Does dark energy obey the inverse-square law?

[MarkE]

“Dark energy is an unknown driving force behind the acceleration of the universe, and we’re measuring the inverse-square law below the dark-energy length scale to look for a possible new gravitational phenomenon.
Kapner and his colleagues use a sensitive device called a torsion balance to test the inverse-square law, attempting to shed some light on dark energy.
And the results regarding the dark-energy length scale? “There are no deviations from the inverse-square law,” Kapner insists. “We see it behaves just as Newton predicted.” The test, he says, establishes that there is nothing new at the dark-energy length scale".
(Source: https://phys.org/news/2007-01-dark-energy-inverse-square-law.html)

Does this mean that dark energy obeys the inverse-square law?
And does this in turn imply that, to understand what dark energy is, we can include what we know about the gravity near black holes (i.e. singularities)?

Edited June 28, 2021 by MarkE

[swansont]

Dark energy causes accelerating expansion, which is not a part of Newtonian gravity.  

[MarkE]

34 minutes ago, swansont said:

Dark energy causes accelerating expansion, which is not a part of Newtonian gravity.  

Newton's inverse-square laws states that a massive body, which is closer to another massive body, experience more inward attraction. So when it approaches a massive body, it will accelerate, which is similar to the redshift that all the galaxies in the universe experience, only not inward, but outward.

So maybe the universe is an inside out black hole of some sort? It kind of makes sense, because when I say 'outward' I mean at the Big Bang, which is known to have arisen from an 'initial singularity'.

Edited June 28, 2021 by MarkE

[exchemist]

16 minutes ago, MarkE said:

“Dark energy is an unknown driving force behind the acceleration of the universe, and we’re measuring the inverse-square law below the dark-energy length scale to look for a possible new gravitational phenomenon.
Kapner and his colleagues use a sensitive device called a torsion balance to test the inverse-square law, attempting to shed some light on dark energy.
And the results regarding the dark-energy length scale? “There are no deviations from the inverse-square law,” Kapner insists. “We see it behaves just as Newton predicted.” The test, he says, establishes that there is nothing new at the dark-energy length scale".
(Source: https://phys.org/news/2007-01-dark-energy-inverse-square-law.html)

Does this mean that dark energy obeys the inverse-square law?
And does this in turn imply that, to understand what dark energy is, we can include what we know about the gravity near black holes (i.e. singularities)?

No, this passage does not say anything about dark energy obeying an inverse square law. What it says is that no deviations from Newton's inverse square law of gravitation were detected.

So this experiment has not shed any light (haha) on dark energy, save, I suppose, in establishing some upper limit to the magnitude of any deviation from Newton's inverse square law that there may be. 

[MarkE]

13 minutes ago, exchemist said:

What it says is that no deviations from Newton's inverse square law of gravitation were detected.

No deviations, so it follows the inverse-square law, then? (Because if you say 'no', shouldn't there be deviations?)

[exchemist]

46 minutes ago, MarkE said:

No deviations, so it follows the inverse-square law, then? (Because if you say 'no', shouldn't there be deviations?)

What "it" are you talking about?  

I repeat, but with emphasis added, no deviations from Newton's inverse square law of gravitation were detected.

In other words, just to spell it out, no influence of dark energy - which the experimenters thought might cause a deviation from Newton's law of gravitation - was detected. 

As nothing apart from Newton's law behaviour was observed, no manifestation of dark energy was detected.

So no information about dark energy can be obtained from this experiment, except in the sense I mentioned, viz. that if there are any deviations from Newton's law, they must be smaller than the detection limit of this experimental setup.

[swansont]

Gravitationally bound systems don't expand.

From the article:

"we’re measuring the inverse-square law below the dark-energy length scale to look for a possible new gravitational phenomenon" (emphasis added)

They aren't looking at distances where expansion is observed. They're saying that dark energy doesn't perturb gravitationally-bound systems.

[MarkE]

1 hour ago, swansont said:

Gravitationally bound systems don't expand.

In time they will, won't they? Leading to the 'heat death' of the universe?

1 hour ago, exchemist said:

no influence of dark energy - which the experimenters thought might cause a deviation from Newton's law of gravitation - was detected. 

Alright, I think I get it now: so the inverse-square law remained the same, with or without dark energy, it did not influence the body-body relationship, right? In that case I've misinterpreted the article, but thanks for pointing it out.

OK so the article doesn't support or refute the question I had. That mean I still have the question.
So I'm wondering what you think about it. Let me repeat what I said:

2 hours ago, MarkE said:

Newton's inverse-square laws states that a massive body, which is closer to another massive body, experience more inward attraction. So when it approaches a massive body, it will accelerate, which is similar to the redshift that all the galaxies in the universe experience, only not inward, but outward.

Well, can the be a connection of some sort? Or should in that case the redshift have to follow the inverse-square law for any connection to exist between
A) the gravitational attraction associated with black hole singularities on the one hand, and B) the gravitational attraction associated with the Big Bang's 'initial singularity' on the other hand (which is exerting a gravitational pull on all galaxies, and so galaxies closer to the Big Bang (which are further away from us) experience stronger attraction, and thus a higher redshift)? 

Edited June 28, 2021 by MarkE

[exchemist]

2 minutes ago, MarkE said:

In time they will, won't they? Leading to the 'heat death' of the universe?

Alright, I think I get it now: so the inverse-square law remained the same, with or without dark energy, it did not influence the body-body relationship, right? In that case I've misinterpreted the article, but thanks for pointing it out.

OK so the article doesn't support or refute the question I had. That mean I still have the question.
So I'm wondering what you think about it. Let me repeat what I said:

Well, can the bere a connection of some sort? Or should in that case the redshift have to follow the inverse-square law for any connection to exist between
A) the gravitational attraction associated with black hole singularities, 
and
B) the gravitational attraction associated with the Big Bang's 'initial singularity' ? 

I'm sorry, I can't follow any of this. Hubble's Law reflects the observation that recessional velocity (as calculated from the cosmological red shift) is linear with distance. So it's not an inverse square relation. 

[swansont]

26 minutes ago, MarkE said:

In time they will, won't they? Leading to the 'heat death' of the universe?

No, it's the galaxies not bound to each other that will continue to recede from each other.

The stars in these galaxies will burn out and eventually new stars will not be able to form.

1 hour ago, MarkE said:

Newton's inverse-square laws states that a massive body, which is closer to another massive body, experience more inward attraction. So when it approaches a massive body, it will accelerate, which is similar to the redshift that all the galaxies in the universe experience, only not inward, but outward.

Redshift is caused by motion away. If the motion is towards each other, there will be a blueshift.

There's also a redfshift as light climbs out of a gravity well.

[MarkE]

1 hour ago, exchemist said:

I'm sorry, I can't follow any of this. Hubble's Law reflects the observation that recessional velocity (as calculated from the cosmological red shift) is linear with distance. So it's not an inverse square relation. 

Galaxies are not merely moving away from us, but at an accelerating pace, exponentially. Similarly, the gravitational field of a black hole attracts matter exponentially. I’m wondering whether the reason for this exponentiallity might be the same, only inside out.

Edited June 28, 2021 by MarkE

[swansont]

41 minutes ago, MarkE said:

Galaxies are not merely moving away from us, but at an accelerating pace, exponentially. Similarly, the gravitational field of a black hole attracts matter exponentially. I’m wondering whether the reason for this exponentiallity might be the same, only inside out.

Black holes attract matter in violation of the inverse-square law (where Newtonian physics would apply)? Citations please.

[MigL]

43 minutes ago, MarkE said:

Similarly, the gravitational field of a black hole attracts matter exponentially.

No, that doesn't happen.
The only reason BHs seem to have extreme gravity is because you can get much closer to the mass than you otherwise could to a non collapsed star.

edit:   cross posted with Swansont

Edited June 28, 2021 by MigL

[joigus]

Dark energy is uniform by its very definition. The inverse square law is only valid for local clustering of energy-momentum, and it's an approximation. When you get close to sources of gravity, it's no longer valid. Example: Mercury's orbit around the Sun, for which the inverse-cube term's effects are sizeable at the time scale of centuries. No gravitational source that I know of has field exponentially-varying with distance.

2 hours ago, MarkE said:

In time they will, won't they? Leading to the 'heat death' of the universe?

Systems dominated by gravity (all stars and black holes) are fundamentally out-of-equilibrium, due to negative heat capacities: They heat up when they lose energy into space, so they're thermally unstable. They don't "thermally die". The concept of heat death of the universe is a theoretical extrapolation that would apply to models of the universe other than the one we presently accept --and never to a standalone star, in any case. It doesn't apply to the present picture of the universe that emerges from cosmological observations AFAIK.

[exchemist]

1 hour ago, MarkE said:

Galaxies are not merely moving away from us, but at an accelerating pace, exponentially. Similarly, the gravitational field of a black hole attracts matter exponentially. I’m wondering whether the reason for this exponentiallity might be the same, only inside out.

So far as I am aware nobody says the process is exponential. But you suggested an inverse square law was followed. And it isn't.

And matter is not attracted by black holes exponentially either. It is attracted according to Newton's inverse square law. 

It looks as if you may not understand what exponential means - which raises the possibility that you don't know what an inverse square law is either. These terms have a mathematical meaning.

 

[MarkE]

47 minutes ago, exchemist said:

So far as I am aware nobody says the process is exponential. But you suggested an inverse square law was followed. And it isn't.

And matter is not attracted by black holes exponentially either. It is attracted according to Newton's inverse square law. 

It looks as if you may not understand what exponential means - which raises the possibility that you don't know what an inverse square law is either. These terms have a mathematical meaning.

 

1, 2, 3, 4, 5 = linear

1, 2, 4, 8, 16 = exponential

1, 2, 3, 5, 8, 13, 21 = exponential (since the Fibonacci numbers also grow at an exponential rate equal to the golden ratio φ)

But the cosmological constant is not exactly constant. It has a (tiny) positive value. So that means that φ today is not φ tomorrow. And since attraction near the singularity of BH is stronger (because it goes into infinity), the gravitational “φ” is increasing its value as well.

So how is the exponentiality of the gravitational attraction of matter approaching a BH different from the exponentiality of galaxies getting pulled closer to the Big Bang? I am not a mathematician, but I really don’t see the difference, they’re both examples of exponential attraction.

Edited June 28, 2021 by MarkE

[swansont]

14 minutes ago, MarkE said:

1, 2, 3, 4, 5 = linear

1, 2, 4, 8, 16 = exponential

1, 2, 3, 5, 8, 13, 21 = exponential (since the Fibonacci numbers also grow at an exponential rate equal to the golden ratio φ)

So how is the exponentiality of the gravitational attraction of matter approaching a BH different from the exponentiality of galaxies getting pulled closer to the Big Bang? I am not a mathematician, but I really don’t see the difference, they’re both examples of exponential attraction.

2^±n is exponential

x^±2 is not

 

[MarkE]

9 minutes ago, swansont said:

x^±2 is not

Not my words:

”It demonstrates that the Fibonacci numbers grow at an exponential rate equal to the golden ratio φ.” (Source)

Edited June 28, 2021 by MarkE

[MigL]

There is a whole range of growth rates between linear and exponential.
As well as growth rates such as hyperbolic, which are faster than exponential.

1 hour ago, MarkE said:

And since attraction near the singularity of BH is stronger (because it goes into infinity)

If anything goes to infinity, that is an indication that your thinking/equations have exceeded their bounds of applicability.

 

[exchemist]

1 hour ago, MarkE said:

1, 2, 3, 4, 5 = linear

1, 2, 4, 8, 16 = exponential

1, 2, 3, 5, 8, 13, 21 = exponential (since the Fibonacci numbers also grow at an exponential rate equal to the golden ratio φ)

But the cosmological constant is not exactly constant. It has a (tiny) positive value. So that means that φ today is not φ tomorrow. And since attraction near the singularity of BH is stronger (because it goes into infinity), the gravitational “φ” is increasing its value as well.

So how is the exponentiality of the gravitational attraction of matter approaching a BH different from the exponentiality of galaxies getting pulled closer to the Big Bang? I am not a mathematician, but I really don’t see the difference, they’re both examples of exponential attraction.

Exponential does not just mean getting bigger and bigger. See the other posts that explain.

To put it In words, rather than in maths, an exponential process is one in which the rate of growth or decline is proportional to the magnitude of whatever it is that is growing or declining. So for example, in radioactive decay the rate of decay is proportional to the amount of substance that has not yet decayed. So the rate of decline itself declines as more and more of the material decays. Or, in the unconstrained growth of a bacterial colony, the rate of growth is proportional to the number of bacteria present at any given moment, because each cell divides at a fixed rate so the more cells there are the faster it grows.

This does not apply to gravitation. The force an object experiences grows as an inverse square of the distance from the attracting body.  That is not an exponential. 

[SergUpstart]

10 minutes ago, exchemist said:

Exponential does not just mean getting bigger and bigger. See the other posts that explain.

To put it In words, rather than in maths, an exponential process is one in which the rate of growth or decline is proportional to the magnitude of whatever it is that is growing or declining. So for example, in radioactive decay the rate of decay is proportional to the amount of substance that has not yet decayed. So the rate of decline itself declines as more and more of the material decays. Or, in the unconstrained growth of a bacterial colony, the rate of growth is proportional to the number of bacteria present at any given moment, because each cell divides at a fixed rate so the more cells there are the faster it grows.

Absolutely right. And the exponent is the main function in the economy.

[swansont]

1 hour ago, MarkE said:

Not my words:

”It demonstrates that the Fibonacci numbers grow at an exponential rate equal to the golden ratio φ.” (Source)

We're not talking about Fibonacci. In any event, it shows the growth is related to φⁿ  which is indeed exponential.

If you click on your link and then the "exponential rate" link and look at the graph, it shows a linear function,  as well as 2ⁿ and x³

You can see that they are not the same growth. 

[MarkE]

Thanks everybody for your responses! Nobody today of course knows what dark energy is, and understands what causes it and why, so I don’t think we can be sure that there’s no link between a BH and dark energy (which, as pointed out earlier, may represent the BB, from all sides around the universe, and therefore shares the singularity nature, because the BB is also referred to as a singularity (the so-called ‘initial singularity’). So what lies beyond the universe may have (attractive) properties.

We also don’t know what lies beyond the observable universe, if anything, so we can’t be sure that the universe is a closed space, and that it is infinite, and because we don’t know this for sure, it might as well be finite, which may imply that the galaxies are not moving away from each other simply because spacetime itself expands, and that the galaxies don’t truly move because they’re just along for the ride, rather, it could also that they are truly moving, because they're attracted to this 'edge' of the universe, which functions as a kind of inside out BH attracting all galaxies from all sides, and therefore the attraction is expected to be stronger further away. 

When I say ‘edge’ or ‘boundary’, I don’t mean something physical as a circumference around the universe. It’s not made of matter, which, to me, only strengthens the similarity between dark energy and a BH because a BH is also can't possibly be made of ordinary, Standard Model, matter.

I never understood an ‘infinite universe’ anyway, how do you visualize such a universe? How would you draw that on paper? 

But I don’t want to do philosophy. I'm not going to choose to 'believe' one explanation over the other, so I’m not choosing sides here, but so far, I have no reason to refute this unorthodox explanation. So, all in all, I remain skeptic in rejecting any correspondence between the nature of BHs and dark energy.
It’s a complicated topic, and nobody today grasps the full picture. But thanks a lot for all your replies, I’m going to take everything into consideration, and read some more books regarding this subject!

[swansont]

24 minutes ago, MarkE said:

Thanks everybody for your responses! Nobody today of course knows what dark energy is, and understands what causes it and why,

Hence the "dark" moniker

24 minutes ago, MarkE said:

so I don’t think we can be sure that there’s no link between a BH and dark energy (which, as pointed out earlier, may represent the BB, from all sides around the universe, and therefore shares the singularity nature, because the BB is also referred to as a singularity (the so-called ‘initial singularity’). 

There's no reason to think there is, either, which is a stronger statement.

The BB extrapolates back to a singularity, but at all times past that (i.e. at all times we have physics that we can discuss) there is dark energy and no singularity. "All sides around the universe" has no meaning.