A Brief History of Time¶
It is interesting to compare The Geometry of the Universe to Stephen Hawking’s, A Brief History of Time.
A best selling book that aimed to be accessible to a very wide audience, aiming to explain nothing less than the entire history of the universe.
Hawking feared every equation would halve his audience, so including only a single equation.
Published in 1988, some 30 years had passed, since Fred Hoyle’s, The Nature of the Universe.
It is a period during which observational astronomy had made dramatic strides.
Hoyle sets the scene for this sixty year adventure, a brief history of our time, describing the 1960’s view of how the universe may have come about.
It includes a chapter entitled, The Expanding Universe, as does Hawking’s brief history.
Hoyle speculated that the aparent expansion would be a balanced if matter was spontaneously created at a fairly modest rate.
Black holes were not a major focus at this time, nor was there mention of dark matter.
By the time of Hawking, black holes had evolved from hypothetical object to indirect observation.
Hawking was very much focussed on unifying quantum mechanics and Einstein’s general relativity. With the big bang theory, comes the belief that at some point the universe was in such a tiny space that quantum weirdness really matters.
At the big bang, quantum effects come into the equation, so to understand the fundamentals of the universe you needed to model the very first instant of the explosion, when everything is so close quantum weirdness enters as you try to model gravity.
Hawking shows connections between event horizons of black holes and the early moments of the universe.
Exploring the mathematics of both general relativity and quantum mechanics Hawking showed how black holes could evaporate over time.
These two books give a good reminder of how new a theory the Big Bang theory is, and also the pace at which we are able to make new observations of the universe during this time.
By 1988, the theory is firmly established, with observations such as the Cosmic Microwave Background having been taken as confirmation of the big bang theory. The background is extaordinarily smooth. It has curious spherical resonances over vast distances.
Hawking mentions the how discovery of quasars led to Hoyle abandonning his continuous creation model. Quasars are highly red-shifted and so are assumed to be very distant objects of extraordinary power. The fact that we do not see these objects nearer to us is deemed to be an indication that quasars were an earlier stage of the evolution of the universe, and hence very much further away.
Fast forward to today. Observational astronomy is living in a golden age with satellite observatories and gravitational wave detectors.
In the early part of Hawking’s career the dark matter problem had not yet entered the mainstream.
It was observations of the characteristic spirals of galactic rotation curves that were not compatible with general relativity.
The conclusion? There must be some magical Dark Matter, carefully placed to make the galaxies spin as they do.
As noted above, Hawking worked in theoretical physics, focussing on quantum theories of gravity, and much of the book focusses on quantum effects and notes similarities between the event horizon of a black hole and the big bang singularity.
It is here that there may be some salvation for much of the work done under the assumption that there was a Big Bang some 13.7 billion years ago: much of the physics of the early universe, if fact, once you get past the inflationary phase, is relevant to the quasar models that Rourke describes.
Hawking asks four questions regarding the origin of the universe:
1. Why was the early universe so hot?
2. Why is the universe so uniform on a large scale?
3. Why did the universe start out with so nearly the critical rate
of expansion that separates models that collapse from those that
go on expanding forever?
4. Despite the fact that the universe is so uniform and homogeneous
on a large scale it contains local irregularities, such as stars
and galaxies.
What is the origin of these density fluctuations?
It is left to Rourke to untangle this puzzle. If you enjoy a good brain teaser then this book is for you.
The short answer, imagine what if there was an essentially infinite space of galaxies, just like we see, what would the whole look like?
Q1. Why was it so hot? It still is, it’s bigger than you realise.
Q2. Why so uniform? It may have been there a very, very long time.
Q3. See Q2. The universe has had a long time to achieve some sort of dynamic equilibrium.
Q4. Everything is still resonating, a self sustaining wobble as seen in the CMB.
Rourke takes the simplest model that fits the equations and observations and shows space time is more complex than we realise.
Happily, with an adjusted perspective, a very elegant and economical model shows how to interpret our observations.
For good measure Rourke addresses all these issues:
* Red Shift
* Quasars
* Cosmic Microwave Background
* Gamma Ray Bursts
* Dark Matter - not required.
One subject not covered by Hawking, is dark matter, much of his early research happened before the galactic rotation problem became widely apparent.
It is helpful to think of dark matter as the error term in general relativity.
Indeed, this is what Rourke does, with a minor adjustment to the standard solutions to Einstein’s equations. An assumption that the rotation of any body also affects the surrounding space time.
Interlude¶
At this point it should be apparent that this is a complex story.
Much of the complexity comes from the incredible success of the last sixty years of astronomical observation: radio telescopes, space telescopes, satellite observations, planetary observations and gravitational wave observatories.
These observations have provided a ripe field for speculation and ingenious solutions.
The big bang theory imposes a 14 billion year time scale on matters and this is increasingly becoming problematic.
The introduction of dark matter further muddies the water as it can always be invoked whenever observations are otherwise hard to explain.
In short, anyone faced with arguing that the Big Bang theory is a mistake is faced with a veritable mountain range of peaks to overcome before being able to make their argument.
Rourke slowly unpicks the puzzle.
There are some bold predictions along the way, in particular about Sag A*, the giant black hole thought to be at the centre of the Milky Way.
The prediction? At a modest 4 million solar masses it is just not big enough to drive a spiral galaxy the size of the Milky Way.
He suggests that there should be a mass of some 10-100 billion solar masses and that the Sun is likely some 50,000 light years from the centre, with Sag A* only about halfway to the centre, and whilst roughly on line to the centre, it is visibly NOT directly on line.
Red Shift¶
The interplay of distance and time.
Symmetries of space time and the mysterious hyperbolic rotations.
de Sitter Space is introduced as the simplest possible space time, based on special relativity.
Quasars¶
and Rourke shows how quasars could in fact be relatively close, low power objects, where the emitted radiation is red-shifted due to the intense gravitational field, in accordance with general relativity.
Cosmic Microwave Background¶
Dark Matter¶
not required!¶
Gamma Ray Bursts¶
Where is the sun?¶
Or more particularly, where is the centre of our galaxy?
How far is the sun from that centre?