A Dark energy = cosmological constant, any problems with that?

[kurros]

So I recently had a conversation with a mathematician friend of mine who studies Einstein's equations, and he asked me this: Why do physicists call it "dark energy"? It isn't like the dark matter problem, where there is almost certainly some massive "stuff" out there gravitationally influencing the motions of stars and galaxies and galaxy clusters and so on. We already have a perfectly good model for "dark energy", he says: GR. It just works already, why all the fuss? The cosmological constant is more or less just a constant of integration that appears naturally. It is just another free parameter, like the speed of light, or Newton's constant. Why not just fix it to what it needs to be and call it a day? Why all the talk of a dark energy "problem"?

For the purposes of this question I am supposing or assuming that the "cosmological constant problem" is actually a different issue. That problem asks why Lambda has the value it does, not why does it exist. Naive QFT calculations give a clearly incorrect answer for a vacuum energy contribution, so just forget about those, QFT or quantum gravity people will fix that one day. We are here asking why not just use the cosmological constant as-is? Why even associate it with QFT vacuum energy? Why all the searching for stuff to add into the energy-momentum tensor to emulate a cosmological constant, or modifications of GR? Of course it would be nice if there are some new quintenssence fields or some modified gravity, or even if it IS the QFT vacuum, or something fun, but don't we already have the solution in front of us?

Just curious how others here would have responded to my friend :). I guess this is a question about what physical motivation there is to suppose that the cosmological constant is something more than just another constant in Einstein's equations.

 

[phyzguy]

I tend to agree with your viewpoint, and other people have agreed as well. I suggest this paper "Why all these prejudices against a constant?" I think the reason that people started calling it "dark energy" is that we really don't know that it is a constant. If you call it the "cosmological constant", you prejudice all future investigations with the assumption that it is a constant. If you call it "dark energy", you open up the possibility of it varying in space and time. Much work is underway to try to determine if it varies, or if it truly is a constant. Time will tell.

 

[PeterDonis]

The cosmological constant is more or less just a constant of integration that appears naturally.

That's true, but it still leaves the question of why it takes the value that we actually observe it to take. Many people don't appear to be satisfied with the answer "just because", so they are looking for some deeper reason.

why not just use the cosmological constant as-is? Why even associate it with QFT vacuum energy?

One way of looking at this is that it depends on which side of the Einstein Field Equation you put the lambda term on. If you put it on the LHS, which IIRC is where Einstein and others originally put it, then it looks like a "property of spacetime"--something that is just "there", that you wouldn't expect to have to explain in terms of some kind of "stuff" (unless you view spacetime itself as a kind of "stuff"). But if you put it on the RHS, and give it the units of energy density (instead of curvature, which would be the natural units for it on the LHS), then it looks like some kind of "stuff", and you naturally start looking for an explanation of where this "stuff" comes from, hence the attempts to associate it with QFT vacuum energy, since that's the only kind of "stuff" we know of that can be there in what looks like a vacuum.

 

[kimbyd]

So I recently had a conversation with a mathematician friend of mine who studies Einstein's equations, and he asked me this: Why do physicists call it "dark energy"? It isn't like the dark matter problem, where there is almost certainly some massive "stuff" out there gravitationally influencing the motions of stars and galaxies and galaxy clusters and so on. We already have a perfectly good model for "dark energy", he says: GR. It just works already, why all the fuss? The cosmological constant is more or less just a constant of integration that appears naturally. It is just another free parameter, like the speed of light, or Newton's constant. Why not just fix it to what it needs to be and call it a day? Why all the talk of a dark energy "problem"?

The problem is the specific value of the cosmological constant that is required to explain the observations. In natural units, its value is approximately $10^{-120}$.

Typically when there is a very large or small number in physics, there's a reason why that number is large or small. The justification is that if there is some process that sets the values of numbers like the cosmological constant, then unless that process is doing something really intricate and interesting, the natural expectation is to get dimensionless numbers around 0.1-10 or so. Go much larger or much smaller than that, and there's probably something interesting that's being missed.

So, many physicists have been working hard to come up with alternative models that don't contain constants that are so ridiculously tiny.

 

[anorlunda]

One way of looking at this is that it depends on which side of the Einstein Field Equation you put the lambda term on. If you put it on the LHS, which IIRC is where Einstein and others originally put it, then it looks like a "property of spacetime"--something that is just "there" ... But if you put it on the RHS, and give it the units of energy density ... then it looks like some kind of "stuff"

Ah, very insightful You wrote before about interpretations of GR. Would freedom to choose LHS/RHS preference be an interpretation?

 

[PeterDonis]

You wrote before about interpretations of GR.

I did? I wrote an Insights article about interpretations of QM, but I don't think I've written one about interpretations of GR. Unless you're thinking of the series I wrote on "Does Gravity Gravitate?" That's sort of about "interpretations" of GR.

Would freedom to choose LHS/RHS preference be an interpretation?

It could be thought of that way, I suppose, yes.

 

[anorlunda]

I did? I wrote an Insights article about interpretations of QM, but I don't think I've written one about interpretations of GR. Unless you're thinking of the series I wrote on "Does Gravity Gravitate?" That's sort of about "interpretations" of GR.

This is what I was thinking of Peter when I said that you wrote about interpretations. I thought that too was instructive because I had never considered interpretations in GR context before.

Ah, ok. Yes, from a philosophical point of view, I agree the question is undecidable. The spacetime curvature interpretation of GR is, strictly speaking, an interpretation, not a claim about "how things really are". It just happens to be a very, very useful interpretation, so much so that physicists routinely talk about it as if it were a fact.

 

[PeterDonis]

This is what I was thinking of Peter when I said that you wrote about interpretations.

Ah, got it. Putting the Lambda term on the LHS or RHS of the EFE is really a separate "interpretation" question from the one I was talking about in that thread. If you interpret the Einstein tensor as describing, not spacetime curvature, but some kind of field, you still have a choice of whether to put the Lambda term on the LHS and call it part of the same field, or on the RHS and call it part of the source of the field.

 

[kurros]

The problem is the specific value of the cosmological constant that is required to explain the observations. In natural units, its value is approximately $10^{-120}$.

Typically when there is a very large or small number in physics, there's a reason why that number is large or small. The justification is that if there is some process that sets the values of numbers like the cosmological constant, then unless that process is doing something really intricate and interesting, the natural expectation is to get dimensionless numbers around 0.1-10 or so. Go much larger or much smaller than that, and there's probably something interesting that's being missed.

So, many physicists have been working hard to come up with alternative models that don't contain constants that are so ridiculously tiny.

Hmm, ok sure, but as far as I know most of the proposed dark energy candidates don't actually solve the cosmological constant problem, do they? I though most of them still just require fine tuning. Are there any candidates which naturally predict a super tiny value?

 

[kurros]

I tend to agree with your viewpoint, and other people have agreed as well. I suggest this paper "Why all these prejudices against a constant?" I think the reason that people started calling it "dark energy" is that we really don't know that it is a constant. If you call it the "cosmological constant", you prejudice all future investigations with the assumption that it is a constant. If you call it "dark energy", you open up the possibility of it varying in space and time. Much work is underway to try to determine if it varies, or if it truly is a constant. Time will tell.

Well that's fair I suppose, and was more or less the answer I gave my friend, I was just wondering if I was missing something :). We don't put the same effort into looking for a varying Newton constant or speed of light, for instance, though of course people occasionally do that. I guess doing that is definitely modifying gravity though, whilst we can imagine a dynamic "cosmological constant" without abandoning GR.

 

[kimbyd]

Hmm, ok sure, but as far as I know most of the proposed dark energy candidates don't actually solve the cosmological constant problem, do they? I though most of them still just require fine tuning. Are there any candidates which naturally predict a super tiny value?

It depends upon what you mean by "solve". There haven't been any alternative proposals which are clearly superior for sure (i.e., most tend to be rather ad-hoc with little to no physical justification). But that's not really relevant to the motivation for trying to find such a model.

 

[kurros]

Can we make a thermodynamic or perhaps metaphysical argument that dark energy should be dynamic? For example, it represents a kind of continuous energy injection into the universe, which feels like an odd thing for a constant to do. No other parameters do anything like that. Of course energy in GR is a tricky thing so maybe this is not such a useful way to look at it.

 

[PeterDonis]

For example, it represents a kind of continuous energy injection into the universe

No, it doesn't. A constant energy density everywhere means nothing is "injected". It's just there, the same everywhere.

Btw, "injecting" energy would violate local energy conservation, so it's impossible in GR anyway.

 

[kurros]

Well it kind of does. It's not a local energy injection, but it *is* acting like an effective force pushing galaxies apart. You could make a dark energy power station that could extract energy from the accelerating cosmic expansion if you built one big enough. The most naive thought experiment is to "anchor" two galaxies to each other with a super long cable. There will be a tension induced in this cable by the accelerating cosmic expansion, which you could use to run a generator until you run out of cable. (I'm not sure if there is something more clever that can be done to generate power forever, perhaps there isn't. And perhaps you can't get back more energy than it takes to transport your cable to the other galaxy in the first place. I'm not sure.)

Of course all the galaxies are already moving apart just from "standard" cosmic expansion so there is already plenty of energy you could extract just from that motion, however suppose we somehow brought them to rest relative to each other. If they are far enough apart that they aren't gravitationally bound, then they will start moving away from each other due to dark energy. So energy is "injected" in this sense.

We could imagine a universe with a really enormous cosmological constant, so that you could even feel this force on a human scale. Like you could hold your arms up and feel them getting dragged away from each other by the cosmic expansion. I guess that does suggest your couldn't do useful work with it though, it'd just be like a very weird component of the local gravitational field; you'd have to move objects together before you could extract energy from them being pushed apart, same as you have to pump water up a hill before you can extract energy from it flowing back down. Hmm, I'll have to think about it a bit more...

 

[nikkkom]

We could imagine a universe with a really enormous cosmological constant, so that you could even feel this force on a human scale.

That's what inflation _is_: mathematically it's the same as dark energy, just way, way larger magnitude.

 

[kurros]

Sure, sure, I was thinking a little less large than that though :). Large enough to feel it on human scales, but not so large that it blasts all matter apart and launches it across cosmological scales in an instant :).

 

[PeterDonis]

it *is* acting like an effective force pushing galaxies apart

But without changing any energy density, which means "effective force" is not really a good analogy. It's also not a good analogy because the galaxies do not feel any force pushing them apart; they are moving on geodesics. The dark energy simply makes the spacetime geometry such that the geodesics diverge.

The most naive thought experiment is to "anchor" two galaxies to each other with a super long cable. There will be a tension induced in this cable by the accelerating cosmic expansion

A small tension, but it will be constant, not increasing with time. The cable just makes the two galaxies into one object, which will have some internal stress in it because it has to resist the tidal gravity that is causing geodesics to diverge. But you won't be able to use this as a continuous power source; the most you could do would be to break the cable and release its stored energy one time.

So energy is "injected" in this sense.

No, it isn't. This is a bad analogy and you should not use it. See above.

We could imagine a universe with a really enormous cosmological constant, so that you could even feel this force on a human scale.

No, you wouldn't feel the force. See above.

 

[Bandersnatch]

No, you wouldn't feel the force. See above.

Why wouldn't one feel tidal gravity? Isn't that what spaghettification is all about?

 

[PeterDonis]

Why wouldn't one feel tidal gravity?

You feel a force if you aren't moving on a geodesic--or more precisely, if not all parts of you are moving on geodesics. But the force you feel (in the case where tidal gravity is present) is not "tidal gravity"; it's the internal forces between the different parts of your body that are keeping those parts from all following the geodesics that they would follow if they were moving purely in response to tidal gravity. If we are talking, not about one object bound by internal forces, but separate objects that are accelerating (in the coordinate sense) away from each other due to dark energy, those objects feel zero force even though they are certainly being affected by tidal gravity (since that's what the dark energy is producing).

 

[Bandersnatch]

If we are talking, not about one object bound by internal forces, but separate objects that are accelerating (in the coordinate sense)

Right. But the bit you were responding to was an example of a human with outstretched arms - so very much an object held together by internal forces.

 

[PeterDonis]

the bit you were responding to was an example of a human with outstretched arms - so very much an object held together by internal forces.

Yes, so the first part of my post would apply; the force the human feels is the internal forces, not tidal gravity. But as the human comes closer to the singularity at the center of a black hole, the internal forces holding him together have to increase (because the tidal gravity is increasing), and ultimately they reach their limit and the human's body comes apart. After that, the various pieces are moving on geodesics (though they won't be for very long since the singularity is close).

 

[JMz]

Typically when there is a very large or small number in physics, there's a reason why that number is large or small.

Except for gravity, even the non-Λ part: Gm_e²/(hc) ~ 10^-45. So far, "it just is". :-(

 

[kimbyd]

Except for gravity, even the non-Λ part: Gm_e²/(hc) ~ 10^-45. So far, "it just is". :-(

Oh, theorists are very much interested in trying to solve that problem as well, and it has been the source of quite a few theoretical ideas, such as the proposal of large extra dimensions.

 

[JMz]

Oh, theorists are very much interested in trying to solve that problem as well, and it has been the source of quite a few theoretical ideas, such as the proposal of large extra dimensions.

Yes, indeed! (I once worked on one of those, a few aeons ago. The CMB was at five K back then. ;-) But so far, nothing definitive.

 

[kurros]

But without changing any energy density, which means "effective force" is not really a good analogy. It's also not a good analogy because the galaxies do not feel any force pushing them apart; they are moving on geodesics. The dark energy simply makes the spacetime geometry such that the geodesics diverge.

It does change energy density, the energy density of matter goes down as a result. As for "feeling" a force, this is not really the relevant issue since you can say the same thing about any gravitational force. In fact you can say it about any matter moving as a result of any uniform force acting on all its parts at once. If you were a ball of equally charged particles sitting in an electrostatic field then you wouldn't "feel" anything as you accelerated, since to "feel" something you would need to experience some internal stresses, which you would not if all your particles remain stationary relative to each other even as the whole accelerates. Of course your constituents repel each other so this isn't a great analogy, but there are no forces exactly like gravity in this respect. The point is just that this doesn't change whether you view gravity as a force equivalent to the others, or as spacetime curvature. But this is all a bit beside the original point.

A small tension, but it will be constant, not increasing with time. The cable just makes the two galaxies into one object, which will have some internal stress in it because it has to resist the tidal gravity that is causing geodesics to diverge. But you won't be able to use this as a continuous power source; the most you could do would be to break the cable and release its stored energy one time.

You don't need the tension to increase, you just need the force to act over a distance to do work and generate power, which it will so long as you have more and more cable to "feed" out of the two galaxies as they are pull apart by dark energy (or by the tidal forces induced by diverging geodesics; it is equivalent). So you can certainly generate power, but only until you run out of cable. And it is entirely possible that you cannot generate more energy than it took to connect the two galaxies in the first place, or than it takes to harvest more cable etc. So I concede that it may not indicate a "real" injection of energy into the universe, it is possibly just a bizarre way of recovering some stored potential energy. But energy conservation doesn't really work like normal in GR, particularly in expanding spacetimes, so I'm not 100% sure.

 

[PeterDonis]

It does change energy density, the energy density of matter goes down as a result.

As a result of expansion, yes. But that happens regardless of whether there is dark energy; it's not due to any "transfer" of energy to or from dark energy. (It can't be since the density of dark energy is constant.)

As for "feeling" a force, this is not really the relevant issue since you can say the same thing about any gravitational force.

Exactly: in GR gravity is not a force either. It's spacetime geometry.

If you were a ball of equally charged particles sitting in an electrostatic field then you wouldn't "feel" anything as you accelerated

Yes, you would. The proper acceleration of a charged object in an electrostatic field is nonzero.

since to "feel" something you would need to experience some internal stresses, which you would not if all your particles remain stationary relative to each other even as the whole accelerates

Yes, you would. The key is not whether the particles are stationary relative to each other; it's whether their separations are the same as they would be in free fall. They aren't.

whether you view gravity as a force equivalent to the others

You can't view gravity as a force equivalent to the others, because it isn't. Only gravity can be modeled as spacetime curvature; the others can't.

You don't need the tension to increase, you just need the force to act over a distance to do work and generate power, which it will so long as you have more and more cable to "feed" out of the two galaxies as they are pull apart by dark energy (or by the tidal forces induced by diverging geodesics; it is equivalent).

Sorry, you are simply mistaken. Tidal gravity (which includes the effects of dark energy, as you correctly note) does not itself exert a force on anything. See my exchange with @Bandersnatch earlier in this thread (posts #18 through #21).

Note that in the scenario I discussed with @Bandersnatch (an astronaut falling towards the singularity of a black hole), the tidal gravity over a fixed separation increases with time; that's why the internal stresses in the astronaut's body have to increase. But in the case of dark energy, the tidal gravity over a fixed separation is constant; that's why the tension in the cable you postulate is constant. But that means that, as far as the two galaxies + cable system is concerned, everything is static and there is only a fixed amount of stored energy (the energy stored in the cable), which can be released once and that's it.

it is entirely possible that you cannot generate more energy than it took to connect the two galaxies in the first place

Which is, as I've already noted, the fixed amount of energy stored in the cable (because it's under tension). Which you can put in once, and take out once, and that's it.

energy conservation doesn't really work like normal in GR, particularly in expanding spacetimes

That's true as far as global energy conservation is concerned, but it doesn't affect the two galaxies + cable scenario; all of the stored energy there can be localized (the tension in the cable), so it doesn't raise any of the issues that come up globally in GR.

 

[kurros]

As a result of expansion, yes. But that happens regardless of whether there is dark energy; it's not due to any "transfer" of energy to or from dark energy. (It can't be since the density of dark energy is constant.)

Exactly: in GR gravity is not a force either. It's spacetime geometry.

Yes, you would. The proper acceleration of a charged object in an electrostatic field is nonzero.

Yes, you would. The key is not whether the particles are stationary relative to each other; it's whether their separations are the same as they would be in free fall. They aren't.

You can't view gravity as a force equivalent to the others, because it isn't. Only gravity can be modeled as spacetime curvature; the others can't.

Sorry, you are simply mistaken. Tidal gravity (which includes the effects of dark energy, as you correctly note) does not itself exert a force on anything. See my exchange with @Bandersnatch earlier in this thread (posts #18 through #21).

I'm not sure where you were going with that exchange. And I'm not at all sure what you are claiming here. Tidal gravitational forces clearly can exert forces on things, that's why they can create the tides on Earth, and rip apart stars as they fall into black holes. If dark energy can generate tidal forces like these, which we seem to agree that it can, then I don't see why it would not pull on the rope in my thought experiment. In fact you agreed that it *does* pull on the rope, there is a tension induced, so I am again left at a loss as to what you mean here.

Note that in the scenario I discussed with @Bandersnatch (an astronaut falling towards the singularity of a black hole), the tidal gravity over a fixed separation increases with time; that's why the internal stresses in the astronaut's body have to increase. But in the case of dark energy, the tidal gravity over a fixed separation is constant; that's why the tension in the cable you postulate is constant. But that means that, as far as the two galaxies + cable system is concerned, everything is static and there is only a fixed amount of stored energy (the energy stored in the cable), which can be released once and that's it.

What do you mean? You think if we let out more rope then the tension will not increase again? Why? Our two far-separated galaxies, initially at rest relative to each other, will experience an acceleration relative to each other due to dark energy, will they not? Or their geodesics will diverge, if you prefer. It was my understanding that they will. If not, then I don't see how there would be a tension on the rope/tether in the first place. Are you saying that if we bring two objects to rest relative to each other then they will remain at that fixed distance, despite cosmic expansion (ignoring their mutual gravitational attraction)?

 

[PeterDonis]

Tidal gravitational forces clearly can exert forces on things, that's why they can create the tides on Earth

Sorry, again you are mistaken. Please go back and read my exchange with @Bandersnatch again.

In the case of tides on the Earth, the water in the Earth's tidal bulge moves outward, relative to the Earth, because of the natural geodesic motion due to the spacetime curvature (tidal gravity) created by the Moon (and the Sun, but we'll focus on the Moon here) and by the Earth. That water feels no force due to the tidal gravity. The only force it feels is the net (non-gravitational) force due to hydrostatic pressure exerted by the water (or ocean bottom) underneath it; that force prevents the water from completely following the natural geodesic motion due to the spacetime geometry in its vicinity.

(Note, also, that the water in the Earth's tidal bulge does not have internal tension the way a solid object like a rope would. That makes the analysis of the two cases differ in some respects. See below.)

In fact you agreed that it *does* pull on the rope, there is a tension induced

I agreed that there is tension in the rope; but the reason there is tension in the rope is not that tidal gravity is exerting a force on it, or on the galaxies. It is that the rope is preventing the two galaxies from following the natural geodesic motion due to the spacetime curvature in their vicinity. If the rope were not there, the two galaxies would separate. With the rope there, the two galaxies reach an equilibrium in which their separation is constant and the rope is stretched beyond its unstressed length, just enough so that the tension in the rope imposes the right proper acceleration on the galaxies to keep them at a constant separation.

Once again, gravity in GR is not a force. I don't think you have fully understood the implications of that fact.

You think if we let out more rope then the tension will not increase again?

I think you have not thought the scenario through. Consider the situation I just described above: the two galaxies are at constant separation, with the rope stretched beyond its unstressed length just enough so that its tension keeps the galaxies at constant separation. In this situation, everything is in equilibrium and there is a constant amount of energy stored in the rope. (If you don't see how this situation is an equilibrium, then stop and convince yourself of this before reading further. It is a crucial point.)

Now, suppose we start in this equilibrium situation, and then let out some more rope. What will happen? First, what does "letting out more rope" mean? It means that we have increased the unstressed length of the rope. That means there will be a new equilibrium configuration now, with the galaxies at a larger separation, and with a different amount of tension in the rope. The new tension in the rope will have to be larger than it was before (because the proper acceleration required to hold the galaxies at constant separation increases with the separation). So yes, you are correct that if we let out rope, the tension will increase.

However, you are claiming something more: that we can somehow extract work from this process. How?

 

[George Jones]

Sorry, again you are mistaken.

What about the terminology used on pages 860-861 of Misner, Thorne, and Wheeler?

 

[Dr Whom]

Dark matter. It produces gravitational effects, which as far as we know means it has mass, but it does not interact electromagnetically as all familiar matter does. We can't see it but it exists, hence dark matter. Just like black holes!
http://drwhom.eu3.biz/pages/Dark Matters.htm
Dark energy. The most recent measurements, to everyone's surprise, so the universe is expanding at an every increasing rate, despite the presence of a lot of matter, both light and dark, that should be slowing it down. This is behaviour described in General Relativity by a constant of integration, the Cosmological one, having a positive value. Usually, acceleration requires energy. Like dark matter, we can't see any sources for this energy, hence dark and energy. An intriguing alternative is some form of higher dimensional rotation.
http://drwhom.eu3.biz/pages/TBWS - 05 Dark Energy.htm

 

[PeterDonis]

What about the terminology used on pages 860-861 of Misner, Thorne, and Wheeler?

I don't have my copy right now, but I'll take a look when I get a chance. If it's a place where the term "force" is used to mean something other than "causes nonzero proper acceleration", then I agree that the terminology in the literature is not entirely consistent on this point.

 

[kurros]

Sorry, again you are mistaken. Please go back and read my exchange with @Bandersnatch again.

In the case of tides on the Earth, the water in the Earth's tidal bulge moves outward, relative to the Earth, because of the natural geodesic motion due to the spacetime curvature (tidal gravity) created by the Moon (and the Sun, but we'll focus on the Moon here) and by the Earth. That water feels no force due to the tidal gravity. The only force it feels is the net (non-gravitational) force due to hydrostatic pressure exerted by the water (or ocean bottom) underneath it; that force prevents the water from completely following the natural geodesic motion due to the spacetime geometry in its vicinity.

(Note, also, that the water in the Earth's tidal bulge does not have internal tension the way a solid object like a rope would. That makes the analysis of the two cases differ in some respects. See below.)
I agreed that there is tension in the rope; but the reason there is tension in the rope is not that tidal gravity is exerting a force on it, or on the galaxies. It is that the rope is preventing the two galaxies from following the natural geodesic motion due to the spacetime curvature in their vicinity. If the rope were not there, the two galaxies would separate. With the rope there, the two galaxies reach an equilibrium in which their separation is constant and the rope is stretched beyond its unstressed length, just enough so that the tension in the rope imposes the right proper acceleration on the galaxies to keep them at a constant separation.

Once again, gravity in GR is not a force. I don't think you have fully understood the implications of that fact.
I think you have not thought the scenario through. Consider the situation I just described above: the two galaxies are at constant separation, with the rope stretched beyond its unstressed length just enough so that its tension keeps the galaxies at constant separation. In this situation, everything is in equilibrium and there is a constant amount of energy stored in the rope. (If you don't see how this situation is an equilibrium, then stop and convince yourself of this before reading further. It is a crucial point.)

Now, suppose we start in this equilibrium situation, and then let out some more rope. What will happen? First, what does "letting out more rope" mean? It means that we have increased the unstressed length of the rope. That means there will be a new equilibrium configuration now, with the galaxies at a larger separation, and with a different amount of tension in the rope. The new tension in the rope will have to be larger than it was before (because the proper acceleration required to hold the galaxies at constant separation increases with the separation). So yes, you are correct that if we let out rope, the tension will increase.

However, you are claiming something more: that we can somehow extract work from this process. How?

I'll reply in more detail tomorrow, but I am just describing something exactly like a mass hanging from a rope on earth. We can and do extract energy from such a system by allowing the mass to fall and the rope to turn a turbine. I see no reason the exact same thing would not work in the dark energy situation I described. I do not see from your current argument what would prevent such a thing.

 

[kimbyd]

I'll reply in more detail tomorrow, but I am just describing something exactly like a mass hanging from a rope on earth. We can and do extract energy from such a system by allowing the mass to fall and the rope to turn a turbine. I see no reason the exact same thing would not work in the dark energy situation I described. I do not see from your current argument what would prevent such a thing.

That energy would all come from the relative motion of the two galaxies. It would have nothing (directly) to do with dark energy. All that dark energy does is increases the tension on the rope by such a minuscule amount that it likely would have no measurable impact.

The dark energy also does change the relative motion over time between the two galaxies.

 

[PeterDonis]

I am just describing something exactly like a mass hanging from a rope on earth.

No, you're not. If a rope is suspended on Earth, its point of suspension has nonzero proper acceleration whether the rope and the mass are present or not. It is that outside source of proper acceleration that provides the force which suspends the mass, and against which work is done if the mass is allowed to descend. But in the scenario we're discussing, in the absence of the thread, both "points of suspension"--the two galaxies--have zero proper acceleration. The only possible source of proper acceleration is the thread itself.

So what you should be imagining as an analogy is a huge spaceship floating in free fall, and two masses connected by a thread floating inside the ship. If the ship is subject to a constant tidal gravity (for example, if it's in a circular orbit about a planet and is large enough for the planet's field to vary detectably inside the ship), what will be the equilibrium state of the two masses and the thread?

 

[alantheastronomer]

Dr' Whom in post #30 has the right idea - We observe the universe to be expanding, but we don't have an explanation for what the physical cause of that expansion might be? Hence we call it "dark energy".

 

[kurros]

No, you're not. If a rope is suspended on Earth, its point of suspension has nonzero proper acceleration whether the rope and the mass are present or not. It is that outside source of proper acceleration that provides the force which suspends the mass, and against which work is done if the mass is allowed to descend. But in the scenario we're discussing, in the absence of the thread, both "points of suspension"--the two galaxies--have zero proper acceleration. The only possible source of proper acceleration is the thread itself.

But there *is* a thread, and it is pulling the masses off their geodesics, both in the Earth and dark energy examples. I don't see any difference except for the direction of "falling".

So what you should be imagining as an analogy is a huge spaceship floating in free fall, and two masses connected by a thread floating inside the ship. If the ship is subject to a constant tidal gravity (for example, if it's in a circular orbit about a planet and is large enough for the planet's field to vary detectably inside the ship), what will be the equilibrium state of the two masses and the thread?

There will be tension, and you should be able to do work with it. It seems the same. It could do so much work that it rips the ship apart, in the extreme case. (edit: and dark energy could rip you apart too, if the cosmological constant was really huge. So it seems like it *can* do work. Of course you could never form in the first place with a huge cosmological constant, but if someone did the work needed to put you together in such a universe then dark energy could certainly then use that stored energy to rip you apart again).

 

[kurros]

That energy would all come from the relative motion of the two galaxies. It would have nothing (directly) to do with dark energy. All that dark energy does is increases the tension on the rope by such a minuscule amount that it likely would have no measurable impact.

The dark energy also does change the relative motion over time between the two galaxies.

Haha sure, it is miniscule, but this is an in-principle sort of question :).

 

[JMz]

...we don't have an explanation for what the physical cause of that expansion might be? Hence we call it "dark energy".

How so? We have one perfectly good explanation: It's Einstein's own Λ. It's true that people can come up with other explanations -- and that work is certainly worthwhile.

But you could likewise make the case that the gravitational coupling parameter G is not independent of time, or that the speed of light is not constant for all observers. However, those are the standard explanations, they are in agreement with virtually all current observations, and they don't come with any physical cause either, at least not so far. Yet we don't consider the lack of a cause to be a problem.

@kurros's friend is right: This isn't a problem, it's simply a discovery.

The one good reason to treat it otherwise is --

many physicists have been working hard to come up with alternative models that don't contain constants that are so ridiculously tiny.

 

[Orodruin]

Dr' Whom in post #30 has the right idea - We observe the universe to be expanding, but we don't have an explanation for what the physical cause of that expansion might be? Hence we call it "dark energy".

This is also not correct. The universe could be expanding even if there was no dark energy. Dark energy is needed only for accelerated expansion.

 

[kurros]

Ok so here is a better reply to what you said earlier:

Sorry, again you are mistaken. Please go back and read my exchange with @Bandersnatch again.

In the case of tides on the Earth, the water in the Earth's tidal bulge moves outward, relative to the Earth, because of the natural geodesic motion due to the spacetime curvature (tidal gravity) created by the Moon (and the Sun, but we'll focus on the Moon here) and by the Earth. That water feels no force due to the tidal gravity. The only force it feels is the net (non-gravitational) force due to hydrostatic pressure exerted by the water (or ocean bottom) underneath it; that force prevents the water from completely following the natural geodesic motion due to the spacetime geometry in its vicinity.

I think you are getting too caught up in the language here. I'll agree that yes you are strictly correct, but I don't think it is incorrect to call that situation "feeling a tidal force". It is just a frame of reference difference, like feeling a centrifugal force when you ride the gravitron. Yes, you actually feel the walls pushing you off your geodesic, but there is no real reason not to talk about the "fictional" force that exists in the spinning reference frame.

I agreed that there is tension in the rope; but the reason there is tension in the rope is not that tidal gravity is exerting a force on it, or on the galaxies. It is that the rope is preventing the two galaxies from following the natural geodesic motion due to the spacetime curvature in their vicinity. If the rope were not there, the two galaxies would separate. With the rope there, the two galaxies reach an equilibrium in which their separation is constant and the rope is stretched beyond its unstressed length, just enough so that the tension in the rope imposes the right proper acceleration on the galaxies to keep them at a constant separation.

Once again, gravity in GR is not a force. I don't think you have fully understood the implications of that fact.

Exactly, without the rope the galaxies would follow their natural geodesic motion. Exactly like a mass hanging on a rope on Earth would fall downwards along its natural geodesic motion if the rope was not there. Both cases seem completely analogous, and I see no reason why you can turn a turbine in one scenario and not the other.

I think you have not thought the scenario through. Consider the situation I just described above: the two galaxies are at constant separation, with the rope stretched beyond its unstressed length just enough so that its tension keeps the galaxies at constant separation. In this situation, everything is in equilibrium and there is a constant amount of energy stored in the rope. (If you don't see how this situation is an equilibrium, then stop and convince yourself of this before reading further. It is a crucial point.)

It doesn't matter how much energy is stored in the rope. That isn't where the energy comes from. Like on earth, when you create the gravity-battery situation described earlier, it doesn't matter how much energy is stored in the cable. What matters is the mass hanging from the cable and the distance over which you let it fall. That determines the potential energy difference, which is the maximum you can recover in power generation. It should be exactly the same in the dark energy scenario. I'm not 100% sure where the potential energy is stored, but I guess it might just be stored in the configuration of matter you start with. You start with two galaxies "near" each other, and they want to "fall" away from each other. So there is a certain amount of stored potential energy there.

Now, suppose we start in this equilibrium situation, and then let out some more rope. What will happen? First, what does "letting out more rope" mean? It means that we have increased the unstressed length of the rope. That means there will be a new equilibrium configuration now, with the galaxies at a larger separation, and with a different amount of tension in the rope. The new tension in the rope will have to be larger than it was before (because the proper acceleration required to hold the galaxies at constant separation increases with the separation). So yes, you are correct that if we let out rope, the tension will increase.

However, you are claiming something more: that we can somehow extract work from this process. How?

Same as on Earth. Attach our end of the rope to a turbine and let it spin as the rope uncoils. Though I guess in this analogy the turbine is attached to the falling mass. For an even closer analogy you might imagine a space elevator. It takes energy to lift stuff up to our anchor in geostationary orbit, but we can certainly recover energy by attaching a rope to stuff as it falls back down the elevator, and turning a generator as it falls back down. Even more, we could generate power by attaching a tether on the *outside* of our anchor, above geostationary orbit, and allowing the centrifugal force of the orbit to drag a mass outwards while turning a generator. All this seems fine as far as I can see. It can be hard to pinpoint where the energy comes from sometimes, but it can be done.

 

[PeterDonis]

there *is* a thread, and it is pulling the masses off their geodesics, both in the Earth and dark energy examples.

No. In the Earth example, the rope is not what is pulling the mass off of a geodesic: it's whatever structure is holding up the rope's attachment point. In the two galaxies example, there is no such attachment point for the rope.

I don't think it is incorrect to call that situation "feeling a tidal force".

It is if it leads you to an incorrect analysis of a scenario, which it is doing.

Both cases seem completely analogous, and I see no reason why you can turn a turbine in one scenario and not the other.

That's because the term "tidal force" is misleading you.

It doesn't matter how much energy is stored in the rope. That isn't where the energy comes from.

This is true in the Earth example. It is not true in the galaxies connected by rope example.

It takes energy to lift stuff up to our anchor in geostationary orbit, but we can certainly recover energy by attaching a rope to stuff as it falls back down the elevator, and turning a generator as it falls back down.

This is not analogous to the galaxy scenario either. The galaxies were not "lifted" to their positions, and you're not recovering any energy by letting them "fall".

Please take a step back and think carefully about the one valid analogy I suggested to you, the one that actually involves tidal gravity, and nothing else. That is the situation with the two galaxies and the rope: there is tidal gravity, and nothing else. No planet, no potential well, nothing. Just tidal gravity and nothing else. To support your claim you need to show that you can extract an arbitrary amount of work by paying out rope in that situation. Nothing else will do.

 

[kimbyd]

Dr' Whom in post #30 has the right idea - We observe the universe to be expanding, but we don't have an explanation for what the physical cause of that expansion might be? Hence we call it "dark energy".

To expand a little on Orodruin's response, dark energy doesn't cause the expansion at all. It modifies the rate of expansion, making it higher in the late universe than would otherwise be the case.

 

[kurros]

No. In the Earth example, the rope is not what is pulling the mass off of a geodesic: it's whatever structure is holding up the rope's attachment point. In the two galaxies example, there is no such attachment point for the rope.

Yes there is, the attachment point is the other galaxy. There is an acceleration off their geodesics occurring. Acceleration times mass times distance is work. Where is the problem?

This is not analogous to the galaxy scenario either. The galaxies were not "lifted" to their positions, and you're not recovering any energy by letting them "fall".

Please take a step back and think carefully about the one valid analogy I suggested to you, the one that actually involves tidal gravity, and nothing else. That is the situation with the two galaxies and the rope: there is tidal gravity, and nothing else. No planet, no potential well, nothing. Just tidal gravity and nothing else. To support your claim you need to show that you can extract an arbitrary amount of work by paying out rope in that situation. Nothing else will do.

I see no problem in the purely tidal situation either. There is a tension in the rope, a force, if you apply it over a distance then that is work. Why wouldn't it be? And we already do extract power from tidal gravity, that's what tidal power on Earth is. The mechanism is a bit different but the power is still generated due to tidal forces. If there is some problem with any of this then you'll have to be much more clear about what it is.

Here's a similar siutation: https://physics.stackexchange.com/q...e-break-due-to-the-tidal-forces-or-not/214363. Are you trying to tell me that you cannot do work by allowing that rope to unspool while turning a turbine? I'm sorry but I see absolutely no problem with that at all.

 

[nikkkom]

How so? We have one perfectly good explanation: It's Einstein's own Λ. It's true that people can come up with other explanations -- and that work is certainly worthwhile.

But you could likewise make the case that the gravitational coupling parameter G is not independent of time, or that the speed of light is not constant for all observers. However, those are the standard explanations, they are in agreement with virtually all current observations, and they don't come with any physical cause either, at least not so far. Yet we don't consider the lack of a cause to be a problem.

If we accept a premise that there was an early inflationary phase, then it hints that "Λ" is not a constant, it depends on vacuum state you are in - IOW: it probably comes from the vacuum energy density: inflationary vacuum has a high one, our current vacuum has a very tiny, but nonzero one. Heuristically this makes sense, as inflationary vacuum probably has some huge VEVs, and current fields' VEVs are either zero (leptons and photons) or much lower than Planck.

We "only" need to learn how to actually calculate vacuum energy density, correctly in UV limit.

 

[kurros]

If we accept a premise that there was an early inflationary phase, then it hints that "Λ" is not a constant, it depends on vacuum state you are in - IOW: it probably comes from the vacuum energy density: inflationary vacuum has a high one, our current vacuum has a very tiny, but nonzero one. Heuristically this makes sense, as inflationary vacuum probably has some huge VEVs, and current fields' VEVs are either zero (leptons and photons) or much lower than Planck.

We "only" need to learn how to actually calculate vacuum energy density, correctly in UV limit.

I'm not sure it has anything to do with VEVs of fields, does it? I mean the Higgs field has a VEV of 246 GeV, but this is nothing to do with dark energy. I presume because we can consider the Higgs field to be at the minima of its potential, so it is in fact in a minimum-energy state, despite that state being at non-zero field values. So it is about the potentials of our fields. In contrast, in inflation the inflaton starts off at the top of some big potential energy hill.

 

[nikkkom]

I'm not sure it has anything to do with VEVs of fields, does it? I mean the Higgs field has a VEV of 246 GeV, but this is nothing to do with dark energy.

Directly, no. Indirectly, I assume the math will work out so that large VEVs usually correspond to large vacuum energy density.

In contrast, in inflation the inflaton starts off at the top of some big potential energy hill.

I don't think so. Inflationary state may be a (false) vacuum, i.e. a local _minimum_.

 

[Orodruin]

Indirectly, I assume the math will work out so that large VEVs usually correspond to large vacuum energy density.

This assumption is generally not correct.

 

[kurros]

Directly, no. Indirectly, I assume the math will work out so that large VEVs usually correspond to large vacuum energy density.

I don't see why? 246 GeV is rather high energy, vastly higher than we see for the cosmological constant, so on the face of it it seems like this isn't the case.

I don't think so. Inflationary state may be a (false) vacuum, i.e. a local _minimum_.

Local being the key word. If there is a deeper minimum somewhere else then there is still a potential energy difference between the states, with the false vacuum being higher energy.

 

[nikkkom]

I don't see why? 246 GeV is rather high energy, vastly higher than we see for the cosmological constant, so on the face of it it seems like this isn't the case.

246 GeV is rather low energy compared to the natural scale, the Planck. Basically, our current vacuum state and physics we observe is very "cold", way way down below Planck.

Also, "cosmological constant" nee "dark energy" can not be directly compared with VEVs because they have different units. It's like comparing meters with volts. Dark energy has energy _density_ (energy per unit volume), not energy.

Local being the key word. If there is a deeper minimum somewhere else then there is still a potential energy difference between the states, with the false vacuum being higher energy.

Earlier you said "in inflation the inflaton starts off at the top of some big potential energy hill". That description definitely does not describe a local minimum.

 

[nikkkom]

> Indirectly, I assume the math will work out so that large VEVs usually correspond to large vacuum energy density.

This assumption is generally not correct.

Sure. "I have a hunch" is not scientifically valid. Only the mathematically consistent, real theory's predictions are scientifically valid. I'm looking forward to the time we'll have one which can calculate vacuum energy density from first principles.