# Estimating The Fractal Dimension of the Spiders of Mars

Above is an image of “dry ice spiders” on Mars. Every spring the Sun warms up the Martian south polar icecap and causes jets of carbon-dioxide gas to erupt through the icecap. These jets carrying dark sand into the air and spraying it for hundreds of feet around each jet forming these wonderful spider-like structures. Notice how they look very much like fractals.

Just for fun, and because I had a week off, I wondered if I could calculate, or really estimate the fractal dimension of these structures. To do this, I decided to use the box-counting dimension, which gives a bound on the fractal dimension. Rather than give a careful description here I will point to the following link.

I did this in a few stages using Mathematica. First I needed to get a form of the image that can be used.

The image of the left is what I then used as the fractal that I wanted to estimate the box-counting dimension of. The image of the right is the overlay of the original image and the “extracted” image. This shows that it is not perfect, but it will do for now.

Then I needed to write a Mathematica notebook that will give an estimate of the box-counting dimension. Of course, before I applied it to the spider question, I tested it on fractals with know fractal dimensions. It worked very well in general. Thus, I am confident that the estimate for the spider landscape is reasonable (modulo details of how I created the simpler black and white image).

So, what do I get for the box-counting dimension?

dimbox= 1.758 ± 0.013

Before anyone takes that figure too seriously, one should study many more of these spiders and see what range of values ones gets. Also the sensitivity to how I have “extracted” the fractal from the original should be tested. I have no idea if this has been done before or if it is interesting to anyone, like i said just for fun.

# Moon pictures

Just a few snaps of the moon with my new camera, Cannon Powershot 420 is. It has been a while since I last observed or photographed the moon.

27th December 2017

28th December 2017

1st January 2018

5th January 2018

6th January 2018

# The Polish and Welsh contributions to the discovery of gravitational waves

I just want to acknowledge the contributions of two teams to the discovery of gravitational waves. These groups are only part of the wider community and I highlight them for purely personal reasons.

The Polish group

The Virgo-POLGRAW group,  lead by   Prof. Andrzej Królak at IMPAN.

The Welsh group

The Cardiff Gravitational Physics Group,  and within that the Data Innovation Institute lead by Prof Bernard F Schutz.

# Quantum gravity

 The subject of a quantum theory of gravity is interesting, technical and very difficult. However, there are three basic principles that we expect such a theory to obey.

Creating a full quantum theory of gravity seems to be out of our reach right now. String theory comes close, but the full theory here is not understood. Loop quantum gravity also offers a good picture, but again technicalities spoil achieving the goal.

I am no expert in quantum gravity, but I thought it maybe interesting to outline three basic ‘rules’. The full quantum theory of gravity should be:

1.  Renormalisable (maybe not perturbatively) or finite.
2. Background independent.
3. Reducible to general relativity (plus small corrections) in a sensible classical limit.

As a warning, I will not be too technical here, but will use some standard language from quantum field theory.

Renormalisable
The standard methods of quantum field theory are to expand the theory about some fixed configuration, usually the vacuum, and consider small fluctuations about this reference configuration. However, in doing so some techniques are needed to remove the appearance of infinite values of things you would like to measure in the lab. These methods are collective known as ‘perturbative renormalisation’. For example, we know that the quantum theory of electrodynamics can be handled properly using these methods.

However, general relativity as described by Einstein is not amenable to methods of perturbative renormalisation. Well, this is true if we want a full theory. What one can do is consider quantum general relativity as an effective theory. That is we accept that at some energy scale the theory will breakdown, but as long as we are not at that scale the theory is okay. By adding a ‘cut-off’ we can understand quantum general relativity using Feynman diagrams to ‘one-loop’ and calculate graviton scattering amplitudes and so on.

Interestingly, there is some evidence that general relativity or something close to it is nonperturbatively renormalisable; this is known as asymptotic safety. With no details, the idea is that quantum general relativity is not ‘sick’ and well-defined, just not as a perturbative theory like quantum electrodynamics. This is fascinating as it means that a proper quantum theory of gravity may not be a theory of gravitons after all! Recall that small ripples in the electromagnetic field are quantised and understood to be photons. Maybe it is not really possible to describe quantum gravity in a similar way where small ripples in space-time are quantised.

Alternatively, a full theory of quantum gravity could be finite. That is we can employ perturbative methods, but do not need renormalisation techniques. Amazingly, we know of supersymmetric Yang-Mills theories that are finite. Moreover, superstring theory is also finite (I am unsure as to how rigours the proof are here, but the string community generally accept this as fact). It maybe possible that the full theory of quantum gravity is finite from the start. This suggests that looking at supersymmetric theories of gravity is a good idea, but by no means the only thing one can think about.

In short, any full quantum theory of gravity must allow us to calculate things we can hope to measure.

Background independence
This means that the theory should not depend on any chosen background geometric fields. In particular, this is taken to mean that the theory should not require some chosen background metric.

String theory as it stands fails on this. However, string theory is usually employed using perturbation theory and so some classical background is chosen, often 10-d flat space-time.

Loop quantum gravity seems better in this respect, but it has other problems.

In short, any full quantum theory of gravity should not require us to fix the geometry (and maybe topology) from the start.

Reduce to general relativity
General relativity has been so successful in describing classical gravitational phenomena. It is tested to some huge degree of accuracy and so far no deviations from it’s predictions have been found. General relativity is a good theory within the expected domains of validity.

Thus, any quantum theory of gravity must in some classical limit reduce to general relativity, up to small corrections. These quantum corrections must be small enough as not to be seen already in astrophysics and cosmology.

If a quantum theory of gravity cannot be shown to reduce to general relativity in some limits (there maybe several ways of doing this) then we cannot be sure that we really have a quantum theory of gravity.

Today we know that string theory gives us general relativity + small corrections. In essence this is because the spectra of closed string theory contains a spin-2 boson, via rather general arguments we know that this has to be the graviton and the field equations are essentially the Einstein field equations. (Remember this is all in perturbation theory).

Recovering general relativity from loop quantum gravity has yet to be done. This I would say is a sticking point right now.

In short, any full quantum theory of gravity must reproduce the phenomena of general relativity is some classical limit(s).

# Newton to appear at a pub in Cardiff!

 As part of this year’s Cardiff Science Festival the Institute of Physics has organised for Prof. Mike Edmunds to perform his one man play about Sir Isaac Newton at Porter’s Bar in Cardiff on Wednesday, 16 July 2014 from 18:30 to 20:00.

This event is completely FREE, but spaces are limited. Please follow the link below for more details.

# Nicolaus Copernicus' birthday

 Today, the 19th February is the birthday of Mikołaj Kopernik, maybe better known in the west as Nicolaus Copernicus. Kopernik was born on the 19th February 1473 in the city of Toruń, in the province of Royal Prussia, in the Crown of the Kingdom of Poland.

The heliocentric hypothesis
De revolutionibus orbium coelestium (1543) is the book in which which Kopernik offered an alternative model of the Solar system to Ptolemy’s geocentric system. Kopernik’s new model places the Sun and not the Earth at the center of the Solar system and represented a new shift in thinking. Importantly, the heliocentric model fits the astronomical observations much more naturally than the geocentric model which required strange phenomena like epicycles.

Nicolaus Copernicus Monument in Warsaw
In Warsaw there is Bertel Thorvaldsen’s monument which was completed in 1830. The monument comes with the words “Nicolo Copernico Grata Patria” (Latin: “To Nicolaus Copernicus from a Grateful Nation”) and “Mikołajowi Kopernikowi Rodacy” (Polish: “To Mikołaj Kopernik from his compatriots”).

Early in the Nazi German occupation of Warsaw in 1939, the Germans replaced the Latin and Polish inscriptions on the monument with a plaque in German: “To Nicolaus Copernicus from the German Nation”.

On 11 February 1942 Maciej Aleksy Dawidowski removed the German plaque!

During the 1944 Warsaw uprising the momentum was damaged and shortly after the Germans decided to melt it down for scrap metal. The Germans sent the monument to Nysa (southwestern Poland), but they had to retreat before they could melt it down. The Polish people returned the monument to Warsaw on 22 July 1945. The monument was renovated and unveiled again on 22 July 1949.

In 2007 a bronze representation of Kopernik’s solar system, modeled on an image in his De revolutionibus orbium coelestium, was placed on the square in front of the monument.

You can see some pictures of me next to the monument here.

# Galileo's birthday

 Today, the 15th February is Galileo Galilei’s birthday. He is often referred to as the farther of modern physics. He is of course also know for his discoveries using his telescope including the Galilean Moons of Jupiter, the rings of Saturn, the phases of Venus many geographical features of the Moon. Galileo as born on the 15th February 1564 in Pisa, Italy.

His legacy for theoretical physics
Galileo’s legacy for physics was his blend of mathematics with experimentation. Most of the contemporary science at the time was rather qualitative and Galileo was one of the first to believe that the laws of nature can take a mathematical form.

Galileo Galilei Wikipedia.

# New exhibition at Jodrell Bank near Manchester

 Big Telescopes, Big Science is a brand new exhibition which will be unveiled in February at Jodrell Bank visitors centre. the exhibition will include hands-on activities showing how telescopes work and how it is possible to use many smaller telescopes to act as one large telescope.

There will also be running family science shows as part of the half term activities.

# Professor Copeland wins Rayleigh Medal and Prize

 Professor Edmund Copeland of the University of Nottingham has won the 2013 Rayleigh Medal and Prize as awarded by the Institute of Physics.

Professor Copeland was awarded the prize for his work on particle/string cosmology from the evolution of cosmic superstrings, to the determination of the nature of Inflation in string cosmology and to constraining dynamical models of dark energy and modified gravity.

A personal note
I first met Professor Copeland back in 2005 when was at the University of Sussex. I was there studying for my masters degree. He then, in the same year moved to Nottingham to establish the Particle Theory Group.

2013 Rayleigh Medal and Prize, IOP website.

Prof. Copeland’s homepage

# Large meteor over South Wales

A meteor was spotted traveling across the night sky by people across many parts of the UK including Cornwall, Hampshire, Lancashire, Worcestershire and South Wales.