Half a Problem Solved?

I have intended to write something for quite a while about something that I wrote in Mathematics to Address an Apparent Problem with Imagining a Universe has been bugging me.  That post was “a very brief explanation as to how mass/energy enters to the (…) universe at a rate of one unit of mass/energy per unit of time”.

 

The problem here is that the mathematics tells us that, to remain flat in the presence of expansion, a universe with a volume equal to the Hubble volume (where the Hubble “constant” is the inverse of the age of the universe) must accrue an additional unit of (Planck) mass/energy every two units of (Planck) time.  If the universe got one unit of mass/energy per unit of time, then it would never have done more than collapse in on itself because it would have had a density twice that of a black hole.

 

In Mathematics to Address an Apparent Problem with Imagining a Universe, I wrote:

 

We can get circles from a sphere by sectioning it.  The greatest circle we can create has the same radius as the sphere itself.  The sectioning effectively creates two hemispheres.  Note that I remain aware that the surface area of the curved section of the hemisphere is not equal to the surface area of the circle created by the section.  By analogy, the universe could be notionally sectioned by a spherical section, creating two halves, meaning two (three-dimensional) Hubble volumes, meaning that the nice one “unit” of energy for each “unit” of time during which the radius increases by one “unit” of length is obtained for the universe as a whole.

 

 Usch.

 

Recently, PBS Space Time published the video Could the Universe be Inside a Black Hole? which ended with a question about what exists outside of the black hole.  I slapped together a quick (and somewhat imperfect) comment to the effect that outside our universe – if it were to be a black hole – is not a where-question but rather a when-question.  There were universes before ours and there will be universes after ours, but they would be orthogonal to our universe.

 

I also riffed, in that comment, about the problem above that has been bugging me, writing:

 

My working hypothesis at the moment is that if you project four space (spacetime) onto three space (space), there are two equal solutions.  To understand this imagine looking at a monochrome sphere - ignoring any shading - and it would look like a circle.  That circle incorporates precisely half of the sphere with a complete other circle on the other side that you can't see.

 

This still doesn’t get me to where I want to be, because there is a suggestion of contiguous spacetime, with a surface volume that would have a density that is equivalent to that required (for flatness) for half that volume and I am back to having a similar problem – too much space now rather than too much mass/energy.

 

However, it did get me thinking and – coincidentally – there was something else that has been bugging me for a while.  I hinted at it in The Messiness of Layered Spheres, the notion I had in my head, was that for each instant (Planck time) that the universe expanded, there would be a cascade of Planck volumes filling in the gaps created by the expansion.  But it’s messy and the mechanism was utterly obscure.

 

Recently, although little less recently than the PBS video, I also saw an episode of QI in which Alan Davies argues with Sandi Toksvig about the shape that of the cells that bees make.  Hexagonal, obviously.  But no.  The cells are circular, they just make hexagons because that’s the shape that arises when you pack circles (and are minimising the use of resources such as wax).  Those facts together got me thinking about things a differently.

 

I provided some visualisations about the lifecycle of a universe back in Apparent Problems with Imagining a Universe, with the last image looking like this:

The idea is that time in the universe to the left is upwards, and time in the universe to the right is rightwards (thus orthogonal).  Implied is that the spatial dimensions are also orthogonal with no intention to imply that any spatial dimension in the second universe would be aligned with the temporal dimension in the first.

 

The equations that support this notion relate to the approach of the event horizon of black hole:

 

and

 

These become zero at the event horizon (where r = 2GM/c²) and then, inside the event horizon, become the square root of a negative number.  Now, when we are first introduced to the idea of the square root, we are channelled into the thinking that, for example, the square root of 4 = 2.  However, it is more accurate to think that the two solutions to the square root of 4 are +2 and -2 – because (+2)² = 4 and (-2)² = 4.  That is, the absolute value of the square root of 4 is 2, but it could be positive or negative.

 

I was thinking that what goes on, on the other side of the event horizon, was a new universe shooting off in the i direction (that is, orthogonally, so really off in the i, j, k, τ direction).  However, it makes more sense mathematically if there are two directions – the i, j, k, τ direction and the negative i, j, k, τ direction*.

 

That would imply that our universe is one of a matched pair – linked in a way, without any way to communicate or interact – which are being “fed” at a rate of one unit of mass/energy per unit of mass time, equally split between the two of us, resulting in both universes being eternally flat. 

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Why were the bees relevant?  Because I realised that I had been trying to solve the wrong question - How do bees make hexagons?  They don't, they make circles.

It puts me in mind of one of my favourite jokes.  How do you get down from an elephant?  You don't, you get down from a duck.

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* This is deliberately vague.  I'm still thinking about it.  One issue that remains is that neither +τ nor -τ would have precedence, which opens up the possibility that neither would have precedence over any other potentially orthogonal temporal dimension.  A possible solution to that is that at the event horizon all time and space is effectively compressed to zero - meaning that everything on the outside would have been fed through a singularity simultaneously and the orientation of i, j, k, τ and their opposites selected - and set - instantaneously.  As far as the universe(s) on the inside of the event horizon is (are) concerned, the orientation of i, j, k, τ (and their opposites) are and have always been what they are.

 

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Update: 3 April 2022

 

I just listened to the Skeptic's Guide to the Universe episode from 2 April 2022 (audio) - which was live and recorded some days earlier, somewhere in northeastern US.  Bob Novella speaks of a new theory in published in the Annals of Physics (reported at Live Science), in which there is a mirror (or anti-)universe running "backwards in time".  The physicists involved have come to this conclusion a different way, because they were looking for CPT (charge, parity, time) symmetry as an explanation for dark matter.

 

There are some interesting (and parallel) ramifications of the theory, including "a CPT-respecting universe naturally expands and fills itself with particles, without the need for a long-theorized period of rapid expansion known as inflation".  Compare this with my model (Universe (in) a Black Hole - published 7 June 2019) in which our universe is "fed" with one unit of Planck mass/energy per two Planck units of time (see Is the Universe Getting More Massive? (Flatness, not Fatness) – published 30 July 2019) and the expansion follows the Hubble radius = Schwarzschild radius metric, where the Hubble radius is the speed of light multiplied by the age of the universe - which implies that there is no inflation (see My Universal (and Expanding) Struggles – published 9 July 2019).

 

Fascinating stuff.  Note that the model that these physicists are suggesting (at least according to Live Science) is one in which there is a pair of universes in which one consists (largely) of matter and the other (largely) of antimatter, which would explain the dearth of antimatter in our universe.  I don't think that my model necessarily implies that - I think that both universes would have mass/energy of some sort, as necessary to obtain one Planck unit of mass/energy per unit of Planck time.  It should be noted that antimatter has positive mass and that equal parts of matter and antimatter do not cancel each other out, when they collide each is annihilated but they release energy.  You could say that their matter (and antimatter) nature is destroyed, but not their energy.

Pre-Creation (How Good Can God Be?)

I want to consider whatever there was, in the theist conception, prior to creation.  Note: I use the term "prior to" deliberately rather than the term "before", because creation probably implies a beginning of time, in which case there would be no "before" (such as we could understand it).

The idea, as I understand it, is that it is impossible for there to be an infinitely long causal chain back into the past and that, within this universe, all effects (without exception) are preceded by a cause.  Note: I am not interested in Aristotelian "causes" here, which are presented as answers to a "why" question such that considering them would be equivocation.  I very much mean a cause as in the combination of pre-existing conditions and some sort of force acting on something.

The notion of pre-existing conditions and a force acting on something is taken to show that while there must have been some "first cause", that "first cause" could not have come from within this universe.  Note: I am not implying a "first cause" from "outside" the universe, since at this point, notionally, the universe does not (yet, see first note) exist.

This "first cause", it is then claimed, must be a creator god.  Note: I am not implying that this is a specific god, one that maybe has the name "God" or one that Adam and Moses chatted with, so I have no intention to capitalise the term when I use it.

It is further claimed, by most theists, that this creator god is extremely, maximally or all-: powerful, knowing and good.  Some go further, saying that this god is perfect.  I know that, when challenged, some theists suggest a less extreme version of a god, in order to avoid certain problems, but I strongly suspect that in private such theists relax back into believing the full deal.  Let's just say that this hypothetical creator god is, at a minimum, powerful and knowledgeable enough to create this universe and then consider how good such a creator god could be, given that it started with the most rasus of all possible tabulæ rasæ.  Note: This is a questionable metaphor because "rasus" indicates that the "tabula" [slate] has been "scraped" clean, implying that the slate had been in a different state earlier, but I'm just trying to say in an oblique way that this creator has the blankest of all blank canvases before it, that there is nothing before it but potential, and perhaps not even potential, since any potential that exists supposedly exists, as yet unmanifested, within the creator god and that creator god has not yet created anything yet that could be "before" it.

One final, or rather first, thing.  In our understanding of physics, time could have started just prior to the big bang, but it doesn't necessarily have to have started just then.  In the hypothetical that I am considering right now, however, to all extents and purposes time does start with “creation” - because otherwise the causal chain would extend further back, and we're specifically looking at when the chain starts.  I'm willing to accept that the creator god could create time first, with nothing else (so no matter or energy and no space in which to put it), and use the fruit of that initial creative act to "spend time" considering what move to make next.  I'm not saying that a creator god needs to do that, but we're going to consider decision making on the part of the creator god and, as far as we understand it, decision making takes time.

So, we have the creator god.  Nothing is created.  The creator god is sufficiently perfect as to make a universe of some kind.  Is this creator god good?

It seems that we can only tell by employing an awkward, circular definition of good, saying that this creator god is good because it does creator god stuff and creator god stuff (namely creation) is, by definition, good, or good by consideration of what actions this creator god takes - judging it by its fruits, you could say.

But then we come to suffering.  Suffering is, in itself, a bad thing.  I doubt that anyone would argue that suffering, in itself, is a good thing.  It is certainly possible that, if on balance there is more good than bad that accrues from a certain act, then that act can be considered "good" even if it resulted in suffering (in some sort of "the ends justify the means" sort of way).  However, at this point in our hypothetical history, there is nothing and there is, therefore, no suffering at all.

What justification would this creator god have for changing from that primordial, zero-suffering state to a state in which, inevitably, sentient creatures would emerge and suffer, some horribly?  Note: I am not saying here that it's necessarily the case that the creator god should not have created at all, but rather emphasising the (hypothetical) fact that the creator god had an entirely blank canvas (albeit an entirely metaphorical one).  Nothing had yet been created, not even the physical laws of this universe, and the creator god had almost entirely unlimited options (remember that this is a sufficiently powerful and knowledgeable creator god, not an omnipotent or omniscient one).  The creator god could have created, for example, a single intelligent being with which to interact.  It might be argued that loneliness of that being might be an issue, but that is a post hoc quibble.  A deliberately created being, created by a sufficiently powerful and knowledgeable creator god with the sole purpose of interacting perfectly with its creator, would not suffer loneliness - it'd be in (sufficiently) perfect communion with the (sufficiently) perfect creator god.

Some apologists might miss the point (intentionally or not) and suggest that the creator god does not need to justify itself to lowly mortals like myself.  That may well be true, but such a tyrant god is not an inherently good god.  And in any event, I'm not arguing here that this hypothetical creator god does not exist, I am merely pondering on how good it could possibly be.

So, how good can it be?

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There's the common argument that this god wants to enter into a loving relationship with us all, and that this is a great gift, offered freely.  Nevertheless, this is satisfying a want on the part of the creator god, and any good that is associated with this offer comes only after our creation.  Therefore, we suffer (and I reckon we all suffer to a greater or lesser extent) to satisfy the wants of a creator god, even if we might subsequently get a boon that seems somewhat secondary (our happiness is subordinate to that of a vastly superior being, after all).  However, I am not considering the post-creation situation – I'm considering the pre-creation situation in which a creator god has the opportunity to decide between A) creation of sentient beings which would then be placed in a quandary, risking future eternal bliss or future eternal suffering (or permanent oblivion), while experiencing a poor, nasty, brutish, and short lives on the material plane; B); creation of sentient beings who would not then be placed in such a quandary and would not then experience poor, nasty, brutish, and short lives (on any plane) or, C) abstention from the creation of sentient beings altogether.

My thinking is that the creator god could be good.  But it would not be good if it chose option A.

Time to Take WLC to Task (Again)

I initially wrote this on Craig-Land, in a post that I titled Is WLC anti-science or unscientific or ascientistic, or something else?  I must have just been riled up, because I’ve had to edit it quite a bit, removing extraneous words and trying to provide some context.

It might seem to be a little bit technical and esoteric for a forum inhabited by amateur apologists, but remember that they aspire to incorporate science into their endeavours and to bend the findings of science to serve their agenda.

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My departure point here is WLC's Q&A response on relativity.

In short, WLC is not arguing against relativity per se, but he is arguing for one interpretation of relativity over the other (or, rather, the other two).

The first interpretation that WLC deals with is Einstein's, which WLC implies was from his 1905 paper.  The trouble is that the interpretation that WLC is talking about isn't in that paper.  There's nothing in there that implies that Einstein thought that "there is no over-arching way the world is".  The closest is perhaps this statement in Section 2 of Part I (The Kinematical Part) – On the Relativity of Lengths and Time:

So we see that we cannot attach any absolute signification to the concept of simultaneity, but that two events which, viewed from a system of co-ordinates, are simultaneous, can no longer be looked upon as simultaneous events when envisaged from a system which is in motion relatively to that system.

But this is true in all three interpretations.

I thought that maybe Einstein said something like that which WLC claims in his argument with Bergson in 1922, but even that doesn't seem to be so.  At best, Einstein indicated that he held that the time of the philosophers does not exist and that there remains only a psychological time that differs from the physicist’s.  Perhaps WLC extrapolated from this.

Anyways, WLC calls Einstein's interpretation (one which he may well never have held) "really kooky" and thus dismisses it, purportedly leaving only the interpretations of Minkowski and Lorentz.  However, suggesting that Einstein's conception was different to Minkowski's is ridiculous since Einstein incorporated Minkowski’s four-space into his work on General Relativity.  Sure, he didn't initially go along with it, but once he understood the principles, Einstein not only adopted them but showed that it all works.  The "really kooky" interpretation was no more than an intermediate thing, if even that.

The major problem comes in when WLC is trying to choose between Lorentz and Minkowski and I think that it is at this point that he (WLC) become profoundly unscientific or anti-science.

In order to make the choice, WLC relies on his belief that there is a god of a particular sort with particular characteristics, as his final paragraph shows:

For I claim that God’s timeless existence, given that there is a temporal world, is possible only if a tenseless view of time is correct; whereas if a tensed view is right, God exists temporally in absolute time. Since I am firmly convinced that a tensed view of time is correct, I think that Lorentz was, in fact, right, and that God accordingly exists in time

So, he plumps for Lorentz (which gives him a god existing temporally in absolute time).  Hopefully readers can see what WLC did there, he argued "the god of WLC -> Lorenz".

Furthermore, he's arguing that if Lorenz is wrong and space really is Minkowskian, then the god of WLC cannot exist.  I think this is a little short-sighted of him (WLC, that is).

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WLC also presents a false dilemma between "tensed time" in which past and future are real (whatever "real" might mean in this context) and "tenseless time" which he characterises as "just an illusion of human consciousness".

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So, is WLC anti-science, willing to toss science aside if it is inconvenient with respect to his god beliefs?  Or is he simply unscientific, which would possibly imply that he is pseudo-scientific willing to use science-like pronouncements with little if any scientific basis?  Or is he ascientistic, merely charting a difficult course which requires you to use the boat of philosophy here, then leap onto a scientific cart there, and finally ride the rhetorical slippery-dip to a presupposed conclusion (rather than the scientists who are plodding along in the cart the whole way, wondering who that crazy hitch-hiker was)?  Or maybe ... maybe he's a charlatan making it up as he goes along, using whatever tricks he thinks will convince the punters?  Or something else perhaps?

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There is in fact a way to view fourspace (a form of "tenseless time") which is entirely compatible with a god, in fact it's a view that many physicists reject quite fervently perhaps because it opens the door to a Minskowian variant of a god.  I've talked previously about the expansion of space being time.  Implicit in that model is the idea that there is expansion and a rate of expansion.  This might still not leap out at the reader, but it should be more clear from what I wrote in On Time.  I talk there about an invariant space-time speed, including the speed of time (which would be c in a rest frame).  For this to be meaningful there would be some sort of meta-time against which time in our universe would be expanding and time in our universe would be passing.  (This might just be a metaphorical thing of course, but for a god to use it, it'd have to be real, we humans simply wouldn't have any access to it.)

From outside the universe, a god would notionally be able to observe everything simultaneously.  It could tweak events in the "past" and watch (in meta-time) how they play out in the "future".  This has the benefit of avoiding the horns of the predestination-free will dilemma.  Humans in a universe like this one could have absolute free will, but the god watching from outside would be able know the consequences nevertheless, since all of history (including future history) is there before its gaze, simultaneously in meta-time.  Theists could use this model to explain why there were far more interventions (miracles, visitations etc) in the past and none recently.  All the necessary tweaking, or at least major tweaking, has already been done.

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Note that while I do think we all have an invariant space-time speed (c), meaning that I can agree with both Minkowski and Lorenz, I don't think that there's a god out there tweaking our universe.