There is a paper in the American Journal of Physics that got some news attention in mid-October 2023. The version that I first saw excitingly implied that it provided evidence that the universe is a black hole, which naturally caught my eye. (Anton Petrov also put out a video about it.)
This is the image that was being heralded:
Up in the top right corner, we can see the Hubble radius,
which is the age of the universe times the speed of light (which is also the
speed of light divided by the Hubble parameter). Above that and to the left is a region marked
as “forbidden by gravity”, basically indicating that anything in this region of
the chart would be denser than the densest of black holes (a non-rotating black
hole).
We will return to that, but the first thing that leapt out
to me about this chart was the fact that atoms, the Covid virus, an unspecified
bacterium, an unspecified flea, the (average) human, an unspecified whale,
planets, moons, the Earth, main sequence stars and the Sun are all in a
straight line. That line seems to have
the gradient log10M/log10r≈3 with little or no offset. This makes eminent sense since there’s an
established relationship between the mass of something and its volume, mediated
by its density. What might not be so
immediately obvious is the question of the offset.
Let us introduce the density as ρ, and note that we are
talking about a radius, such that the associated volume is 4πr3/3, so M=ρ.4πr3/3= (ρ.4π/3).r3 and therefore
log10M=log10((ρ.4π/3).r3)=log10(ρ.4π/3)+log10(r3)=3log10r+log10(ρ.4π/3)
If there were little or no offset, this would imply that log10(ρ.4π/3)≈0 and so ρ.4π/3≈1, or ρ≈0.25. However, in the paper, it’s noted that the line
is consistent with the density of water (1g/cm3). This represents an offset of log10(4π/3)=0.6.
I looked at the background data (provided in a zip file) and noted
that they estimated the radius of spherical humans, blue whales and fleas using
the following process – To get the radius, take the length, divide by 2, that
gives you a "ball", then divide by 2 again because we want the
radius, not the diameter of the ball.
The figures that they used were (where yellow fill means that the values
are received, and white means they are calculated, noting that the virion here
is a Covid virus particle):
I went into a bit more effort and got (using the same colour coding):
Even though the virion and human densities is very wrong from their estimate, and the whale was somewhat wrong, there was very little effect on the relationship:
Note that the blue line in my chart represents black holes
of different mass and the thin red line is log10M=3log10r+0.6
with the dots near it coming from the table above. The other dots, left to right are, the Milky
Way galaxy, the current Hubble radius and the “observable universe” (inflated
radius of 46.5 ly).
We’ll get back to the “observable universe” later.
The second thing that leapt out at me was that there are
other apparent lines on the chart, albeit shorter. These lines have the same
gradient but a different intercept with log10M=0. There’s a vague line created by globular
clusters, a more distinct line for galaxies and clusters of galaxies, and then
a line for super-clusters right up against critical density (the density of the
Hubble radius). The offset for galaxies
seems to imply a density in the order of about 10-25g/cm3. Note
that there are voids illustrated that are below the critical density, which
makes sense given that if some areas are higher than the critical
density overall for a larger region, then some areas must be lower than this
density – and these would be voids.
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So … the observable universe. According to calculations performed by Ned Wright (although he might not be
the original), the observable universe has a radius of about 47 billion light
years – if one includes the assumption of accelerating expansion from about 5
billion years ago, as required to get the appearance, today, of constant expansion
at the speed of light since 13.787 billion years ago, due to the disturbances
caused by a period of inflation and two different periods of slower expansion. In
The Problem(s) with the Standard
Cosmological Model, I explained why I have issues with that explanation
but if we accept that the observable universe is that big and note that the
argument for that radius is based on the assumption of a critical density which
is pretty much the density that we observe, then we have a problem.
The large orange dot in my chart above shows where the
observable universe plots to, given its density and its radius (and thus its volume). It can be seen to sit above the black hole
line and thus in the “forbidden by gravity” zone, or (a little less clearly):
And, if you read Ned Wright further, you will note that he
goes on to say that the universe, as a whole, is more than 20 times the volume
of the observable universe. This is a
low-end estimate if space.com is to be believed, given
that they report a measurement of 7 trillion light years across, or 3.5
trillion light years as a radius. They
also suggest that another possible figure is 1023 light years, but
this is clearly muddled since the universe would have expanded faster
than the speed of light during any inflation event (not at the speed of light). Plotting these three values as well,
maintaining the same critical density (which is an assumption that is common to
all three), we get:
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So, something seems wrong here. It does make me wonder, given that the paper says
“we plot all the composite objects in the Universe: protons, atoms, life forms,
asteroids, moons, planets, stars, galaxies, galaxy clusters, giant voids, and
the Universe itself”, they don’t plot the universe itself, not even the
“observable universe” … unless the authors’ view is that the Hubble radius is
the radius of the universe.
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One issue raised by various people, including Anton Petrov, is that for the
universe to be (inside) a black hole then there could be nothing outside of it,
which introduces the issue of how the density would suddenly plummet to zero at
the boundary. Generally, it is thought
that the density outside of the Hubble radius is the same as inside (because we
are not privileged, our part of space in not special) – and this is the basis
on which I chart the “observable universe” above the black hole line.
Note that Anton at one point misrepresents the Hubble radius
as the radius of the “observable universe”.
The Hubble radius is 13.787 billion light years, not 93 billion light
years.
Note also that, just after 11:00, he says that when
a black hole gets big enough you can technically go inside it and feel nothing,
so I am not convinced by the argument that outside the Hubble radius would have
to have zero density for us to be in a black hole.
If the region inside the Hubble radius constitutes a black
hole (which it does, since it has the radius, mass and density of a black hole
of its radius, mass and density), then it’s possible to have black holes inside
of black holes, since there’s a supermassive black hole at the centre of many
galaxies and probably many other, smaller black holes in other locations. Consider then the possibility that the Hubble
radius itself is inside another, larger black hole.
Say, for example, that there’s a greater black hole the size
of the “observable universe” at 93 billion light years. What would its density be? The calculation for the density is ρ=3c2/8Gπr2, which for 93 billion
light years is 8.3×10-31g/cm3, or a little under one
tenth the critical density of the universe of ρc=9.4×10-30g/cm3 while
having a volume that is 38 times greater.
Then consider the nesting of many effective black holes
between the Hubble radius and the radius of the “observable universe” and think
of one that is only slightly larger than the Hubble radius – 15 billion light
years. The density of that black hole
would be 8.0×10-30g/cm3 or about 85% as dense as where we
find ourselves, with a total volume that is 30% greater.
So then the question is, how dense would it have to be
beyond the Hubble radius to still constitute a black hole at 15 billion light
years out? I estimate that it would be
in the order of 30% of the critical density.
And for a 93 billion light year radius, the average would be 6%. The bottom line is that density doesn’t need
to suddenly drop to exactly zero, even though we do introduce an apparent
problem with privilege since the region inside the Hubble radius is special
(due to being towards the centre of a zone that is of higher density than the
surrounding area).
This is not, however, the only solution. The other solution, more consistent with the
notion of FUGE, and the implication of the
paper’s writers, is that there’s nothing outside of the Hubble radius – not even
empty space. The problem with that is that it also seems to indicate that we are in a privileged location, because we appear
to be at the centre of such a universe - unless the geometry is such that all points within appear to be central.
