The Goldilocks Enigma – Part Four

by Laura Knight-Jadczyk

In the previous post, we talked about the beginnings of cosmology as described by Paul Davis.  Davies took on the task of ‘Explaining the Universe’ which means describing the Standard Model and how it came to be.  We learned that there appears to be no ‘center’ to the universe and everywhere you look, the space between galaxies gets bigger and bigger as time goes by.  Thus, there is the expanding balloon analogy which says that the universe can be finite without having a center or an edge.  It also makes us realize that, whatever the ‘Big Bang’ was, it wasn’t exactly an explosion the way we think of explosions.

Davies tells us that a telescope is a ‘timescope’, that when we observe images of distant galaxies, we are seeing them as they appeared long before Earth existed.  That is due to the fact that it takes time for the visual to reach us at the speed of light. 

As light traverses the expanding universe its wavelength stretches along with the stretching space. ….The amount of red shift depends on how long ago (and hence how far away) the light was emitted.  Working back towards the big bang, the red shift gets bigger and bigger. … Going much farther back in time (and out into space), we reach the epoch from which the CMB emanates.  … CMB has travelled to earth relatively undisturbed since about 380,000 years after the big bang.  Before that time the temperature was too high for atoms to exist because the electrons would have been stripped away from the nuclei by the intense heat, i.e. the atoms were ionized.  Physicists refer to a gas in this state as plasma.  Plasmas scatter light strongly and so they are opaque: that is why we can’t peer inside the sun…  when WMAP detects the CMB, it is in effect seeing as far back in time as is possible… No ordinary telescope or microwave antenna, however powerful, can penetrate the glowing fog beyond. 

Going in another, but related, direction for a moment: I read an interesting article the other day:  James Webb telescope discovers earliestgalaxy in the known universe — and its shockingly big .   In this article we are told:

According to new research, astronomers using the powerful infrared telescope have revealed what appears to be the two earliest, most distant galaxies in the known universe, dating to just 300 million years after the Big Bang.

Besides being exceptionally old, the newly discovered galaxies — named JADES-GS-z14-0 and JADES-GS-z14-1 — are also unusually large for such an early time in cosmic history, according to the discovery paper published May 28 to the preprint server arXiv. With the larger of the galaxies measuring an estimated 1,600 light-years across, the discovery adds to a mounting pile of evidence that the earliest galaxies in the universe grew up much faster than leading theories of cosmology predict to be possible.

That is interesting enough, but here is another problem I read about recently: Astronomers say we may live at the center of a cosmic void 2 billion light-years wide that defies the laws of cosmologyAstronomers say we may live at the center of a cosmic void 2 billionlight-years wide that defies the laws of cosmology  which says:

·       Evidence suggests that our galaxy is inside a cosmic void, a vast expanse of relatively empty space.

·       According to our laws of cosmology, however, this void should not exist.

·       New research says that such a void may explain unusual behavior in nearby galaxies. 

According to a growing list of evidence, we live in the crosshairs of a giant cosmic void — the largest ever observed. Astronomers first suggested such a void in 2013 and the evidence for its existence has been stacking up ever since.

But the kicker is that this giant void shouldn't exist in the first place. If it does exist, that means something is probably amiss with our understanding of the cosmos.

According to a fundamental theory of cosmology called the cosmological principle, matter in the universe should be uniformly distributed on very large scales.

The reason this matters is that by assuming uniformity, scientists can apply the same laws of physics to nearby objects as objects at the fringes of the early universe. In other words, everything operates under the same universal laws.  …

However, multiple observations over the last decade suggest that matter in the universe may clump into regions of high- and low densities, meaning it's not so uniform, after all.

"By now it's pretty clear that we are in a significant underdensity," Indranil Banik, a postdoctoral research fellow at the University of St. Andrews, told Business Insider.

"There's a few people that are still opposed to it to a limited extent. For example, some people have correctly argued that such a void shouldn't exist in the standard model, which is true. That unfortunately doesn't prove it's not there," he added.

Banik co-authored a paper published late last year in the peer-reviewed journal Monthly Notices of the Royal Astronomical Society that suggests we may live near the center of this void — called the KBC void — about 2 billion light-years across. Wide enough to fit 20,000 Milky Way Galaxies in a row stretching from one end to the other. …

The KBC void isn't totally empty. It can't be, because we live in it. But, if Banik and his colleagues' calculations are correct, the void would be about 20% emptier than space outside its border.

That may not seem like a big deficit, but it's enough to cause some confusing behavior in our local cosmic neighborhood, according to the recent study.

In particular, nearby stars and galaxies are moving away from us faster than they should be. Cosmologists have a value, called the Hubble constant, which they use to help describe how fast the universe's expansion is accelerating.

The Hubble constant should be the same value wherever you look, whether it's close by or very far away. The problem is that the galaxies and stars in our local neighborhood appear to be moving away from us faster than the Hubble constant predicts, essentially defying our law of cosmology that describes how the universe grows and evolves.

Astronomers can't agree on what's causing this discrepancy in the Hubble constant, and the contention has become known as the Hubble tension.

Banik and his colleagues suggest that the void could be a solution because high-density regions with stronger gravity outside the void could be pulling galaxies and stars toward them.

Banik argues that these outflows could explain why cosmologists have calculated a higher value for the Hubble constant when looking at nearby objects. Stuff moves faster in the void, flying out of our empty region towards crowded outer space.

New research suggests the KBC void is a 2 billion light-year-wide expanse of relatively empty space, and our galaxy sits right near the center of it. Pablo Carlos Budassi / Wikimedia Commons  © Pablo Carlos Budassi / Wikimedia Commons

Back to our main topic.  According to the Standard Model, which Davies is describing, light can have travelled at most 13.7 billion years and we cannot see beyond that point and so, for a while, it was said that the universe is that old. (Well, getting older every second!)  Nowadays, we can see much further thanks to the Hubble telescope.  Apparently Hubble can see at least 28 billion years back in time.  We also have to keep in mind that even as light is moving across the universe, space itself is expanding ahead of it and therefore, travel time is greatly extended.

Scientists have estimated that the observable universe contains about 10⁵⁰  tons of visible matter which combines to create a powerful gravitational field which warps the geometry of space.  “So, what is the shape of space,” Einstein asked himself in 1917.  Because gravitation warps the geometry of space, in Einstein’s mathematical model of the universe, this warping, averaged over billions of light years, makes space a hypersphere. According to Einstein, one can set off in one direction and keep going and going and end up back where you started.  The universe is unbounded, but finite.

 

As Davies says, we don’t know what lies over the cosmic visual horizon but it is probably more of the same, especially considering the Einstein cosmic balloon model.  That being said, what is inside the balloon?  What is inside Einstein’s ‘hypersphere’? 

Well, apparently, we can’t know that because we are trapped on the 3 dimensional surface of the sphere.  And the same holds true for the ‘exterior’ of the balloon.  We really are like the beings in the novella “Flatland”   only it’s a little more complicated because we are 3D beings in a 3D world, and we are talking about hyperdimensions basically all around us.  Paul Davies thinks this is irrelevant:

Try to put yourself in the position of a pancake-like creature restricted to life on the surface of a round balloon.  The pancake might conjecture about what lies inside the balloon (air, empty space, green cheese…), but whatever there is doesn’t affect the pancake’s actual experience because it cannot access the space inside the balloon, or receive any information from it.  … the pancake doesn’t need a god’s eye view of the balloon to conclude that its world is spherical – closed and finite, yet without boundary.  The pancake can deduce this entirely by observations it can make from the confines of the spherical surface: the sphericity is intrinsic to the surface, and does not depend on it being embedded in an enveloping three-dimensional space.  How can the pancake tell?  Well, for example, by drawing triangles and measuring whether the angles add up to more than 180’.  Or the pancake could circumnavigate its world.  In the same vein, humans could deduce that we are living in a closed, finite, hyperspherical Einstein space without reference to any higher-dimensional embedding or enveloping space, merely by doing geometry within the space.  So, the existence or otherwise of an ‘interior’ or ‘exterior’ region of the Einstein universe, not to mention what it consists of, is quite simply irrelevant.  But if you would like to imagine inaccessible empty space there for ease of visualization, they go ahead.  It makes no difference.

Yet, Davies then begins to discuss other dimensions than the 3 we experience.  Since we can’t see them, they must be hidden.  But how?  According to Davies, there are two ways.  The first was suggested by Oskar Klein in the 1920s.  His idea was to consider a hose which, from a distance, looks like a line.  When you get closer, the ‘line’ turns out to be a two-dimensional sheet rolled into a tube.  A point on the line would then turn out to be a circle around the circumference of the tube.  His suggestion was that what we take to be points of 3D space are actually little circles going around a 4^th dimension.  This ‘rolling up’ of dimensions is called ‘compactification’ and there is no limit to the number of extra dimensions that can be compactified though there are a variety of ways they can compactify.  The different shapes that can result are referred to as ‘topologies’.  The more dimensions, the more possible topologies.  So, when talking about the shape of space, you have to specify how many ‘large’ (i.e. seen) dimensions there are, and how many are compactified (i.e. unseen).

The second way that extra dimensions might be hidden from view would be if we are trapped in the three dimensions we observe and are not able to move in the extra dimensions.  Such trapping would also trap light since we cannot see the 4^th dimension.  The idea that we are prisoners in our 3D reality emerges naturally in what are known as ‘brane theories’.  There it is suggested that our 3D universe is a ‘three brane’ embedded in four space dimensions.

Davies concludes that there seems to be a reason that nature has decreed that we live in a three dimensional world (however many hidden dimensions there are).  According to English mathematician, Gerald Whitrow, if space had four dimensions and the laws of gravitation and electromagnetism remained unchanged, the inverse square law would become an inverse cube law, and the Earth would have spiraled into the Sun long ago along with many other disasters. Life would be impossible in space with any more ‘large’ dimensions than three.  So, as Davies notes: three dimensions are ‘just right’ like baby bear’s porridge was for Goldilocks.

To be continued .......

P/S. 01-06-24 18:49 (A.J.) compactified extra dimensions or branes floating a higher dimensional realm? I think I would not be surprised if Nature is using both possibilities, as well as other that we are not thinking about yet.

P.S. 04-06-24 17:10 (A.J.)

Parts 3 and 4 of the series of Jay Campbell's podcasts with Laura:

P.S. 06-06-24 (A.J.)

Reading Hermann Weyl "Space Time Matter", Dover 1952. There, p. 284:

"The world is a (3 + 1)-dimensional metrical manifold; all physical field-phenomena are expressions of the metrics of the world. (Whereas the old view was that the four-dimensional metrical continuum is the scene of physical phenomena; the physical essentialities themselves are, however, things that exist “ in “ this world, and we must accept them in type and number in the form in which experience gives us cognition of them: nothing further is to be “comprehended” of them.) We shall use the phrase “state of the world-aether” as synonymous with the word “ metrical structure,” in order to call attention to the character of reality appertaining to metrical structure ; but we must beware of letting this expression tempt us to form misleading pictures."

But "experience" goes  far beyond 3+1 dimensions! Weyl apparently restricted the concept of "experience" to "material experience".  Weyl was a mathematician, so he should know that mathematics, for example" is very important, but mathematical experience is a simple example of a non-material category. We desperately need physics and mathematics of other realms/densities.

P.S. 06-06-24 Reading J.-F. Pommaret "Nonlinear conformal electromagnetism and gravitation". There:

"Let us start this paper with a personal but meaningful story that has oriented my research during the last forty years or so, since the French ” Grandes Ecoles ” created their own research laboratories. Being a fresh permanent researcher of Ecole Nationale des Ponts et Chauss´ees in Paris, the author of this paper has been asked to become the scientific adviser of a young student in order to introduce him to research. As General Relativity was far too much difficult for somebody without any specific mathematical knowledge while remembering his own experience at the same age, he asked the student to collect about 50 books of Special Relativity and classify them along the way each writer was avoiding the use of the conformal group of space-time implied by the Michelson and Morley experiment, only caring about the Poincar´e or Lorentz subgroups. After six months, the student (like any reader) arrived at the fact that most books were almost copying each other and could be nevertheless classified into three categories:

• 30 books, including the original 1905 paper ([9],[23]) by Einstein, were at once, as a working assumption, deciding to restrict their study to a linear group reducing to the Galilei group when the speed of light was going to infinity. It must be noticed that people did believe that Einstein had not been influenced in 1905 by the Michelson and Morley experiment of 1887 till the discovery of hand written notes taken during lectures given by Einstein in Chicago (1921) and Kyoto (1922).

• 15 books were trying to ” prove ” that the conformal factor was indeed reduced to a constant equal to 1 when space-time was supposed to be homogeneous and isotropic.

• 5 books only were claiming that the conformal factor could eventually depend on the property of space-time, adding however that, if there was no surrounding electromagnetism or gravitation, the situation should be reduced to the preceding one but nothing was said otherwise.

The student was so disgusted by such a state of affair that he decided to give up on research and to become a normal civil engineer. "