well you know you don’t have to read my article if you don’t like it. you claim i’m solving a problem that’s only a small problem, not a big problem. meanwhile i assume that you’re not bothering if people play video games instead? because people need to take their minds of their immediate reality for a while? or sth

actually, there’s quite a few places all over the internet where this is being discussed, if you just google for “cosmology energy conservation”. spontaneously i found these sites:

• https://www.reddit.com/r/cosmology/comments/1jnk2qy/energy_conservation_on_cosmological_scales/
• https://preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ (oh btw that blog post gets more readable if you use your browser’s “reader view” or try to print it into a PDF file)

Now while i acknowledge that reddit is not the peak insight level, and i can’t tell about that blog post, it does quite clearly state things such as:

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.)

I can go look for more discussion about this topic if you want to. Or you can just google it yourself. The issue is a bit complicated because it involves complicated mathematics though. So, the quote from the blog post is accurate: “cosmologists have not done a very good job of spreading the word about [this]: energy is not conserved in general relativity.”

also to be more picky about it: the second law of thermodynamics precisely states that energy cannot be converted with a 100% efficiency from heat into mechanical work / electrical energy. This (topic of energy non-conservation in cosmology) is yet a step further, because it argues not so much that 1 J of heat can be converted into 1 J of mechanical work, but instead it asks whether 1 J of heat can be converted into 2 J of heat. So it’s not about different types of energy being able to be converted into each other, but about the non-conservation of the sum of all of these energies.

edit:

• https://en.wikipedia.org/wiki/Conservation_of_energy#General_relativity

General relativity introduces new phenomena. In an expanding universe, photons spontaneously redshift and tethers spontaneously gain tension; if vacuum energy is positive, the total vacuum energy of the universe appears to spontaneously increase as the volume of space increases. Some scholars claim that energy is no longer meaningfully conserved in any identifiable form.

If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics, notably the Friedmann–Lemaître–Robertson–Walker metric that appears to govern the universe, do not satisfy these constraints and energy conservation is not well defined.

yeah, actually, i am. or at least i suspect so.

the thing with energy conservation is that it mostly comes from noether’s theorem (or variants thereof) that state that as long as the laws of physics don’t change over time, no new energy can be created. you’ve probably heard about it. Noether’s theorem.

Now, what i’m suspecting is (but i have yet to do the calculation) is that while there is a conserved quantity in cosmology (as long as the rate of expansion stays constant), it is not what most people would identify as “usable energy” in their everyday life. So, you might have a quantity E that describes the total amount of energy in the universe, or in a region of spacetime that is defined by some comoving boundaries, but it does not translate to the intuitive picture of energy (light energy, mechanical work, heat energy) that most people use for practical computation. This could be possible e.g. because there’s an additional, negative energy stored in the “gravitational field”, which just means, we add an additional quantity (called the gravitational field) sothat the total sum of all energies stays constant. Yet, paradoxically, that additional gravitational field energy does not actually affect a local observer in any practical way. Just like you wouldn’t notice it at all, if the electrical potential dropped by the same amount everywhere in space at the same time, because the measurable electrical field strength is only the gradient (change over distance) of the electric potential, so if the potential drops by a constant everywhere, the gradient does not change. Still, if you have filled your universe with more positive charges than negative charges, the total electrostatic energy of the universe still drops (according to mathematics). The same happens with the gravitational field.

So, we have two types of energy: a useful one and one that we can probably not even measure, and while the sum of the two is conserved, either of them is not. And that’s what’s at play here.

edit: you might want to read https://en.wikipedia.org/wiki/Conservation_of_energy#General_relativity

General relativity introduces new phenomena. In an expanding universe, photons spontaneously redshift and tethers spontaneously gain tension; if vacuum energy is positive, the total vacuum energy of the universe appears to spontaneously increase as the volume of space increases. Some scholars claim that energy is no longer meaningfully conserved in any identifiable form.

If the metric under consideration is static (that is, does not change with time) or asymptotically flat (that is, at an infinite distance away spacetime looks empty), then energy conservation holds without major pitfalls. In practice, some metrics, notably the Friedmann–Lemaître–Robertson–Walker metric that appears to govern the universe, do not satisfy these constraints and energy conservation is not well defined.

For asymptotically flat universes, Einstein and others salvage conservation of energy by introducing a specific global gravitational potential energy that cancels out mass-energy changes triggered by spacetime expansion or contraction. This global energy has no well-defined density and cannot technically be applied to a non-asymptotically flat universe; however, for practical purposes this can be finessed, and so by this view, energy is conserved in our universe. Alan Guth stated that the universe might be “the ultimate free lunch”, and theorized that, when accounting for gravitational potential energy, the net energy of the Universe is zero.

which is basically what i tried to argue in the earlier half of my comment, i think.

yeah, i was implicitely assuming the lambda-CDM model with a positive lambda, such that expansion continues forever at an exponential rate. while not 100% sure that this is the right model to describe how the universe behaves, it is the current standard model that most people use. it’s valid to criticize that choice of model as an (not justified enough) assumption.

frankly, we don’t have enough data to say with certainty how the universe is gonna develop long-term. and maybe it won’t actually continue to expand forever. i’m just assuming this here because most people do. and you have to start somewhere.

edit: in fact i’m glad that you asked :) it means that you’re an attentive reader. always check the assumptions that are implicitely made.

in other words, to put it in more drastic terms: your framing that humans won’t survive the next 10 billion years anyway and even if we do, we’re ultimately gonna die after that, makes it in fact more likely that we won’t survive that long.

yeah i get what you’re saying. i really do. however, the thing is, it’s not entirely pointless what i said. human society has often developed in accordance with philosophical principles. people will act more likely in ways that ensure that they have a long-term future, if they can reasonably believe that they can have (or at least have a vision of) their long-term prosperity. You get what i’m saying? drunkyards both in america and in russia are more likely to poison themselves with alcohol if they don’t see “the good ending”. the same is happening on a political, geopolitical level. people are more likely to act sane if they can see the bright future ahead.

currently, the physics narrative about the long-term development of the universe is bleak. you learn in school that eventually the universe is gonna end in a long, boring cold death. You can see how that paints a negative picture of the future in people’s heads? “nothing i do matters because in the end we’re all gonna die” -> people do stupid things because they don’t care. that’s not psychologically healthy. we need to rewrite the narrative in a positive way. and that’s what i’m doing by showing that it is theoretically possible, theoretically conceivable, worth to consider the option that there is a long-term positive future. that’s how human psychology works, both in geopolitics and for the individual drunkyard (on a smaller scale). so the drunkyard might care about his family, the geopolitics cares about the fate of the universe, kinda.

uhm actually, changing coordinate systems we do all the time. Just that we use a number to describe some location, does not mean that that number immediately translates to some measurable quantity. Often we choose abstract coordinate systems to simplify calculations (such as polar coordinates or comoving coordinates). Then, if we want to actually measure things, we have to translate these coordinates into physically measurable variables, which is a translation to another coordinate system. That is what’s happening here. the “proper distance” is the physically measurable quantity (as would be measured by a ruler). the “comoving distance” is an abstract coordinate system, that is not directly a measurable quantity. That’s what’s happening here.

yeah, one would intuitively think so. very understandable. the interesting thing is, as long as everyone does it, the universe would not contract from it. the detailed explanation is a bit complicated but becomes clear when one observes that every intersection point’s comoving coordinates stay constant over time as long as the wires pull on each side with equal force. It’s one of these paradoxes (things that seem one way but go another way) of physics.

edit: i should mention that that might be a confusing answer to you. “comoving coordinates” are a mathematical trickery to deal with the coordinate system in more abstract terms. it does not denote the “distance” between intersection points (the “distance” does increase over time still).

ok, thanks :) is there something that you would like to know more about specifically? i might be able to give you some hints as well

so your whole comment is very belittling and i would not give that advice to a five-year old child because while you do say “thank you for your contribution”, you did not actually interact with the content. i assume you glanced over it and said “well that won’t work because … idk. if it worked, i’d have already heard about it”. that does not stimulate discussion but hinder it.

As an example of the distinction, though there are a lot of different elements out there in our universe, we have to make materials using the properties that those elements have available to us, we can’t make up the properties that we want the material to have first then try and force the elements to do precisely what we want them to.

so first of all, actually this is precisely what has happened in science multiple times over. the chemical element germanium was theoretically predicted first (by mendelejev) and only after that was it experimentally discovered. the planet neptune was first posited to exist based on mathematical calculations, only after that has it been found in the night sky. so yes, we do routinely make predictions about absurd and exotic stuff and only after that actually start looking for it.

If the second law of thermodynamics states that entropy is always tending to a maximum, and that increasing disorder defines the arrow of time, how is it possible that life even exists? Humans are insanely complex, and exist by taking simple atoms and molecules and combining them in an intricate ordered structure. The different layers of external and internal complex structure is incalculable; we are extremely highly ordered in a universe forcing disorder.

Also this has nothing to do with thermodynamics. Thermodynamics historically developed to describe hot gases and combustion engines, things on everyday-life scales. It’s never made to describe processes on cosmological scale. I hope that you do not seriously apply that theory outside of its intended context, because those results would be meaningless. There is no indication that cosmological processes would have to adhere to the second law of thermodynamics (or if you do have such indication, please send it to me, i’d like to see it). Please make as little unnecessary assumptions as possible.

Also important, like theneverfox said, the universe has ways of closing off these kinds of loop holes. Imagine creating a whip from this material you describe. When you would make that whip long enough (and compared to the scale you describe it can be tiny), you’d easily be able to get the end beyond the speed of light when whipping it. Obviously this can’t work, so we know this material simply cannot exist. Nothing with a tensile strength like you describe can exist, not even in theory and applying some fantasy magic. It would break the laws of physics. (And not even getting into the amount of energy per volume such a material would have is beyond black hole levels, so that’s a whole thing)

interesting argument with the whip, i’ll think about it.

however your second point about the amount of energy per volume that such a material would have, i calculated that and it’s about equal to the rest mass of the material. in other words, charging it with energy the way i intended would roughly double its total mass. not create a black hole.

(that’s because you’re siphoning off that energy to create more mithril wire. so the stored energy has to be at minimum equal to the rest mass of the new mithril wire. i hope that makes sense.)

comoving distances are a way to describe coordinates. they do not represent what you would measure with a ruler. instead, a ruler would measure the proper distance (which is explained further down in the article). and that does increase with time due to expansion.

yeah, the long chain of protons and neutrons is an interesting idea. I’ll think about it :)

For example, if an undiscovered element is required, does that mean it would need to be generated from nothing, so to speak, with a particle accelerator?

Yes. That is specifically what i assumed. W2 is the rest mass of the mithril chain link, i.e. the (minimum) energy required by a particle accelerator to produce that material out of nothing.

no, look. there’s a thing called proper distance that does increase over time. you’re mixing up things here.

the planets of the solar system do not move further away from the sun over time. they are gravitationally bound. that is because while there is a pseudo-force pulling them apart, due to how weird orbital mechanics are, that does not actually lift them to a higher orbit. for the planets to change to a higher orbit, they would have to accelerate forward instead. it’s weird, i know.

anyways, the wires do get stretched over time.

cosmic expansion (if you represent it as a pseudo-force) increases linearly with distance, meanwhile gravity gets weaker quadratically with distance. that means, at a certain point, cosmic expansion is going to be stronger than gravity. here’s a visualization for you:

(forgive that i didn’t pretty up the diagram much. i just don’t care enough to label everything properly. you get the idea)

uhh, i get your point, but my point wasn’t to “build a machine that works”. rather, i’m having a mathematical background (personally) and doing an “existence proof” here: i show that something is possible, not that something is efficient or can be easily built. many such proofs exist throughout the field of mathematics, and also physics, to show the consistency or inconsistency of some other, more practical theory. this is often useful because even when you cannot find an object itself, knowing that it must exist can have distinct benefits.

i’m gonna exemplify this with the proof that the square root of 2 is irrational. the proof assumes that two natural numbers a and b exist such that sqrt(2) = a / b. Then it derives a contradiction from that and that’s how we know that sqrt(2) is irrational. At no point were the numbers a and b ever found. Hence, by your metrics, such a proof is “useless” (because it does not construct a or b). but, the value is not to find a number, but to proof that it does / does not exist. different category of goal here.

The cherry on top is that we don’t really understand cosmic expansion or the forces behind it… We have models that work to a point, but only to a point. We know our models are wrong (or say least incomplete), so there’s no guarantee it’ll continue when the stars go dark

yeah, that’s a fair argument and i considered it as well. you’re right, we don’t fully understand how cosmic expansion is gonna develop in billions of years, however, there’s roughly 3 scenarios:

1. cosmic expansion comes to a halt after a while
2. cosmic expansion continues at an even rate, i.e. the Hubble parameter remains a constant non-zero value
3. the hubble parameter oscillates up and down over time

all three cases are interesting. in the 1. case (which is surprisingly difficult to describe) some parts of the universe continue to contract while others continue to expand. ultimately we might be able to survive indefinitely in this universe by constantly exploring new areas (there’s no “off limits” area if the universe doesn’t expand continuously).

the 2. case is discussed in this article.

in the 3. case, you could extract energy out of a “change of the laws of physics over time”, i.e. if gravity has different strength each day, you could move a boulder up on a mountain when it’s weak and down when it’s strong and generate power that way. similar thing is possible if hubble parameter is non-constant over time. i won’t go into detail because do you really care about the details of that maths?

Even if your “mithril” could exist, this thought experiment doesn’t even cover the question of whether this system of chains would yield enough energy to justify the amount of energy that would be spent creating and maintaining this cosmic-scale mechanism.

actually that’s the whole point of the second half of the article. did you even read it?

frankly, that’s bullshit. locally, the wires would be under stress if they’re stretched.