# Physical laws for a matter-filled universe

The Setting:

I have an idea for a universe that, in an inversion to our own, is filled for the most part with matter in solid, liquid, gaseous or plasma form, while vacuum and degenerate matter is present but relatively rare as matter appears to be in our own universe.

This universe would contain many bubbles and tunnels of vacuum that would interpenetrate the matter, with less dense elements closer to vacuum than denser elements. Accumulation of matter would not for the most part lead to degenerate states, but degenerate matter may exist. Most of the matter present would be analogues of our elements, though variants may exist.

Matter may be stationary or moving relative to other matter, and matter whose centre of mass is not moving may or may not have spin.

This universe has four large spatial dimensions and two time dimensions, though the time dimensions behave as one for most purposes.

In adherence to the strong anthropic principle, this universe must be habitable by a species that is a four-dimensional analogue of humans.

EDIT:

I see this universe as being quite claustrophobic, with most of it being filled with solid and liquid matter, with twisting tunnels and bubbles containing gas, plasma and/or vacuum interpenetrating the volume the way stars are interspersed in the vacuum of our universe. These bubbles and tunnels would not remain static over time, but would move very slowly on a human timeframe.

Edit 2:

It is quite important that this universe be at least 95% filled with matter, of which at least 75% would be solid, the rest being in other states. It is also important that bubbles appear with at minimum the same approximate frequency as stars in our universe, or up to 100-fold greater frequency, and that the bubbles be connected by thinner tunnels, that should for the most part not be straight. Most of the bubbles and many of the tunnels should be supplied with some sort of light/heat source. A cyclical variation in illumination is also desirable, though this need not be constant.

The Question:

What set of physical laws could achieve this universe? These laws must be sufficient to simulate at least a section of the coarse structure and basic principles of this universe in a cellular automaton program, though they may be a simplified version - I'm not asking for the code or exact constants, just a basic description of how they could work.

In addition, to fill the requirements of the strong anthropic principle (this need not be simulatable), where does light and heat come from? How would day/night or light/dark cycles occur? How would the different elements occur, be synthesised and/or destroyed? How could 'earth'-quakes occur?

• Two time dimensions? There are some issues with that. It's possible, I suppose (see here, for example - some models allow that). – HDE 226868 Feb 26 '15 at 2:04
• The two time dimensions is similar to Itzhack Bars two-time dimensions, and is present to allow for time travel, for purposes of the universe it would act as if it had one time dimension. – Monty Wild Feb 26 '15 at 2:29
• Is the universe expanding, contracting or static? – HDE 226868 Feb 26 '15 at 3:52
• @HDE226868, it doesn't matter. It is probably static. – Monty Wild Feb 26 '15 at 4:00
• @MontyWild the Wikipedia page is technical. However Google also turns up Wave propagation: Odd is better, but three is best. Look at what happens (2D case) when you throw a stone in a pond: the pulse is not a single ridge and valley, but the area between the initial wave and the origin continues to ripple. – JDługosz Mar 24 '15 at 2:30

Let's build a universe.

To describe this universe, we need a metric. I won't go into details about the precise definition - for more, see Wikipedia, as well as Physics and Mathematics. In this case, we need a metric of dimension (4 + 2) (i.e. four dimensions of space and two of time). This will be represented in a 6-by-6 matrix: $$g=\begin{bmatrix} g_{t_1t_1} & 0 & 0 & 0 & 0 & 0 \\ 0 & g_{t_2t_2} & 0 & 0 & 0 & 0 \\ 0 & 0 & g_{rr} & 0 & 0 & 0 \\ 0 & 0 & 0 & g_{\theta\theta} & 0 & 0 \\ 0 & 0 & 0 & 0 & g_{\phi\phi} & 0 \\ 0 & 0 & 0 & 0 & 0 & g_{\varphi\varphi} \end{bmatrix}$$ This corresponds to a line element1 of $$ds^2 = - dt_1^2 - dt_2^2 + dr^2 + r^2 (d\theta^2+ \sin^2\theta (d\phi^2+\sin^2 \phi d\varphi^2))$$ using n-spherical coordinates and a metric signature of (-,-,+,+,+,+), which happens to be my personal preference. You can use (+,+,-,-,-,-), if you want.

That describes an empty, four-dimensional Riemannian manifold in 4-dimensional n-spherical coordinates. It's your universe. The problem is, there's nothing in it. For that, we turn to the Friedmann–Lemaître–Robertson–Walker (FLRW) metric.

One of the beautiful things about the FLRW metric is that it's an exact, homogenous, isotropic perfect fluid solution of the Einstein Field Equations that can be used for modeling universes. Another beautiful thing is that it's so simple, compared to some of the other wacky stuff that you can get out of the EFEs. A third beautiful thing is that the FLRW metric yields the Friedmann equations. But I'll get to that a bit later.

Thank you so much for saying that the two time dimensions can act as one. This simplifies things greatly, because it means that they behave identically. In other words, $g_{t_1t_1}$ is the same as $g_{t_2t_2}$. It's great.

Now the FLRW metric includes a scale factor, $a(t)$, which is a function of time and describes the expansion or contraction of the universe (or neither, if $a(t)=1$). The reason that it's good that the two time dimensions are the same is because if they weren't, I'd have to write the scale factor as $a(t_1,t_2)$. That's not great, because the Friedmann equations involve derivatives of $a(t)$. Partial derivatives would make things more complicated. Anyway, on to the Friedmann equations.

There are just two: $$\frac{\dot{a}^2+kc^2}{a^2}=\frac{8 \pi G \rho + \Lambda c^2}{3}$$ and $$\frac{\ddot{a}}{a}=-\frac{4 \pi G}{3} \left(\rho + \frac{3p}{c^2} \right) + \frac{\Lambda c^2}{3}$$ The meanings of the variables are given nicely on Wikipedia.

These two equations describe how the universe expands or contracts. They can tell us quite a lot about its behavior. If you want to make the universe interesting, do try it. But if you want a static universe, then $a=1$, and all derivatives are $0$.

The FLRW metric is a perfect fluid solution, which is quite handy here. Wikipedia again gives an interesting relation. Take a fluid with pressure $p$ and density $\rho$. The equation of state is $$p=w \rho c^2$$ We can then write $a(t)$ as (through an irrelevant derivation) $$a(t)=a_0 t^{\frac{2}{3(w+1)}}$$ So solve for $w$ above, and you can find your scale factor. This means, actually that your universe may be expanding or contracting. From here, we can calculate all sorts of cool things.

With a scale factor of $a \neq 1$, the FLRW metric is $$ds^2 = - dt_1^2 - dt_2^2 + a(t)(dr^2 + r^2 (d\theta^2+ (\sin^2\theta d\phi^2+\sin^2 \phi d\varphi^2)))$$ and, substituting in for $a(t)$, $$ds^2 = - dt_1^2 - dt_2^2 + a_0 t^{\frac{2}{3(w+1)}}(dr^2 + r^2 (d\theta^2+ (\sin^2\theta d\phi^2+\sin^2 \phi d\varphi^2)))$$ That's your universe.

We have to figure out a plausible way for the bubbles and tunnels to form. In our universe, gas clouds form because of gravity. Then stars form. Here, though, gravity would be trying to collapse the matter around the empty spaces.

You could go for something like Dan's "Harmonics", or you could treat the "vacuum" as another fluid. In fact, you have too, because you have to explain why the fluid around these pockets doesn't collapse. Here's an example.

Take a gas cloud. This cloud has a few quantities: temperature ($T$), pressure ($p$) and density ($\rho$), as well as maybe a few other non-vital characteristics.2 Changes in one will influence changes in the other two. To start with, though, these properties are constant.

Now, the cloud has pressure. This means that every bit of it pushes against regions of space nearby it. This, along with the other bits, means that unless gravity is strong enough to keep the cloud in hydrostatic equilibrium - or, in fact, to make it undergo gravitational collapse - the cloud may expand outwards.

In this case, the situation is that of a cavity inside a gas cloud. There's nothing to stop the gas from moving in, whereas there is pressure from the gas in the cloud. These openings will be crushed very quickly. So you need these bubbles to be more like a fluid that the absence of one.

Another thing to add is that the fluid in this universe should be more or less uniform. For example, in our universe, any bit of vacuum is, in general, much the same as any other bit of vacuum. Why should this be any different in this universe? What makes any bit of this fluid special when compared to any other bit? You need some processes to occur to destroy the local homogeneity and isotropy of the fluid. On large scales, though, these properties can not be violated - otherwise the conditions for the FLRW metric are not met.

I'd like to go on with a discussion of a passage from Wikipedia:

In 1920, Paul Ehrenfest showed that if there is only one time dimension and greater than three spatial dimensions, the orbit of a planet about its Sun cannot remain stable. The same is true of a star's orbit around the center of its galaxy. Ehrenfest also showed that if there are an even number of spatial dimensions, then the different parts of a wave impulse will travel at different speeds. If there are 5 + 2k spatial dimensions, where k is a whole number, then wave impulses become distorted. In 1922, Hermann Weyl showed that Maxwell's theory of electromagnetism works only with three dimensions of space and one of time. Finally, Tangherlini showed in 1963 that when there are more than three spatial dimensions, electron orbitals around nuclei cannot be stable; electrons would either fall into the nucleus or disperse.

Max Tegmark expands on the preceding argument in the following anthropic manner. If T differs from 1, the behavior of physical systems could not be predicted reliably from knowledge of the relevant partial differential equations. In such a universe, intelligent life capable of manipulating technology could not emerge. Moreover, if T > 1, Tegmark maintains that protons and electrons would be unstable and could decay into particles having greater mass than themselves (This is not a problem if the particles have a sufficiently low temperature).

Translation:

Ehrenfest's work has one huge consequence: orbital mechanics are not fun. Stable orbits are out the window. This means no planetary systems whatsoever - and given the nebular hypothesis, this means that it would be tough for planets to even form! So scratch and life like we know it - although I take it you already expected that. Your description is of something wildly different from our universe - extremely chaotic. I think you expected that.

Weyl's work (available here, if you're willing to trudge through it, which I'm currently not) chucks electromagnetism as we know it out the window. I have yet to find the relevant section, so it's unclear if electromagnetism cannot exist in any form or whether Maxwell's formulation is merely inadequate. Let's just not expect anything special.

Tegmark's work may be the most relevant (though I'm skeptical of some of his other work - I won't take that against him). If he's correct, then your two time dimensions must behave exactly as one. Or you can change up your elementary particles. Otherwise, no stable atoms. This answers the "How would the different elements occur, be synthesised and/or destroyed?" bit. They wouldn't. Add to that the bit about Tangherlini - whose work I'm not familiar with - and you can kiss elements goodbye.

On to what your universe will actually be like.

I'll start at the smallest scale: elementary particles.

If Tegmark is right, electrons and protons (and therefore, most likely, quarks) must go out the window. The same goes for the electron's heavier cousins, the muon and the tau. Quarks take away all the baryons (composite particles made up of quarks), leaving us with neutrinos. I don't know if those, too, may not exist. If so, their interactions would be very dull! Neutrinos seldom interact with anything.

We could come up with a whole new set of elementary particles, or we could use a little loophole. See, according to the Freidmann equations (and their variants), if $a(t) \propto t^{2/3}$, then the universe is dominated by matter. If $a(t) \propto t^{1/2}$, then the universe is dominated by radiation.

Hearken back to the work around $p=w \rho c^2$, and the later derivation. In that, the scale factor is $$a(t)=a_0 t^{\frac{2}{3(w+1)}}=a_0 t^{\frac{2}{3w+3}}$$ For the universe to be radiation dominated, the thing that $t$ is raised to must be proportional to $1/2$. An easy way of doing this is to set $w$ to $1/3$. We then find that $t$ is, in fact, raised to the power of $1/2$, and so our universe is radiation dominated.3

Note that our universe entered a stage like this very early in its history. Its primary constituents? Photons and neutrinos. Sounds a bit like ours. The cool thing? When our universe was about 378,000 years old, it underwent recombination. Up until that point, it was filled with an opaque (to light) plasma. That was when the CMB was formed.

At this point, it's looking a lot like our universe in its earliest days.

On to some of your specific points.

What set of physical laws could achieve this universe?

You can set virtually any laws you want. For example, the equation of state used above doesn't have to be accurate. Maybe there's another constant shoved in there. Maybe general relativity doesn't work, and so the FLRW metric doesn't accurately describe the universe. Take your pick. You can create new constants for this universe, and by doing so create new laws and interactions. The number of dimensions doesn't matter.

You do have to be careful about making sure that the laws lead to the desired scenario. For example, if you were to introduce a force that pushes matter away - sort of like anti-gravity - then your scenario doesn't make sense. Everything is trying to get away from everything else. All of a sudden, pressure skyrockets, and things start to get weird. Weirder than you intended, that is.

If you end up coming up with some basic laws, then I can get back to you on what else would happen.

In addition, to fill the requirements of the strong anthropic principle (this need not be simulatable), where does light and heat come from?

I don't know about you, but I would not want to live here. Life as we know it could not survive here. Photons and neutrinos (well, their equivalents in this universe) aren't the best food.

Fortunately, you didn't ask about life; you asked about light and heat. Those are easier. The universe is filled with radiation, although if it hasn't undergone recombination, it may be opaque to photons. But it's quite possible that, in some places, photons can flow freely, spreading heat with them. Shine light on anything and it will heat up, and vice versa.

Not a very hospitable place, I'll grant you.

How would day/night or light/dark cycles occur?

You need to figure out just how the heck you have a planetary system form. Before, I discussed how that would not be possible. Maybe an isolated ball of rock could form. But that would be difficult. It would have a nice sky, though. Maybe reminiscent of Dave Bowman's journey in 2001: A Space Odyssey.

Same goes for

How could 'earth'-quakes occur?

You can't have earthquakes without Earth.

How would the different elements occur, be synthesised and/or destroyed?

I'll end on a positive note, because, as usual, it seems I've inadvertently written a pessimistic answer. Damn. I'll add to it by recalling the work of Tangherlini, which says that elements will not form. Shoot.

But here's the positive note: You can create elementary particles that circumvent that (somehow). Science can be a real pain in the neck sometimes, but you have to remember that you are always in control. In a world like this, you can create whatever you want. Remember the metric? That gives one description of the universe. One. And look at all the variables that can change. I barely used any actual numbers in this answer. They're there for you to fill in.

Create your own laws. Your own particles. Your own universe. And you've got a universe that I'd be happy to live in, because it came from unbounded imagination. That's pretty awesome.

1 For more information on this particular line element, see Wolfram Math World.
2 We can, by the way, related these properties via the ideal gas law, $PV=nRT$. You just need to derive density from the law.
3 And so $p= \frac{1}{3} \rho c^2$.

# Second Try

I apologize for the potentially confusing second answer, but at the moment, my original one is rather long-winded, and I'd like to go in a whole new direction from it. To avoid confusion, I'll start anew. If people want, I can delete this and merge it1 into the other answer, but for simplicity and readability I'd like to give it its own section

Correct me if I'm wrong, but it seems that you want a set of rules that, if given at the very start, could predict how your universe would evolve, both on large and small scales (though perhaps more on small scales). In other words, a deterministic universe that could be simulated on a computer (I'm not suggesting a relation to any of the questions).

Properties

Matter has to have some properties that dictate how it interacts with other bits of matter. Not all bits of matter are influenced by the same things: For example, in our universe, some particles have electric charge while others do not. Yet we can still describe them in terms of electric charge: $q=0$. So I'll say that these properties - represented as variables, though some are variables and some are constants for a given particle - can apply across-the-board.

• Gravitational mass, $m$: This is a universe where active and passive gravitational mass are the same, though inertial mass may not be.
• Inertial mass, $m_i$: I'd like to keep this equivalent to gravitational mass, but it may not be the case. The choice is yours.
• Position, coordinate system of your choice: I'd use spherical (hyperspherical, in this case) coordinates globally, as I discussed in my original answer, but you can use $x,y,z$-coordinates in any scenario, if you want. It's simple for discussing two-dimensional interactions.
• Speed/velocity, $v$: Particles can move; therefore, they have a velocity. From this and mass we can say that they have momentum ($p$) and kinetic energy ($KE$). Higher time derivatives also exist (the two time dimensions behave as one), so particles also have acceleration ($\dot{v}=a$), jerk ($\dot{a}=j$), etc.
• Temperature, $T$: Particles can vibrate; therefore, they have a temperature.

Properties not in our universe2:

• Ikimgiir charge, $i$: A property describing how likely a particle is to interact with other particles via the ikimgiir force, as described later. Ikimgiir charge ranges from $0$ to $1$.
• Kaaziikkhaaku, $k$: A property describing how a particle may attach to another particle of the same type and form a composite particle, as described later.

There are also other properties (pressure, density, etc.) that can be derived on large scales. In fact, velocity and high time derivatives of position are really also derived quantities.

Forces:

• Gravity: Gravity works the same here as in our universe, and can be described by general relativity (albeit by a 4 + 2 metric). It's simpler, though, to use a classical approximation on smaller scales. So our law here is $$F=G\frac{M_1m_2}{r^3}$$ with $G$ being any value you choose. It falls off with $r^2$ and not $r^2$ because of a generalization of the inverse-square law to higher dimensions.
• Ikimgiir: Ikimgiir describes the process of forming those cavities you mentioned. I said that the charge ranges from $0$ to $1$. That's because it's similar to a probabilistic measure. The charge is measured across all particles as a normal distribution: There are fewer particles with low ikimgiir charges and fewer particles with higher ikimggir charges. This distribution, though, can vary across types of particles. For example, particle type A might have a different distribution than particle type B. So in reality, the distribution does not range from $0$ to $1$, but from some number $k$ to $-k$, where $k<0$. The area under the curve is $1$.

A generalized distribution is $$f(x, \mu, \sigma) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x- \mu)^2}{2 \sigma ^2}}$$ $\sigma$ and $\mu$ can vary between particle type, though there is no continuous function connecting them. They exist in discrete types of your choosing.

The force from ikimgiir is probabilistic3, too, and it depends on a variable called $z$. You see, each particle has a different $z$ that it has its entire span of existence that is independent of $f$. The latter is a probabilistic distribution of the strength of the interaction whenever it happens; the former is a probabilistic distribution of when it will happen.

We describe $z$ using a cumulative distribution function, where $x \to t$ and the graph is renewed whenever a particle exerts the ikimgiir force. This function describes how likely it is that such an event has happened since the last time the particle exerted such a force (or since its creation), starting from $t=0$. Therefore, the probability at $t=0$ is, for a given particle, 50%.

So the ikimgiir force can be described in terms of $i$, $f$ and $z$ But we still need to describe its effects on other particles. When a particle exerts an ikimgiir force, it creates a spherical cavity. The size of this cavity is governed by a number, $a$, and $f$. $a$ is a universal constant, and represents the maximum size of the cavity (in the case of $f=1$). The radius of the cavity is $f \cdot a$. The final volume of the cavity is the volume of a 4-dimensional ball4.

The ikimgiir force acts on particles only when the cavity is expanding, and only on particles on the edge of the cavity. For particles at an instantaneous distance from the center of the cavity, $r_{inst}$, the force is $$F_I=\frac{i}{r_{inst}^3}$$ where $i$ is the charge of the particle causing the cavitation. This is an inverse-cube law. Particles not on the cavity edge do not feel this force, but they are pushed away by particles touching the cavity.

Kaaziikkhaaku

This isn't a force, but a property. It describes how likely a particle is to combine with another particle (of the same time) and form a composite particle. $k$ is the same for all particles of a given type, and is just a probability (e.g. 50%, 78%, etc.). Kaaziikkhaaku only applies when two particle are within a certain distance of each other.

1 . . . which is what I have just done.
2 Names taken from a random syllable generator here.
3 Okay, so we've sacrificed a bit of determinism here.
4 I say "ball" and not "sphere" because in mathematics, "sphere" actually refers to the dimension of the outside boundary of what we would normally call a sphere. For example, the boundary of a baseball is a 2-sphere.

• ^ What he said. – Serban Tanasa Feb 27 '15 at 2:43
• By the way, bravo to anyone who struggles through all of this. @SerbanTanasa - Thanks. – HDE 226868 Feb 27 '15 at 2:43
• Yeah, I considered tackling this, glanced at what would be the multiple time dimensions equations, died inside a little, and decided to leave it to braver souls! – Serban Tanasa Feb 27 '15 at 2:49
• @SerbanTanasa It's very easy if you just treat them as one. I don't think the Friedmann equations would have held in multiple time dimensions, like I said; it's a lot easier to treat them as one. – HDE 226868 Feb 27 '15 at 2:50
• @HDE226868, this is a great answer, but rather lower level than I was looking for. I'm presupposing that there is matter, and looking for a set of rules that would organise that matter as I described. I had also considered having positive eigenvalues for time as in Greg Egan's Orthogonal universe gregegan.customer.netspace.net.au/ORTHOGONAL/ORTHOGONAL.html – Monty Wild Feb 28 '15 at 2:18

Ok. So I'm going to use a shortcut here and use most of our physics, making only minor changes that I think could result in what you want. I'm also going to ignore most of the required 4D differences with the power of handwavium since I don't think I'm up to designing a universe from scratch.

So other than the new dimensions, this universe only has three major differences from ours in terms of physics:

1. Gravity does not exist as a function of matter - it doesn't distort spacetime.
2. The universe is static in size and is not expanding. It does not have borders and is instead self-circular (go far enough in one direction and you end up back where you started).
3. A new force, Harmonics, exists.

Harmonics is a force similar to gravity, but instead of being caused by matter it's a fundamental aspect of spacetime. Think of it as harmonic waves of spacetime distortion throughout the universe. Each spatial dimension has a different harmonic frequency, but they are related (for example, a 1:2:3:4 ratio). These waves create patterns of reinforcement and interference, so some areas end up strong, while some are canceled out and don't have any real "gravity". Additionally, harmonic also functions in both time dimensions, but with much-reduced values. This gives you something similar to "orbits" and keeps, for example, your planets from being a constant distance from their suns.

This gives you stars (lots of distortion), vacuum, (areas surrounded by strong distortions), and smaller objects (some distortion), and extremely rarely black holes/neutron stars (extreme distortion). Areas with the right mix in each direction end up pulling/pushing so that nothing ever ends up collecting, so you end up with your giant gas clouds throughout the universe. Habitable planets are those that collect in the habitable frequencies of their parent star, but they don't orbit the star - instead they will "shuffle" back and forth in place (as will the star) in accordance with the time-dimension harmonics.

In the beginning, this universe will be extremely patterned and consistent. However, collections of stars will be slightly smaller or larger, and once those undergo enough fusion and you start seeing supernovae, the impact from those will disturb other stars and start messing things up. By the time your lifeforms exist it will be a mess, but still much more consistent than our universe.

• I had in mind something much more claustrophobic. Have a look at my edited question. – Monty Wild Feb 26 '15 at 3:12
• Ah. Yeah I went with this way because it gives light, heat, and elements (through star fusion), but lets you mix things up more because gravity is more constant. The problem is stars are pretty fundamental to our universe, I'll have to think about ways to get a real inversion. – Dan Smolinske Feb 26 '15 at 3:16

I'm adding this as a separate answer because it takes an entirely new approach.

I've thought of two new possibilities that might offer something closer to the question's current direction. I'm not sure how plausible either is if you dig down into the gritty details, but I think they'll work for your purposes.

## The Universe Star

Imagine a universe nearly the same as our own, but with two distinct differences:

1. The gravitational constant is either weaker or drops off at a higher coefficient (so r^3, r^4, etc... instead of r^2). I'm unsure which would work better, but I'm leaning toward the higher coefficient as a side-effect of having extra space and time dimensions.
2. The big bang had almost no kinetic component.

Then there is simply a giant ball of hydrogen. Instead of expanding, it will say in one place and start to coalesce. Eventually, the entire universe will be a single, mind-boggling vast star.

Over billions of years, this star will go through the normal phases we see in our universe, and will start fusing elements. However, due to luck, gravity is low enough that it will never explode and go nova. Instead, the heavy elements will start forming near the center and will continue to accrete. Eventually, our star will have a giant core of rock - let's say roughly the size of our galaxy - composed almost entirely of various higher elements.

Due to variations, heat, and chemical and nuclear reactions, this rock will not be uniform. Pockets of elements will form and move around, and due to heat, you'll get variations of gases and liquids as well. Since gravity is lower, the rock is self-supporting and is able to withstand its own weight (this is possible in our universe too, but requires extremely light and strong materials). Heat will radiate inwards from the outer edge where fusion is still occurring, and from massive nuclear and chemical reactions.

For light, your sapients will likely need to use infrared mostly, rather than visible light. Alternatively, they could probably use other radiation frequencies - radar, or microwave - or operate entirely off of acoustics.

## The Big Pop

This uses the same constraints from the Universe Star (lower gravity and no kinetic component to the big bang) but adds one additional change: instead of forming as elemental hydrogen, the entire universe "pops" into place as a single, giant rock composed of various higher elements.

Because many of these elements are unstable, they will decay, react to each other and create heat and radiation. This will set off other elements, creating nuclear reactions throughout the entire universe.

For billions of years, these reactions and decays will continue. This will cause it to expand somewhat, allowing it to cool eventually to the point where life is possible.

At this point, you will have a rock with a size on the order of galaxies, composed of various elements. Most will be higher, but you will get pockets of lower element gases and liquids. Life will form in these, living off of chemical reactions and leftover nuclear heat and radiation.

Tunnels and Pockets

This applies to both of the above answers. There will be large (solar-system sized) regions of relatively stable rock. These rocks will border other rocks and will move semi-independently. Think plate tectonics, but with galaxies. The border between these will be mostly compressed together, but the movement and grinding will create gaps that your sapients can exploit. These gaps will be what tends to fill with useful elements, gases, liquids, and life.

• You're right; gravity drops off with different powers of $r$. – HDE 226868 Mar 24 '15 at 15:41
• @HDE226868: I suspect that with r^3 you might need a lower gravitational constant, although really I'm not sure how reasonable either of these is, so it might be handwavium either way. I suspect there's either an extremely fine or non-existent line between "livable" and "would explode"... – Dan Smolinske Mar 24 '15 at 15:52

My own take on this is that the universe starts out pretty much empty. We then apply the following rules:

1. Vacuum randomly and spontaneously generates elementary particles that can combine to form atoms, though the presence of matter suppresses this.

2. Vacuum repels matter. Matter does not attract other matter, instead suppressing the vacuum repulsion (though not perfectly) if there is sufficient matter present.

With the universe filling with matter, and matter trying to move away from vacuum, matter would be pushed together into clumps. As matter accumulated, the vacuum would form bubbles, with lighter elements around the perimeter and heavier elements .

1. Matter impacting other matter at sufficient velocity can cause nuclear fusion.

The matter spontaneously generated in a vacuum will be accelerated toward the nearest clump of matter. The velocities involved can result in atomic fusion and the synthesis of heavier elements.

At this point, we have a universe that will simply fill up with matter that will gradually transmute to heavier elements, with a few bubble-like voids.

1. A novanoid (appearing as a regular pentachoron with negative mass) may be spontaneously generated in any volume regardless of the presence of matter that is sufficiently far from any other novanoid, and there is a small chance, increasing as a novanoid approaches another novanoid, that the novanoids will be destroyed.

2. Matter is repelled from a novanoid with greater force than matter is repelled from vacuum, and the repulsiveness of vacuum and novanoids is cumulative.

3. Novanoids generate Kizerain, Eskaxis, Qiameth, Surogou and Nekmit charges (abbreviated to K, E, Q, S and N respectively), each at a separate rate unique to the novanoid.

4. When sufficient K, E, Q, S or N charge has accumulated at a novanoid, it will discharge following the path of least resistance to a corresponding pentachoron vertex on the same or another novanoid, given that charge has significant momentum and is ejected regular to the pentachoron vertex. Correspondences are: K -> E -> Q -> S -> N -> K. Discharge is not instantaneous, and takes 1/3 to 2/3 of the charge time for that charge to accumulate, though discharge rate is also constant to the novanoid. The orientation of the charge-emitting vertices of a novanoid is random at its generation and is otherwise invariant.

5. The K, Q, and N charges emit black-body radiation at a temperature inversely proportional to the distance they must travel to their discharge points (hotter when distances are shorter), and E and S charges emit black-body radiation at a temperature proportional to the distance they must travel to their discharge points (hotter when distances are longer). This ranges from 0K at 0/infinite range to approximately 25000K. As this is 4D-space, light intensity falls off following the inverse-cube law.

6. K and Q -charge will fully ionise and repel any matter in contact with it. E and S charge will attract and fuse matter that it passes through, generating heavier elements. N-charge cools matter, matter having having a negative temperature with respect to N-charge, and N-charge will pass through matter leaving it undisturbed other than being cooled.

7. Charge-Light passes through an additional small dimension, and can therefore pass through matter, though reflected light passes through normal space.

8. K and E -charges travel in spirals (left and right-handed respectively) around the path of least resistance, the width of the spiral inversely proportional to the distance between source and sink. The other charges travel directly along the path of least resistance.

The novanoids and the charge that they emit will enhance some of the vacuum bubbles, and will generate spiralling or straight(ish) tunnels, as well as creating heavier elements. As novanoids are not entirely static, their bubbles and tunnels will move along with them. The discharges will generate light on a cyclical basis, forming the basis for day/night cycles. As novanoids appear and disappear, new bubbles and tunnels may form, and old tunnels and bubbles may fill or collapse. Movement of novanoids and their associated charge-tunnels occurs at a rate approximating that of continental drift, and their lifespans approximate that of geological ages to planetary lifetimes.

1. The universe is expanding slowly. As it expands, the expansion places tensional stress on the solid matter matrix between the voids, and at irregular intervals, the matter matrix will rupture, relieving the stress, initially producing vacuum-filled voids between previously-adjoining volumes, providing new sites for vacuum-matter genesis. The recoil shock of matter-matrix ruptures would be experienced as earthquakes.

So, we have a universe that is mostly solid matter, interpenetrated by a multitude of twisting tunnels, and illuminated periodically by vast charge-arcs that slowly change the shape of the tunnels. I anticipate that the diameters of the bubbles would be on the order of stars' diameters, and the diameters of tunnels would be on the order of planets'.

Some sections of the matter matrix may rotate due to the influence of vacuum and novanoid repulsion, along with the influence of charges, to cause moving particles to impact a volume of matter and transfer their momentum in an asymmetrical fashion. This may form solid, rotating balls, or they may be interpenetrated by charge-caused tunnels and/or vacuum bubbles.

You can get the opposite universe effect but not use chemical element matter as we know it. The universe can be filled with stuff that can vary from place to place, and has effects that act as a medium for other things whether dissolved other stuff, changes to properties or energy that can propogate as waves. The properties of the media are observed as differences to the things that inhabit it; perhaps different things are selective in which mediums they can pass through or move into without disrupting their state of being. But a void would be a hard boundry that nothing can pass through, and the geometry can be mapped out by feeling around the edges.

What would it be like if our universe was like that? We have fields and particles that populate the vacuum, but the vacuum has properties. If space was a substance and you got to a region where it was different, the laws of motion and chemestry would change.

Imagine tiny particles that move inside a crystal, and the atoms of the matrix control how they cluster and interact with each other. That is easy tomunderstand, though I think having energy in the form of state changes and dynamics is better, and the phenomena can only exist within the context of the medium, like sound waves or crystal dislocations or semiconductor "holes".