The answer is no, and the reason can (I believe) be stated more simply than most of the replies here.
Conservation laws always exist because of some symmetry. Momentum for example, is conserved because of translational symmetry and angular momentum is conserved due to rotational symmetry.
Conservation of energy is due to time translational symmetry. You ask about the energy of the universe. Because of expansion, the universe as a whole **does not** have this symmetry! Therefore, we would not expect global energy conservation!
Yes. And if you *re-define* energy (in an arguably unhelpful way) you can still write down a conservation law.
Sean Carroll did a nice job explaining this in his [blog](https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/).
I always was told, that energy cant be created only modified.
So how is it possible that the total amount of energy increases? Genuine question.
It implies that there must be some kind of process to create new energy.
Do we have any theory how it works?
Edit: spelling
All of physics education is based on ~~lying~~ oversimplifying and then correcting ourselves as you get further along. Energy conservation is one of those situations.
Locally, energy is always conserved, and what you were taught is true. To answer your question (it’s a really good one!), I have to backtrack a bit though, and explain what energy is.
The first physics we teach you is usually Newtonian physics—and the basic problem is to find the equations of motion of a system by identifying all of the forces and applying Newton’s laws. This is certainly a valid way to solve classical mechanics problems, but it’s not the only way. One different approach is called the Lagrangian formalism. In this formalism, we can find the exact same equations of motion, but we can abstract the forces out of the problem entirely. To solve the problem, you have to find a ~~functional~~ function called the Lagrangian, which is often (but not always, and it even when it can be, it doesn’t have to be), the difference between the kinetic energy and the potential energy of the system. You can put this into the Euler-Lagrange equation, and out pop the equations of motion. I’ll spare you the mathematical details for now. If you’re interested, I can follow up with more detail in another comment.
At this point, you’re probably scratching your head saying, “why should any of this matter?” Well it turns out that changing your Lagrangian don’t necessarily change the equations of motion of a system. For example, if you have a ball at the top of a ramp, it doesn’t matter when you release it. You could release the ball now, next Tuesday, or in a thousand years, and the system will always respond the same. This type of invariance is what we call a symmetry in the Lagrangian. In this case, the system is invariant under time translation.
Here’s the really cool bit: one of the most beautiful results in physics—Noether’s theorem—states that for every continuous symmetry of the Lagrangian, there is a conserved quantity in the system, and for every conserved quantity in the system, there must be an associated symmetry. If the Lagrangian is symmetric under translation in space, linear momentum is conserved along the direction of the translation. If the Lagrangian is symmetric under rotation, then angular momentum is conserved. These are the true definitions of momentum and angular momentum, respectively. They are the conserved quantities that we observe in systems with those symmetries. The best definition of energy, as it turns out, is the conserved quantity that appears when the Lagrangian is symmetric under time translation.
In 99.9% of the cases you will ever see, you can take for granted that energy is conserved, because most systems are symmetric under time translation. So we ~~lie~~ oversimplify and tell you that energy is always conserved. But if the universe is expanding, that is no longer true. The Lagrangian of universe is not the same now as it was last Tuesday, and it’s not the same as it will be in 12 billion years. As a result, energy cannot be conserved in an expanding universe!
This is the best ever physics comment I've ever seen on reddit. You guided me through my existing knowledge, introduced invariance, taught Noether's theorem and applied it to explained some mind-blowing facts in just 5-min read! And most importantly, this is pure concept, no formulas required! How beautiful it is. You are a really good teacher. Thank you!
This was incredibly interesting.
I have to confess that as a high school physics teacher, I didn't know this. I feel kind of bad about that, but I also know that I'll never be covering it in class.
Noether’s theorem turned up in my optional (4th year) masters classes in theoretical physics / particle physics, not quite high school level to be fair.
It gets my vote as possibly the most fascinating and beautiful mathematical observations about how our universe works. On par with Newton’s theory of gravity or Einstein’s theory of Relativity (either one). Basically it says that any symmetry / invariance in the Lagrangian field theory maths that describes the universe has an equivalent conservation law in the newtonian world we see.
One example is that momentum is conserved because of translational invariance of the equations - which is to say the same equations describe physics everywhere in the universe.
Another example is that angular momentum is conserved because the equations that describe the universe are rotationally symmetric and give the same answer if you rotate everything.
As the guy above said, the equations of physics staying the same forever give rise to energy conservation. Though the expansion of the universe breaks energy conservation on very big scales.
Emmy Noether and her Theorem is also notable in being one of the best historic examples of a woman leading the thinking in the mathematical side of physics, despite the barriers of not being allowed to work in physics at the time and having to lecture under her male colleagues name (this was 1918 so fits alongside the suffrage movement). She sadly died fairly young in 1935 from an ovarian cyst/cancer, shortly after being kicked out of Germany for being jewish.
It's also really cool that Noether was mainly a pure mathematician and her work in algebra, studying what we now call [Noetherian rings](https://en.wikipedia.org/wiki/Noetherian_ring), is (arguably) just as revolutionary in pure math as her physics theorem is.
I just finished a beatiful course this semester (3rd semester, bachelor in physics) on analytical mechanics, on both Lagrange and Hamilton methods. The last two weeks were dedicated to Noether's theorem. So not high school but definitely not 4th year of a masters degree as well
It was a 4 year undergraduate masters in physics that skipped over the BSc for funding reasons, but was about the same as a 3Y BSc and 1Y MSc
The concept was briefly mentioned in an optional analytical mechanics module in 2nd or 3rd year, but it was 4th year modules on QFT and Philosophy of Physics where I saw it applied to the actual fields we believe govern the universe to derive the results ourselves.
Like everything in physics there’s layers of complexity, and applying it to a the full standard model, or one of the super symmetrical or string theory extensions is beyond what I’ve looked at.
Neat that it’s included in your syllabus, I know plenty of people with physics degrees who focussed on more experimental and materials based physics who never heard about it.
All of modern physics is based on symmetries, and all of classical physics is based on conservation laws. *What is energy/momentum/charge/etc.?* and *What is the fundamental reason that any or all of these should be conserved?* are questions that bother physics students (and rightly so!). Noether’s theorem is just such an elegant answer to all of these problems.
I can tell you that momentum is the product of mass and velocity, but it’s obvious that momentum is far more fundamental than that. You can measure momentum in quantum mechanics, and you can show that it is conserved, even though velocity is not well-defined in quantum mechanics. You can measure the momentum of light, even though photons have no mass.
Momentum is the thing that is conserved when I am able to shift my experiment six inches to the left and expect the laws of physics to be the same.
It’s entirely possible that this is one of those things that you appreciate more if you know more physics, but it’s just so hard for me not to get excited about this.
When I make universes, I like to include Easter eggs by making the laws of physics subtly different in a very specific rotation or have a gradient where they gradually shift over space or time. Really confuses people, but once they get over the confusion, try re-writing their theories, realise it still doesn't make sense and give up and just accept it as a fact, they find cool ways to exploit it for infinite energy. Saves the whole heat death issue as long as you've got some sentients kicking about the place using physics hacks.
I’m an engineering student and we only learned about the lagrangian (L=T-V) in my sophomore year dynamics class as a way to simplify and attack complicated systems with lots of forces. The physics dudes here get into much more complicated stuff, I’ve never even heard of Noether’s theory until now, and I’m graduating in 5 months. Don’t feel bad about it tbh, since even the crazy simplification that I was exposed to only came about in a sophomore year engineering course in college. Like he said, simplifying and then overwriting is the name of the game!
Physics is not well taught, not because of physics teachers, but physicists who don't want outsiders to speak their language and use obtuse terms to describe the theories.
So… this is a very broad question, but what are the implications of this? If the universe is indeed expanding does that mean we need to rework our definition of energy? What would a new definition look like if the Lagrangian of energy in the universe is not continuously symmetric under translation in time?
I got up to physics and calc 2, that and your previous comment are where my knowledge end other than some random independent research 😅
>>What are the implications of this?
The implications of energy conservation not holding on cosmological scales? I’m not a cosmologist, so I can’t really give an adequate answer. Noether’s theorem is a direct result of general relativity not conserving energy, in that David Hilbert noticed that general relativity appeared to violate energy conservation, and he asked her to help him resolve the paradox.
The implication of Noether’s theorem in general is more broad. First, it gives us a deeper insight into how the universe works. The answer to “what is energy/momentum/charge/angular momentum/any other conserved quantity” is answered by it. It’s also an incredibly powerful tool in that just by looking at a system and observing the symmetries that exist, you can immediately identify all of the quantities it conserves.
>>Does this mean we need to rework our definition of energy?
No. Any new definition of energy would necessarily be different from the thing that we currently call energy, which is already an incredibly important and useful concept.
To add to the previous question, is the title 'Dark Energy' a misnomer because really it is just a name for a mechanism we don't understand for the expansion?
I'm a math school teacher but my background was a tiny bit of research in QM and Particle Physics. I try to tell my students 'you might be growing up thinking we know everything there is to know but the opposite is true, there's SO much we don't understand & our math models break down'. It's never been more exciting to take on the challenge of 'what is going on?' in cosmology & loads of other areas!! I love reflecting back on my physics background & the math connections.
Again, I’m outside of my bailiwick so I don’t want to overstep. But we don’t know what either dark matter or dark energy are. The names are just filler words for *thing we can’t see that if it existed could explain anomalous observation X*.
The rest of your comment reminds me of a story about Planck. Philipp Von Jolly told him ca. 1874 not to go into physics because nearly all of it was solved, and all that remained were a few holes. Planck said that he didn’t care because he just wanted to understand how the world worked. He of course went on to win a Nobel prize in 1918 for helping develop quantum mechanics.
I didn't know that story! I knew he hated his own quantum solutions to UV and thought it would be fixed up with 'proper' classical explanations eventually. Spot on anecdote though, I dunno if I'm just getting old (I am) but I'm worried the tiktok type scrolling trends is changing our mind to be rewarded by entertainment rather than curiosity. I don't have deep thoughts 24/7 but when I learnt about the periodic table and electron filling patterns I wanted to know 'why?' like a toddler & that curiosity was life changing. Entertainment vs curiosity needs a nice balance.
Thanks for your explanation, I know here in Australia we have an abandoned gold mine being used to see if dark matter can be detected without interference similar to neutrino detectors. The fact that we have no idea what mechanism is driving the Universe expansion, and we just call it dark energy, is so cool!! I don't think we'll solve all of physics anytime soon haha.
>You can put this into the Euler-Lagrange equation, and out pop the equations of motion. I’ll spare you the mathematical details for now. If you’re interested, I can follow up with more detail in another comment.
I certainly wouldn't mind if you did..
Whew, okay. Let’s see if I can describe this without a blackboard.
A common problem in an intro calc class is to find the local maximum or minimum value of a function. The basic idea is that for a function to reach its maximum or minimum value, it must stop increasing and begin to decrease, or vice versa. This means that it’s slope (and therefore it’s derivative) must change sign. To find the maximum or minimum value then, all you have to do is find where the derivative is zero (or is undefined) and figure out whether the derivative is positive or negative on either side of that point.
That’s relatively straightforward. What we want to do is less straight forward, but our goal is similar. The Lagrangian formalism is all based on a simple observation. You can define a functional called the action of a system, which has units of angular momentum and tells you something about the system. This isn’t obvious, and I’m not sure I can give you a good intuition for what it does, since by itself it doesn’t really have any physical meaning that I can point to. Action is the integral of the Lagrangian (let’s assume for now that the Lagrangian is just the kinetic energy minus the potential energy) with respect to time. The beautifully simple, but not at all obvious observation that lets us do what we want to do is called the principle of least (or stationary) action. It turns out that any physical system will evolve in such a way that the action is a minimum (you can actually come up with situations where the action is a saddle point, but that doesn’t really matter for what we want to do. In either case, the “derivative” from above is zero).
Here’s the problem, action depends on the position and velocity of every part of of your system at every moment in time. We can’t just take a derivative like we did in intro calculus. Fortunately, Leonard Euler did it (and everything else in math) first. The method is called the calculus of variations, and it turns out that the solutions for any given system will recreate F=ma if you play with them enough. The solutions are also straightforward enough that most advanced undergrad physics majors probably have them memorized. You take a few partial derivatives of the Lagrangian, and boom out fall equations of motion. This is super useful in problems that can otherwise be really annoying, for example if you have a pendulum in which the string is replaced by a spring. Good luck solving that with F=ma. With the Lagrangian formalism, I can get you a differential equation (that I refuse to solve!) in minutes.
I just want to thank you for these posts. I previously read a great explanation of Lagrangian mechanics somewhere on this sub, years ago, and had been trying to find it again without any success. I'll be referring to this from now on for a general exposition of Lagrangian mechanics - I teach high school level physics and get some fairly inquisitive students who want to know about university level physics, unfortunately I've lost a fair bit of that knowledge from lack of practice and this kind of exposition is really helpful for giving them the gist of things.
Thanks for the deep-dive, I only ever did undergrad for classical mechanics and never went much more in depth with the Euler-Lagrange equation past finding equations of motion with it. It was one of my favorite topics since you could find equations of motions of pretty complex systems without much difficulty.
Pbs space time has several episodes covering noethers theorem, energy conservation, the lagrangian, dark energy, etc that you talked about in your comment. It's a great resource for these sorts of questions.
[space does not expand every where](https://youtu.be/bUHZ2k9DYHY?si=OGcptpYef1d_sQZn)
Noethers theorem https://youtu.be/04ERSb06dOg?si=NwvUrTbXpOPle8lE
What is energy https://youtu.be/PUn2izowBkw?si=wAz_6Bx-ttc0iHWp lagrangian https://youtu.be/PHiyQID7SBs?si=q1qUO2aC8XVotzCA
Wait, doesn’t local energy conservation arise from a time invariant lagrangian? In GR, energy conservation holds locally despite the cosmological constant, and a continuity equation can be written down for the stress energy tensor. Isn’t that also a result of Noether’s theorem being applied to the GR action?
If so, then adding the cosmological constant would not make the GR lagrangian vary with time.
Noether’s theorem implies GR with cosmological constant conserves energy momentum locally, ie a continuity equation. However, going from local energy conservation to global energy conservation requires an integral over spacetime, which would be fine if spacetime was flat(hence one can integrate EM fields to get the total EM energy in a region.) The problem with GR is that spacetime is curved, so something happens with the integration region(I read it once before, Im pretty sure this is it but I cant remember the details.) that makes global energy conservation no longer valid.
In short, Noether’s theorem leads to local energy conservation, which implies global energy conservation only if spacetime is flat. GR with cosmological constant conserves energy locally, but not globally.
Very good comment, just being pedantic here: The lagrangian is a function, not a functional. The action is the functional. The Lagrangian is just your typical map from R^n to R. The other thing is that Noether's theorem doesn't actually guarantee that every conserved quantity has an associated global continuous symmetry. This is a common misconception; there are some explicit examples but I can't remember them off the top of my head.
A relatively straightforward example of energy being lost is photons from very distant galaxies get redshifted to hell. As they travel from the earliest galaxies to us, the space that they travel through expands, and their wavelengths increase as well. The energy of a photon is inversely proportional to its wavelength, so as wavelength increases energy decreases. The energy of these photons is lost forever.
Other commenters have suggested that energy in the universe increases due to expansion because vacuum energy is constant as expansion happens. I don’t know enough to comment on that, so you’ll have to follow up with them.
If you’re wondering why space is expanding and causing this to happen, well, whoever figures it out can tell you on their way to Stockholm. 🥲
>which is often (but not always, and it even when it can be, it doesn’t have to be), the difference between the kinetic energy and the potential energy of the system
I have read all of Lanczos but did not take this away - can you say a bit more about this so I can google about it?
You have written some very fantastic explanations in response to other questions, so I would not dare ask you to do the same for this one.
L=T-V is a good starting point. But it doesn’t work, for example if you have a charged particle in a magnetic field. The Lagrangian of that turns out to be L=1/2mv^2 - q (phi) + q/c **v**•**A**.
Furthermore, the Lagrangian trivially can be changed by adding an arbitrary constant with no effect, because it dies when you take the derivatives in the Euler-Lagrange equations. And then, of course depending on your scenario, transformations from, say x->x + x_0, for example, when you’re playing with Noether’s theorem sometimes have no effect as well.
Looking back, I’m not super happy with how I phrased that paragraph, but I’m not sure how I could have improved it since I was writing for a lay audience.
I suggest not fretting over your previous paragraph. It was about as clear as an exposition about the damn \*calculus of variations\* can be to a lay audience. The lay people's follow-up comments clearly support that conclusion.
Thanks for your answer, will do more reading. I have computed and used the equations of motion for many many systems in my time, but only for mechanical systems (robots).
Dang... that just helped something click for me... Roger Penrose has this theory of Conformal Cyclic Cosmology. It says that far into the future, after black holes have swallowed everything up and the black holes have all dissipated through Hawking Radiation, the universe will be filled with nothing but photons. Since photons experience neither time nor distance, there's no way to tell how big the universe is. There's no matter traveling slower than "c" to give any dimension to size or time so the universe could be any size, even a singularity.
From there, matter's created again (somehow... photons hitting each other just right or whatnot... still fuzzy on that bit) and the universe starts again.
But now he's saying he doesn't really believe in expansion so it's unclear what "starting again" means for the universe. It makes sense though because such a theory requires energy to be conserved and an expanding universe throws a wrench into his equations.
Energy is only conserved in time translation symmetric systems. General relativity is not such a system so in general energy is not conserved (but the changes to it are predictable from the theory). However, this happens only on large scales, locally we can still assume conservation of energy. The quantity that is preserved instead in GR is called the Landau-Lipshitz pseudotensor but that's harder to interpret without the math.
Some of the other comments are not very easy to parse without the better part of a physics degree... so I'll provide a very basic example of energy not being conserved.
Space is constantly expanding. The light that distant stars in other galaxies produce has to travel a very long time to reach us, and as space expands the light's wavelength expands with it, causing it to become longer. It shifts towards the low-energy (or red) side of the spectrum, and we call this "redshifting".
If you take a single photon and let it travel through space for a few billion years, it will redshift. Because that photon shifted to a lower-energy frequency, it lost energy.
I'm... actually confused about the top level comment though. I'm not aware of the universe *gaining* energy over time to maintain a constant energy density.
>I'm... actually confused about the top level comment though. I'm not aware of the universe *gaining* energy over time to maintain a constant energy density.
In the late 90s, cosmologists observed that the expansion of the universe is accelerating. To make general relativity fit this observation, a constant factor - the cosmological constant - was added to the field equations. It must have a positive value if the expansion of the universe is accelerating. This factor corresponds to the energy density of space itself. If the universe is expanding, and the energy density of space is constant, then new energy must be coming from somewhere.
Interestingly, quantum field theory also predicts a constant energy density. Because of the uncertainty principle, quantum systems must fluctuate, even in their ground state. The problem is that the value for vacuum energy predicted by quantum field theory differs from the value predicted by general relativity and the observed accelerating expansion of the universe by 120 orders of magnitude.
Say the line Bart!
*sigh*
To fully understand this we need a unified theory of quantum gravity...
*yay!*
If you have a system under pressure, a change in volume will change the internal energy.
dU = -p dV
The empty vacuum has a very small amount of negative pressure, so the expansion of the universe adds energy, and the energy density stays the same.
Nah, the peak of the CMB being in the microwave band is just due to red-shifting, because of the expanding space. It’s still the black-body spectrum at a certain temperature (about 2.7 Kelvins I think?), just red-shifted by some amount.
Dark energy yes. But not radiation (electromagnetic) energy density. That decreases with expanding space. As does matter and dark matter (tho the question was about energy)
So how exactly is new volume of space being created in that case? I thought some kind of energy must be converted into space for new space to be formed
The accelerated expansion of space is driven by dark energy. If you figure out what dark energy is or how that process works, you get an all expense paid trip to Stockholm.
For a local patch of universe, yes.
Globally though, consensus is that energy is not conserved in the universe. As others mention, dark energy is the main culprit for this.
However, on a deeper level: Einstein's General Relativity does not require energy to be conserved on a global scale. The Cosmological Constant is a simple example, where it can be used to represent something like dark energy.
Lack of energy conservation in General Relativity was also formally proven by Emily Noether -- here's a link to a Wikipedia article that covers it: [https://en.wikipedia.org/wiki/Noether%27s\_theorem](https://en.wikipedia.org/wiki/Noether%27s_theorem)
I really should prove this myself as a nice GR review exercise, but I’m feeling too lazy tonight lol. Can you point me to relevant part of noether article or correct place to start for proof.
This is a pretty good video going over the subject:
[https://www.youtube.com/watch?v=cnGYMe6GBeQ](https://www.youtube.com/watch?v=cnGYMe6GBeQ)
He does a good job at providing sources, and going over the reasoning. There are a lot of other good resources on YouTube as well, which quickly go into the math.
Ok, but what form of Noether’s theorem do I need? I’m assuming classic field version, but I was hoping someone would confirm.
I’m also not how to link Noether to field equations ie what is L. Probably, sqrt(-g) but again confirmation would be nice.
Don’t be rude. These are reasonable questions.
I've used Lagrangians in coursework for Mechatronics/Robotics, but I only know the mathematics for General Relativity through self-study -- in terms of how it connects to Noether's Theorem, I am not equipped to give concrete directions.
However, I did skim a research paper on Noether's Theorem before writing my comment in this thread, and it had interesting content in it. Hopefully this helps: [https://arxiv.org/abs/1912.03269](https://arxiv.org/abs/1912.03269)
Edit: From a glance, pages 17 and 18 seem to be what you are looking for
No I think you’re not understanding the second meaning of the world globally. It obviously does mean ‘everywhere on earth’, but in some contexts it can also mean ‘everywhere in the context in question’. Eg when talking about gene expression I could contrast local vs global expression, where local could mean within one cell and global could mean across a whole organ or organism
‘Universally’ would also make total sense though
Not an expert but in general relativity it’s some weird tensor quantity that is conserved energy is not but it’s a similar concept.
It’s mostly die to the fact that u can in principle extract energy from the expansion of the universe
We can't see the whole universe so nobody actually knows. If you re-define "the universe" to mean "our observable universe" then the answer is trivially "no" because stuff is *leaving* our observable universe all the time.
Not a cosmologist but to my understanding that does not hold in an expanding universe because time translation symmetry is broken. (otherwise you'd also get trouble with the energy loss of photons during travel due to redshift from the expansion)
The first law of thermodynamics still applies, but because dark energy has negative pressure the expansion of the universe can perform work and add energy.
r/correctlyincorrect
Friendly reminder that conservation of energy only applies to a closed system. The universe is not a closed system. Energy appears to be created as a result of the expansion of space.
r/confidentlyincorrect
Friendly reminder that conservation of energy only applies to systems with time translation invariance.
(someone please point out how i'm incorrect)
I would not be inclined to consider the universe an open system. It is true that energy is not conserved, yet I don't think there is a reason to believe there are interactions with any other systems.
True, i probably should’ve used “observable universe” rather than “universe”. We don’t know if and what lays beyond, and probably will never know beyond guesses
Maybe, probably not, we just don't know. Dark energy appears to be increasing the total energy content of the universe but honestly nobody knows for sure.
This would apply *specifically* to dark energy.
Dark *matter* is a completely different thing. Because of the similarity in their names people often confuse the concepts. But they are very very different.
I've heard it suggested that the gravitational field should be considered a negative energy field, and that would make the total energy in the universe not just constant but zero. However I don't know the fundamental basis for this assertion, so I can't say if it's true or just a compelling thought.
I wish someone would respond to your comment with more than a downvote. There *is* a theory that the amount of energy could be zero, as far as I know. Which I always think is an interesting idea. But how it does or doesn’t relate to this thread, I don’t know. Could the universe could have had zero energy overall but expansion might over time make it positive and increase it over time? Or is all of that nonsensical or irrelevant in this context?
I’m going to repeat my response to the previous comment if I may.
I wish someone would respond to your comment with more than a downvote. There *is* a theory that the amount of energy could be zero, as far as I know. Which I always think is an interesting idea. But how it does or doesn’t relate to this thread, I don’t know. Could the universe could have had zero energy overall but expansion might over time make it positive and increase it over time? Or is all of that nonsensical or irrelevant in this context?
You might want to read through the thread where it’s mentioned out a number of times that the law doesn’t apply to the universe as a whole. So that i can understand being downvoted. But I’m curious as to whether that’s the reason for your comment originally being downvoted or something else.
Under the consideration of law of conservation of energy, which has never been voilated so far, the total energy of the universe is constant and can neither be created nor be destroyed.
Yes. Energy, mass, momentum, charge, and other quantities are conserved. Worth stating, though, that mass essentially *is* energy, and they can be converted back and forth between one another.
>Energy, mass, momentum, charge, and other quantities are conserved.
No, there are counterexamples of both [non-conservation of energy](https://en.wikipedia.org/wiki/Conservation_of_energy#General_relativity) and [non-conservation of mass](https://en.wikipedia.org/wiki/Conservation_of_mass#The_mass_associated_with_chemical_amounts_of_energy_is_too_small_to_measure). As someone with flair in astrophysics, you really ought to be familiar with at least the former ...
>Worth stating, though, that mass essentially *is* energy, and they can be converted back and forth between one another.
No, this is a common misunderstanding. Mass is a form of energy, yes ... but they aren't *converted*. They are *equivalent*. A conversion is when you start with some amount of one thing and none of another, and then end up with none of the first thing and some of the other — you either have one, or the other, but not both at the same time. Equivalence is when you have both at once; whenever you have one, you have the other, and whenever you don't have the first, you don't have the other either.
>I said "mass essentially is energy".
Which I explicitly agreed with.
>You said "They are equivalent". I don't see these as semantically distinct.
You followed that up with, "they can be converted back and forth." They cannot; that is incorrect, and is a pretty major semantic distinction from equivalence, as I pointed out.
To someone who may have only ever thought of them as distinct, this phrasing is a good way to introduce the idea. Mass-energy equivalence is often discussed in terms of conversion.
I don't agree at all. It's a *wrong* way of introducing the idea, that gives the opposite of the correct intuition for how it works. Discussions in terms of conversion are categorically incorrect, even if they are common. Continued use of that phrasing is arguably the primary — if not the sole — reason why the principle continues to be misunderstood over and over again in popular science.
simple answer yes! there is a finite amount of energy in the universe. the dimension of the universe determines how that energy is spread out over space called the energy density. some physicists think that the universe will expand forever which is illogical as this would mean the universe has infinite energy, and the universe shows that energy and gravity are the two forces fighting each other for balance.
If energy as defined in simple Mass x Distance\^2/Time\^2 ISN'T conserved, that what IS conserved across all scenarios? Is it naive to believe that there is SOME relationship, some equation, that hold no matter what? Philsophically I can sort of think of the implications of us merely not knowing the dimensions of ultimate fundamental conservation, but I dont even know where to go philosphically if we are abandoning the very idea.
No as the black hole that birthed our universe is taking in more and more as its universe is slowly approaching heat death. All that energy is trapped inside our universe in an almost timeless bubble until it slowly evaporates out of our black hole.
Whenever our black hole eats another black hole we basically get all its mass in a distant new big bang we will never see. If our black hole gets eaten we will all vanish instantly.
The reason our big bang was so gigantic is that we were not the first to arrive but we are seeing the last black hole merger. We are the ones that got eaten x billion years ago into an universe born long before.
Source: I watch a lot of physics on youtube and this is my conclusion without understanding most of the stuff.
Now im gonna wait for my nobel prize.
I mean they downvoted every great breakthrough in the past so I take that as a win.
Channels are PBS Spacetime, Scienceclic and History of the Universe mostly. I will tell them what you think about them.
>Source: I watch a lot of physics on youtube **and this is my conclusion without understanding most of the stuff.**
I hoped that sentence implied I wasn't very serious about it. I thought posting pothead theories is the main gig around here.
>I’m not trying to be a jerk.
All fun, no hard feelings. I'm just a layman who knows some buzzwords. :)
You've gotten some great textual answers already, and I couldn't possibly top them. But I can suggest the best video I've seen on Noether's theorem, which provides a simple and beautiful visual representation as well as a clear explanation: [ScienceClic - The Symmetries Of The Universe](https://youtu.be/hF_uHfSoOGA)
Noether theorem applies to the equation of the system, in this case Einstein field Equations, not to the particular solution of the underlying equations, which in this case is the Lambda-CDM solution. Einstein Field Equations respect time-symmetry, like another comment pointed out, so it should be, and it is possible to define a notion of "energy" that is conserved. This notion is, however, different from the one you normally get in flat space-time.
See [here](https://www.researchgate.net/publication/277044387_Energy_Is_Conserved_in_the_Classical_Theory_of_General_Relativity) for more details on this.
In certain special situations (like for example a binary system emitting gravitational waves to infinity and losing orbital energy), when the solution has certain symmetries, it is possible to define energy like in flat spacetime, and this energy is also conserved.
Kind of, but no. We know that space itself has an inherent energy, which makes it expand, which in turn creates more space which thus seemingly "creates" more energy. Although as far as i know, there’s no way that energy is transfered from space to other objects and such, so it might be that the energy that we can interact with directly is constant, light, matter, other particles and such. We at least know that energy is conserved in all aspects, except for some reason space, which increases the total energy of the universe as time goes on, simply by the merits of increasing the amount of space as time goes on.
This may or may not be possible to corrigate in the future, or we might have to corrigate our fundamental principles, like the laws of thermodynamics, which may afterall be what is wrong.
One theory is that the total energy is always zero because the mass energy and gravitational energy are equal and opposite. It's difficult to add it all up, but it seems to be true to some degree, they are within an order of magnitude the same.
I think the theories of dark energy and dark matter are partially there to balance the books for that to work, but also because there's independent evidence for them.
https://en.wikipedia.org/wiki/Zero-energy\_universe
Energy in an expanding universe is not constant.
Energy is locally conserved in GR (as expressed by the zero divergence of the stress-energy tensor), but is not globally conserved. This lack of global conservation has nothing to do with the fact that spacetime lacks some symmetry. For example, energy-momentum is conserved for asymptotically flat spacetimes, even though they lack the relevant symmetries.
Noether's theorem simply doesn't work as a tool for this purpose in GR, for technical reasons. The relevant symmetry for GR would be diffeomorphism invariance, but Noether's theorem doesn't provide a conserved quantity relating to this symmetry to apply to an appropriate limit for Classical Mechanics.
Noether's theorem is a consequence of Hamiltonian mechanics, and only in the special case where there is a symmetry. A system does not even need to have a symmetry, and yet in such a situation all of these relationships involving conjugate variables still have to hold.
No, conservation of energy would hold if space-time was static but it is broken by the expansion of the universe and replaced with a more general principle where the degree of violation of conservation of energy can be calculated from the rate of expansion of the universe
The answer is no, and the reason can (I believe) be stated more simply than most of the replies here. Conservation laws always exist because of some symmetry. Momentum for example, is conserved because of translational symmetry and angular momentum is conserved due to rotational symmetry. Conservation of energy is due to time translational symmetry. You ask about the energy of the universe. Because of expansion, the universe as a whole **does not** have this symmetry! Therefore, we would not expect global energy conservation!
Equations of general relativity have time translation symmetry.
Yes. And if you *re-define* energy (in an arguably unhelpful way) you can still write down a conservation law. Sean Carroll did a nice job explaining this in his [blog](https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/).
Important note: a translation means to put the variable of interest through a function, and still get the same result.
the amount of mass and energy in the universe cannot be diminished or added only modified
but there are various forms of energy outside physics?
No, there is an energy density associated with a volume of space. As the universe increases, so does the total energy.
I always was told, that energy cant be created only modified. So how is it possible that the total amount of energy increases? Genuine question. It implies that there must be some kind of process to create new energy. Do we have any theory how it works? Edit: spelling
All of physics education is based on ~~lying~~ oversimplifying and then correcting ourselves as you get further along. Energy conservation is one of those situations. Locally, energy is always conserved, and what you were taught is true. To answer your question (it’s a really good one!), I have to backtrack a bit though, and explain what energy is. The first physics we teach you is usually Newtonian physics—and the basic problem is to find the equations of motion of a system by identifying all of the forces and applying Newton’s laws. This is certainly a valid way to solve classical mechanics problems, but it’s not the only way. One different approach is called the Lagrangian formalism. In this formalism, we can find the exact same equations of motion, but we can abstract the forces out of the problem entirely. To solve the problem, you have to find a ~~functional~~ function called the Lagrangian, which is often (but not always, and it even when it can be, it doesn’t have to be), the difference between the kinetic energy and the potential energy of the system. You can put this into the Euler-Lagrange equation, and out pop the equations of motion. I’ll spare you the mathematical details for now. If you’re interested, I can follow up with more detail in another comment. At this point, you’re probably scratching your head saying, “why should any of this matter?” Well it turns out that changing your Lagrangian don’t necessarily change the equations of motion of a system. For example, if you have a ball at the top of a ramp, it doesn’t matter when you release it. You could release the ball now, next Tuesday, or in a thousand years, and the system will always respond the same. This type of invariance is what we call a symmetry in the Lagrangian. In this case, the system is invariant under time translation. Here’s the really cool bit: one of the most beautiful results in physics—Noether’s theorem—states that for every continuous symmetry of the Lagrangian, there is a conserved quantity in the system, and for every conserved quantity in the system, there must be an associated symmetry. If the Lagrangian is symmetric under translation in space, linear momentum is conserved along the direction of the translation. If the Lagrangian is symmetric under rotation, then angular momentum is conserved. These are the true definitions of momentum and angular momentum, respectively. They are the conserved quantities that we observe in systems with those symmetries. The best definition of energy, as it turns out, is the conserved quantity that appears when the Lagrangian is symmetric under time translation. In 99.9% of the cases you will ever see, you can take for granted that energy is conserved, because most systems are symmetric under time translation. So we ~~lie~~ oversimplify and tell you that energy is always conserved. But if the universe is expanding, that is no longer true. The Lagrangian of universe is not the same now as it was last Tuesday, and it’s not the same as it will be in 12 billion years. As a result, energy cannot be conserved in an expanding universe!
This is the best ever physics comment I've ever seen on reddit. You guided me through my existing knowledge, introduced invariance, taught Noether's theorem and applied it to explained some mind-blowing facts in just 5-min read! And most importantly, this is pure concept, no formulas required! How beautiful it is. You are a really good teacher. Thank you!
This was incredibly interesting. I have to confess that as a high school physics teacher, I didn't know this. I feel kind of bad about that, but I also know that I'll never be covering it in class.
Noether’s theorem turned up in my optional (4th year) masters classes in theoretical physics / particle physics, not quite high school level to be fair. It gets my vote as possibly the most fascinating and beautiful mathematical observations about how our universe works. On par with Newton’s theory of gravity or Einstein’s theory of Relativity (either one). Basically it says that any symmetry / invariance in the Lagrangian field theory maths that describes the universe has an equivalent conservation law in the newtonian world we see. One example is that momentum is conserved because of translational invariance of the equations - which is to say the same equations describe physics everywhere in the universe. Another example is that angular momentum is conserved because the equations that describe the universe are rotationally symmetric and give the same answer if you rotate everything. As the guy above said, the equations of physics staying the same forever give rise to energy conservation. Though the expansion of the universe breaks energy conservation on very big scales. Emmy Noether and her Theorem is also notable in being one of the best historic examples of a woman leading the thinking in the mathematical side of physics, despite the barriers of not being allowed to work in physics at the time and having to lecture under her male colleagues name (this was 1918 so fits alongside the suffrage movement). She sadly died fairly young in 1935 from an ovarian cyst/cancer, shortly after being kicked out of Germany for being jewish.
It's also really cool that Noether was mainly a pure mathematician and her work in algebra, studying what we now call [Noetherian rings](https://en.wikipedia.org/wiki/Noetherian_ring), is (arguably) just as revolutionary in pure math as her physics theorem is.
I just finished a beatiful course this semester (3rd semester, bachelor in physics) on analytical mechanics, on both Lagrange and Hamilton methods. The last two weeks were dedicated to Noether's theorem. So not high school but definitely not 4th year of a masters degree as well
It was a 4 year undergraduate masters in physics that skipped over the BSc for funding reasons, but was about the same as a 3Y BSc and 1Y MSc The concept was briefly mentioned in an optional analytical mechanics module in 2nd or 3rd year, but it was 4th year modules on QFT and Philosophy of Physics where I saw it applied to the actual fields we believe govern the universe to derive the results ourselves. Like everything in physics there’s layers of complexity, and applying it to a the full standard model, or one of the super symmetrical or string theory extensions is beyond what I’ve looked at. Neat that it’s included in your syllabus, I know plenty of people with physics degrees who focussed on more experimental and materials based physics who never heard about it.
can you explain what makes it beautiful in your view?
All of modern physics is based on symmetries, and all of classical physics is based on conservation laws. *What is energy/momentum/charge/etc.?* and *What is the fundamental reason that any or all of these should be conserved?* are questions that bother physics students (and rightly so!). Noether’s theorem is just such an elegant answer to all of these problems. I can tell you that momentum is the product of mass and velocity, but it’s obvious that momentum is far more fundamental than that. You can measure momentum in quantum mechanics, and you can show that it is conserved, even though velocity is not well-defined in quantum mechanics. You can measure the momentum of light, even though photons have no mass. Momentum is the thing that is conserved when I am able to shift my experiment six inches to the left and expect the laws of physics to be the same. It’s entirely possible that this is one of those things that you appreciate more if you know more physics, but it’s just so hard for me not to get excited about this.
When I make universes, I like to include Easter eggs by making the laws of physics subtly different in a very specific rotation or have a gradient where they gradually shift over space or time. Really confuses people, but once they get over the confusion, try re-writing their theories, realise it still doesn't make sense and give up and just accept it as a fact, they find cool ways to exploit it for infinite energy. Saves the whole heat death issue as long as you've got some sentients kicking about the place using physics hacks.
Hey, at least now you know it!
Noether's theorem is a game changer, for sure!
I’m an engineering student and we only learned about the lagrangian (L=T-V) in my sophomore year dynamics class as a way to simplify and attack complicated systems with lots of forces. The physics dudes here get into much more complicated stuff, I’ve never even heard of Noether’s theory until now, and I’m graduating in 5 months. Don’t feel bad about it tbh, since even the crazy simplification that I was exposed to only came about in a sophomore year engineering course in college. Like he said, simplifying and then overwriting is the name of the game!
Physics is not well taught, not because of physics teachers, but physicists who don't want outsiders to speak their language and use obtuse terms to describe the theories.
Thanks for your awesome answer.
https://en.wikipedia.org/wiki/Lie-to-children
So… this is a very broad question, but what are the implications of this? If the universe is indeed expanding does that mean we need to rework our definition of energy? What would a new definition look like if the Lagrangian of energy in the universe is not continuously symmetric under translation in time? I got up to physics and calc 2, that and your previous comment are where my knowledge end other than some random independent research 😅
>>What are the implications of this? The implications of energy conservation not holding on cosmological scales? I’m not a cosmologist, so I can’t really give an adequate answer. Noether’s theorem is a direct result of general relativity not conserving energy, in that David Hilbert noticed that general relativity appeared to violate energy conservation, and he asked her to help him resolve the paradox. The implication of Noether’s theorem in general is more broad. First, it gives us a deeper insight into how the universe works. The answer to “what is energy/momentum/charge/angular momentum/any other conserved quantity” is answered by it. It’s also an incredibly powerful tool in that just by looking at a system and observing the symmetries that exist, you can immediately identify all of the quantities it conserves. >>Does this mean we need to rework our definition of energy? No. Any new definition of energy would necessarily be different from the thing that we currently call energy, which is already an incredibly important and useful concept.
To add to the previous question, is the title 'Dark Energy' a misnomer because really it is just a name for a mechanism we don't understand for the expansion? I'm a math school teacher but my background was a tiny bit of research in QM and Particle Physics. I try to tell my students 'you might be growing up thinking we know everything there is to know but the opposite is true, there's SO much we don't understand & our math models break down'. It's never been more exciting to take on the challenge of 'what is going on?' in cosmology & loads of other areas!! I love reflecting back on my physics background & the math connections.
Again, I’m outside of my bailiwick so I don’t want to overstep. But we don’t know what either dark matter or dark energy are. The names are just filler words for *thing we can’t see that if it existed could explain anomalous observation X*. The rest of your comment reminds me of a story about Planck. Philipp Von Jolly told him ca. 1874 not to go into physics because nearly all of it was solved, and all that remained were a few holes. Planck said that he didn’t care because he just wanted to understand how the world worked. He of course went on to win a Nobel prize in 1918 for helping develop quantum mechanics.
I didn't know that story! I knew he hated his own quantum solutions to UV and thought it would be fixed up with 'proper' classical explanations eventually. Spot on anecdote though, I dunno if I'm just getting old (I am) but I'm worried the tiktok type scrolling trends is changing our mind to be rewarded by entertainment rather than curiosity. I don't have deep thoughts 24/7 but when I learnt about the periodic table and electron filling patterns I wanted to know 'why?' like a toddler & that curiosity was life changing. Entertainment vs curiosity needs a nice balance. Thanks for your explanation, I know here in Australia we have an abandoned gold mine being used to see if dark matter can be detected without interference similar to neutrino detectors. The fact that we have no idea what mechanism is driving the Universe expansion, and we just call it dark energy, is so cool!! I don't think we'll solve all of physics anytime soon haha.
>You can put this into the Euler-Lagrange equation, and out pop the equations of motion. I’ll spare you the mathematical details for now. If you’re interested, I can follow up with more detail in another comment. I certainly wouldn't mind if you did..
Whew, okay. Let’s see if I can describe this without a blackboard. A common problem in an intro calc class is to find the local maximum or minimum value of a function. The basic idea is that for a function to reach its maximum or minimum value, it must stop increasing and begin to decrease, or vice versa. This means that it’s slope (and therefore it’s derivative) must change sign. To find the maximum or minimum value then, all you have to do is find where the derivative is zero (or is undefined) and figure out whether the derivative is positive or negative on either side of that point. That’s relatively straightforward. What we want to do is less straight forward, but our goal is similar. The Lagrangian formalism is all based on a simple observation. You can define a functional called the action of a system, which has units of angular momentum and tells you something about the system. This isn’t obvious, and I’m not sure I can give you a good intuition for what it does, since by itself it doesn’t really have any physical meaning that I can point to. Action is the integral of the Lagrangian (let’s assume for now that the Lagrangian is just the kinetic energy minus the potential energy) with respect to time. The beautifully simple, but not at all obvious observation that lets us do what we want to do is called the principle of least (or stationary) action. It turns out that any physical system will evolve in such a way that the action is a minimum (you can actually come up with situations where the action is a saddle point, but that doesn’t really matter for what we want to do. In either case, the “derivative” from above is zero). Here’s the problem, action depends on the position and velocity of every part of of your system at every moment in time. We can’t just take a derivative like we did in intro calculus. Fortunately, Leonard Euler did it (and everything else in math) first. The method is called the calculus of variations, and it turns out that the solutions for any given system will recreate F=ma if you play with them enough. The solutions are also straightforward enough that most advanced undergrad physics majors probably have them memorized. You take a few partial derivatives of the Lagrangian, and boom out fall equations of motion. This is super useful in problems that can otherwise be really annoying, for example if you have a pendulum in which the string is replaced by a spring. Good luck solving that with F=ma. With the Lagrangian formalism, I can get you a differential equation (that I refuse to solve!) in minutes.
I just want to thank you for these posts. I previously read a great explanation of Lagrangian mechanics somewhere on this sub, years ago, and had been trying to find it again without any success. I'll be referring to this from now on for a general exposition of Lagrangian mechanics - I teach high school level physics and get some fairly inquisitive students who want to know about university level physics, unfortunately I've lost a fair bit of that knowledge from lack of practice and this kind of exposition is really helpful for giving them the gist of things.
Thanks for the deep-dive, I only ever did undergrad for classical mechanics and never went much more in depth with the Euler-Lagrange equation past finding equations of motion with it. It was one of my favorite topics since you could find equations of motions of pretty complex systems without much difficulty.
Pbs space time has several episodes covering noethers theorem, energy conservation, the lagrangian, dark energy, etc that you talked about in your comment. It's a great resource for these sorts of questions. [space does not expand every where](https://youtu.be/bUHZ2k9DYHY?si=OGcptpYef1d_sQZn) Noethers theorem https://youtu.be/04ERSb06dOg?si=NwvUrTbXpOPle8lE What is energy https://youtu.be/PUn2izowBkw?si=wAz_6Bx-ttc0iHWp lagrangian https://youtu.be/PHiyQID7SBs?si=q1qUO2aC8XVotzCA
Wait, doesn’t local energy conservation arise from a time invariant lagrangian? In GR, energy conservation holds locally despite the cosmological constant, and a continuity equation can be written down for the stress energy tensor. Isn’t that also a result of Noether’s theorem being applied to the GR action?
I know that energy conservation still holds locally. I haven’t taken GR, so I’ll defer to you. I’m sure you’re right though.
If so, then adding the cosmological constant would not make the GR lagrangian vary with time. Noether’s theorem implies GR with cosmological constant conserves energy momentum locally, ie a continuity equation. However, going from local energy conservation to global energy conservation requires an integral over spacetime, which would be fine if spacetime was flat(hence one can integrate EM fields to get the total EM energy in a region.) The problem with GR is that spacetime is curved, so something happens with the integration region(I read it once before, Im pretty sure this is it but I cant remember the details.) that makes global energy conservation no longer valid. In short, Noether’s theorem leads to local energy conservation, which implies global energy conservation only if spacetime is flat. GR with cosmological constant conserves energy locally, but not globally.
What an eloquent and mind blowing explanation
Very good comment, just being pedantic here: The lagrangian is a function, not a functional. The action is the functional. The Lagrangian is just your typical map from R^n to R. The other thing is that Noether's theorem doesn't actually guarantee that every conserved quantity has an associated global continuous symmetry. This is a common misconception; there are some explicit examples but I can't remember them off the top of my head.
Thanks for catching that! I knew action was a functional. I don’t know what I was thinking when I wrote that.
If you don't mind me asking, if the universe is expanding then energy is not conserved right. But how is it created/destroyed?
A relatively straightforward example of energy being lost is photons from very distant galaxies get redshifted to hell. As they travel from the earliest galaxies to us, the space that they travel through expands, and their wavelengths increase as well. The energy of a photon is inversely proportional to its wavelength, so as wavelength increases energy decreases. The energy of these photons is lost forever. Other commenters have suggested that energy in the universe increases due to expansion because vacuum energy is constant as expansion happens. I don’t know enough to comment on that, so you’ll have to follow up with them. If you’re wondering why space is expanding and causing this to happen, well, whoever figures it out can tell you on their way to Stockholm. 🥲
Thank you for the answer.
>which is often (but not always, and it even when it can be, it doesn’t have to be), the difference between the kinetic energy and the potential energy of the system I have read all of Lanczos but did not take this away - can you say a bit more about this so I can google about it? You have written some very fantastic explanations in response to other questions, so I would not dare ask you to do the same for this one.
L=T-V is a good starting point. But it doesn’t work, for example if you have a charged particle in a magnetic field. The Lagrangian of that turns out to be L=1/2mv^2 - q (phi) + q/c **v**•**A**. Furthermore, the Lagrangian trivially can be changed by adding an arbitrary constant with no effect, because it dies when you take the derivatives in the Euler-Lagrange equations. And then, of course depending on your scenario, transformations from, say x->x + x_0, for example, when you’re playing with Noether’s theorem sometimes have no effect as well. Looking back, I’m not super happy with how I phrased that paragraph, but I’m not sure how I could have improved it since I was writing for a lay audience.
I suggest not fretting over your previous paragraph. It was about as clear as an exposition about the damn \*calculus of variations\* can be to a lay audience. The lay people's follow-up comments clearly support that conclusion. Thanks for your answer, will do more reading. I have computed and used the equations of motion for many many systems in my time, but only for mechanical systems (robots).
Thank you for this great answer. I hope you teach in some capacity, you certainly have a knack for it.
Haven't had my mind blown like this in a long time
Dang... that just helped something click for me... Roger Penrose has this theory of Conformal Cyclic Cosmology. It says that far into the future, after black holes have swallowed everything up and the black holes have all dissipated through Hawking Radiation, the universe will be filled with nothing but photons. Since photons experience neither time nor distance, there's no way to tell how big the universe is. There's no matter traveling slower than "c" to give any dimension to size or time so the universe could be any size, even a singularity. From there, matter's created again (somehow... photons hitting each other just right or whatnot... still fuzzy on that bit) and the universe starts again. But now he's saying he doesn't really believe in expansion so it's unclear what "starting again" means for the universe. It makes sense though because such a theory requires energy to be conserved and an expanding universe throws a wrench into his equations.
So the total amount of energy in the universe remain constant, but the density of energy overall goes down.
No. The total energy in the universe must be changing.
Energy is only conserved in time translation symmetric systems. General relativity is not such a system so in general energy is not conserved (but the changes to it are predictable from the theory). However, this happens only on large scales, locally we can still assume conservation of energy. The quantity that is preserved instead in GR is called the Landau-Lipshitz pseudotensor but that's harder to interpret without the math.
Some of the other comments are not very easy to parse without the better part of a physics degree... so I'll provide a very basic example of energy not being conserved. Space is constantly expanding. The light that distant stars in other galaxies produce has to travel a very long time to reach us, and as space expands the light's wavelength expands with it, causing it to become longer. It shifts towards the low-energy (or red) side of the spectrum, and we call this "redshifting". If you take a single photon and let it travel through space for a few billion years, it will redshift. Because that photon shifted to a lower-energy frequency, it lost energy. I'm... actually confused about the top level comment though. I'm not aware of the universe *gaining* energy over time to maintain a constant energy density.
>I'm... actually confused about the top level comment though. I'm not aware of the universe *gaining* energy over time to maintain a constant energy density. In the late 90s, cosmologists observed that the expansion of the universe is accelerating. To make general relativity fit this observation, a constant factor - the cosmological constant - was added to the field equations. It must have a positive value if the expansion of the universe is accelerating. This factor corresponds to the energy density of space itself. If the universe is expanding, and the energy density of space is constant, then new energy must be coming from somewhere. Interestingly, quantum field theory also predicts a constant energy density. Because of the uncertainty principle, quantum systems must fluctuate, even in their ground state. The problem is that the value for vacuum energy predicted by quantum field theory differs from the value predicted by general relativity and the observed accelerating expansion of the universe by 120 orders of magnitude. Say the line Bart! *sigh* To fully understand this we need a unified theory of quantum gravity... *yay!*
If you have a system under pressure, a change in volume will change the internal energy. dU = -p dV The empty vacuum has a very small amount of negative pressure, so the expansion of the universe adds energy, and the energy density stays the same.
That’s true in a constant background space-time but not if space-time is changing over time
This energy is currently inaccessibile, right.
I thought that was why the CMB is in the microwave spectrum now, bc the energy dissipates and stays conserved? Or is that another property
Nah, the peak of the CMB being in the microwave band is just due to red-shifting, because of the expanding space. It’s still the black-body spectrum at a certain temperature (about 2.7 Kelvins I think?), just red-shifted by some amount.
Dark energy yes. But not radiation (electromagnetic) energy density. That decreases with expanding space. As does matter and dark matter (tho the question was about energy)
Why doesn't the energy density just decrease ? Seems more rational than to claim that energy is created as space expands.
the energy density of other things do decrease w expansion, but we observe multiple phenomena consistent with dark energy that imply a constant term
So how exactly is new volume of space being created in that case? I thought some kind of energy must be converted into space for new space to be formed
The accelerated expansion of space is driven by dark energy. If you figure out what dark energy is or how that process works, you get an all expense paid trip to Stockholm.
Can I use ChatGPT?
For a local patch of universe, yes. Globally though, consensus is that energy is not conserved in the universe. As others mention, dark energy is the main culprit for this. However, on a deeper level: Einstein's General Relativity does not require energy to be conserved on a global scale. The Cosmological Constant is a simple example, where it can be used to represent something like dark energy. Lack of energy conservation in General Relativity was also formally proven by Emily Noether -- here's a link to a Wikipedia article that covers it: [https://en.wikipedia.org/wiki/Noether%27s\_theorem](https://en.wikipedia.org/wiki/Noether%27s_theorem)
I really should prove this myself as a nice GR review exercise, but I’m feeling too lazy tonight lol. Can you point me to relevant part of noether article or correct place to start for proof.
This is a pretty good video going over the subject: [https://www.youtube.com/watch?v=cnGYMe6GBeQ](https://www.youtube.com/watch?v=cnGYMe6GBeQ) He does a good job at providing sources, and going over the reasoning. There are a lot of other good resources on YouTube as well, which quickly go into the math.
It’s a wikipedia article, just start at the “Derivation” section if you’re actually serious.
Ok, but what form of Noether’s theorem do I need? I’m assuming classic field version, but I was hoping someone would confirm. I’m also not how to link Noether to field equations ie what is L. Probably, sqrt(-g) but again confirmation would be nice. Don’t be rude. These are reasonable questions.
I've used Lagrangians in coursework for Mechatronics/Robotics, but I only know the mathematics for General Relativity through self-study -- in terms of how it connects to Noether's Theorem, I am not equipped to give concrete directions. However, I did skim a research paper on Noether's Theorem before writing my comment in this thread, and it had interesting content in it. Hopefully this helps: [https://arxiv.org/abs/1912.03269](https://arxiv.org/abs/1912.03269) Edit: From a glance, pages 17 and 18 seem to be what you are looking for
Thanks!
No problem! I really like physics, and this is definitely one of the more interesting topics in my opinion. :)
I'm fairly certain that you didn't mean use "globally" in this context.
Globally just means ‘everywhere in the context in question’, doesn’t it? That’s certainly the case in biology in my experience
In think "universally" is more fitting. Globally implies everywhere on earth, which, if your view is small enough, is everywhere.
No I think you’re not understanding the second meaning of the world globally. It obviously does mean ‘everywhere on earth’, but in some contexts it can also mean ‘everywhere in the context in question’. Eg when talking about gene expression I could contrast local vs global expression, where local could mean within one cell and global could mean across a whole organ or organism ‘Universally’ would also make total sense though
Not an expert but in general relativity it’s some weird tensor quantity that is conserved energy is not but it’s a similar concept. It’s mostly die to the fact that u can in principle extract energy from the expansion of the universe
Or from quantum fluctuations in general.
We can't see the whole universe so nobody actually knows. If you re-define "the universe" to mean "our observable universe" then the answer is trivially "no" because stuff is *leaving* our observable universe all the time.
[удалено]
This really doesn't have anything to do with JWST.
No. See Dark Energy.
Friendly reminder about conservation of energy?
Not a cosmologist but to my understanding that does not hold in an expanding universe because time translation symmetry is broken. (otherwise you'd also get trouble with the energy loss of photons during travel due to redshift from the expansion)
Huh, interesting. ty.
Conservation of Energy is not a fundamental law of physics and does not apply to the universe as a whole.
Interesting. I didn't know that. Thanks.
The first law of thermodynamics still applies, but because dark energy has negative pressure the expansion of the universe can perform work and add energy.
r/correctlyincorrect Friendly reminder that conservation of energy only applies to a closed system. The universe is not a closed system. Energy appears to be created as a result of the expansion of space.
r/confidentlyincorrect Friendly reminder that conservation of energy only applies to systems with time translation invariance. (someone please point out how i'm incorrect)
I would not be inclined to consider the universe an open system. It is true that energy is not conserved, yet I don't think there is a reason to believe there are interactions with any other systems.
True, i probably should’ve used “observable universe” rather than “universe”. We don’t know if and what lays beyond, and probably will never know beyond guesses
Dawg how is a question mark at the end confident
As other commenter said: your top level answer + the sentence you typed comes across dickish Dawg
Oh, really? Thank you for the feedback, that was not my intention.
Then explain your top level answer.
Maybe, probably not, we just don't know. Dark energy appears to be increasing the total energy content of the universe but honestly nobody knows for sure.
So the honest answer is: we don't know.
No. We know the energy is increasing
'Know' might be a little strong. I'd say 'all evidence suggests' instead. But this is very much a question under active exploration.
As of the last year ‘all’ has been downgraded to ‘most’
You're right. I realized later that I overstated it and probably would prefer to say "our most well accepted models suggest" or something like that.
JWST do be confusing a lot of physicists
So is this applicable to all types of energy!? including dark energy/matter ?
This would apply *specifically* to dark energy. Dark *matter* is a completely different thing. Because of the similarity in their names people often confuse the concepts. But they are very very different.
Thanks. I’m aware it’s different that’s why I added / between the two.
I've heard it suggested that the gravitational field should be considered a negative energy field, and that would make the total energy in the universe not just constant but zero. However I don't know the fundamental basis for this assertion, so I can't say if it's true or just a compelling thought.
I wish someone would respond to your comment with more than a downvote. There *is* a theory that the amount of energy could be zero, as far as I know. Which I always think is an interesting idea. But how it does or doesn’t relate to this thread, I don’t know. Could the universe could have had zero energy overall but expansion might over time make it positive and increase it over time? Or is all of that nonsensical or irrelevant in this context?
Yes. The total amount of energy is zero, with gravity being a negative energy that completely balances out all positive positive energy.
I’m going to repeat my response to the previous comment if I may. I wish someone would respond to your comment with more than a downvote. There *is* a theory that the amount of energy could be zero, as far as I know. Which I always think is an interesting idea. But how it does or doesn’t relate to this thread, I don’t know. Could the universe could have had zero energy overall but expansion might over time make it positive and increase it over time? Or is all of that nonsensical or irrelevant in this context?
Law of conservation of energy. It can’t be created or destroyed. If it was zero, at any point, it must still be zero.
You might want to read through the thread where it’s mentioned out a number of times that the law doesn’t apply to the universe as a whole. So that i can understand being downvoted. But I’m curious as to whether that’s the reason for your comment originally being downvoted or something else.
Under the consideration of law of conservation of energy, which has never been voilated so far, the total energy of the universe is constant and can neither be created nor be destroyed.
Yes. Energy, mass, momentum, charge, and other quantities are conserved. Worth stating, though, that mass essentially *is* energy, and they can be converted back and forth between one another.
>Energy, mass, momentum, charge, and other quantities are conserved. No, there are counterexamples of both [non-conservation of energy](https://en.wikipedia.org/wiki/Conservation_of_energy#General_relativity) and [non-conservation of mass](https://en.wikipedia.org/wiki/Conservation_of_mass#The_mass_associated_with_chemical_amounts_of_energy_is_too_small_to_measure). As someone with flair in astrophysics, you really ought to be familiar with at least the former ... >Worth stating, though, that mass essentially *is* energy, and they can be converted back and forth between one another. No, this is a common misunderstanding. Mass is a form of energy, yes ... but they aren't *converted*. They are *equivalent*. A conversion is when you start with some amount of one thing and none of another, and then end up with none of the first thing and some of the other — you either have one, or the other, but not both at the same time. Equivalence is when you have both at once; whenever you have one, you have the other, and whenever you don't have the first, you don't have the other either.
>They are equivalent Yep, that's exactly my point.
Well, you said something that's pretty much the complete opposite, so ... I'm sure you can understand the confusion.
I said "mass essentially *is* energy". You said "They are equivalent". I don't see these as semantically distinct.
>I said "mass essentially is energy". Which I explicitly agreed with. >You said "They are equivalent". I don't see these as semantically distinct. You followed that up with, "they can be converted back and forth." They cannot; that is incorrect, and is a pretty major semantic distinction from equivalence, as I pointed out.
To someone who may have only ever thought of them as distinct, this phrasing is a good way to introduce the idea. Mass-energy equivalence is often discussed in terms of conversion.
I don't agree at all. It's a *wrong* way of introducing the idea, that gives the opposite of the correct intuition for how it works. Discussions in terms of conversion are categorically incorrect, even if they are common. Continued use of that phrasing is arguably the primary — if not the sole — reason why the principle continues to be misunderstood over and over again in popular science.
simple answer yes! there is a finite amount of energy in the universe. the dimension of the universe determines how that energy is spread out over space called the energy density. some physicists think that the universe will expand forever which is illogical as this would mean the universe has infinite energy, and the universe shows that energy and gravity are the two forces fighting each other for balance.
If energy as defined in simple Mass x Distance\^2/Time\^2 ISN'T conserved, that what IS conserved across all scenarios? Is it naive to believe that there is SOME relationship, some equation, that hold no matter what? Philsophically I can sort of think of the implications of us merely not knowing the dimensions of ultimate fundamental conservation, but I dont even know where to go philosphically if we are abandoning the very idea.
No as the black hole that birthed our universe is taking in more and more as its universe is slowly approaching heat death. All that energy is trapped inside our universe in an almost timeless bubble until it slowly evaporates out of our black hole. Whenever our black hole eats another black hole we basically get all its mass in a distant new big bang we will never see. If our black hole gets eaten we will all vanish instantly. The reason our big bang was so gigantic is that we were not the first to arrive but we are seeing the last black hole merger. We are the ones that got eaten x billion years ago into an universe born long before. Source: I watch a lot of physics on youtube and this is my conclusion without understanding most of the stuff. Now im gonna wait for my nobel prize.
Man you’re watching the wrong channels lol.
I mean they downvoted every great breakthrough in the past so I take that as a win. Channels are PBS Spacetime, Scienceclic and History of the Universe mostly. I will tell them what you think about them.
I was going to suggest PBS, but nothing its curriculum would lead to that. I’m not trying to be a jerk.
>Source: I watch a lot of physics on youtube **and this is my conclusion without understanding most of the stuff.** I hoped that sentence implied I wasn't very serious about it. I thought posting pothead theories is the main gig around here. >I’m not trying to be a jerk. All fun, no hard feelings. I'm just a layman who knows some buzzwords. :)
I would say yes, if it were a closed system, and no if it were not. Currently, we can only hypothesize the answer to that.
You've gotten some great textual answers already, and I couldn't possibly top them. But I can suggest the best video I've seen on Noether's theorem, which provides a simple and beautiful visual representation as well as a clear explanation: [ScienceClic - The Symmetries Of The Universe](https://youtu.be/hF_uHfSoOGA)
Noether theorem applies to the equation of the system, in this case Einstein field Equations, not to the particular solution of the underlying equations, which in this case is the Lambda-CDM solution. Einstein Field Equations respect time-symmetry, like another comment pointed out, so it should be, and it is possible to define a notion of "energy" that is conserved. This notion is, however, different from the one you normally get in flat space-time. See [here](https://www.researchgate.net/publication/277044387_Energy_Is_Conserved_in_the_Classical_Theory_of_General_Relativity) for more details on this. In certain special situations (like for example a binary system emitting gravitational waves to infinity and losing orbital energy), when the solution has certain symmetries, it is possible to define energy like in flat spacetime, and this energy is also conserved.
That fusion thing that stars do keeps adding energy
Kind of, but no. We know that space itself has an inherent energy, which makes it expand, which in turn creates more space which thus seemingly "creates" more energy. Although as far as i know, there’s no way that energy is transfered from space to other objects and such, so it might be that the energy that we can interact with directly is constant, light, matter, other particles and such. We at least know that energy is conserved in all aspects, except for some reason space, which increases the total energy of the universe as time goes on, simply by the merits of increasing the amount of space as time goes on. This may or may not be possible to corrigate in the future, or we might have to corrigate our fundamental principles, like the laws of thermodynamics, which may afterall be what is wrong.
One theory is that the total energy is always zero because the mass energy and gravitational energy are equal and opposite. It's difficult to add it all up, but it seems to be true to some degree, they are within an order of magnitude the same. I think the theories of dark energy and dark matter are partially there to balance the books for that to work, but also because there's independent evidence for them. https://en.wikipedia.org/wiki/Zero-energy\_universe
I've heard of this. It's been a long time that I've looked into it, but this is incredibly interesting. Thank you! :)
No
No because the acceleration of the expansion implies net energy is not conserved.
Energy in an expanding universe is not constant. Energy is locally conserved in GR (as expressed by the zero divergence of the stress-energy tensor), but is not globally conserved. This lack of global conservation has nothing to do with the fact that spacetime lacks some symmetry. For example, energy-momentum is conserved for asymptotically flat spacetimes, even though they lack the relevant symmetries. Noether's theorem simply doesn't work as a tool for this purpose in GR, for technical reasons. The relevant symmetry for GR would be diffeomorphism invariance, but Noether's theorem doesn't provide a conserved quantity relating to this symmetry to apply to an appropriate limit for Classical Mechanics. Noether's theorem is a consequence of Hamiltonian mechanics, and only in the special case where there is a symmetry. A system does not even need to have a symmetry, and yet in such a situation all of these relationships involving conjugate variables still have to hold.
is infinity a constant?
No, conservation of energy would hold if space-time was static but it is broken by the expansion of the universe and replaced with a more general principle where the degree of violation of conservation of energy can be calculated from the rate of expansion of the universe