How well has the force of Dark Energy been calculated?

[LuckyNate]

What i would like to know is, how far apart would 2 masses of 1kg each have to be, for the effects of their gravitational attraction to be overcome by the force of the Dark Energy (i.e. to begin moving away from, rather than toward one another?)

The basic question I am trying to pick away at is, does the dark energy have a force that is gravity like (somehow affected by the square of or square root of distance) or does it just add up over distance? also is there going to be some sort of threshold or horizon out there at a certain distance from a mass where the dark energy is somehow pushing against the edge of its gravitational field (if my assumption that the empty space is pushing out against anything with mass is correct)?

 

[voxilla]

Dark energy is an attempt to explain why our exploded big bang universe is undergoing an accelerated expansion.
An other attempt is that our big bang universe is surrounded by similar big bang universes, and those pull by gravity on our big bang universe, explaining why ours has and accelerated expansion.

 

[LuckyNate]

Dark energy is an attempt to explain why our exploded big bang universe is undergoing an accelerated expansion.
An other attempt is that our big bang universe is surrounded by similar big bang universes, and those pull by gravity on our big bang universe, explaining why ours has and accelerated expansion.

Thanks very much for this aside on what dark energy is...hopefully now someone can post an actual answer to one of the questions I've posted.

 

[voxilla]

Thanks very much for this aside on what dark energy is...hopefully now someone can post an actual answer to one of the questions I've posted.

I'm just trying to imply that dark energy and gravity are the same.

 

[LuckyNate]

vox they are not the same...gravitation is inherent in mass, and curves the surrounding space-time...the dark energy appears to be an inherent energy present in the empty space-time itself, the question i need answered is 'how strong is the dark' energy and 'how its force plays out (is it analogous to magnetism, gravitation, etc.)' If you can't directly give an answer to this question or at least confirm that the answer is not yet known, then please don't reply.

 

[alexg]

The expansion of the universe adds up over distance, at a rate of 73.8 kilometers per second per megaparsec.

Gravity overwhelms expansion out to a distance of about 200 million light years, the size of the Local galactic supercluster.

I once ran a calculation on the expansion rate between the Earth and moon, if gravity was ignored, and I got a rate of a tenth of a diameter of a proton per second. It's astounding weak, but since it's additive with distance, and there's so much distance, there's an awful lot of expansion going on.

 

[voxilla]

If you can't directly give an answer to this question or at least confirm that the answer is not yet known, then please don't reply.

My answer is that the answer to your question is that this depends where you place your 2 masses of 1 kg in space.

 

[LuckyNate]

The expansion of the universe adds up over distance, at a rate of 73.8 kilometers per second per megaparsec.

Gravity overwhelms expansion out to a distance of about 200 million light years, the size of the Local galactic supercluster.

Is this threshold (200 million light years out) described by the mass of the localized supercluster?
if so, would the limiting distance be smaller for smaller masses?
can we try the math? 2 masses of 1kg each are touching in open space...how far apart will i have to pull them before they stop attracting due to gravitation and begin moving apart due to dark energy? will there be a distance at which the 2 forces (gravitation and dark energy) are totally balanced? if so what is that distance?

 

[voxilla]

will there be a distance at which the 2 forces (gravitation and dark energy) are totally balanced? if so what is that distance?

It really depends how your 2 1kg masses are placed relative to the proximity of 2 black holes with largest local attraction.

 

[LuckyNate]

It really depends how your 2 1kg masses are placed relative to the proximity of 2 black holes with largest local attraction.

for this thought experiment, let us imagine there are no other pieces of mass nearby enough to exert any appreciable gravitational attraction on my two masses except on one another, or better yet, that no other masses exist in the space I'm using. i myself am not exerting any gravitational force on the masses either...so the only force of gravitation that the two masses will feel are from one another, and the only dark energy that they will feel will be the inherent dark energy present in regular space-time. in this sort of an arrangement, how far apart will the 2 masses need to be in order to start moving apart from dark energy rather than moving together from gravitational attraction. Again, please, if you don't know how to answer please don't bother to try.

 

[alexg]

I've found a figure for the strength of Dark Energy given as 2 x 10^-35 m/s^2.

Plug that into F = G(m1m2/r^2) as F, G =6.674 x 10^-11, m1 and m2 are both 1, and I get a figure of 3.3 x 10^12 meters or .00036 light years.

I think its in the ball park.

 

[LuckyNate]

just about 3:08 light hours away...wow that means cosmological 'empty spaces' have to be immense for even the smallest effects of the dark energy to be felt.
Sadly, this doesn't make it much easier for me to wrap my head around, I was hoping for a more grassroots number like, "The distance from New York to Chicago" or something.
With these kinds of numbers even the smallest mass overpowers the dark energy easily, makes one wonder how clean is the empty space after all? It must be incredibly empty for the gravity to not overtake it with ease, because apparently even the smallest masses can overcome it gravitationally, even over great distances.

 

[voxilla]

That would all be true if space was empty, but it is not ...

 

[LuckyNate]

That would all be true if space was empty, but it is not ...

"What you've just said is one of the most insanely idiotic things I have ever heard.
At no point in your rambling, incoherent response, were you even close to anything that could be considered a rational thought.
Everyone in this room is now dumber for having listened to it.
I award you no points, and may God have mercy on your soul."

I think you are missing the point of this discussion.

The main core of what I was trying to get at was "In terms that a regular person can grasp, how strong is the Dark Energy?" I think that question was well and thoughtfully answered by alexg (thanks alexg) and if more people spent their time trying to help others learn in this way we could all benefit.

 

[chronon]

I've found a figure for the strength of Dark Energy given as 2 x 10^-35 m/s^2.
.

That doesn't look right, the units should be time^-2.

Assuming that it means 2 x 10^-35 s^-2 gives r^3=6.674 E-11/2E-35 =3.33E+24, so r=1.5E8 metres - half a light second.

 

[LuckyNate]

That doesn't look right, the units should be time^-2.

Assuming that it means 2 x 10^-35 s^-2 gives r^3=6.674 E-11/2E-35 =3.33E+24, so r=1.5E8 metres - half a light second.

I myself was wondering if that number didn't seem too high, it felt to me like space wasn't empty enough for it to work.

Your numbers indicate that at about one third the distance from Earth to the moon, two 1kg masses will stop attracting and balance out the force of gravity versus the expansion...this sounds like a more reasonable figure to me, one that allows the force of gravity to be overpowered by the expansion at believable distances between dust particles and gas atoms floating around in space but also makes the expansion seem stronger than i thought originally.

Here we have another thoughtful answer given by an informed council. Thanks Chronon. Can anybody else throw their 2 cents in? which of these estimates is closer?

 

[alexg]

I like Chronon's numbers better myself. When I tried to use 10^40 kg for both m1 and m2 (estimated the mass of two galaxies), I got a figure for r that was waayyyy too high.

One question I have though is why is it r^3, and not r^2?

 

[voxilla]

"What you've just said is one of the most insanely idiotic things I have ever heard.
At no point in your rambling, incoherent response, were you even close to anything that could be considered a rational thought.
Everyone in this room is now dumber for having listened to it.
I award you no points, and may God have mercy on your soul."

I think you are missing the point of this discussion.

The main core of what I was trying to get at was "In terms that a regular person can grasp, how strong is the Dark Energy?" I think that question was well and thoughtfully answered by alexg (thanks alexg) and if more people spent their time trying to help others learn in this way we could all benefit.

Be careful about flaming, or you might receive an infarction, or whatever they call that here on this forum.

The answer given here to your question is correct in your thought experiment conditions.

 

[chronon]

Actually, I can see a problem with my estimate. It implies the distance at which gravitational attraction and dark energy repulsion goes as the cube root of the mass of an object, so for the Milky Way (mass ~ 2E42 kg ) they would balance at about 2 million light years - about the distance to the Andromeda galaxy. However, the effect of dark energy is negliglble compared to gravity between the Milky Way and the Andromeda galaxy.

 

[chronon]

One question I have though is why is it r^3, and not r^2?

The gravitational force between the masses decreases as the square of the distance between them, while the force due to dark energy is proportional to the distance, so that their ratio goes as the cube of the distance.

 

[alexg]

hmmmm... I'm beginning to have doubts about this method. The numbers just don't seem right.

 

[LuckyNate]

The gravitational force between the masses decreases as the square of the distance between them, while the force due to dark energy is proportional to the distance, so that their ratio goes as the cube of the distance.

this doesn't sound correct to me, after all...
in both cases (x^2 + x) ≠ x^3 and (x^2 -x) ≠ x^3
so if the two forces are regarded as both positive or one positive and the other negative in neither case will they make x^3
again i am no mathematician, but i know addition and subtraction (of the dark energy over distance) doesn't multiply or divide the force or the distance of gravitational attraction.
Then again, maybe I'm just reading the equation and/or logic incorrectly... think on it and let me know what you come up with.

 

[chronon]

If you have a mass M, then the gravitational acceleration at distance r from is will be GM/r^2 towards it, and the acceleration due to dark energy will be αr away from it, where α is a constant of proportionality, so the total acceleration will αr-GM/r^2. You want to know where these cancel each other, i.e. αr-GM/r^2=0, giving r^3=GM/α

 

[phinds]

I have no quantitative information to add, but I'll toss in my favorite comment on the expansion of the universe. I forget the exact wording, but it's something like this:

Even though the universe is expanding, it's still not going to be any easier to find a parking place.

Sounds silly, but the POINT of the discussion it was in is that if you could magically paint parking space lines in space deep between galaxies, it would take something like a billion years before they would have moved far enough apart to let you park another car.

 

[alexg]

I won't go through the tedium of doing it again, but using a Hubble constant of 78 km/sec/megaparsec, I calculated that expansion would (sans gravity) move the Earth and moon apart at a rate of 1 tenth of a proton's diameter per second.

 

[BillSaltLake]

Without the extra acceleration, we expect a matter-dominated flat-space solution which yeilds å₀/a₀ (=H₀) = 2/(3t₀). With "dark energy", the observed H₀ is ~ 1/3t₀. Thus, DE is making things separate fractionally at rate Δa/a₀ = Δt/(3t₀), ot 1/3 part per 14 billion per year.
Two masses separated by distance d (meters) will have their separation change due to gravity at Δd = Δt² x (1.67 x 10^-11/2d²), whereas DE adds Δd = Δt x (d/4.2x10¹⁷ sec). Gravity accelerates at Δt² whereas DE is linear in Δt, so there is no "immediate" equlibrium.
A more accurate representation of the lambda term (DE) is a/a₀ = 0.35e^0.85t/to. (This assumes sinh(x)→.5e^x). With this, in time Δt ~ .5t_0, , the DE will begin to outrun the gravitational attraction if the attraction alone had caused the two masses to decrease their separation to half. This would happen at d ~= 7 x 10⁷ m = 40,000 miles.

 

[marcus]

... 2 masses of 1kg each are touching in open space...how far apart will i have to pull them before they stop attracting due to gravitation and begin moving apart due to dark energy? will there be a distance at which the 2 forces (gravitation and dark energy) are totally balanced? if so what is that distance?

I understand "open" space to mean not just outside our galaxy, and our local cluster of galaxies, but also outside any supercluster of galaxies. And DISTANCE can be the technical measure used in stating Hubble law expansion. What you would measure at this given moment if you could freeze the expansion process to give yourself time to measure it, say by radar or a pulse of light. This freeze frame distance is called "proper distance".

Different people use different values of the Hubble expansion rate, I'm used to 71 km/s per Mpc and I see other people sometimes say 74, and others say 70. Let's use 71. It says that if you put two CMB stationary observers one Megaparsec apart proper distance, then the proper distance between them will be increasing at 71 km/s.

The upshot I think is that a pair of kilogram balls each placed at CMB rest 400,000 km apart would continue indefinitely to get farther apart. Hopefully someone else will check my arithmetic, which I put in a separate thread.
https://www.physicsforums.com/showthread.php?t=566059
According to a parallel calculation, 300,000 km would not be far enough. It is not a realistic thought experiment because CMB rest cannot be determined with sufficient precision. Even if you could travel out into open space to position the balls.

I didn't reply to your question exactly as posed:
I'd urge that you should correct any misconceptions in the question itself. Standard mainstream cosmo does not attribute the expansion to the "dark energy" effect. What we observe is expansion of distances and a very very slight acceleration of that.

The acceleration is interesting and has the cosmologists all excited, but the the main pattern of expansion started for some other reason way long ago NOT because of the "dark energy effect" that they measure and talk about nowadays. The expansion of distance is governed by the 1915 Einstein eqn and once the pattern gets started it tends to continue without any "force".

So don't think of expansion as exerting a "force" that is somehow going to be "balanced" by the attraction between the two metal balls. the expansion of distances (between CMB stationary observers) is just a given---a feature of the universe's geometry.

It would be there essentially the same if you could magically turn "dark energy" off, that is, turn the very slight acceleration off.

For over half of the history of the U, the expansion has in fact NOT been accelerating. It has been slowing. The "dark energy" effect has been negligible. Here's a modified version of the question.

... 2 masses of 1kg each are touching in open space...how far apart will i have to place them so they will continue indefinitely moving apart due to the pattern of Hubble-law expansion, and not eventually start falling towards each other? Would there be a stable distance, and if so what is that distance?

I think the natural question to ask is at what distance do you get ordinary expansion exceeding the ESCAPE VELOCITY. In that case the balls would continue to get farther apart forever and never start falling towards each other. I did a very rough ad hoc calculation to get a handle on what distance would be required.

300,000 km is not enough. At that distance, starting from CMB rest the balls begin by getting further apart but eventually start falling towards each other. So no separation smaller than that could be stable. At any greater initial separation they always start by moving farther apart---so starting at CMB rest there is no initial placement distance that will not change.
Again, here's the calculation for the distance 400,000 kilometers (a bit over the distance to the moon).
https://www.physicsforums.com/showthread.php?t=566059