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 is not a law, it is hypothesis for building theories. Ufortunately, in modern science this was limited to only one theory that put a severe constraints and limitations on any development of other theories.
Hypothesis of enregy conservation is perfectly valid, and there is no any problems with it. The problem is with modern single theory, that does not have place for any unknown energy conversions, so nobody study them.
Dark matter / dark energy is a crutch for modern theory invented in attempt to somehow fit experimental observations into the moderm theory that declared only correct one. It is just a mathematical "unknown" that mathematicians put on the one or another side of equation to make their equations look corresponding to observations.
General relativity equation turned from a theory into dogma, that is why everything observed had to be squizeed into this theory math at any cost, to not allow any doubts in dogma. "Eisnstein always right" regardless of what we observe in experiments.
So, energy conservation hypothesis just state that energy/matter can't appear from nowhere and disappear into nowhere. Einstein dogmas put hard constraints on the ways energy/matter could convert between different forms, so the only way to fit math with reality is to push inconsistency onto some "dark" thing, that just exist.
Throwing out Einstein dogmas we could easily imagine that there are just other energies / form of matter we didn't discovered yet and there are other undiscovered ways of conversion from known energy/matter forms to unknown forms. But since all research is directed only by Einshtein dogmas, there is no chance this possible ways and forms will ever be studied.
There are also mutiple other ways of how things could be in universe for real, from fractional dimentionalities, to just that constants declared as constants in modern theory are not really constants at all.
Energy conservation hypothesis is very useful for practical applications and nearly everything humanity invented is in one way or another use this hypothesis. So, I don't see any reasons to abandon it. And if energy/matter disappear into nothing or appear from nothing, I'll more likely suggest that we have to look for unknown forms of energy/matter, especially if there is no place for them in Einstein dogmas, than to fall into a trap of discarding perfectly working and practically useful energy conservation hypothesis.
This is brilliant! One issue is that quantum theory itself abandoned Einstein's later work in the 20s and 30s and became "Bohr-Heisenberg always right" so what's being defended is not so much Einstein anymore as a false structure built upon him. (Even when Heisenberg took a wrong turn in his mountaineering and couldn't build the bomb that Oppenheimer could.) But you've got the core dogmatism of the movement absolutely right. Thank you for reading and understanding all that is written here, and I appreciate your comments on other issues as well even when I don't say so.
This is still same dogmatism, quantum mechanic does not fit into general relativity - it is a problem of QM, and never GR. All that quantum field theory, quantum gravity and so on, are attempts to fit quantum world into general relativity, never vice versa. And ths is in situation when number of real, replicateable experiments that confirm quantum mechanics validity are orders of magnitude larger than very few observations (not even controlled experiments) that could be explained by general relativity. Fuck, we practically use quantum mechanics laws even when typing our messages on thins forum, but there is zero real practical applications of general relativity. But it is quantum mechanics should be changed, not general relativity.
Thinking about that, you also could notice that it is not quantum mechanics that put limitations on further technological progress. So, the barely proven theory dictates what things shouldn't be researched should be kept intact, while solid proven theory that doesn't limit our progress should be somehow changed to fit former one. Looks like it is limitations that relativity put on progress are very important for those who keep relativity as dogma.
Something like that.
Thank you for writing interesting things, that make this forum worth reading.
Thank you! I had to read your comment twice, first as if you were sincere and pointing out that even despite the inroads of QM there is still validity to relativity, and only second in the sarcastic sense in which you appear to actually have meant it.
Yeah, I'm still in the defiant Einstein camp. QM works because its math is accidentally right but its explanations of reality are lousy and this has been pointed out from within the mainstream a number of times. Someday we'll get the best of both worlds.
I have more practical approach to science. Any fundamental theory should open a multiple roads for technological progress, not close them. QM in that way is practical, verifiable, working and gives useful results. Einstein relativity only close roads without any practical application.
And no, GPS don't need relativity to work at all, those who try to use GPS as a single example of relativity usefulness, just never took a look into how GPS really works and unaware that it is differential system, not absolute one. It does not matter what absolute time is on satellites, the differences between times received from different satellites are used to calculate position. So, even if clocks run sligtly faster or slightly slower, this will give insignificant error (millimeters) in coordinates. Much more important thing is that all clocks on satellites should run with same rate, and this is solved using atomic clocks onboard.
So, from my point of view, QM wins over *R and it is *R that should be changed so that it will open multiple roads for practical technological progress.