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> In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with ze

> In fact that local conservation of stress-energy density is what requires the energy density of matter (which in cosmology-speak means a perfect fluid with zero pressure) to decrease as the universe expands (as the cube of the scale factor). That makes total sense! Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? What's the energy equivalent of one new cubic meter of space, in Joules? Do we know that? Does it fit the observed matter density, with and without dark matter? It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process.

pdonis 2y ago
> Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? It doesn't work that way. Remember that GR is a theory of spacetime geometry. When we say "the universe is expanding", that's really shorthand for "the spacetime geometry of the universe has a particular shape". It doesn't mean that the universe "adds cubic meters" over time. There is certainly a relationship between the density of matter (or more generally stress-energy density) and the geometric property that informally we refer to as "the rate of expansion of the universe". The equations that express that relationship are the Friedmann equations, which are just the Einstein Field Equation, the central equation of GR, specialized to the kind of spacetime geometry that "expanding universe" refers to. But it's not really useful to think of those relationships as saying that if the matter density decreases by this much, it makes the universe expand that much. > It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process. No, that's not a good way to look at it. A cosmological constant aka dark energy is best thought of as just an unusual form of perfect fluid whose pressure is minus its energy density. Then you just plug that into the Friedmann equations to get predictions for what we should expect to observe, such as "accelerating expansion".
- thriftwy 2y ago
  I don't agree with you. Between us and a redshifted galaxy, for a specific cross-section "tube", there is a dV/dt of new space and a -dE/dt of energy from the redshift. It is possible to calculate both so at least the circumstantial "cubic metres for joules" metric is possible, and interesting. But it seems I'm not geting it out of this discussion. You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. If the density decrease is not linked to the volume increase then you have to explain where that extra energy went. "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place. Unfortunately what I can see is lack of understanding the mechanism and being able to productively reason about that, and stress-energy tensor is sufficiently complicated abstraction that one no longer feels the discomfort of not understanding.
  - pdonis 2y ago
    > I don't agree with you. Then you are disagreeing with our best current physical model of our universe, which does not say what you are saying. > I'm not geting it out of this discussion. You should be aware that General Relativity and modern cosmology are complex subjects, and cannot be understood all at once in the course of an Internet discussion. Do you know how long it took me to properly understand the model that I am giving you a very quick and abbreviated description of? Several decades. So if you're expecting a quick "sound bite" answer that will make sense to you, and you have no background whatever in those subjects, of course you are not going to get what you are looking for. I can't help that. All I can tell you is what our best current models say. > You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. No, that's not what I'm saying. What I'm saying is that the relationship is not a causal relationship, in which the density decrease causes the volume increase. It is just a relationship that is enforced by the overall relationship between the spacetime geometry and the stress-energy tensor. The general form of that relationship is the Einstein Field Equation, and the particular form that applies to our best current model of the universe is the Friedmann equations. Those equations most definitely do give a relationship between density decrease for matter and what you are calling "volume increase"--more precisely the rate of "volume increase" (but the term cosmologists actually use is "scale factor" and "rate of increase of the scale factor"), and that relationship most definitely does include a local conservation law for stress-energy. I apologize if that wasn't clear. > "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place. I'm using "perfect fluid" here as a technical term for a particular form of the stress-energy tensor, where the only two things you need to specify are energy density and pressure. Terms like "matter" and "dark energy" are then just names for particular equations of state, i.e., particular relationships between energy density and pressure. "Matter" means pressure is zero. "Dark energy" means pressure is minus energy density. That is standard usage among cosmologists. As for why the dark energy density stays the same as the universe expands, that's what the Friedmann equations say when pressure is minus energy density. If you don't like the term "perfect fluid" to describe such a thing, that's fine, call it something else if you like. (But don't expect cosmologists to go along with you.) The important point is the physics, not the words we use to describe it. The physics is what I said. You can check it for yourself if you like by looking up the Friedmann equations. > what I can see is lack of understanding the mechanism What I can see, and I can't avoid saying this bluntly, is someone who has no background in physics but still presumes to tell someone who does have such a background what they do and do not understand. Sorry, but you, and again I can't avoid saying this bluntly, simply don't know what you are talking about. I do know what I am talking about. I'm sorry that I can't convey what I know to you in a quick sound bite that will make sense to you, but that's beyond human powers. There's a reason that people spend years or decades studying these subjects, and there's a reason that even the basics are taught in university courses that take multiple semesters to complete and require textbooks and working problem sets and so on.

pdonis 2y ago

> Does this meak we know how much the total density of matter has to decrease in order for universe to expand one cubic meter? It doesn't work that way. Remember that GR is a theory of spacetime geometry. When we say "the universe is expanding", that's really shorthand for "the spacetime geometry of the universe has a particular shape". It doesn't mean that the universe "adds cubic meters" over time. There is certainly a relationship between the density of matter (or more generally stress-energy density) and the geometric property that informally we refer to as "the rate of expansion of the universe". The equations that express that relationship are the Friedmann equations, which are just the Einstein Field Equation, the central equation of GR, specialized to the kind of spacetime geometry that "expanding universe" refers to. But it's not really useful to think of those relationships as saying that if the matter density decreases by this much, it makes the universe expand that much. > It looks to me that "dark energy" / cosmological constant is just a measure of preference for matter+volume (or at least energy+volume) to take the form of volume rather than matter, in an otherwise conserving process. No, that's not a good way to look at it. A cosmological constant aka dark energy is best thought of as just an unusual form of perfect fluid whose pressure is minus its energy density. Then you just plug that into the Friedmann equations to get predictions for what we should expect to observe, such as "accelerating expansion".

thriftwy 2y ago
I don't agree with you. Between us and a redshifted galaxy, for a specific cross-section "tube", there is a dV/dt of new space and a -dE/dt of energy from the redshift. It is possible to calculate both so at least the circumstantial "cubic metres for joules" metric is possible, and interesting. But it seems I'm not geting it out of this discussion. You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. If the density decrease is not linked to the volume increase then you have to explain where that extra energy went. "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place. Unfortunately what I can see is lack of understanding the mechanism and being able to productively reason about that, and stress-energy tensor is sufficiently complicated abstraction that one no longer feels the discomfort of not understanding.
- pdonis 2y ago
  > I don't agree with you. Then you are disagreeing with our best current physical model of our universe, which does not say what you are saying. > I'm not geting it out of this discussion. You should be aware that General Relativity and modern cosmology are complex subjects, and cannot be understood all at once in the course of an Internet discussion. Do you know how long it took me to properly understand the model that I am giving you a very quick and abbreviated description of? Several decades. So if you're expecting a quick "sound bite" answer that will make sense to you, and you have no background whatever in those subjects, of course you are not going to get what you are looking for. I can't help that. All I can tell you is what our best current models say. > You were talking about stress-energy tensor, and it did sound like density decrease is linked to the volume increase in a mathematical sense so that conservation happens. Now you say they are not related in that way. No, that's not what I'm saying. What I'm saying is that the relationship is not a causal relationship, in which the density decrease causes the volume increase. It is just a relationship that is enforced by the overall relationship between the spacetime geometry and the stress-energy tensor. The general form of that relationship is the Einstein Field Equation, and the particular form that applies to our best current model of the universe is the Friedmann equations. Those equations most definitely do give a relationship between density decrease for matter and what you are calling "volume increase"--more precisely the rate of "volume increase" (but the term cosmologists actually use is "scale factor" and "rate of increase of the scale factor"), and that relationship most definitely does include a local conservation law for stress-energy. I apologize if that wasn't clear. > "perfect fluid whose pressure is minus its energy density" does not make sense because you said it is expanding but keeping the same density. If a fluid is expanding but not becoming less dense, it wasn't a fluid in the first place. I'm using "perfect fluid" here as a technical term for a particular form of the stress-energy tensor, where the only two things you need to specify are energy density and pressure. Terms like "matter" and "dark energy" are then just names for particular equations of state, i.e., particular relationships between energy density and pressure. "Matter" means pressure is zero. "Dark energy" means pressure is minus energy density. That is standard usage among cosmologists. As for why the dark energy density stays the same as the universe expands, that's what the Friedmann equations say when pressure is minus energy density. If you don't like the term "perfect fluid" to describe such a thing, that's fine, call it something else if you like. (But don't expect cosmologists to go along with you.) The important point is the physics, not the words we use to describe it. The physics is what I said. You can check it for yourself if you like by looking up the Friedmann equations. > what I can see is lack of understanding the mechanism What I can see, and I can't avoid saying this bluntly, is someone who has no background in physics but still presumes to tell someone who does have such a background what they do and do not understand. Sorry, but you, and again I can't avoid saying this bluntly, simply don't know what you are talking about. I do know what I am talking about. I'm sorry that I can't convey what I know to you in a quick sound bite that will make sense to you, but that's beyond human powers. There's a reason that people spend years or decades studying these subjects, and there's a reason that even the basics are taught in university courses that take multiple semesters to complete and require textbooks and working problem sets and so on.