I spent my early years in the same Yorkshire town as Fred Hoyle, the astrophysicist who coinded the term Big Bang.
It was the time of moon landings and I recall in junior school excited discussions as these things called black holes, they might actually exist. Black holes did not feature much at all in the cosmology of the day.
Some years later I found myself at Warwick University, learning mathematics from a wonderful department put together by Professor Zeeman. He had recently given the Royal Institution Christmas Lectures, which was in part, why ended up at Warwick.
It was Christopher Zeeman who gave a 30 lecture course on the foundations of mathematics.
It was a 30 hour tour through the history of mathematics, building the foundations on which all mathematics stands.
The story was interwoven with the history of the subject. A crisis that emerged as calculus itself was called into question.
The solution was a system based on axiomatics. 15 rules that numbers should obey.
It was shown that such a system did exist, complete with a plan for how to build such a system.
Things were taken one step further and it was shown that any two systems which obeyed the axioms would be equivalent in the sense that it would be possible to map every number in one system to a number in the other, preserving all the mathematical structure.
I feel very much, that some of this rigour is lacking in the astrophysics world.
We have a theory, the Big Bang theory, which fits our observations remarkably well.
- observed correlation of redshift with distance
- Cosmic Microwave Background
- the distribution of hydrogen, helium, lithium and other elements.
In order to fit the observations, a number of additions have had to be made:
- inflationary period
- dark matter
- dark energy
- theories of galactic formation
- Hubble constant tension
Given the numerous issues, it is very much worth asking if there is an alternative theory, one that does not require these adjustments?
Is the big bang theory the only possible explanation of what we see?
It so happens that there is such a theory, for this we first need to go back to Fred Hoyle's static universe.
Hoyle calculated how much matter would need to be spontaneously created to balance the observed expansion. It was only around 1 atom per year for each sky-skraper sized volume of space. He argued that spontaneous creation of such a modest amount of matter was less implausible than the big bang theory.
It was the discovery of quasars, highly red-shifted objects, assumed to be extraordinarily distant and powerful, an earlier phase of the universe, if you like, that was taken as strong evidence for the Big Bang. We do not see these powerful objects closer to us, so it is assumed they represent some earlier stage of evolution of the universe.
Fast forward to 2017 when I discovered, Professor Colin Rourke had a book out, with the title A new paradigm for the Universe.
He was my tutor back in the day at Warwick. He taught calculus with an approach he had developed for the Open University. He also lectured on curves and spaces, a subject that is essential to an understanding of the equations of space-time.
It has taken me many years to fully appreciate the ideas in the book. In which time it has been updated and republished, as The Geometry of the Universe.
It really does describe a paradigm shift, although much of the book is highly relevent to a Big Bang Universe too.
The book introduces the main characters involved in building models for Einstein's General Relativity. There is a whole cast of characters. There was much discusion of different models.
One of the principles behind the book is Einstein’s cosmological principle, that the universe is close to homogeneous and isotropic in the large-scale, on average. Whaterver that means.
Colin Rourke uses the strong cosmological principle to extend the argument to time as well as space, suggesting the universe is likely orders of magnitude older and larger than the big bang theory's 13.7 billion year age.
It is a natural consequence of Einstein's Special Relativity, that time and space become intertwined, so why not extend the cosmological principle to time as well?
There is a lot of evidence that the universe is extremely old. There are many observations that show that the whole system appears to be in a remarkable state of equilibrium. The sort of equilibrium that might take a very long time to establish, given the distances involved.
Many of the issues that arise in the big bang theory disappear, if there is simply more time for everything to happen.
A new theory of galaxy growth and formation is needed, one that is stable over long periods of time.
And then there is redshift.
Well it turns out this is just what we would expect to see. Based on local observations, nearby galaxies are typically in relative motion, relative to the distant stars at about one thousandth the speed of light or so.
The transform that takes a distant galaxies space time to our space time is a Lorentz transform.
We see the path of the galaxy, when viewed in just two dimensions, distance and time, as following a hyperbola, as distance and time intertwine.
Thus the Lorentz transform that takes a source's space-time coordinates and maps it to ours, shows the source's time dilating, relative to ours. In other words, the redshift we observe is just a consequence of special relativity.
Further note, that de Sitter Space produces exactly the right metrics to explore this model of the universe.
The result is that we see a source increasingly red-shifted the further it recedes from us. This emerges from the Lorentz transformations to map the source's time and distance to our space, and taking account of the curvature of space-time.
If we go backwards in time, past the point of closest approach of the galaxy, there is a symmetry with the path in forwards time.
But here, we see a large part of the source's time in a small period of our time.
Rourke suggests that this is what gamma-ray bursts are.
It's long past time for me to get this working in the `dss`_ module.
A galaxy, newly visible to us, bursting on the scene and showing it's history in a burst of light, before receding rapidly into the distance, redder and redder.
And now we are back to Fred Hoyle's continuous creation. Except that it is not magic creation of matter, rather it is matter that has existed for a very long time, a galaxy arriving in our visible universe.
In his marvellous book, The Nature of the Universe, Fred Hoyle had this curious paragraph:
... You will have noticed that I have used the concepts of space and time as if they coud be treated separately. According to the relativity theory this is a dangerous thing to do. But it so happens that it can be done with impunity in our universe, although it is easy to imagine other universes where it could not be done. What I mean by this is that a division between space and time can be made and this division can be used throughout the whole of our universe. This is a very important and special property of our Universe which I think it is important to take into account in forming the equations that decide the way in which matter is created.
I am extremely curious how Hoyle came to this way of thinking.
Whilst it is true that we as an observer can choose three dimensions of space and one of time, and we can use it throughout the universe, the same division is not possible for other observers.
They have there own local division, we have the same speed of light.
There's a transformation between the spaces that preserves distance.
It is curious, since it is precisely when you take account of special relativity, that it is clear why we see redshift, as well as extreme blue shift.
With a big bang theory, a universal time is partially reinstated, yet due to relativity, two observers in relative motion, will still not agree on the time and place of events.
Regardless, the key point is that the redshift we observe is exactly what we would expect to see in a static universe as described above.
These are generally much closer to home. Due to the mass at their centre, light can be highly redshifted. In short, not all red-shift is cosmological.
The idea is that there is a spectrum as a quasar grows into a galaxy. It's central black hole grows over time.
The light from a quasar can be highly redshifted, due to general relativity and the presence of a super massive black hole at its centre.
It can be hard to distinguish the cosmological and gravitational redshift, but James Webb will help enormously with this task.
Quasars are baby galaxies, many are part of the galaxy structure, others ejected from a galaxy.
The book provides a model, for which I believe all that is required is the density and temperature of the medium, and the mass of the central black hole.
There is surely plenty of data from JWST that will allow fitting of models to observations of quasars associated with local galaxies.
Once the Big Bang is abandoned, much of what we observe in the universe is easier to explain.
A good example are the harmonics in the Cosmic Microwave Background. With an older universe, there is now no constraint on how long different parts of the universe have had to communicate and develop harmonics.
The universe isn't a vacuum, it is full of dust. Suppose each particle of dust obeys the Sciama Principle?
The Sciama Principle, that a non-linear motion of a body induces a non-linear motion of the surrounding space.
It is a natural addition to Einstein's General Relativity, where the rotation of a body is assumed to have negligible effect on the surrounding space time.
It is important to note that this was a pre-computer age, so there is a strong focus on a simple model.
That model happened to be extraordinarily good, fitting observations such as the precession of Mercury. It has continued to be confirmed in many scenarios.
The theory runs into trouble with galactic rotation curves, where stars at the edge of galaxies have higher tangential velocities than you would expect for the standard model.
The standard solution has been to infer dark matter's presence.
Rourke says rotation does matter, but it is not normally noticeable unless the mass is very large, or you are close to the mass.
To drive a full sized galaxy you need hundreds of billions of solar masses, which raises important questions about Sgr A*.
I am not aware of the theories relating to how fast these humoungous black holes take to form post big bang.
The standard model has stars clumping together, then starting to spin up, with a central bulge and maybe a bar forming.
In a static universe there is plenty of time for a galaxy to grow, and in turn create new quasars, that may one day grow to be a full sized galaxy.
One thing the space telescope has shown is the dust across the universe.
From rings around Neptune and Jupiter, to the interstellar dust of galaxies.
This dust may be playing a critical role in the propogation of gravitational waves.
The Kerr metric is typically used to model the rotation
I have decided to just keep appending new versions at the top of this file.
The pictures from the James Webb Space Telescope have been stunning. They have generated a lot of excitement amnongst astrophysicists.
High redshift galaxies, is the big bang theory wrong? The word on the street is that this is just great new data to refine models and find the missing key to the standard big bang model.
My personal view, recently changed to a belief that the universe
From Peebles, Anomalies in Physical Cosmology:
Einstein’s cosmological principle, or assumption, is that the universe is close homogeneous and isotropic in the large-scale average.
To be more explicit about the role of this assumption in the standard ΛCDM theory used in this paper I offer the following definition.
The theory applies the standard physics of matter, radiation, and Einstein’s general theory of relativity with its cosmological constant to a cosmologically flat universe that is a spatially stationary, isotropic, random process with a close to scale-invariant power law power spectrum of Gaussian and adiabatic departures from homogeneity.
This trimmed-down theory has eight free parameters (the density parameters in ordinary matter, dark matter, the CMB, and neutrinos with negligible rest masses; with Hubble’s constant, the primeval Gaussian process amplitude and power law index, and the optical depth for scattering of the CMB by intergalactic plasma).
I ask the question, what would a universe with Einstein's cosmological principla look like?
What if the universe is essentially static, vast and truly ancient.
Suppose that galaxies gradually grow from smaller systems, until they reach a size that is naturally in balance with the surrounding universe.
Stirring dust into stars and planets for a very long time indeed.
Over time, quasars can form along the galaxies arms. They may eventually be ejected from the galaxy and appear as baby galaxies.
These quasars complicate astronomy significantly as they often have redshift that is due to a large mass at their centre. Einstein's general relativity explains how a central mass can slow time significantly. This influence can extend out far enough to shift the light from the active region.
To model a quasar we just need the central mass, and the density and temperature of the surrounding medium. JWST can help greatly with the last two parameters.
It is in general difficult to distinguish a small, nearby quasar from a more distant galaxy, where all the redshift is assumed to be cosmological. The angular size of the objects can clearly help clarify matters.
With JWST we have high resolution images of nearby galaxies, the density and temperature of the dust should be much clearer.
I have been on a journey, and found new perspectives.
It has been a way to see how the world might have changed or not.
Sharing ideas with others, finding out what people are doing and why. What is the perspective, why do they believe what they do.
It has been a wonderful time in our exploration of the universe we find ourselves in.
A space telescope at L2, observing the light in the infra red.
I met Norm Newton, just the perfect name. At a cafe in the Universe, close to home.
My journey had been shrouded in doubt, was the world quite ready to know what they see?
It's stunning, it's crisp, with a gravitational twist, all in the deep infra red.
What's distance, what's frequency as we spin through time.
A mathematician with a furious fascination with the details of topological space. Proving beyond, the shadow of a doubt that all spheres behave in just the same manners.
Yet the deltas exchange and in time build collective understanding.
There's noise everywhere, with some glorious peaks.
When one with such a grasp of how our observations are constrained, whilst explaing the rhythms in space time.
** Work in progress -- much rambling ahead, for now this is just random thoughts to be resorted **
Borrowing the title of Fred Hoyle's epilogue to his Nature of the Universe.
My views have changed significantly, since I first became aware of Colin Rourke's work in cosmology.
It is a curious transformation, in which to fully appreciate the simplest possible universe, we first have to forget much that we assume is undoubtedly true.
Light. Is there anything else?
de Sitter Space is an extremely good approximation to what we see.
It is a vacuum solution to Einstein's equations, with no matter.
Most of the universe, in terms of space, has very little matter. We should expect de Sitter Space to be a good approximation, and indeed it is.
Throughout this space, it is the Cosmic Microware Background that defines the space.
Where does this orignate from? With an essentially static universe we can expect it to be dominated by distant sources.
Assuming the universe is ancient, we can expect waves to form as it is modulated by the intervening matter.
There are harmonics in the CMB, these are unsurprising, given the potential age of the universe. A model should however take these harmonics into account.
An a particle of dust which absorbs a quantum of light, that is rotating with the body, will move some distance before the electron decays and emits the photon.
It will thereby result in an oscillation in the surrounding space time with the same angular velocity as the body, proportional to its mass, and falling off linearly with distance.
The drop off is inversely proportional to distance, because the radiation has a direction, determined by the plane of rotation of the dust.
The gravitational fog, that blurs our vision around the de Sitter Radius, obscures the fact that some of the light which makes up the cosmic microwave background potentially originates from a very long way beyond the de Sitter radius.
It took me a very long time to appreciate this, the 13.7 billion year horizon still being a parameter in de Sitter Space.
The horizon is not an abrupt discontinuity, as would be expected in a big bang theory, but rather a misty horizon that gives glimpses of the universe beyond.
The key is to accept the possibility that the universe is very much older than the window our visible universe appears to give.
Key ideas:
a static universe that is essentially unbounded in size and time
Most of the universe has no matter and de Sitter Space, a solution to general relativity for a universe with no matter, appears to be a very good match for our observations.
Godel universe: causality issue.
Einstein-Cartan theory seems to be essentially the same modification to general relativity that Colin outlines in appendix A.
wikipedia currently has the following note:
Einstein–Cartan theory has been historically overshadowed by its torsion-free counterpart and other alternatives like Brans–Dicke theory because torsion seemed to add little predictive benefit at the expense of the tractability of its equations.
Since the Einstein–Cartan theory is purely classical, it also does not fully address the issue of quantum gravity. In the Einstein–Cartan theory, the Dirac equation becomes nonlinear..
quantum gravity is really not important in this story. By this, I mean, the universe has been in a similar state for so long that we do not need to worry about the time when everything was so close. First we need to get an accurate understanding of the broad structure of the universe.
the quantum field is, of course, important, it is just not a reasonable objection to a macro theory of gravity.
define a sphere around each galaxy, the radius at which microwaves dominate the energy.
Why microwave? Energy lost through curvature, each source can only contribute a finite amount of energy.
Rate of arrivals of new galaxies.
Balance with outflowing, red-shifted field.
These are baby galaxies. They are often associated with a nearby galaxy, or indeed embedded within the structure of a full galaxy.
Light from small quasars is typically significantly red-shifted due to the proximity of the active sphere generating the light to the centre of the black hole.
The classical solutions to Einstein's equations make no assumptions about how mass is distributed within a rotating body.
The assumption is that only the total mass affects the gravitational field and that mass can be assumed to be concentrated at the centre of the body.
A body's affect on the rest of the universe matches the rest of the universe's effect on the body.
Think about the Earth and the Moon.
Assume that there exists a field that defines an extremely high frequency oscillation.
The bodies modulate the signal.
A body of mass M rotating with angular velocity omega induces an oscillation of the same frequency in the surrounding space.
What is the angular velocity of the Sun?
It appears to rotate in around 27 days, but what other rotations are there within the Sun?
What about the individual atoms, with electrons orbitting them?
They are rotating too.
Imagine a body such as the Earth and the moon, as the moon orbits the earth.
It takes a second or two for a wave to make a round trip from earth to moon.
The moon, conveniently, seems to be rotating with its orbit, always with the same dark side hidden.
To first order, the oscillations of atoms define the field, leading to general relativity.
The sum of these oscillations presumably producing a thermal spectrum.
Two bodies a distance r apart are able to accelerate towards each other by an amount proportional to m_1 * m_2 / (r * r).
How? Gravity causes each body to reflect back to the other it's rotation, weighted by the above amount: the product of the two masses divided by the square of the distance between them.
Each mass reflects back the wave it sees from the other, the size of the reflection being proportional to the bodies mass, with the effect dropping off inversely with distance.
For the full round trip that gives the formula above.
The result is that standing waves will emerge, such as the ocean tides, which allow the bodies to move in harmony.
The fundamental wavelength being r/c.
What I am trying to argue here is that just the "massive bodies reflect back what they see" -- which is implicit in the Weak Sciama principle????
So Newtonian Gravity falls out naturally to first order.
Now, note that any body obviously has other rotations than those of its atoms.
The moon does a full rotation roughly every 28 days, as does the Sun.
Both presumably are seen to earth as rotations, or oscillations, around that period.
But 28 days is very much longer than the period it takes an atom to oscillate.
Following Planck's law and assuming the energy a mass generates with a given wavelength is inversely proportional to the wavelenth, would give one way to make the various rotations commensurate.
In other words explain why only the oscillations of the atoms need to be taken into account to get a very good approximation of reality: General Relativity.
To go to the next level, other oscillations need to be included. In the case of a galaxy, there is assumed to be a giant rotating mass at the centre.
[n] dumbell systems: two roughly equal sized stars.
Implication for black holes: all the mass concentrated around the surface?
Oscillations.
Thing of event horizon as the point where light is slowed so it rotates with the black hole?
Still rotating, you can't unmake your deal with the universe.
By that, having used up energy to rotate really fast you can't crawl up into a black hole and pretend it never happened, at least that would require work. Rather the body just continues as nothing has happened.
Microwaves can and do mediate the signal?