FUGE Clarifications

Out of interest, I put the link to Flat Uniform Granular Expansion into Google’s NotebookLM tool and listened to the two person “deep dive” that it generated (transcript here).  Generally, I was happy with it – even if it was very heavy on me being “out there”.  In a few instances however, the AI appears to have hallucinated, reaching conclusions that aren’t in the text and ascribing them to me.  However, it’s possible that I managed (unintentionally) to imply certain aspects that can be extracted by the human reader as well so here are some clarifications.

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Origin of the FUGE model

The logic that leads to the FUGE model begins with three observations: the universe is expanding, the universe is flat and the age of the universe is approximately 13.8 billion years.

A flat universe has critical density.  Critical density is proportional to the square of the Hubble parameter (with all other components being constants).  Also, critical density is equal to the density of a Schwarzschild black hole with a radius equal to the Hubble length (which is merely the speed of light divided by the Hubble parameter).  The value of the Hubble parameter is equivalent to the inverse age of the universe.  (Note that the preceding link uses a Hubble parameter value of 67.8 km/s/Mpc which was determined by the Planck collaboration in 2015.  There is however a tension given that increasing accurate values for the Hubble parameter value are zeroing in on different values. Data from the JWST, SH0ES and more recent data from DESI indicate a value closer to 74 km/s/Mpc – which corresponds to a Hubble time of 13.3 billion years.  The Hubble parameter value which precisely corresponds with 13.8 billion years is 70.8 km/s/Mpc – which is clearly within the margin of error given the results that have been achieved.)

Then I propose a hypothesis – what would it look like if the universe was expanding such that its radius was increasing at the speed of light?  The value of the Hubble parameter would always be the inverse of the age of the universe.  And, the radius of the universe would always be the age of the universe times the speed of light.

But, if the universe were flat, then the density would have to be critical (and according to Sean Carroll, if flat then the universe has always been and will always be flat).  Note however that the critical density is proportional to the square of the Hubble parameter, which is inversely proportional to the radius of the universe – so the critical density is inversely proportional to the square of the radius.  However, the density of a fixed mass in a sphere (such as a Schwarzschild black hole) is inversely proportional to the cube of the radius.

This means that the mass-energy content of an expanding volume that maintains critical density must be increasing.  Then it’s relatively simple mathematics to show that mass-energy in a sphere at critical density, if it increases in radius by one Planck length must increase by the equivalent of half a Planck mass to remain critical.  To be increasing at the speed of light, the increase of one Planck length has to happen in one Planck time.

Another aspect of being flat is that the universe is smooth – as lumpiness at a sufficiently large scale could lead to curvature.  It follows therefore that the rate and distribution of mass-energy entering the universe would be smooth.

If we start with those conclusions, which are based on observations, the critical density and the volume being defined by the age of the universe, we arrive at a total mass-energy in the universe being equal to the baryonic (ordinary) matter attributed to the observable universe.  It is from this that the suggestion in the Standard Model that the total mass-energy of universe is about twenty times that of the baryonic matter appears to be a problem.  The FUGE model does not arise from eliminating Dark Matter and Dark Energy, but rather it is the case that the model doesn’t accommodate either of them.  The suggestion is that the phenomena which those dark substances were postulated to explain would have to be explained otherwise (if indeed they need explaining).

Note again that the critical density is equal to the density of a Schwarzschild black hole with a radius that is equal to the radius of a FUGE universe.  As the universe increases in size, while it does increase in mass, it decreases in density.  The same applies to a black hole (the Schwarzschild black hole, being one that is neither rotating nor charged, is the largest you can have with a given mass).  A universe which is at least 46 light years across, per the Standard Model, with a density of approximately 10^-26 kg/m³, is about one hundred times more dense than a black hole of that size.  (Note that if the universe were infinitely large, then this might not be a problem, it might only be a problem if there is a notional boundary, as there would be if the universe was initially constrained in a relatively small volume from which it expanded, as per the both the Standard Model and the FUGE model.)

 

Age of the universe

In the FUGE model, the universe is in the order of 14 billion years old.  It is not past eternal.  That said, if our universe were being “fed” by a “progenitor universe” that is/was orthogonal to ours, then that universe could be effectively eternal (in its own orthogonal history) with its eternity being entirely (and orthogonally) coincident with the initiation of our universe.

That said, our universe certainly had a beginning in the FUGE model with what is sometimes called an “instanton” – a Planck sphere (a sphere with a radius of a Planck length) containing the mass-energy equivalent of half a Planck mass at time t = one Planck time.

Note that in the FUGE model, you could work out how old the universe is in two ways.  You could look at the Hubble parameter or you could look at the density of the universe.  If the Hubble parameter were approximately 70 km/s/Mpc in a FUGE universe, then the universe would be approximately 14 billion years old.  If the density were approximately 9×10^-26 kg/m³ in a FUGE universe, then the universe would be approximately 14 billion years old.

 

Contents of the Universe (and the Distribution thereof)

The FUGE model does not, in itself, make comment on the nature of the mass-energy in the universe, nor its distribution.  All that the model suggests is that half a Planck mass is added to it every Planck time, and this has been the case for approximately 14 billion years.

The notion that the universe was opaque until about 380,000 years after the instanton is not problematic.

 

Threads?

No idea where this came from.  The expansion of space in the FUGE model is granular, in that individual “grains” of space are added stochastically (or randomly) to the volume.  The grains of space which appear are not linked, so it would be wrong to think of them as threads.  Note that it would result in a simultaneity problem if they were linked or coordinated in any way – with a whole new form of spooky action at a distance.

 

The Big Bang

When I first heard the artificial podcasters suggest that the FUGE model does away with the Big Bang, I reacted.  I didn’t mention the Big Bang in the Flat Uniform Granular Expansion article at all.  However, thinking about it, it could be that they were right, depending on the definition of the Big Bang.  If, and only if, you include inflation as a necessary component of the Big Bang theory, then the FUGE does not include the entirety of the Big Bang.  If, on the other hand, you consider the Big Bang to be “a physical theory that describes how the universe expanded from an initial state of high density and temperature” (per Wikipedia), then the FUGE model is consistent with the Big Bang.  An instanton is as dense as you can get, and the corresponding temperature for the mass-energy in an instanton is the Planck temperature, which is as hot as you can get at about 1.4×10³² kelvin (remember things cool down as you expand them, although we usually only notice this with gas it applies across the board for any form of matter that is compressible).

I would have to disagree with the podcast on this point, but only to the extent that they should have mentioned inflation, rather than the Big Bang.

Note also that I would have to disagree that the CMB is evidence of the Big Bang in the form that they must be referring to.  That is to say, the CMB is not evidence of inflation.  That is almost precisely backwards – inflation was introduced as an explanation for the statistical isotropy of the CMB.  If there is another mechanism to explain that phenomenon, then we can lose inflation.  However, the CMB is in fact evidence of the version of the Big Bang that the FUGE is consistent with (that the universe used to be a lot smaller and hotter about 13-ish billion years ago).  It is not, as the pseudo podcasters suggested, a “a result of the thermalization of all that energy that's constantly being added to the universe” – that is pure hallucination on the part of the controlling AI.

 

Red shift

Again, I reacted to this – especially as the artificial podcasters make it the central plank of their final part of the podcast.  I didn’t make any comments about redshift that were specific to the FUGE model.  The only mention was in terms of the sorts of observations that Hubble was making back in the 1920s, that all the stars around us are redshifted and the further away they are the more redshifted they are, and therefore the universe is expanding.

That said, there is a link in the article to The Conservatory - Notes on the Universe, which does hint at redshift.  However, this article doesn’t even mention the term and the one reference to stretching involves a god of physics making a circle out of nothing.  The only suggestion I make in that article is that if we consider a “carrier photon” on which the mass-energy of the universe were carried, after having added half a wavelength every Planck time, since the instanton, then that carrier photon would have an energy that is equivalent to the mass of the universe (which I know sounds crazy, it’s just that the mathematics stacks up).

I made no comment about the redshift of a photon emitted at the CMB in either article.  But I did in another article, which I am not going to link here, but you can find if you are interested (just look for the term “redshift”).  For dramatic reasons I got distracted in that article, which it isn’t really about redshift at all, it’s more about another model that I found when looking into the topic.  Although it does eventually curve back into considerations of redshift in a FUGE universe, that article makes no suggestion that redshift works the way that the podcasters mention.  Instead, I arrived at the equation z=t/(t₀-t) using a number of different approaches.

It is possible that yet another of my articles was accessed by the AI.  There is one that is about a claimed relationship between the temperature of the CMB and Hawking temperature, but also mentions redshift.  This could conceivably have been source of the comment:  “So instead of being leftover heat from the Big Bang, the CMB in (a) FUGE (universe) is more like a constant hum from all th(e) new energy being added to the universe.”

In that article there is this sentence: “The currently observed CMB, per Tatum's implied mechanism, is not from recombination per se but is instead a summation of all the redshifted temperatures across the Hubble radius (which is to say across the past).”  This was not something I said on my own part, but rather was musing on an implied mechanism that seems to be buried in Eugene Tatum’s Flat Space Cosmology.  Later in the article, I go on to clarify, in reference to the relationship between CMB temperature and Hawking temperature, that “the relationship does not quite make sense” and that “I cannot, at this time, work out how the temperature contributions would collate in precisely the right way to give the result that Tatum suggests and this is a major stumbling block as far as my accepting the reality of the relationship goes”.

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I added this article to the AI (along with the Flat Uniform Granular Expansion article), and it still hallucinates - suggesting a past eternal, that the FUGE model has mechanisms to explain the acceleration of universal expansion for which Dark Energy is a proposed explanation and that the phenomenon explained by Dark Matter is accounted for in the FUGE model.  I want to clarify again for any human readers, the FUGE model does not include a past eternal (at least not in our time dimension) and the FUGE model does not allow for Dark Energy or Dark Matter that would require the universe to be 20 times more massive.

The FUGE model, if correct, would require alternate explanations for the related phenomena, perhaps something akin to MoND to replace Dark Matter (other alternative theories may be available) and acceptance that the measured acceleration of the universe is merely an artefact of that measurement - thus negating the need for Dark Energy (see also Dark Energy - Observational Skeptism).  The FUGE model does not, however, provide mechanisms for Dark Energy or Dark Matter.