and proportional to the distance? If not, then why not add the formula for electrical attraction and repulsion (and those for strong and weak forces) as well to this sum?

2. What does it mean that the universe consists of 27% (light and dark) matter and 73% vacuum energy? From the formula, a comparison between the two terms only makes sense if a particular value of r is chosen. And the only reasonable value I can think of to choose would be the radius of the visible universe. But still, how do we know these proportions? We can measure (very unaccurately) the acceleration in the distant universe and derive a value for lambda from there. And we might estimate all gravitating matter by observing the dynamics of clusters etc. Is this the way this calculation is done? I can't imagine we can acquire an accurate result from this.

 

[bcrowell]

Finally, the propagation speed of a gravity field is certainly equal to that of an electromagnetic field, i.e. the speed of light. Although gravity can be seen as a distortion of the curvature of space, there is an alternative description that makes use of gravitons, particles that carry the force just like photons carry the electromagnetic force. I don't know why but experts seem to be pretty confident that these particles are massless, and therefore must travel with speed of light.

You don't have to resort to quantum gravity to understand why small-amplitude gravitational disturbances propagate at c. (We don't have a working theory of quantum gravity, and there are fundamental reasons to believe that gravitons can never be directly detected, even by fairly godlike means.) The Einstein field equations are a classical field equation, and they predict that small-amplitude disturbances propagate at c.

The reason we're confident that the graviton, if it exists, must be massless is because it would be the quantization of a classical field which is already known for classical reasons to have waves that travel at c.

I would hesitate to describe it that way. Dark energy, as a source of stress-energy, is no different than radiation or dust, in that it is a density that occupies space, i.e. it occupies the RHS of Einstein's Equations. If the origin of dark energy is indeed quantum vacuum energy, then it is in some sense a fundamental ingredient, but I still wouldn't qualify it as a fundamental characteristic of spacetime itself.

I could be wrong, but I believe the following is correct. Einstein originally thought of the cosmological constant as being a fixed property of space, not just another matter field. When people today use the term "dark energy," is has connotations that they're thinking of it as a matter field. It would be a completely meaningless semantic distinction except that if it's a matter field, then it could have dynamics of its own. When people talk about a cosmological constant, they're thinking of it as a constant, so it can't have its own dynamics.

 

[Tanelorn]

Thanks Ben and bapowell for your replies regarding my question about the characteristics of space.

I have been listening to an audio version of "Ether and the Theory of Relativity" an address delivered on May 5th, 1920, in the University of Leyden
by Albert Einstein. Is the following about the existence of some kind of ether still believed correct?

"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."

 

[bcrowell]

Thanks Ben and bapowell for your replies regarding my question about the characteristics of space.

I have been listening to an audio version of "Ether and the Theory of Relativity" an address delivered on May 5th, 1920, in the University of Leyden
by Albert Einstein. Is the following about the existence of some kind of ether still believed correct?

"Recapitulating, we may say that according to the general theory of relativity space is endowed with physical qualities; in this sense, therefore, there exists an ether. According to the general theory of relativity space without ether is unthinkable; for in such space there not only would be no propagation of light, but also no possibility of existence for standards of space and time (measuring-rods and clocks), nor therefore any space-time intervals in the physical sense. But this ether may not be thought of as endowed with the quality characteristic of ponderable media, as consisting of parts which may be tracked through time. The idea of motion may not be applied to it."

We've drifted onto a topic that's unrelated to the original topic of this thread, so if you want to discuss this further, I'd suggest starting a new thread.

FAQ: Didn't Einstein say that general relativity was an aether theory? Is general relativity compatible with an aether?

No, Einstein didn't say that general relativity was an aether theory. Einstein wrote a 1924 paper in which he made the philosophical point that although relativity killed off the luminiferous aether as the supposed medium of electromagnetic vibrations, it still imbued the vacuum with specific physical characteristics, such as curvature and energy. The basic point of the paper is that we can't decide, purely based on philophical ideas like Mach's principle, whether the vacuum has its own properties; we actually have to go through the usual scientific cycle of theory and experiment in order to find out the answer. Internet kooks love to misinterpret and overinterpret this paper, or to misrepresent it by saying that Einstein referred to GR in general, throughout his career, as an aether theory.

A more subtle question is what kinds of aether theories can be constructed, and how they relate to (or don't relate to) general relativity. Philosophers and historians of scientists have debated whether any real aether theory ever actually existed, and what that would mean. Earman (1989) investigates earlier work by Trautman (1966), and concludes: "[A]bsolute space in the sense of a distinguished reference frame is a suspect notion, not because armchair philosophical reflections reveal that it is somehow metaphysically absurd, but because it has no unproblematic instantiations in examples that are physically interesting and that conform even approximately to historical reality." Debate on this philosophical and historical issue continues,[Rynasiewicz 2003] but one should keep in mind that this discussion is all about theories that have been falsified by observation since the Michelson-Morley experiment. Jacobson (2008) has investigated a theory in which Lorentz invariance is approximate, and is broken in the gravity sector at large Lorentz boost velocities. This theory includes phenomena like aether dust settling onto a planet and giving it an aether charge. Jacobson's model has two adjustable parameters which, if nonzero, differentiate it from general relativity, and which are constrained by astrophysical observations. It is important to note that the model is not compatible with Galilean relativity, and it predicts all the same counterintuitive phenomena as standard relativity, including, e.g., the twin paradox, length contraction, and black holes.

A. Einstein, "Über den Äther," Schweizerische naturforschende Gesellschaft 105 (1924) 85

original text - http://www.wikilivres.info/wiki/Über_den_Äther

English translation of [Einstein 1924]- http://www.oe.eclipse.co.uk/nom/aether.htm

commentary by John Baez on [Einstein 1924] - http://web.archive.org/web/20070204022629/http://math.ucr.edu/home/baez/RelWWW/wrong.html

A. Trautman, in B. Hoffmann (editor) Perspectives in Geometry and Relativity, Bloomington, 1966, p. 413.

J. Earman, World Enough and Space-Time, Absolute versus Relational Theories of Space and Time. Cambridge, 1989, MIT.

Rynasiewicz, "Field Unification in the Maxwell-Lorentz Theory with Absolute Space," Philosophy of Science 70 (2003) 1063, available at http://philsci-archive.pitt.edu/archive/00001096/ . Rynasiewicz starts by summarizing two important earlier papers that are now difficult to obtain: Trautman 1966 and Earman 1989.

Ted Jacobson, "Einstein-aether gravity: a status report," 2008, http://arxiv.org/abs/0801.1547

 

[Tanelorn]

ok thanks Ben, this had been gnawing at the back of my mind since the properties of space thread, probably still is..

 

[bapowell]

However, two questions remain unsolved for me.

I think much of your confusion stems for your attempt to understand cosmology and gravitation in general using the laws of Newton. The example I showed above is a Newtonian approximation that only makes sense in the case of weak gravitational fields; after all, GR indeed reduces to Newtonian gravity in this limit. However, more generally one must apply GR in order to understand the gravitational dynamics of the universe at large.

1. Why do we regard the gravitational attraction and the cosmological repulsion as aspects of one and the same force (field)? Or, to put it otherwise, would it be alright if I would say that there is a fundamental force called gravitation that is always attracting, proportional to mass and inversely proportional to distance squared, and that there is another fundamental force called the cosmological force that is always repulsive and proportional to the distance? If not, then why not add the formula for electrical attraction and repulsion (and those for strong and weak forces) as well to this sum?

This expression determines the acceleration due to gravity that arises from two distinct stress-energy ingredients: ordinary matter and a cosmological constant, again, with the caveat that one is working in the weak field limit. The gravitational properties of the two components are opposite -- one attractive and the other repulsive.

2. What does it mean that the universe consists of 27% (light and dark) matter and 73% vacuum energy? From the formula, a comparison between the two terms only makes sense if a particular value of r is chosen. And the only reasonable value I can think of to choose would be the radius of the visible universe. But still, how do we know these proportions? We can measure (very unaccurately) the acceleration in the distant universe and derive a value for lambda from there. And we might estimate all gravitating matter by observing the dynamics of clusters etc. Is this the way this calculation is done? I can't imagine we can acquire an accurate result from this.

It is not appropriate to apply this formula to the large scale evolution of the universe, and it is only on these large scales that the decomposition of the universe into matter and dark energy is relevant. This decomposition is best understood by examining the properties of the cosmic microwave background within the context of the isotropic and homogeneous Friedmann cosmology.