## The Universe as a Gas Can – Part I: Entropy

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**Warning- The following article contains conjecture – An Idea - and is not to be taken as scientific fact **

This supposition reasoning of the universe begins with a hypothetical container. The container is not a spatial container, but an energetic one. This container originally contained a value of all the energy in in the universe, which we can call X-energy.

The actual spatial dimensions of the container are unimportant. Maybe it was the size of a pin head, maybe it was a big as the physical universe.

Matter is said to have formed after the Big Bang https://www.big-bang-theory.com/ when the universe cooled. We know that E = mC squared. This means that when we take the value of the speed of light, square it and then multiply that by the mass of an object, that is how much energy is represented by the object. It’s an awful lot of energy tied up as matter.

Energy exists in many forms, such as heat, light, chemical energy, and electrical energy. Thermodynamics is the study of energy.

The Second Law of Thermodynamics states that "in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state." This effect is commonly referred to as entropy.

Energy may be lost from systems to the universe in many ways including as heat or light. It is not until we put more energy back into our local energetic systems that we can get them to resume their energetic function. The release of this unusable energy back into the universe is entropic. It has been suggested that eventually even the energy of matter, including matter itself will fall foul of entropy and undergo energetic decay.

It is my contention that when matter was created, the energy value of the universe, as detected by the container that held it, fell (the energy of matter could not be read). The remaining value of the energy of the Universe (U) became X-energy (the total energy of the universe) minus Y-energy (the energy of matter). This was the energy equivalent of sucking gas out of a gas can. The energy container can be visualized as buckling. This visualization is important to understand that an opposite drive could be created at this point to restore the container to its original energy value. While the gas can may be imaginary, the drive is not. I propose that this drive to restore the container to its original value explains Entropy.

Let’s look at that equation again: U = X – Y (remaining universal energy = total that there should be minus what is tied up in matter. I know what is tied up as matter is mc squared, so the equation becomes: U = X – mc2

Interestingly when we compare equations we can see this becomes a simple derivation of Helmholtz free energy : The equations for calculating the free energy of a system are: A = U – TS where A is the remaining energy after the internal energy – or how much energy there should be (U) has had subtracted from it TS which is temperature and entropy.

U = X – mc2 compares to A = U – TS

Anyway, this is an interesting aside for now. My point is that entropy may be a drive to restore the energy value of the universe by sucking it back out of matter so it can be read by the container again. It is an ontological attempt to explain entropy.

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This is pretty much what cosmology says. The Big Bang started in a state of thermal equilibrium - an even bath of radiation with all the same temperature. Then the radiation cooled to a point where a fair chunk of it condensed out as matter.

In that respect, the universe fell out of equilibrium and so there is an entropic equilibrium to restore. All the matter will want to find ways to turn back into radiation and catch up with the general cosmic flow again if it can. Hence stars, for instance. And black holes can also radiate so will eventually evaporate over sufficient time.

As an aside, consider how heat content and spatial extent are mirror images of each other at the Planck scale of the Big Bang.

The Planck temperature is defined by a wavelength with a frequency of one Planck distance. So it is all about the size of a single energetic vibration that can be packed into a single unit of space. This single wave is so compressed that it represents the hottest or most blueshifted light.

So the lack of room for light to move at the moment of the Big Bang is also what set its heat to the maximum energy scale or temperature that radiation can have.

You can see there is a very direct connection here between the container and its contents.

The Heat Death is then likewise defined by a Universe arriving at a state where any remaining photons are so redshifted that they are a single wavelength stretched the size of the visible universe. The radiation now has a temperature of virtually absolute zero degrees K.

So it is absolutely the case that there is a relation between the available space for radiation and its consequent energy scale.
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You little ripper! - as we say in Australia.

** An expression of great joy. **
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So it is absolutely the case that there is a relation between the available space for radiation and its consequent energy scale.

So the upshot is that the reason for the expansion of the universe is about entropy. If we knew the correlate between mass, entropy and space, we could calculate how much space it would take to drain the energy back out of matter.

If that’s correct, then it would seem to follow that the expansion of space would cease once that figure is reached (the Heat Death is reached) - but I know that the cessation of expansion isn't supposed to happen. This can only mean that the full conversion never happens.

Do you know the problem. Is it the wavelength of radiation - can it never become linear and thus disappear back into the initial condition? The exponential curve that never hits zero? Why would it keep expanding do you think? (I don't buy momentum from the Big Bang)

So the lack of room for light to move at the moment of the Big Bang is also what set its heat to the maximum energy scale or temperature that radiation can have.

It almost sounds like a false start doesn't it. Let me ask you a question. You've seen those drawing of a gravity well with mass sitting plum in the centre? Do you think that if we just created the well, matter might appear?
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If that’s correct, then it would seem to follow that the expansion of space would cease once that figure is reached (the Heat Death is reached) - but I know that the cessation of expansion isn't supposed to happen. This can only mean that the full conversion never happens.

This is getting into very tricky to explain areas but we now have evidence of a "dark" energy or positive cosmological constant that is driving the accelerated expansion of the Universe. So that faint extra push in fact ensures a heat death at some future predictable moment in time.

Our corner of the universe is bounded by a still expanding event horizon - what we call the hubble radius that defines the visible universe. So because the universe is expanding spatially, everything towards the edge of our point of view just gets faster and faster until it is effectively going faster than the speed of light. At that point it vanishes from view. It disappears over the horizon of the hubble radius. We can no longer have any interaction with it.

In a universe without an extra dark energy push, a perfectly balanced universe would be coasting to a halt at the end of time. Eventually everything that has been disappearing over the horizon would reappear because the metric expansion would be steadily slowing, running out of steam, and that would give time for even the most distant light to start reaching us again.

But with dark energy, instead the hubble radius/event horizon would still be there. The larger universe would still be super-luminally out of reach for us. However the horizon itself would cease to expand and instead come to a halt at a fixed distance. And that then means the entropy of the visible universe could not physically get any lower. A fixed horizon means as much would entropy would be re-entering as leaving. So the total becomes a final condition.

Think about it as running down an up escalator. At some point, you are running at the same speed as the escalator going the other way and so you just stay in the same place. Despite all the action.

And we can measure where we are in this story using the principle of holographic event horizons.

The existing entropy content of our visible universe is represented by the "container" of an event horizon that has swallowed up 10^122 degrees of freedom. Eventually all the cosmic back ground radiation will add to that, swell the horizon. But only by a surprisingly small amount - a contribution of just 10^88 extra degrees of freedom. That's a round-up error of 34 decimal places.

Even the evaporation of all the super-massive blackholes in our corner of the universe would only add 10^103 degrees of freedom - a clerical adjustment to the 19th decimal place of the total sum.

So we pretty much are at the Heat Death as things stand, even if those super-massive blackholes are going to take about another 10^103 years to fully decay.

Do you know the problem. Is it the wavelength of radiation - can it never become linear and thus disappear back into the initial condition? The exponential curve that never hits zero? Why would it keep expanding do you think? (I don't buy momentum from the Big Bang)

The momentum of the Big Bang explains most of the story. The little extra contribution from "dark energy" has become the new mystery. But it could just be a tamed remnant of inflation or the simple product of quantum uncertainty at the vacuum level. There are certainly plausible theories.

The other bit of the new physics is realising that event horizons radiate. That is why the universe would be able to reach some actual final heat death temperature - as the only thing glowing would be the "container" itself. The cosmic event horizon at its fixed position would emit black-body radiation as a normal quantum process. It is just that the photons would be so absolutely cold or stretched that they would have a wavelength the size of the visible universe itself.

Which is what I pointed out about the symmetry between the Big Bang and its Planck scale heat, and the Heat Death, where once again the energy inside the container matches the size of the container in its frequency.

So some new deep connections have been discovered. Even physicists and cosmologists are still trying to figure out a definite meaning for them.

If you are interested, check out Charlie Lineweaver - of your favourite university, ANU. He wrote a good Sci Am piece and has a ton of great papers on his webpage.
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the energy inside the container matches the size of the container in its frequency.

Frequency. This is an excellent description of space that has turned some mental tumblers. Before the big bang there would have been an absolutely compressed frequency which would put energy out of the spatial plane entirely. That's how it arose from nothing. It would have had a frequency of one meaning it was a line with a point moving vertically up and down it. Thus space is the background for an echo or a reverberation. Energy is creating its own context. I'll let that idea percolate for a bit.

Tonnes of good stuff to digest in your post. :)
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We are going from amplitude 1 wavelength 0 to amplitude 0 wavelength 1. The energy of the universe is reorientating itself. That's what the universe is, the reorientation of energy. Matter and emergent systems make more sense now. Matter is not the enemy of energy. It is the holding configuration, rendering it relatively inert for a time, to allow the reconfiguration. Entropy is the master control. The 'anti-entropic' heirachical states merely allow a variably timed redistribution of energy.
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It would have had a frequency of one meaning it was a line with a point moving vertically up and down it.

Think also of the fact that a sine wave is formed by the rotation of the unit circle....

So taking the particle viewpoint - the fundamental U1 symmetry that accounts for the nature of radiation - there is a duality here that explains things. The shortest frequency is also the quantum spin - a rotation with Planck scale.

A limitation to spatial extent - a fundamental smallness - is cashed out in the other direction by a matching largeness of the rotational confinement. Spin starts out with its highest possible value. And so the first sine wave echo to resonate in the Planck-scale cavity is as hot as it gets in being also as curved as it gets. (Spacetime curvature equalling energy density in the general relativity view.)

Once you put the bits and pieces together, you begin to see the pattern of relations that compose the Planck scale. All the aspects of the Cosmos that seem broken apart and unrelated are unified, different ways of looking at the same thing, at the Planck scale.

This has become explicit in the way modern physics has evolved. It is the reason why quantum gravity would count as a final gluing together of the Planckian parts - https://en.wikipedia.org/wiki/CGh_physics
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Spacetime curvature equalling energy density in the general relativity view

Yes, I see the bridge. I'm not there quite yet though. The quantum spin that creates the frequency of the Planck scale temperature, does it still exist or is it conceptual? The rest of the radiation of the universe is the result of the growing expansion of the wheel? As the energy density of the universe weakens the circle grows? Energy density is highest where space is the most curved - macroscopically that would be in gravity fields I guess. So in a way it answers whether bending space would cause mass to appear - Yes - mass as a radiating body. The deeper the curvature the tighter the frequency of radiation.

Thus quantum gravity would glue together the Planckian parts because quantum gravity represents the most extreme bending of space possible and thus able to create Planck temperatures?
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The quantum spin that creates the frequency of the Planck scale temperature, does it still exist or is it conceptual? The rest of the radiation of the universe is the result of the growing expansion of the wheel?

This particular part of the story is more my speculative argument. I'm not really aware of any explicit development of it in the literature.

But anyway, the argument would be that spacetime has its two critical symmetries once it is expanded and flat. Rotation and translation are the two inertial forms of motion that are symmetry preserving actions and so not entropic. Any material body can move in a straight line at a constant speed forever. And also rotate in the same spot forever. So even in classical Newtonian mechanics, this duality of translation and rotation is a very deep fact.

And then all the particles of nature are explained as varieties of fundamental spin symmetry. And their spin is complex as a massive particle - one able to be moving slower than the speed of light - could be spinning in three possible directions. A massless particle - which must travel at c - can only spin in two (for the complicated reason you can never accelerate faster than the particle and "reverse its spin" in its forward direction of travel by looking at it from in front.)

So if we start with the Big Bang as a primal fluctuation - just an action and a direction - then it might be both a primal rotation and a primal translation at the same time. (After all, why discriminate by labelling it one kind of action or conserved symmetry rather than the other?) But the translation - a free action involving moving in some straight line - is as small as it ever could be in this first moment. While the rotation is as big as it ever could be already. A full turn is possible in the tightest space.

Then as the Universe expands and cools, you have a swing the other way. Now any remaining translational action can travel as far as its pleases. But all rotational action - in terms if intrinsic quantum spin - is left behind, located in an increasingly shrunken fashion. Translation's gain is rotation's loss.

Radiation - as particles travelling through a void - of course combines translation and rotation. A photon is a wave with a rotating phase. The spin carves a helix along a path. The spin stays constant in size - the quantum spin of a particle just has a number (0, 1/2, 1, 1.5, 2). But the path is being stretched by the expansion of space, and so the helix or wave form is redshifted and loses effective energy.

You can imagine the difference if spin could change its rate. If the spin rate increased to match the stretching effect, then the helix would write the same corkscrew on the universe. It would be like shrinking the rolling circle that creates the sine wave to tighten up the frequency it is losing.

(And if spin could slow, it would be like the rolling circle getting bigger, so delivering the red-shift in a non-expanding universe - the kind of complementary effect you were going for with contracting spatial co-ordinates. Again, the sign that a view is fundamentally right is that it can be inverted and still give you the same essential story. This formal duality principle is the big thing that sparked string theory's second revolution and is why AdS/CFT correspondence in holographic theory is such a big result. So seeking duality is definitely the approved way to think.)

So to sum up, any primal action at all requires also the dimensional container to give it shape. So quantum action and spatiotemporal structure must go hand in hand from the get-go. And the Planck scale encodes that dichotomy in incorporating both the h that scales quantum action and the G that scales gravity (and so defines what counts as a flat container).

Then a second primal dichotomy is the one between rotation and translation as actions that are both conserved due to spacetime symmetries. Both are possible, and thus both are happening, from the get-go of the first Big Bang fluctuation. But rotation starts with the volume turned up to 10 and then gets "lost in space". And translation starts with no room to express itself, but eventually comes to be the dominant mode of action. Particles which then carry both kind of actions (as little rotatable and translatable packets of excitation) carve out helical paths that looked increasing stretched and red-shifted as spatial extent grows while rotational possibility remains rooted right where it started.

Bear in mind that quantum spin is a lot more complicated than I've just described it. I've just stuck to the story of photons as the simplest possible case.
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Just to make sure I've got your idea right.

And then all the particles of nature are explained as varieties of fundamental spin symmetry. And their spin is complex as a massive particle - one able to be moving slower than the speed of light - could be spinning in three possible directions. A massless particle - which must travel at c - can only spin in two (for the complicated reason you can never accelerate faster than the particle and "reverse its spin" in its forward direction of travel by looking at it from in front.)

So these are higher order spins. We have the spin of the object about its own central axis, the spin of the object about its translational axis (the helix), a third spin could be the rotation of the helix through space and so on (like a chromosome wrapping around histones). It's funny to find higher order systems in something as simple as spin. The other spin, viewing it as you go past the object would seem like a perceptual change though, not an actual one.

So the pre-Big Bang, 'maximum' spin conformations and speeds and very tight hard reversible translations (creating the reverse spin conformations except in the innate spin). Like an out of control washing machine thrashing furiously.

These actions are timeless, anti-entropic, however, later as space expands the higher order spin conformations become stretched translationally. Translation itself undergoes space expansion. If there was no translational expansion of rotation then the relative effect on the wavelength would be compressive. Radiation would be blue shifted to the Planck temperature. Translation of rotation at a rate faster than the expansive rate of the universe would red shift it. Which does seem to be happening.

But what of the innate spin - it wouldn't undergo translational expansion. It would remain constant. So, it is this spin that is a universal constant while the fact that translation matches (or does it) space expansion renders it also a constant.

Is that it?
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The reversible nature of translation and rotation (except for innate spin) at the time before the big bang would have seemed like a switch blinking on and off, into and out of existence. As the translations grew larger the time between the blinks grew longer and the blink itself became more sustained. Finally the translation became so large it broke a restorative constraint, becoming non-reversible and dragging rotation out with it.
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What does it even mean to talk about the world and the way it existed before human experience, language, and concepts? This scientific view of the world just assumes there was an already laid out, independent world, which we just by happenstance have a view upon, almost like an external observer from another reality 'looking in'.

We can only talk about this supposed pre-human physical world, using language taught and passed on through people's, cultures, practices, and histories - all entirely human. Is there some sort of independently existing past out there in some void beyond this 'lifeworld' we inhabit, to which our words fly out and refer to?

I feel as if this scientific, materialist view of the world is tantamount to religious delusion. People talk about the big bang the same they talk about God's "let there be light" - it's a creation story. Yes, this scientific approach toward the past has explanatory and predictive value, but that does not mean the unobservables used within the approach actually exist out there.
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but that does not mean the unobservables used within the approach actually exist out there.

You are confused about the philosophy of science. As a method, it is explicit that it simply forms theories of the thing in itself.

Having laid that epistemic foundation, it can then get on with developing theories that have maximal objectivity - ideas that are measurably the most viewpoint invariant.
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Any blinking at all would require the dimensionality that would make it a thing. So the blinking would itself be the first symmetry breaking - a raw first emergence of an action with a direction. Then after that would come the second distinction of actions that conserve rotational symmetry and actions that conserve translational symmetry.

At the Planck scale, rotation and translation would look the same - just a blink, a pulse of action or energy, as you put it. But as soon as space started to grow in scale, there would be these two energy conserving directions in which things could spill.

Spin then gives shape to the particles which are the located excitations. The standard model describes the fundamental gauge symmetries that allow particles to exist. Then translation allows those localised excitations to propagate and disperse.

So one direction of motion produces particles. The other lets them spread and fragment to create an en-mattered void that is running down an entropic gradient.
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Having laid that epistemic foundation, it can then get on with developing theories that have maximal objectivity - ideas that are measurably the most viewpoint invariant.

But that's not what people mean when they talk about scientific objectivity, including within this thread. When people talk about the Big Bang, they talk about it as if it was an event that really happened, out there in some independently existing past, billions of years before the existence of humans (and the concept "billions of years").
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Huh? People only began to talk about the Big Bang when the evidence began to build for it. They had to start making the best sense of the observed facts.

Even if you want to pretend to be a strict idealist here, there would still be the same need to account for the structure of our experience. We can't just wish all those red-shifted galaxies to instead be blue-shifted.

So sure, it is important to understand scientific knowledge is socially constructed. But that doesn't mean it's just some fantasy story with no basis in reality. It means that there is in fact a right way to socially construct knowledge if the goal is "objectivity". And that way is ... science.
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I spent the better part of two days working with rotation and translation ideas to little avail. In the end I think it is the question you are trying to solve with it that I don't quite understand. Why it is conserved in space?- is that it? My conclusion was - that it is only conserved in idealic circumstances. I don't see how it is conserved otherwise. For example we know that a material body will accelerate (or decelerate) as well as alter course in a gravitational field, thereafter adopting higher or lower translational velocities (slingshotting) and we know space is curved, and if it passes the even horizon of black hole nothing gets out. In linear non-gravitational space I think the conservation rule holds. Do you disagree?

And if there is the third option of expansion - as there really must be just because it is both what we can see, and what is most probable given the Universe has been around long enough for us to be even wondering - then this expansion must be most remarkably fine-tuned. The expansion - or indeed now, the acceleration - is adjusted to be exactly the amount needed to make the Universe almost perfectly flat and future eternal.

The details are worth going into as this is a cosmic scale whodunnit. It shows how poor our metaphysical intuitions can be. It shows why proper science is actually needed. :)

The actual physics has long moved on. The question now is why is it faintly accelerating by some precisely correct amount to make up for the 70 per cent of "missing mass". There is plenty of speculation about possible answers, but right now it is simply a really big and interesting gap in our scientific knowledge.

And have come up with this:

The idea that the universe is expanding beyond that accounted for by entropy obviously suggests another unaccounted for energy - the dark energy you talked about. I had an idea, and I've been researching as I write this and so far my hunches are panning out as I go along (ironically I find it quite frustrating). Maybe I am just treading a well worn path here.

At the beginning of the universe it was not just temperature that dropped, but also pressure (just came across negative pressure). When we have a rapid drop in pressure things bubble (I can't think of a more scientific term). What if spacetime bubbled (we know its curved). A bubble would be an area of less dense space, which would want to collapse back out, thus providing a push. Punctuating the area around the bubbles would be higher density areas where matter formed (gravity) - like the parts giving shape to the inside of an egg carton. So while matter wants to go from a dense to a less dense energy form, dark energy wants to go from less dense to more dense.

If we consider more dense space as having curvature - gravity, then less dense space would have an inverse curvature - an anti-gravity effect. Thus matter can arise in gravity - curvature (as I've suggested before) - OK, I've just found out that dark matter has a force that repels gravity.
These large bubbles would explain why there is more dark energy than matter energy, why the energy value of the universe continues beyond the container of entropy, and why dark energy has such a low density. As it collapses we would expect velocity of collapse to increase, consistent with the expanding velocity of the universe. It also explains why the expanding universe does not enlarge matter.

I found a reference to quantum foam relating it to space density which also kind of fits in. I have just found this good reference here which actually fits the bill too. Actually, like I thought, it might be a well worn path I'm describing, more speculation, but I'll pass it on to you anyway.

Aside:
As you know, I like to work on visualizing these types of problems but most of the time they've been solved- I think I'm on the right track here, but I don't think it's ground breaking. You're more up to date than me with the state of science, can you suggest an unsolved physics puzzle?
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Why it is conserved in space?- is that it?

The proper answer is very technical - https://en.wikipedia.org/wiki/Noether%27s_theorem

In linear non-gravitational space I think the conservation rule holds.

Yes. And then energy is not necessarily conserved under GR as the reference frame is free to flex. That is, GR doesn't provide you with a fixed geometry that could make local symmetry a hardwired thing.

When we have a rapid drop in pressure things bubble

You mean if they contain dissolved gas. So a quite specific phenomenon, called cavitation, that has no real connection.

A bubble would be an area of less dense space, which would want to collapse back out, thus providing a push. Punctuating the area around the bubbles would be higher density areas where matter formed (gravity) - like the parts giving shape to the inside of an egg carton.

Unfortunately for that theory of yours, the Universe looks fantastically even in its expansion. That is what the CMB maps are about. So the dark energy must be evenly spread. Your approach says everything would instead be remarkably patchy. That would be obvious too see.
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I typed in space bubble theory and got this:
https://en.wikipedia.org/wiki/Eternal_inflation
Although I don't see why a bubble would have to contain gas. It would not be hollow, just relative low density areas of space all collapsing to provide a uniform outward push (at least in a 2d reference frame).

Like this:
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You might also find this interesting. It talks about creating cavitation as a function of wavelength and (of course) frequency. It also talks about conservation of energy as it relates to cavitation size, although it does not address the density of the medium - or any changes therein. It also talks of power, which we would substitute for energy.

We know that when space began everything was tripping over itself to get out (high density) and as it broke free it became less dense.

And just now, typing expansion of bubbles (to see if I could simulate the push) gave me this.
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And just now, typing expansion of bubbles (to see if I could simulate the push) gave me this.

Hah. I wasn't going to mention that to avoid complicating things. But you realise that is a way to do without dark energy at all? So a patchy distribution of regular matter would leave under-dense regions that could expand faster.
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Yeah, the conclusion left me scratching my head.
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Actually, now that I re-read it, it seems to fall in line with what I said at the beginning - that mass would form in the gaps, don't you think? I don't see why both theories can't be right. The large low density space areas are dark energy. And looking at the pictures they're showing of the network of galaxies, it seems to match right up.
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This image of the galaxies is the missing ratio?
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Again, dark energy would be inherent in space - the quantum vacuum - itself. That is why it could create a basic tension or negative pressure that accelerates expansion. But it would also have to be everywhere evenly. Space couldn't be full of cosmic scale holes, could it?

But if you love bubbles, they appear in a variety of cosmological scenarios, like reheating - https://arxiv.org/abs/0707.0839

As a mechanism, it is not outlandish.
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It is inherent in space. The negative pressure is due to the shape, which is an antrgravitational shape. So imagine them as energy balls in space that you can only go over. It keeps pushing things around them like a forcefield. And I think it could create an accelerating expansion because the tangent on the collapsing bubble would move from vertical to the horizontal plane as it collapses, causing greater horizontal speed. Expansion would be uniform because all the sides are touching. Mass remains unaffected because it is in the ditches and doesn't expand (remember we talked about if you could create matter by bending space). The universe photo is the egg carton. I'll check out the link tomorrow. This is good fun.
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I just realised I may have not explained it adequately. It is inherent because the bubbles are 'in' space - it is the curvature of space. An outward rather than inward curvature. The negative pressure is because it is collapsing while the universe is expanding.
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If it is true, do you see the beauty of it? Mass is governed by entropy which wishes to bring gravity (ultimately) up to flat space by dissolving the energy out of matter. Dark energy also wants to flatten itself out in order to become flat space but in the reverse. Gravity flattens out of its well, dark energy flattens its mole hill. A process of ironing the kinks out.
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Dark energy also wants to flatten itself out in order to become flat space but in the reverse. Gravity flattens out of its well, dark energy flattens its mole hill.

But gravity wants to curve spacetime into a tight ball - a singularity. And dark energy is the opposite in wanting to curve spacetime hyperbolically - a constant bending away from itself. So we have a positive and negative curvature deal that balances out and leaves a flat Euclidean spacetime.

It is more complicated than that. But it is crucial that gravitating mass produces positive curvature (like a sphere surface) while dark energy is about negative curvature (like the surface of a saddle).
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But gravity wants to curve spacetime into a tight ball - a singularity. And dark energy is the opposite in wanting to curve spacetime hyperbolically - a constant bending away from itself.

At first glance it appears as if they have swapped places. If you took your analogy of the sphere and the saddle, that is just the same as the energy ball/egg of dark energy and the matter shape of the egg carton respectively. Because they are coming out in exactly the opposite places like this it suggests it is a problem of imagining or assigning the wrong an inverse property the attribute (so instead of using gravity you use antigravity for example). The basic shapes are correct though.

That gravity wants to curve space time into a tight ball is just saying it wants to increase the density of space around it. All force lines feed in (that is why it can also be visualised as a well). Dark Energy is exactly the opposite and wants to curve spacetime the other way - low density with the field lines moving out of it (a bubble). There is no conflict here I can see between what you say and what I say that cannot be solved by realising that we can describe an object in terms of its background or intrinsic volume (opposite but the same).

Entropy of course doesn't want space to curve into a tighter ball. It wants to free the energy locked in high density space and give energy that to low density space so that all space becomes nice and even. We know entropy bleeds energy out of matter. We know the curvature of space in terms of gravity is produced by mass. If mass is bleeding energy its gravitational field lowers. The gravity well rises toward the surface (the ball becomes less tight) because of the net effect of entropy.

Entropy would also be acting on dark energy, not to release energy but gain energy in terms of space density, which would be something we could look at and think about.

I am glad you said they balance each other, because I have been wanting them to form that relationship. They don't match each other spatially but in terms of net energy- note I say net energy. This is important to create a neat energy sine wave. ). Gravity is very tight, high density energy but of short duration (a deep narrow trough), while dark energy would be expanded low density energy over a much longer duration (a shallow wide bowl). But gravity and dark energy can share the same total energy value.

As the entropy does it's work the sine way flattens. When it has flatlined, it is game over and the flip of the wave from frequency 1 wavelength 0 to frequency 0 wavelength 1 is complete (but I don't think it ever will because I don't think this is a property a radiating sine wave can adopt - the eternal redshift we talked of earlier).

Is there something about it that still bothers you? It seems like a nice little energy symmetry.
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