Will the Universe Inevitably Contract?

In Could the Universe have Created Itself?, I commented that to the effect that the universe, or at least the part of the universe that matters, will inevitably contract.  This sounds like a big claim given that there are cosmologists out there arguing for at least four different end states of the universe: Big Freeze (the universal destiny previously known as heat death), Big Crunch, Big Rip and Big Slurp (which is a rather ridiculous term referring to a catastrophic vacuum metastability event, but I guess it’s in keeping with the other terms).  Note that the Big Bounce is just a cycling of Big Bangs and Big Crunches, so each instance of the universe would end in a Big Crunch.

I’m not arguing for a Big Crunch per se, but rather a combination of the Big Crunch and the Big Freeze (and maybe even aspects of the Big Rip, but I don’t think so).  We could call it the Big Hole because it would be one black hole in an otherwise empty, eternal universe.

So, why is this inevitable?

First, I need to clarify my assumptions.  I’m working with my model of the universe, which is expanding with time (at the speed of light) in which the expansion is retarded by concentrations of mass-energy (and this manifests as gravity).  We know that the universe isn’t expanding evenly because if it did, then we wouldn’t have noticed it happening.  What we do notice is that the gaps with next to no mass-energy in them (between galaxies) are expanding more than the regions with higher concentrations of mass-energy.  I’m also assuming that this recession is not the only form of motion in the universe – for example, despite being some distance away, the Andromeda galaxy is not receding from us but is rather approaching us at high speed.  There’s some recession going on for sure, but galaxies also have motion on space as well.  Some galaxies are in orbit around other galaxies, such as the Large Magellanic Cloud which is a satellite galaxy of the Milky Way.

Imagine a circle on which there are evenly spaced points and then expand that circle:

Then imagine instead a circle on which two points are marginally closer to each other, and that the closer two points are, the less the distance between them increases (note that I have amplified the effect here by not modifying any of the blue points, focussing instead on only the green and orange points):

Then imagine that the points are all moving around, even if only a little.  Eventually, you’ll get clumping.  It might take a very long time, but in what I am modelling, we have (future) eternity to work with.  Eventually, everything in the universe will be clumped together, and eventually that will all be compressed into a(n in-universe) black hole.

I agree that, if the universe was simply expanding, then everything would end up just receding away from everything else and we’d end up with either a Big Freeze or a Big Rip.  But the universe is not simply expanding – there’s something about concentrations of mass-energy that makes the expansion uneven.

It’s possible that what I have described here is pretty much a Big Crunch, but I don’t envisage a scrunching up of all spacetime in the black hole, or into a singularity, just the mass-energy.  I lean instead towards a final equilibrium state with just enough space to maintain the appropriate density for whatever mass the black hole ends up with (the original mass-energy, plus whatever additional energy, if any, was added via quantum processes during the “life” of the universe).

Could the Universe have Created Itself?

Skydive Phil has a new Before the Big Bang episode out, “Can the Universe Create Itself?”  In The Boundary Proposal and i-Time, before having seen the video, I suggested that the answer would be no.  Now, after having seen it, my answer remains a steadfast no.  Note that I have changed the tense in the title of this article, effectively making it a different question, but the answer to both questions is no.

I think that the star of the video, Gott (amusingly the German word for “god”, noting that all nouns in German are capitalised), was addressing a different question: could the universe have emerged from a closed timelike curve? or, could a universe which is temporally unbounded have a beginning in the finite past?  The answer to both of these, according to Gott, is yes.

My issue, however, is that all the clever folding of space (and balancing of different types of vacuums to result in zero energy and zero pressure) doesn’t provide you with an escape from the problem of (infinite) regress in which you keep going back to an initial state and ask how that “initial” state got there – at which point you admit to a new “initial” state.  Even if there was a primordial closed timelike loop out which our universe sprung (somehow resulting in the hot dense, pre-Big Bang state), you can ask how that closed timelike loop got there.  And was (is?) the medium in which that closed timelike loop existed (exists?)?  Clearly it’s not “in space”, but it would be a loop of something, presumably, “in” something.

I agree that, given the assumption of an initial closed timelike loop, we could have a universe that just happens due to a quantum fluctuation but I don’t think we really have an argument here against a theist (the believer in a different kind of Gott) who might argue for a quantum engineering version of the Creator, one that carefully sculpts a very specific closed timelike loop – from nothing and in nothing – out of which the pre-determined universe springs entirely in accordance with some divinely inscrutable plan.

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I have a somewhat different view on cosmogony, the origins of the universe.  As I described in The Boundary Proposal and i-Time, I see this universe as being inside a black hole.  I also see the universe that is “outside” (and in a sense “outwhen”) our black hole as also being inside a black hole, although I don’t have the same level of evidence to support that notion – I am just assuming the consistency of relativity (some of the initial conditions would be not need to be consistent across universes).  And so on, each universe is encapsulated in a black hole nestled in the next universe up.  (I say “up” because a black hole is a gravity well and you go down into wells.)

Although this universe (and all universes in this chain) may be future eternal, we can nevertheless consider them as being a sequence of expansion-contraction phases (ECPs) – because the part that matters, the mass-energy will inevitably contract even if the empty space around it expands forever.

My concept is that it is possible, if unlikely, under quantum physics for things to wobble into existence.  Not things like Boltzmann brains, which are far too complex to actually eventuate, but tiny amounts of mass-energy.  Even if only miniscule amounts of mass-energy eventuate in each link of the universal chain, the chain is not limited as far as the number of links (the ECPs) so eventually, you will end up with a universe as large as ours.

I have no idea how much mass-energy could come into existence via quantum mechanical processes in each universe, but if we limit it to, for example, one joule per ECP, then to arrive at a universe our size would take 10⁷⁰ ECPs.  This is a lot of iterations and it becomes less surprising that, eventually, a species such as ours should eventuate.  It could be that less mass-energy is added each time, perhaps the least amount of energy possible at the time it comes into existence - which today would be c.h/(width of the universe) and that is a pretty small amount of energy.

Now this idea can be applied to another problem – if only very small amounts of energy are added each time, how could it be that the first black hole formed?  If there was only a tiny bit of energy at first it would not be enough to form a black hole, because you need at least a Planck mass in a Planck volume (which is notionally the smallest volume).  However, if the lowest amount of mass-energy that can be added by quantum mechanics to a universe is defined by c.h/(width of the universe) then, when the universe is as small as it can be, at Planck volume, the width is one unit of Planck length and in that case the lowest possible amount of energy is precisely one unit of Planck energy, precisely what you need for your first black hole.  This first black hole would commence the ECP process, which is initially instantaneous (actually one unit of Planck time), until there is another quantum mechanical event that adds another minimum amount of energy.  So the number of ECPs between us and that first quantum mechanical event could be, well … astronomical.  Beyond astronomical.

In my model, the universe does not create itself, but its beginnings are extremely humble, it is equivalent to a multiverse – but at least partially sequential (I have no issue with each individual black hole spawning their own chain of future eternal universes, prior to be being subsumed in the final universal black hole) – and it gives support to the idea that a universe as suitable for life as ours could indeed arise merely by chance, even if “fine tuning” for it were necessary.

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I did mention above that the universe, or at least the part of it that matters, will inevitably contract.  This sounds like it might be a big claim, so I will try to address that another day.

The No Boundary Proposal and i-Time

Skydive Phil and co recently released a couple of new videos in their Before the Big Bang series.  They have upped their tempo a little, with two episodes being released in less than four months.

I’ve not yet had time to look at “BtBB6: Can the Universe Create Itself?” (to which the answer would initially seem to be no, but I’ll reserve further comment until I’ve watched it).  I have, however, enjoyed “BtBB5: The No Boundary Proposal” and I must congratulate Phil on getting such luminaries together – including Stephen Hawking.

I do have a vested interest though, or two.

The first is that the model aligns very closely with something that I’ve pondered myself, which I’ll go into in a moment.  The second is that the No Boundary (or Hawking-Hartle) Proposal rips a hole in two of WLC’s favourite arguments, namely the one when he trundles out the BGV theorem and uses it to argue for his god and the one where he argues that the universe is contingent (while excluding necessity as underlying the beginning of the universe).

I’ll simply throw that out there and encourage the reader to watch the video.  Just keep in mind that if there is no conceptual issue with a natural universe that is not past eternal, then the BGV argument is short circuited and that if a natural universe can be necessary by virtue of physics, then the argument from contingency fails.  Or, at the very least, WLC and his ilk are constrained to a form of argument from incredulity (and/or from personal ignorance).

Now, the physics of the No Boundary Proposal.  I will say up front that I never considered an initial 4-space (ie a four-dimensional manifold) somehow transforming into a 3-space plus time, but I certainly have considered i-time.  Let me start from somewhere close to the beginning, or perhaps a long way before the beginning.  Bear with me if it seems like I am taking a weird detour.

One of the characteristics of a black hole is its density.  Density is simply the mass of something divided by its volume, so a very heavy (or, more correctly, very massive) thing in a small volume has high density, and something with mass spread out over a large volume has low density.  Lead is dense, air is not.

We tend to think of stars as very dense, and they certainly have a dense core, while black holes are thought of as either collapsed stars or, in the case of a supermassive black hole, many stars crushed together so tightly that nothing emerges from them – not even light.  So you'd be forgiven for thinking that black holes are very dense.  Not so fast ...

A star has a fuzzy boundary, so the answer to how dense it is is not as simple as with something more distinct like, say, a lump of granite.  Our sun has a core with a density in the order of 150 g/cm³ (liquid water is about 1 kg/litre, or 1 g/cm³) but if you measure from the “surface” of the sun, the photosphere, the average density is only 1.4 g/cm³ which is one quarter the density of the Earth at 5.51 g/cm³.  But at the photosphere, the sun has a density of 0.0000002 g/cm³ compared to the density of the atmosphere at sea level of 0.001225 g/cm³.  Only above 60km above sea level do you start to see atmospheric density in the order of the density of the sun at its "surface" (and then there's another 40km further to go until you are officially in space).

The sun doesn't really stop at the photosphere though, because there is also the corona, which extends out millions of kilometres from the sun (and is actually hotter than the "surface" of sun, up to 450 times hotter).  Note that the radius of the sun is a little under 700,000km, so the corona covers a much greater volume.  Then there is also the area in which solar wind is a factor, which could be argued as being the heliosheath and is sort of equivalent to the atmosphere of a planet (it's a "protective" bubble against the interstellar medium).  This heliosheath extends far out beyond Pluto or about 120 au (astronomical units, so 120 times further out than Earth).

Unlike a star, a black hole has a very well-defined boundary, known as the event horizon which itself can be defined by the Schwarzschild radius or the distance from the centre of the mass of a (non-rotating, spherically symmetric) black hole at which a photon can only just escape (because the escape velocity is the speed of light).  The Schwarzschild radius is directly proportional to the mass (M*2G/c²).  The volume defined by a radius is, however, proportional to the inverse of the radius cubed (4/3.π/r³).  The upshot is that the density of black hole is proportional to the inverse square of the mass – as the mass increases, the density of the black hole goes down (proportional to the square of the increase of the mass).

If you plug in the mass of the universe into the equation (3c⁶/(32G³.M²), you get a density in the order of the density of the universe – implying that we may be in a black hole.

(Note: if the black hole in question is rotating or not spherically symmetric, the argument that we are inside a black hole only improves.)

If we are indeed inside a black hole, the question then arises as to what is outside the black hole.

Let’s leave that question aside for a moment and consider instead what happens to time as you approach the Schwarzschild radius (or event horizon) of a black hole.  The equation for this is given by t_o = t_f.√(1-r_s/r) which basically tells us that, as your distance from the centre of the black hole (r) approaches the Schwarzschild radius (r_s), the time you experience (t_o) decreases as compared to that of a distant observer (t_f) – or time slows down as you approach the event horizon.  This is a phenomenon referred to in the movie Interstellar where travellers deep in the gravity well of a very heavy (massive) planet left their buddy up in space alone for ages while they only experienced a relatively short time on the (liquid) surface.

But this is all about what happens outside the black hole, on the “safe” side of the event horizon at r_s.  If you look at that equation again, you’ll see that something funky happens with time when r < r_s.  You get the square root of a negative number, which is imaginary time, or i-time.  Inside a black hole, time shoots off orthogonally from time outside the black hole, and it does so with no limit because as r->0, r_s/r->infinity (and (1-r_s/r)-> negative infinity and √(1-r_s/r)->i-infinity).

There’s a spatial effect as well.  Compared to a distant observer, rulers in a gravitational well (as in close to a black hole) shrink and once, inside past event horizon, they expand out into i-space.  In other words, within a black hole, there is effectively infinite space and infinite time, but it’s all orthogonal to what is outside.

Now consider the view from inside a black hole.  The entire history of the universe outside will effectively happen instantaneously at t=0, everything that is ever sucked into the black hole will appear instantaneously, having been ripped apart by the transition through the event horizon, with no information remaining in it. There will, be at t=0, basically no space (there’s a limit to how little space there is due to how much mass-energy can fit into it) but as space expands out (orthogonally to space outside the black hole) you basically end up with a Big Bang.  There is a natural correlation between a t=0 and a severely limited amount of space, there’s also a natural arrow of time, and a natural expansion.

So that’s basically how I think of the Big Bang, with each universe eventually (after an eternity) ending up ripped apart inside a new black hole which has a new Big Bang and the routine keeps going, with multiple eternities (and maybe even multiply infinite space, although that is less certain to me, particularly given the initial non-zero space condition).  The thing that I find so interesting with the No Boundary Proposal is not so much that it parallels my model (which it only does to some small extent), but rather that there is a willingness to consider what I call i-time especially given that it is an unavoidable consequence of my model.  There’s also the fact that, as far as we inside our black hole are concerned, the universe outside is as good as a four-dimensional manifold – what happens (or rather happened) out there is all done and dusted, set in stone in a way because it’s all in the past from our perspective (and it all happened instantaneously at t=0) and, from our perspective, the entire history of that external universe is in imaginary time, since that time is orthogonal to our time.

The benefit of my model is there’s a clear explanation as to the transition to our time and our space.  The down side is, well, there are truly brilliant brains looking at the maths behind the four-dimensional manifold and they seem to think that it works.  There’s just my brain looking at my model.