The notion of dark energy is peculiar, even by cosmological standards.
Cosmologists have foisted the idea upon us to explain the apparent accelerating expansion of the Universe. They say that this acceleration is caused by energy that fills space at a density of 10-10 joules per cubic metre.
What’s strange about this idea is that as space expands, so too does the amount of energy. If you’ve spotted the flaw in this argument, you’re not alone. Forgetting the law of conservation of energy is no small oversight.
I like to think that, if I were not a professional cosmologist, I would still find it hard to believe that hundreds of cosmologists around the world have latched on to an idea that violates a bedrock principle of physics, simply because they “forgot” it. If the idea of dark energy were in conflict with some other much more fundamental principle, I suspect the theory would be a lot less popular.
But many people have just this reaction. It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920’s: energy is not conserved in general relativity. (With caveats to be explained below.)
The point is pretty simple: back when you thought energy was conserved, there was a reason why you thought that, namely time-translation invariance. A fancy way of saying “the background on which particles and forces evolve, as well as the dynamical rules governing their motions, are fixed, not changing with time.” But in general relativity that’s simply no longer true. Einstein tells us that space and time are dynamical, and in particular that they can evolve with time. When the space through which particles move is changing, the total energy of those particles is not conserved.
It’s not that all hell has broken loose; it’s just that we’re considering a more general context than was necessary under Newtonian rules. There is still a single important equation, which is indeed often called “energy-momentum conservation.” It looks like this:
{refer to article}
The details aren’t important, but the meaning of this equation is straightforward enough: energy and momentum evolve in a precisely specified way in response to the behavior of spacetime around them. If that spacetime is standing completely still, the total energy is constant; if it’s evolving, the energy changes in a completely unambiguous way.
In the case of dark energy, that evolution is pretty simple: the density of vacuum energy in empty space is absolute constant, even as the volume of a region of space (comoving along with galaxies and other particles) grows as the universe expands. So the total energy, density times volume, goes up.
This bothers some people, but it’s nothing newfangled that has been pushed in our face by the idea of dark energy. It’s just as true for “radiation” — particles like photons that move at or near the speed of light. The thing about photons is that they redshift, losing energy as space expands. If we keep track of a certain fixed number of photons, the number stays constant while the energy per photon decreases, so the total energy decreases. A decrease in energy is just as much a “violation of energy conservation” as an increase in energy, but it doesn’t seem to bother people as much. At the end of the day it doesn’t matter how bothersome it is, of course — it’s a crystal-clear prediction of general relativity. And one that has been experimentally verified! The success of Big Bang Nucleosynthesis depends on the fact that we understand how fast the universe was expanding in the first three minutes, which in turn depends on how fast the energy density is changing. And that energy density is almost all radiation, so the fact that energy is not conserved in an expanding universe is absolutely central to getting the predictions of primordial nucleosynthesis correct. (Some of us have even explored the very tight constraints on other possibilities.)
Having said all that, it would be irresponsible of me not to mention that plenty of experts in cosmology or GR would not put it in these terms. We all agree on the science; there are just divergent views on what words to attach to the science. In particular, a lot of folks would want to say “energy is conserved in general relativity, it’s just that you have to include the energy of the gravitational field along with the energy of matter and radiation and so on.” Which seems pretty sensible at face value.
There’s nothing incorrect about that way of thinking about it; it’s a choice that one can make or not, as long as you’re clear on what your definitions are. I personally think it’s better to forget about the so-called “energy of the gravitational field” and just admit that energy is not conserved, for two reasons.
First, unlike with ordinary matter fields, there is no such thing as the density of gravitational energy. The thing you would like to define as the energy associated with the curvature of spacetime is not uniquely defined at every point in space. So the best you can rigorously do is define the energy of the whole universe all at once, rather than talking about the energy of each separate piece. (You can sometimes talk approximately about the energy of different pieces, by imagining that they are isolated from the rest of the universe.) Even if you can define such a quantity, it’s much less useful than the notion of energy we have for matter fields. The second reason is that the entire point of this exercise is to explain what’s going on in GR to people who aren’t familiar with the mathematical details of the theory. All of the experts agree on what’s happening; this is an issue of translation, not of physics. And in my experience, saying “there’s energy in the gravitational field, but it’s negative, so it exactly cancels the energy you think is being gained in the matter fields” does not actually increase anyone’s understanding — it just quiets them down. Whereas if you say “in general relativity spacetime can give energy to matter, or absorb it from matter, so that the total energy simply isn’t conserved,” they might be surprised but I think most people do actually gain some understanding thereby.
Energy isn’t conserved; it changes because spacetime does. See, that wasn’t so hard, was it?
From the site of cosmologist/theoretical physicist Sean Carroll
https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/
He has some special formatting for equations and stuff that can’t be easily copied over, so check the site if you’re looking for that
It’s still not clear to me why you dont consider “spacetime expansion” as an explanation for the observation of cosmological redshift. Without needing to get into any math, how are you explaining a rate of redshift that increases with distance (as the cosmological constant model predicts, and as we observe)?
I do agree that expansion explains redshift. Coincidentally, God tells me that he stretched out the heavens, so that's in agreement with the observations. Then this expansion slowed down dramatically.
What's in question is whether it's expanding right now, how much, and whether the expansion is accelerating or decelerating, and that part isn't measured by redshift but by a longer chain of inferences.
Oh. Thats your issue…
How do you figure that you can still observe galaxies that are further away having higher rates of redshift, if expansion stopped at some point in the past? Surely that would be seen in observation of the furthest objects - if expansion stopped in the past, then the accelerating expansion would hold until some distance where it failed to hold. Yet we don’t observe that. We observe an accelerating expansion as far as we can see, a distance which increases as our tech improves.
I don’t think this is the case at all. I mean, assuming we’re talking about scientific theories and not feelings
No, the current theory is that expansion was orders of magnitude higher in the Big Bang, slowed down dramatically, and then began accelerating again 4-5 billion years ago ("Expansion of the universe"):
The redshift is the evidence for the Big Bang expansion. Onetime expansion makes everything redshifted, the further away the more so. Comparing models shows that the acceleration hypothesis puts the origin the furthest back in the past, while a simple flat universe (critical density ratio of one) puts it much closer to the present, and the Big Crunch theory (which is still viable) puts it even closer. A fraction of the dot of "today" is all the data we actually have, the rest is theoretical. Last I heard, the critical ratio was so close to one that people can't tell if it's over or under, which makes a big difference in models; the claim of adding recent acceleration to the redshift, as you can see in the graph, is a patch onto a patch. When you actually see the limited amount of data these things are guessed from you marvel that any of them is taken as an established theory.
What you probably mean to say is that the redshift increases with distance, not that its acceleration increases with distance (which is the theoretical part).
I don't have an immediate answer for whether the proposed change in redshift at 4-5 bya is due to an assumption change at that point in the observational distance, or due to an actual change in the stretching that might be explained in a Biblical epoch, or whether it actually does (against my expectations and predictions from data) constitute serious evidence against my current model. But knowing how many other things have been faked I'm pretty confident the actual math will once again align when I have time to get it together.
Inflation and expansion shouldn’t be conflated like that, they're quite different. Different domains, different effects, different proposed causes. Just like with dark energy and dark matter. Just because two things might sound surficially related doesn’t mean they are.
No, I meant exactly what I said, higher rates of redshift. Which is precisely what we observe. If there was a one time expansion which stopped then all of the distant standard candles we measure would be brighter than we measure them as being. Yes, the rate is inferred (aka we can’t measure the difference in redshift from one second to another, yet), via metrics we can actually measure, like 95% of things in science. I’ve yet to hear an explanation from you as to how things further away are all observed as having greater rates of redshift than things closer. That wouldn’t happen with a one time expansion. Period.