Dark energy = cosmological constant, any problems with that?

In summary, the cosmological constant problem is the question of why lambda has the value that it does, not the question of why it exists.
  • #1
kurros
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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.
 
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  • #2
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.
 
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  • #3
kurros said:
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.

kurros said:
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.
 
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  • #4
kurros said:
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.
 
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  • #5
PeterDonis said:
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?
 
  • #6
anorlunda said:
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.

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

It could be thought of that way, I suppose, yes.
 
  • #7
PeterDonis said:
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.
https://www.physicsforums.com/threads/classical-physics-is-wrong-fallacy-comments.942207/page-3#post-5961672 said:
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.
 
  • #8
anorlunda said:
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.
 
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  • #9
kimbyd said:
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?
 
  • #10
phyzguy said:
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.
 
  • #11
kurros said:
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.
 
  • #12
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.
 
  • #13
kurros said:
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.
 
  • #14
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...
 
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  • #15
kurros said:
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.
 
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  • #16
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 :).
 
  • #17
kurros said:
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.

kurros said:
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.

kurros said:
So energy is "injected" in this sense.

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

kurros said:
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.
 
  • #18
PeterDonis said:
No, you wouldn't feel the force. See above.
Why wouldn't one feel tidal gravity? Isn't that what spaghettification is all about?
 
  • #19
Bandersnatch said:
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).
 
  • #20
PeterDonis said:
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.
 
  • #21
Bandersnatch said:
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).
 
  • #22
kimbyd said:
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: Gme2/(hc) ~ 10-45. So far, "it just is". :-(
 
  • #23
JMz said:
Except for gravity, even the non-Λ part: Gme2/(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.
 
  • #24
kimbyd said:
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.
 
  • #25
PeterDonis said:
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.
 
  • #26
kurros said:
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.)

kurros said:
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.

kurros said:
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.

kurros said:
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.

kurros said:
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.

kurros said:
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.

kurros said:
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.

kurros said:
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.
 
  • #27
PeterDonis said:
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)?
 
  • #28
kurros said:
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.)

kurros said:
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.

kurros said:
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?
 
  • #29
PeterDonis said:
Sorry, again you are mistaken.

What about the terminology used on pages 860-861 of Misner, Thorne, and Wheeler?
 
  • #30
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
 
  • #31
George Jones said:
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.
 
  • #32
PeterDonis said:
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.
 
  • #33
kurros said:
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.
 
  • #34
kurros said:
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?
 
  • #35
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".
 
<h2>1. What is dark energy and how does it relate to the cosmological constant?</h2><p>Dark energy is a theoretical form of energy that is thought to make up about 70% of the total energy in the universe. It is believed to be responsible for the observed acceleration of the expansion of the universe. The cosmological constant is a parameter in Einstein's theory of general relativity that describes the energy density of the vacuum. Dark energy is often equated with the cosmological constant because they share similar properties, but they are not necessarily the same thing.</p><h2>2. How does dark energy affect the expansion of the universe?</h2><p>Dark energy is thought to be the driving force behind the accelerated expansion of the universe. It is believed to counteract the gravitational pull of matter and push galaxies further apart, causing the expansion of the universe to accelerate over time.</p><h2>3. Are there any problems with the theory of dark energy being equivalent to the cosmological constant?</h2><p>While the theory of dark energy being equivalent to the cosmological constant is currently the most widely accepted explanation for the observed acceleration of the universe, there are still some unanswered questions and potential problems with this theory. For example, the amount of dark energy predicted by the cosmological constant is significantly larger than what is observed in the universe, leading to the "cosmological constant problem." Additionally, there are other theories that attempt to explain the acceleration of the universe without the need for dark energy.</p><h2>4. How is dark energy being studied and measured?</h2><p>Dark energy is a difficult concept to study and measure because it cannot be directly observed. However, scientists can study its effects on the expansion of the universe through various methods, such as observing the brightness and distances of supernovae, mapping the large-scale structure of the universe, and studying the cosmic microwave background radiation.</p><h2>5. What are some potential implications of the existence of dark energy?</h2><p>If dark energy is indeed the cause of the accelerated expansion of the universe, it could have significant implications for our understanding of the fundamental laws of physics. It could also potentially impact our understanding of the fate of the universe and the possibility of a "Big Rip" scenario in which dark energy becomes so dominant that it tears apart all matter in the universe. Additionally, further research on dark energy could potentially lead to new technologies and advancements in our understanding of the universe.</p>

1. What is dark energy and how does it relate to the cosmological constant?

Dark energy is a theoretical form of energy that is thought to make up about 70% of the total energy in the universe. It is believed to be responsible for the observed acceleration of the expansion of the universe. The cosmological constant is a parameter in Einstein's theory of general relativity that describes the energy density of the vacuum. Dark energy is often equated with the cosmological constant because they share similar properties, but they are not necessarily the same thing.

2. How does dark energy affect the expansion of the universe?

Dark energy is thought to be the driving force behind the accelerated expansion of the universe. It is believed to counteract the gravitational pull of matter and push galaxies further apart, causing the expansion of the universe to accelerate over time.

3. Are there any problems with the theory of dark energy being equivalent to the cosmological constant?

While the theory of dark energy being equivalent to the cosmological constant is currently the most widely accepted explanation for the observed acceleration of the universe, there are still some unanswered questions and potential problems with this theory. For example, the amount of dark energy predicted by the cosmological constant is significantly larger than what is observed in the universe, leading to the "cosmological constant problem." Additionally, there are other theories that attempt to explain the acceleration of the universe without the need for dark energy.

4. How is dark energy being studied and measured?

Dark energy is a difficult concept to study and measure because it cannot be directly observed. However, scientists can study its effects on the expansion of the universe through various methods, such as observing the brightness and distances of supernovae, mapping the large-scale structure of the universe, and studying the cosmic microwave background radiation.

5. What are some potential implications of the existence of dark energy?

If dark energy is indeed the cause of the accelerated expansion of the universe, it could have significant implications for our understanding of the fundamental laws of physics. It could also potentially impact our understanding of the fate of the universe and the possibility of a "Big Rip" scenario in which dark energy becomes so dominant that it tears apart all matter in the universe. Additionally, further research on dark energy could potentially lead to new technologies and advancements in our understanding of the universe.

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