'Local' Dark Energy effect, if any?

[justwondering]

If there is Dark Energy expansion of space throughout this Universe why is it not noticed, at least to some extent, within our Solar system? Can it only be noticed on a Grand Scale?

 

[Chalnoth]

If there is Dark Energy expansion of space throughout this Universe why is it not noticed, at least to some extent, within our Solar system? Can it only be noticed on a Grand Scale?

Well, the basic issue here is that in most models, dark energy doesn't "cluster", it just stays at the same value everywhere, or very nearly so. Because of this, the density of dark energy within our own solar system is probably so absurdly minuscule that we'd never notice its effects.

Of course, it is possible that dark energy does interact to some degree, and therefore cluster to some degree. There are a number of theorists examining such models. But basically just the fact that all solar system experiments done to date are consistent with General Relativity and our understanding of the mass makeup of the planets indicates that dark energy must have a minuscule effect. Bear in mind, after all, that we haven't even been able to detect the effect of dark matter within our own solar system, and dark energy's effects are likely to be significantly weaker.

 

[Phrak]

Well, the basic issue here is that in most models, dark energy doesn't "cluster", it just stays at the same value everywhere, or very nearly so. Because of this, the density of dark energy within our own solar system is probably so absurdly minuscule that we'd never notice its effects.

Of course, it is possible that dark energy does interact to some degree, and therefore cluster to some degree. There are a number of theorists examining such models. But basically just the fact that all solar system experiments done to date are consistent with General Relativity and our understanding of the mass makeup of the planets indicates that dark energy must have a minuscule effect. Bear in mind, after all, that we haven't even been able to detect the effect of dark matter within our own solar system, and dark energy's effects are likely to be significantly weaker.

As I understand it, dark energy should have the same stress-energy tensor as light, but isotropic, if evenly distributed throughout the universe. But maybe I should be asking, instead. Where does dark energy appear in the stress-energy tensor?

 

[Chalnoth]

As I understand it, dark energy should have the same stress-energy tensor as light, but isotropic, if evenly distributed throughout the universe. But maybe I should be asking, instead. Where does dark energy appear in the stress-energy tensor?

No, that's not the case. The ratio of pressure to energy density for radiation is 1/3. Dark energy, to explain the accelerated expansion of the universe, must have a ratio of pressure to energy density that is less (i.e. more negative) than -1/3. For the cosmological constant, the ratio is -1.

 

[SW VandeCarr]

Force: MLT^(-2); Pressure: ML^(-1)T^(-2); Energy: ML^(2)^T(-2); Energy Density: ML^(-1)T^(-2) = Pressure

 

[Chalnoth]

Force: MLT^(-2); Pressure: ML^(-1)T^(-2); Energy: ML^(2)^T(-2); Energy Density: ML^(-1)T^(-2) = Pressure

Right. Pressure and energy density have the same units. What's your point?

 

[SW VandeCarr]

Right. Pressure and energy density have the same units. What's your point?

I sent the message before it was complete by accident (multi-tasking). My point was that pressure and energy density differ only in the way we describe the process of measurement: pressure as force per unit area, energy density as energy per unit volume. Of course we can have dimensionless ratios, but I don't understand the ratios you describe for radiation. The way you use the terms pressure and energy density either doesn't reflect the fact they are essentially the same thing, or (more likely) there are aspects of modern cosmology that I'm not understanding. The dimension of the diagonal cell values 11,22,33 (corresponding to the x,y,z directions ) of the stress-energy tensor are often referred to as "pressure", but this is not distinguished from energy density to my knowledge.

 

[Chalnoth]

I sent the message before it was complete by accident (multi-tasking). My point was that pressure and energy density differ only in the way we describe the process of measurement: pressure as force per unit area, energy density as energy per unit volume. Of course we can have dimensionless ratios, but I don't understand the ratios you describe for radiation. The way you use the terms pressure and energy density either doesn't reflect the fact they are essentially the same thing, or (more likely) there are aspects of modern cosmology that I'm not understanding. The dimension of the diagonal cell values 11,22,33 (corresponding to the x,y,z directions ) of the stress-energy tensor are often referred to as "pressure", but this is not distinguished from energy density to my knowledge.

The 00 component is energy density. Yes, it's distinguished.

 

[SW VandeCarr]

The 00 component is energy density. Yes, it's distinguished.

Yes and no. Energy density is on the main diagonal. It is dimensionally equivalent to pressure, so at some fundamental level it is the same thing. There may be good reasons for distinguishing them. The other off-diagonal components do not have the same dimensions as the main diagonal components (however I'm not sure of the dimensions of shear stress).

Look, I'm just trying to understand this. Perhaps you or someone else can help me out. Why are they distinguished?

 

[Chalnoth]

Yes and no. Energy density is on the main diagonal.

I don't know why you would think that.

It is dimensionally equivalent to pressure, so at some fundamental level it is the same thing. There may be good reasons for distinguishing them. The other off-diagonal components do not have the same dimensions as the main diagonal components (however I'm not sure of the dimensions of shear stress).

Huh? Of course they have the same units. Here, shear stress:
http://en.wikipedia.org/wiki/Shear_stress

Also, the 01, 02, 03 and 10, 20, 30 components of the stress-energy tensor are linear momentum. But those also have the same units (because the speed of light is set to one). Basically, all of the components of the stress-energy tensor are forced to have the same units because otherwise operations like contraction couldn't be performed.

Look, I'm just trying to understand this. Perhaps you or someone else can help me out. Why are they distinguished?

Well, the stress-energy tensor stems from the variation of the action that governs the non-gravitational physics of the matter you're talking about. Variation with respect to time gives you the energy density component. Variation with respect to space gives you the momentum and shear stress components. Variation with respect to time and space gives you the momentum components.

I guess I just don't understand why you think they should be considered the same thing. They're all related by the physics of the material at hand, but this doesn't mean they're identical.

 

[SW VandeCarr]

Huh? Of course they have the same units. Here, shear stress:
http://en.wikipedia.org/wiki/Shear_stress

Also, the 01, 02, 03 and 10, 20, 30 components of the stress-energy tensor are linear momentum. But those also have the same units (because the speed of light is set to one). Basically, all of the components of the stress-energy tensor are forced to have the same units because otherwise operations like contraction couldn't be performed.

I'm talking about physical dimensions in terms of LMT units for any coherent system of measurement, not the units themselves. Without going into the formulas again, can we agree that momentum is not dimensionally equivalent to energy? Therefore momentum density (10, 20, 30) is not equivalent to energy density( 00). Energy flux (01, 02, 03) is not equivalent to energy density, nor is momentum flux (21, 31, 32). Stress is expressed in pressure units, but shear stress (12, 13, 23) is directed along a surface (or tangent to a surface), not toward a surface (ie the shear vector is t(^2)-(t.n)^2 where t is the stress vector and n is the normal to the surface).

I don't understand how setting light speed to one changes this. Dimensional analysis (DA) (as opposed to units of any particular coherent system) regards light speed only has having the dimensions of velocity (MLT(-1)). Standard DA should work for any set of coherent units. It can be extended to thermodynamic, electromagnetic and other phenomenon by adding a few additional appropriate dimensions taken as basic.

 

[Chalnoth]

I don't understand how setting light speed to one changes this.

In GR, computations are performed much more easily if we consider space and time to have the same units. You can always put the factors of c back in later. The point is that if you carefully calculate the stress-energy tensor, all components will always have the exact same units. But you may have some factors of c floating around compared to the more familiar variables the stress-energy tensor components are related to. By setting c=1, we just ignore this fact and move on.

Dimensional analysis (DA) (as opposed to units of any particular coherent system) regards light speed only has having the dimensions of velocity (MLT(-1)). Standard DA should work for any set of coherent units. It can be extended to thermodynamic, electromagnetic and other phenomenon by adding a few additional appropriate dimensions taken as basic.

Right. But it's a pointless exercise here, because a tensor is forced to have the same units for all of its components. Now, the various components of the stress-energy tensor are related by the physics of the stuff in question, but they're not the same.

 

[Phrak]

Light has mass, so dark energy is not equivalent to the stress energy tensor of light, because light is too massive. Is this correct?

I'm having a little trouble with the negative sign. In dagonal form if the pressure were all in the x_1 direction, what is the pressure for dark energy vs. light?

 

[Chalnoth]

Light has mass, so dark energy is not equivalent to the stress energy tensor of light, because light is too massive. Is this correct?

Huh? Light has no mass.

The difference is in the relationship between energy density and pressure. For radiation, pressure is 1/3 the energy density. For dark energy, pressure is close to -1 times the energy density.

I'm having a little trouble with the negative sign. In dagonal form if the pressure were all in the x_1 direction, what is the pressure for dark energy vs. light?

Well, if we just take a homogeneous, isotropic universe, the stress energy tensor for light might look like:

3  0  0  0
0  1  0  0
0  0  1  0
0  0  0  1

...while the stress energy tensor for dark energy might look like:

1  0  0  0
0 -1  0  0
0  0 -1  0
0  0  0 -1

What this means is that if you have a box with some radiation inside, the radiation pushes outwards on the sides of the box. However, if you have a box with some dark energy inside, it tends to pull inward on the sides of the box.

 

[justwondering]

"However, if you have a box with some dark energy inside, it tends to pull inward on the sides of the box."

And THIS causes our Universe to EXPAND faster?

 

[jnorman]

hmmm - inre:
"However, if you have a box with some dark energy inside, it tends to pull inward on the sides of the box."

i don't think i can agree with this. dark energy should be moving along at C. yes? and since dark energy does not interact with anything, it will not be contained within any box, and therefore should have no effect on the box. even if it were somehow contained, any effects would be equalized by pull from DE outside the box anyway. DE really doesn't make any sense to me at all at this point...

 

[justwondering]

"DE really doesn't make any sense to me at all at this point... "

But do you at least think that Dark Energy is real, AND is causing our Universe, but not something so puny as our Solar System, to expand faster.

 

[Chalnoth]

"However, if you have a box with some dark energy inside, it tends to pull inward on the sides of the box."

And THIS causes our Universe to EXPAND faster?

Yes. The reason is that gravity also acts on pressure as well as energy. For a homogeneous, isotropic universe like our own, the "charge" that gravity responds to is the energy density plus the pressure in each direction. So when the sum of the pressure in each direction is more negative than the energy density, the gravitational "charge" is negative, and gravity tends to push that sort of matter apart.

 

[Chalnoth]

hmmm - inre:
"However, if you have a box with some dark energy inside, it tends to pull inward on the sides of the box."

i don't think i can agree with this. dark energy should be moving along at C. yes? and since dark energy does not interact with anything, it will not be contained within any box, and therefore should have no effect on the box. even if it were somehow contained, any effects would be equalized by pull from DE outside the box anyway. DE really doesn't make any sense to me at all at this point...

Perhaps a more realistic way to think about it would be to consider a volume of space with dark energy, with no dark energy outside that volume. The negative pressure indicates that it will collapse in on itself. Compare this to what happens with normal matter and radiation.

If we ignore the interactions of normal matter, which is a really good approximation for what goes on for much larger than galactic scales, then normal matter will just sit within the volume it starts in. The various particles of normal matter will go in orbit around one another, but will neither spread nor collapse. So the zero pressure approximation of normal matter makes sense.

Now, what happens with radiation? This is pretty easy: if we have a volume of space filled with radiation, and none outside, the radiation will rapidly escape and dissipate. So the positive pressure also makes sense here.

Naturally a region with negative-pressure dark energy surrounded by nothing will collapse due to its negative pressure.

 

[SW VandeCarr]

hmmm - inre:
"However, if you have a box with some dark energy inside, it tends to pull inward on the sides of the box."

i don't think i can agree with this. dark energy should be moving along at C. yes? and since dark energy does not interact with anything, it will not be contained within any box, and therefore should have no effect on the box. even if it were somehow contained, any effects would be equalized by pull from DE outside the box anyway. DE really doesn't make any sense to me at all at this point...

Dark energy and dark matter are recent discoveries. Einstein certainly would have known nothing about them. He didn't know that the universe was expanding (although GR predicted an expanding universe, hence the infamous cosmological constant). Perhaps the stress energy tensor isn't conserved. Perhaps GR needs revision.

 

[Chalnoth]

Dark energy and dark matter are recent discoveries. Einstein certainly would have known nothing about them. He didn't know that the universe was expanding (although GR predicted an expanding universe, hence the infamous cosmological constant). Perhaps the stress energy tensor isn't conserved. Perhaps GR needs revision.

It doesn't really matter whether or not Einstein knew anything about these things. General Relativity itself provides unambiguous predictions for what will happen in the presence of such sorts of matter/energy.

But yes, there are a large number of theorists currently working on possible modifications to General Relativity in an attempt to explain both dark matter and dark energy. The attempts to explain dark matter through modified gravity have largely fallen by the wayside, but the initiative is still up and running for dark energy.