Magnetism and the Lunar Eclipse

Being away from home and in a very difficult environment, I have had the opportunity to be mesmerised by the many loving and genuine young people that I have met, so peaceful and kind with some of the most heartbreaking stories I have ever heard. It is wonderful to see the awe in their eyes when I explained to them some of the upcoming events that our galaxy is offering. On Friday the 27th of July at 8.15pm, we will have the chance to witness the Lunar Eclipse begin, reaching full eclipse by 10.30pm and often known as ‘blood moon’ (it will go a deep burnt red due to refraction of light from our atmosphere much like a sunset) that will be the longest lunar eclipse of the century. In addition, the planet Mars will be at opposition when it will be at its most brightest and nearing its closest to earth in 15 years, accompanied with the International Space Station passing on what will be a clear summer’s evening that I will be spending on the rooftop of this dilapidated building in the heart of the Middle East. While light pollution is a significant issue, everyone will get a chance to witness naked eye these phenomenal galactic events that gives them a glimpse into a series of astronomical narratives that will no doubt provoke questions about our planet, orbits and space. These events arrive at the same time I hear the amazing news that my program working with refugees and asylum seekers back home in Australia will be funded, where I will take disadvantaged girls and young women out on hikes, camping and viewings over my telescope where I will teach them about stargazing. It has given me inspiration on my only afternoon off for the week to write this blog post!

I was asked today, “how does all this happen?” and I attempted – albeit due to language barriers rather awfully! – a brief explanation of the moon crossing the ecliptic where the Earth, Sun and Moon are aligned when the moon orbits through the shadow of Earth. Planets orbit around the sun, the gravity pulling and keeping them in orbit and gravity acts as a powerful force between two objects with a mass. You can read more on the eclipse in a previous blog post that I wrote. Magnetism is an entirely separate force despite similarities and it depends more on particular properties rather than simply mass, such as electrons and can both push and pull. Magnetism is present throughout the universe and we can experience it in many ways; when I am out hiking, my compass explains the pressure of magnetism and direction with the movement of the needle as it is attracted by the force.

There are a number of properties and varieties of magnetic forces that explain invisible fields that applies a force that influence objects or material from the magnetism. There are rules that confirm magnetic fields are dipolar and just like earth has both a north and south magnetic pole and the ‘magnetic flux’ explains how the force and attraction between the poles – usually represented by lines as visible in the image below – that can be averaged by the magnetic field and the perpendicular area the field infiltrates. Measurements of the force is determined by the mathematical formula F= qvB (Lorentz Force Law), which is the magnetic force, the charge, the velocity and the magnetic field and the unit of these field are measured in terms of Standard International (SI) units known as tesla.

Earth’s magnetic field is known as a geomagnetic field and magnetosphere the predominate reason for the magnetic field is the liquid iron core surrounding the solid inner core is the source of this phenomenon, the very ‘magnet’ where the electric currents produced by the flow of iron and other metals including nickel cause convection currents from the inertial force of the Coriolis Effect that ultimately splits the field into a surrounding force that envelops Earth and aligns back into the same direction. The changes in temperature and composition of the liquid core creating the currents that rise or sink matter all play a part in Earths magnetic field, that can be captured visually when solar winds collide with it (usually where the magnetic force is much stronger near the north and south poles) and the charged particles trapped by the magnetic field produce the aurora borealis or the aurora australis.


The picture explains the rotational poles but that their alignment geographically differs from our north and south poles on earth, whereby the magnetic south poles resides further north of Antarctic’ South Pole and quite close to the south of Australia while the north magnetic pole is closer to northern Canada and thus south of the North Pole. The magnetic lines explain the streamlined flow of the magnetic field that makes it easier to ascertain the process mathematically. Jupiter has a number of powerful toroidal magnetic fields where the intensity is said to have formed from the dynamic movements of the metallic hydrogen within; the field on the surface of the clouds is almost ten times stronger than earth’s. The Milky Way also has magnetic fields as do galaxies and the universe contains some colossal magnetic fields, where observations of galaxy clusters have found magnetic fields extending millions of light years!

The magnetic force is the attraction or the repulsion (as you experience when attempting to connect two magnets with equal poles) occurs from the magnetic field. The properties of electrical fields (pole) with a positive and negative charge differ with that of magnetic fields (dipole) despite a close correlation, because electromagnetism involves a magnetic dipole producing an electric field as it moves and conversely an electric field can produce a magnetic field meaning the difference is an elementary change in the field. A magnet does not have an electric charge as two separate poles, while a dipole interacts as a charge as visualised in the following image. What this means is that the electrical force itself behaves on a charged particle in the direction of the field and does not need motion while a magnetic force requires this motion and acts perpendicular to the magnetic field.

Gravitational fields also acts as force fields for mass and the gravitational force itself depends on the mass and the mass experiences the gravitational force. The gravitational field has a place in every direction and point in space and known by the formula g = F/m where F is the force of gravity. While this may be a brief example of the difference between magnetism and gravitational fields, it will be a wonderful experience with the full lunar eclipse and Mars showcasing the marvels of the universe over a hot, clear night here in Jerusalem!

Further Reading:

Maurizio Gasperini, Theory of Gravitational Interactions, Springer (2016) 115
Stephen Blundell, Magnetism: A Very Short Introduction, Oxford (2012) 106
Anupam Garg, Classical Electromagnetism in a Nutshell, Princeton University Press (2012) 83

The Cassini-Huygens Mission to Saturn and Titan

Following the painstaking experience watching Titan on Netflix last night (I highly recommend you don’t watch it) which was about the possibility of life on Saturn’ moon following an existential crises plaguing earth, out of sheer agitation I decided to look into this theme and find out more. The Cassini-Huygens mission was a seven year journey of the NASA Cassini Orbiter along with the European Space Agency’ Huygens Probe intended to travel to the Saturn system. Titan IVB-Centaur rocket was launched from Cape Canaveral carrying the orbiter and probe in 1997 and passing Venus, Earth and our moon, an Asteroid Belt and Jupiter, the Huygens Probe successfully landed on Saturn’s moon Titan in 2005. The Cassini spacecraft also managed to capture new and detailed information and images including a number of new moons such as Methone and Pallene, as well as the first spacecraft to orbit Saturn that showcased surprising activity on Enceladus, new rings around Saturn, and a plethora of additional information not previously known by scientists. The 2 hour 27 minute descent to the surface was matched with 72 minutes on the frozen ground until contact with Cassini was lost, and the probe managed to obtain images of Titan’s geology and meteorology to reveal astonishing similarities to Earth. But is Titan really similar to Earth?

The primary scientific goal of the mission was to explore Saturn’s interior and atmosphere, the ring system and the magnetosphere and plasma environment, as well as the magnetic field and origins of Saturn. In addition, a strong focus Saturn’ second largest moon, Titan when the Huygens probe was launched into the moon through the thick atmosphere during its descent to the surface. The probe was intended to study both the atmosphere and the surface composition and contain six instruments that enabled this, such as the Huygens Atmospheric Structure Instrument (HASI) designed to measure the electrical and physical properties of Titan.[1] It was additionally equipped with the following experiments:

Surface Science Package (SSP) aimed at determining the properties of the surface where the probe landed in order to ascertain further details of its composition and measure other aspects of the landing site.

Descent Imager Spectral Radiometer (DISR) that used sensors to uncover spectral measurements of the surface and as it descended toward the surface took images of the spectra.

Gas Chromatograph and Mass Spectrometer (GCMS) that attempted to identify gaseous atmospheric properties and captured material that it analysed as it descended to the surface.

Aerosol Collector and Pyrolyser (ACP) is a device that collected chemical and aerosol samples of the atmosphere and analysed the material taken from the atmosphere.

Doppler Wind Experiment (DWE) detected Doppler shifts that the probe experienced and caused by the atmosphere and winds was measured along with other properties through radio signals.[2]

The atmosphere of Titan contains the chemical composition mostly of nitrogen, but also a mixture of methane, ethane and other hydrocarbons, which makes the composition itself similar to that of Earth that contains 80% nitrogen,[3] particularly as it is the only other planetary body in our solar system that has evidence of liquid on the surface. Images from Cassini show how the surface of the moon contains rivers of ethane and methane and explains why it is the only moon that has clouds and a thick atmosphere. The orbital period of Titan around Saturn nears 16 days and is tidally-locked to Saturn, while the distance to the sun is almost ten times further than earth at 9.54 AU making the solar energy captured by the moon at a much lower rate, however the atmosphere enables Titan to capture solar energy. “It’s partial transparency to significant amounts of sunlight, and its high opacity to longer wavelengths… [s]ome of the energy from the Sun reaches the surface of Titan because solar radiation consists mostly of photons at near-visible wavelengths and the atmosphere is partially transparent at those wavelengths,”[4] that allows only about 10% of the energy to reach the surface. This energy is then absorbed by the surface that releases infrared heat out and back into the atmosphere that re-radiates by out and back down and the phenomenon of this greenhouse effect contributes to the temperature, which is at 92k (-180 degrees Celsius). The atmospheric pressure of Titan is 60% greater than Earth and the radius is almost half, but as the mass of Titan is 1.3452 x 10^23 kg compared to this size, the gravity cannot hold the gas and thus the atmosphere is much greater than that of Earth.

Seasonal variations to do exist on Titan and the Cassini mission aided researchers to ameliorate their understanding of the patterns of atmospheric changes, arriving on the northern hemisphere of Titan during winter.[5] Seasonal changes, however, are incredibly slow as it is driven by the eccentricity of Saturn’ 29.5 yearlong orbit around the sun, and the atmosphere responds to the effects of these changes in rising and falling temperatures as well as day to night variations. The orbital configuration has resulted in an imbalance of methane lakes and rivers in the northern and southern hemispheres of Titan that transports chemicals through evaporation and precipitation differently. The atmospheric pressure on the surface is at 1500mbar and researchers have confirmed the moon experiences cryovolcanism captured by observations from Cassini where the eruption style and composition is similar to volcanoes erupting liquid instead of lava.[6] Among the other important findings include the origins of Titan’ methane and the chemistry of the atmosphere as the gas increased during the descent of the probe, until it reached the surface when a spike was detected at almost 40% increase in methane suggest the possibility during the formation and accretion period, methane became trapped in the ice and reached the surface through cryovolcanism. In addition, radiogenic argon-40 (40Ar) was also detected that further confirms details of Titan’ interior since 40Ar can only form through the decay of potassium-40 (40K) that is found in rocks.[7]

HASI findings also enabled scientists to measure the density of the upper atmosphere and showed the thermosphere to be warmer and with a greater density. Atmospheric circulation and the transportation of heat was captured by the DISR by the “imbalance seen in the radiative flux measurements”[8] and it indicates winds verified by the probe as it encountered the flow from west to east and therefore the same direction as the rotation of Titan. Models have since showed that the captured data confirmed a reversal of direction and different points during the descent of the probe caused by temperature variations between the northern and southern hemispheres and within the Hadley cell that circulates from the north and south poles.[9] The super rotating winds measured the Doppler shift during the descent of the probe and measured large variations in wind speeds as it decreased the closer it reached the surface and the findings also suggest that Titan does not have a mesosphere as was predicted.

The atmosphere of Titan was found to be stratified comparatively to Earth’ troposphere where variations in temperature produce layers and while the amount of sunlight is minimal, the icy moon still contains wind and clouds, where clear by images by Cassini indicate massive dunes on the surface.[10] This provides greater details of the structure of the atmosphere including its temperature, as the DISR captured images of the surface and terrain and showed a plateau of dried river beds and lakes with narrow channels and dendritic networks that parallel the fluvial configuration you’ll find on Earth particularly erosion which DISR detected and indicative of such activity. Buried below the icy surface together with the discovery of what is known as Schumann resonance, very low radio signals in the atmosphere (around 36 Hertz) and for such signals to be reflected, “an ocean of water and ammonia which is buried at a depth of 55-80km below a non-conducting, icy crust”[11] could explain this.

There were a number of reasons for destroying the Cassini orbiter by incinerating it through the powerful atmosphere of Saturn. Not only will it provide additional information to scientists both gaining closer access to the rings of Saturn and the upper atmosphere that provide a glimpse of the interior structure and the opportunity to accurately ascertain the age and composition through closer inspection of the mass of the rings surrounding the planet, but also because of regulations vis-à-vis interplanetary contamination. The preservation of the integrity of the solar system in order to prevent and potentially damage both other planets and our own has led to all spacecraft to undergo sterilisation processes to avoid microbe contamination, particularly of planets or moons that may be capable of organic habitat. The Cassini spacecraft detected a number of new finds on Enceladus that verifies the possible conditions for contamination of microbes from Earth. Cassini itself captured vapour being released from Enceladus that confirmed an oceanic subsurface Knowing that the craft itself has a maximum output of fuel, to prevent any risk of it contaminating the integrity of the moon, scientists decided to plan the death of the device.[12]

While Titan does have similarities to Earth, particularly for having a thick atmosphere and a high percentage of nitrogen, but a number of other missing or differing constituents make these similarities marginal at best. The benefits of the Cassini-Huygens mission to Saturn and Titan enabled scientists to gain further insight to clarify these terrestrial and atmospheric differences.

[1]Fulchignoni, M., Ferri, F., Angrilli, F. et al. Space Science Reviews (2002) 104: 395.
[2] Patrick Irwin, Giant Planets of Our Solar System: Atmospheres, Composition, and Structure, Springer Science & Business Media (2003) 330
[4] Athena Coustenis, Fred Taylor, F. W. Taylor, Titan: The Earth-like Moon World Scientific (1999) 62
[5] Ingo Müller-Wodarg, Caitlin A. Griffith, Emmanuel Lellouch, Thomas E. Cravens, Titan: Interior, Surface, Atmosphere, and Space Environment, Cambridge University Press (2014) 215
[6] R. M. C. Lopes, Cryovolcanism on Titan: New results from Cassini RADAR and VIMS:
[7] Robert Brown, Jean Pierre Lebreton, Hunter Waite, Titan from Cassini-Huygens, Springer Science & Business Media (2009) 182
[8]Ibid., Titan from Cassini-Huygens, 345

The ‘Seeds’ of Super Massive Black Holes

Stellar black holes are scattered throughout the universe, formed under the right conditions when stars reach the end of their life cycle as it collapses into itself when it no longer contains the fuel to counteract the pressure of gravity and resist compression. In order to produce a black hole, the exploding star would need to have a mass greater than our sun (at least twenty times greater) so that there is enough material – which is dispersed following the supernova – to form a black hole and will continue to grow as it consumes material such as gas and stars that draws them into the dense space. Super Massive Black Holes (SMBH) are comparatively galactic monsters that live in the centre of most galaxies and while their origins are indeed more difficult to ascertain, a number of theoretical possibilities continue to elude astronomers. Do they having the humble beginning by starting as stellar black holes that grow over billions of years through accretion and even mergers with other black holes? The confirmation that Sagittarius A* located 26,000 light years away is a SMBH located in our very own galaxy and a number of techniques have been used to ascertain its position, particularly through comparative observations found in the properties of other host galaxies and quasars. The recent quasar, J1342+0928, has given astronomers a glimpse into the possible causes of such huge SMBH.

Albert Einstein predicted the existence of black holes through his general theory of relativity, however it was not until Sir Martin Rees proposed the idea that extremely massive black holes could exist within the Active Galactic Nuclei (AGN)[1] of our own and most galaxies. His theory pieced together a detection of an unknown radio source by Bruce Balick and Robert Brown at the centre of the Milky Way and a possible demonstration that the object with such powerful gravitational force could be caused by an SMBH. AGNs are the centre of an active galaxy and depending on the properties and activity that occur within name, AGNs can be called Quasars, Seyfert Nuclei, Blazers, Liners, Radio Galaxies and BL-LAC objects and a number of other names that verifies the diversity of activity the centre of galaxies can have.[2] Host galaxies themselves also present unique characteristics and types including the elliptical, spiral and irregular galaxies and each have different components. Classification of galaxies was initially developed by Edwin Hubble that divided and then subdivided commonly found features that exhibit unique properties the he coded into a general system; a spiral galaxy, for instance, contains a bulge at the centre, surrounded by a halo and a disk structured as arms like spirals around the galaxy. Further classifications developed as the study of galaxies improved including de Vaucouleurs’s classification of galaxies that helped classify unusual properties or peculiarities, such as Quasars.[3]


Following Balick and Brown’ discovery, there were clear limitations to radio observations to verify whether the source was specifically a SMBH and continued efforts led to NASA’s Chandra X-Ray Observatory to spot never before seen x-ray emissions by penetrating the galactic dust and clouds that blurred the possibility of a closer investigation to this blackness at the heart of our galaxy using radio sources, giving us more insight about the activity and behaviour of SMBH.  The Very Large Array as part of the National Radio Astronomy Observatory (NRAO) includes 27 radio antennas configured to provide images that would give the resolution of one dish at almost 130 metres in diameter.[4] The image below is one such image taken from the observatory in New Mexio and shows a central source – now known to be Sag A* – has forced ionized gas into a mini-spiral rotating around centre and revealing the possible features of a concentration of dark matter, but whether this concentration was a SMBH was not confirmed as well as raising the question and nature of SMBH as apparently motionless. “The implied minimum dark matter density of ~3×10.9 M  pc^-3, however, still allowed a cluster of dark objects, such as neutron stars or stellar mass black holes, as one of the alternatives to a single supermassive black hole because the measurements did not force the cluster’s lifetime to be shorter than the age of the Galaxy.”[5]

Picture 1

As observations have also included evidence of the emission of radiation including Infrared, X-ray and Gamma-Ray sources, other telescopes including the Very Large Telescope (VLA) managed by the European Southern Observatory in the Atacama Desert of northern Chile and the 10m W. M. Keck I telescope on the summit of Mauna Kea in Hawaii has mapped the orbits of stars and objects that are within one parsec (about 3.26 light-years) of the central dark object, enabling astronomers to measure the mass of Sgr A* utilising Kepler’s Laws that calculate the length of time it takes for the orbiting object to encircle the galactic centre together with the semi-major axis, leading astronomers to believe the centre of our galaxy is contained by a SMBH equivalent to 4 million solar masses.[6] “Orbits are derived simultaneously so that they jointly constrain the central dark objects properties: its mass, its position, and, for the first time using orbits, its motion on the plane of the sky.”[7] This is because the dark central object has a powerful mass within such a small radius nearing 100 AU (1 AU is the distance between Earth and the Sun or about 150 million kilometres) that suggested dark matter to be confined in a space of 0.015pc ruling out the possibility of a cluster of stellar black holes as the source, leading to the conclusion that it is a SMBH. The Fermion Ball Hypothesis offers an alternative possibility for the blackness problem as it attempts to explain the supermassive dark object at the centre to be a ball of self-gravitating, non-interacting, degenerate fermions.[8] Fermion balls may have been formed in the early universe and studies show the analysis of the orbits of stars S0-1 and S0-2 around Sgr A* was initially consistent to the FB scenario as the pressure from the degeneracy maintains a balance with the gravitational attraction to the fermions.[9] Continued observations of the S0-2 orbit revealed that a mass of 3.6‡ 0.6 x 10^6 MΘ  is located within a sphere radius of 0.6mps Sgr A*[10] that excludes the possibility of the FB Hypothesis as such a mass density would impact on the fermion ball particles.

These advances in telescopic technology including the use of Very-Long Baseline Interferometry (VLBI) techniques that captures high resolution radio sources from different locations before being combined into following the meticulous measurement of time differences all fed into one central location on a supercomputer with enormous data capacity to enable this to occur efficiently have recently made it possible to capture the shadow of the event horizon, the boundary surrounding the SMBH. As the diameter of the telescope increases the resolution, sensitivity and baseline, and the Event Horizon Telescope (EHT) and the Global mm-VLBI Array (GMVA) combines multiple telescopes around earth to simulate the power that an earth-sized telescope would capture. The boundary surrounding a black hole is an event horizon because while gravity is very strong, objects can still escape from the gravitational pull and thus energy can be detected near the horizon while anything that travels beyond that an observer cannot see.[11]

The Event Horizon Telescope and Global mm-VLBI Array on the Eart

Quasars are the most luminous AGN and they have a very strong correlation to SMBH as the latter is required to give Quasars the immense power that they project. “Quasars rank amongst the most luminous sources of radiation in the universe and are believed to be powered by SMBH.”[12] M–σ or the M-Sigma relation indicates a correlation between the mass of a SMBH and the stellar velocity dispersion in their host galaxies[13] and confirm SMBH to be a fundamental element of host galaxies with Quasars. Quasars are said to exist in predominantly larger galaxies during the active phase of gas accretion and therefore the early life of a galaxy, where particles or matter are heated and accelerated away like a jet or stream of light from the ionization around the boundary of an SMBH at velocities almost at the speed of light and emitting powerful energy and therefore luminosity that exceeds all the sources of light within the entire galaxy.[14] In December 2017, the most distant quasar J1342+0928 at a redshift of z=7.54 was found and provided a glimpse into the cosmological timeline by using Planck parameters that confirmed the age of galaxy to be barely 690 Myr after the big bang[15] with an SMBH that contains a mass of 8e8 Msun (800 million solar masses!).[16] The existence of a SMBH during such an early epoch of the universe’ existence confirms a number of models about how black holes can grow to such a supermassive size as it captures nearby material and ultimately engines the power of a quasar. The standard view is that following supernova explosions, the gravitational interactions form stellar black holes and continue to grow through mergers and accretion, however the accretion theory does not explain the SMBH in quasars so old and powerful as J1342+0928 known as the quasar seed problem, indicating that the conditions to have formed them must have been achieved by direct collapse.[17] A large ‘seed’ to form a black hole as colossal as 100,000+ solar masses and therefore thousands of times bigger than black holes shaped by a supernova is possible in the right conditions during the early universe as it required an equally colossal star collapse that would supress star formation because the temperature of the ultraviolet photos ensure that the surrounding gas remains hot enough. Stars usually form when the cloud cools as the gas is dispersed, but the conditions in the early universe confirm that such a supermassive ‘seed’ could be possible before it begins to attract matter and gas to grow over billions of years into its colossal size.[18]

The catalyst that enables supermassive black holes to form remains unconfirmed, but as technology enables astronomers to locate and verify new hints about the galaxy, we are inching closer and closer to verification of theories


[1] Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research, Ferrarese & Ford 2005, Space Science Reviews, Volume 116, Issue 3-4, pp. 523-624
[2] Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research, Ferrarese & Ford 2005, Space Science Reviews, Volume 116, Issue 3-4, pp. 523-624
[3] Sidney Van den Bergh, Galaxy Morphology and Classification, Cambridge University Press (1998) 13
[5] Stellar Orbits around the Galactic Center Black Hole, Ghez et al. 2005, The Astrophysical Journal, v.620, p.74
[6] Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research, Ferrarese & Ford 2005, Space Science Reviews, Volume 116, Issue 3-4, pp. 523-624
[7] Stellar Orbits around the Galactic Center Black Hole, Ghez et al. 2005, The Astrophysical Journal, v.620, p.74
[8] Neven Bilic, Supermassive Fermion Balls and Constrains From Stellar Dynamics Near Sgr A∗:
[10] Siegfried Röser, From Cosmological Structures to the Milky Way, John Wiley & Sons (2006) 196
[11] Jim Al-Khalili, Black Holes, Wormholes and Time Machines, Taylor & Francis (2016) 64
[12] Formation of z~6 Quasars from Hierarchical Galaxy Mergers, Li et al. 2007, The Astrophysical Journal, v.665, p.187
[13] Raphael Sadoun, M- sigma relation between SMBHs and the velocity dispersion of globular cluster systems: arXiv:1204.0144 [astro-ph.CO]
[14] Andrew C. Fabian, Active Galactic Nuclei: Proc Natl Acad Sci U S A. 1999 Apr 27; 96(9): 4749–4751.
[15] Fulvio Melia, J1342+0928 Confirms the Cosmological Timeline in R_h=ct: arXiv:1712.03306 [astro-ph.CO]
[16] E. Bañados,, An 800 million solar mass black hole in a significantly neutral universe at redshift 7.5: arXiv:1712.01860 [astro-ph.GA]
[17] Bhaskar Agarwal, Formation of massive seed black holes by direct collapse in the early Universe, Dissertation (2013) pp 24
[18] Silvia Bonoli, Massive black hole seeds born via direct gas collapse in galaxy mergers: their properties, statistics and environment,

Thermodynamics and the Arrow of Time

To say an ‘Arrow of Time’ is to say that time itself is linear and one-directional. In thermodynamics, the second law dictates that everything moves in one-direction from a state of order towards disorder and entropy is the statistical measurement of this asymmetry in an isolated system. The universe is, for instance, this isolated system and as a consequence it is impossible to reverse this arrow of time and travel backwards just as much as the continuity of disorder will never decrease. Newton’ equations and other laws in physics, however, can be reversed and thus this ‘order’ is arrived from a state of equilibrium as it moves forward toward disorder. We simply understand the past through entropy and yet, while this may be statistically correct, the Poincare’ recurrence theorem in open systems prove that thermodynamic system may actually be paradoxical. The theorem purports that after a length of time the system may return back to its original or close to its original state, such a hot cup of tea eventually reaching room temperature. Statistical physics that attempts to measure the universe as a finite and objective physical entity together with the evolutionary patterns of nature, reached an impasse since the cosmological theory of the universe with the Big Bang started with chaos and eventually formed this smooth, ordered state that works in contradiction to the second law leading to an reductio ad absurdum. Unless we assume that the big bang itself occurred as a ‘fluctuation’ – indeed, a very rare and unique one – and is thus an addition contained inside one meta-system where a number of universes exist. Ludwig Boltzmann did not believe in the reversibility of statistical thermodynamics; I become conscious or self-aware and thus experience a non-equilibrium with nature or the external world because of a random fluctuation in my brain, but intelligence is only available in my brain and so why everything else in this system – body, organs – and thus consciousness is a random fluctuation. If I want to bake a cupcake, the ingredients – such as flour – can be reversed back to wheat, soil, planet earth, milky way, universe etc &c., – and rather than saying that I need a universe to create a cupcake or that I need to create a universe to make a cupcake, it is easier to explain that a cupcake is made from a random fluctuation. Ultimately, however, we do need a universe, milky way, planet earth, soil, wheat, and flour to make a cupcake and thus every system requires time to move forward as well as backward.

Boltzmann’s entropy formula S = k log W describes the statistical domain of thermodynamic systems [log itself aids with minimising the size of the universe with W being the number of microstates giving a probability at macro-level][1] and that entropy is conserved by the monotonic function of ordered sets as the microstates increase. Any corresponding change at macro-level is causally connected to a change with a microstate within the system, but this interconnected dependence between the two states naturally shows that the macro-state itself contains maximal entropy. That is, thermodynamic equilibrium of system is consistent with the constraints of the second law of thermodynamics and that the formula is the statistical evidence of this. In its simplest, ergodicity is merely analogous to ascertaining the averages of behaviour within a system, measuring transformations, recurrence, arbitrary convergence etc &c. or quite simply the dynamics and that over time the probability of visiting every required state occurs. A macro-state in equilibrium is largest in size, thus over ‘time’ [that is, time-average probability] the system spends visiting the phases as it reaches this equilibrium and thus maximum entropy is, well, ergodic. Even so, it is still incredibly difficult resolving arbitrary estimates coupled with the fact that cases involving the second law of thermodynamics do not necessarily require erodicity at all. But when considering the constituency of time in this framework, the idea that the direction or arrow of time will eventually lead a system toward maximum entropy and ergodicity may, in reverse, explain time.

Ergodicity itself is somewhat Epicurean, not to say that it has any connection with Epicurus’ Nature of the Cosmos, but rather the philosopher himself – more notably adhered by Lucretius – believed that it is a mark of an intelligent mind to think of multiple possibilities – from the absurd to the rational – so as to identify and explain a solution to a cosmological problem;[11] even occasionally, multiple descriptions can prove a theorem adequate and inadequate at the same time. Lucretius’ cosmological phenomenology is based on his thought experiment regarding infinite space, whereby should one travel to the end of the universe and throw a spear through it, what would happen to the spear?[12] Either it will hit it and fall, or it will go through the boundary – that the boundary of a finite universe is ultimately illusory – and toward another space that we are not aware of; what this would mean is that all possibilities and possible worlds outside of the finite space that we understand is actually possible.

Therefore the universe is infinite and according to Newton this must be true; his failure, however, was the proposition that the universe was static purported by his assumption of the stars being fixed relative the inertial frame, namely because the distribution of mass would be unstable. The problem of symmetry, however, regarding a state where the universe is accelerating, is how the direction for which this acceleration is determined. In order to substantiate the validity that there is actually a physical system, the universe requires isotropy and since we can acknowledge that when we look out to the universe that in every direction we can observe the CMB radiation, one can conclude that it may very well be a symmetric space.


Nevertheless, for the sake of avoiding the likelihood of falling down the existential rabbit hole before becoming overwhelmed by the vanity of, well, everything, let us assume that the universe can be modelled as a dynamical system, contained in an isotropic, homogenous and maximally symmetric but statistically within a finite structure and governed by an arrow of time, and in doing so the analysis of erodicity and entropy within such a model seem almost possible. The problem is that, if the arrow of time purports that time itself is moving forward in one direction, that the universe is expanding alongside time as it reaches its maximum state of high entropy, it would mean that therefore the universe had a past and so to not defy the second law of thermodynamics, the early universe would have to be at a state of low entropy. In an environment where the observable universe is much denser or smaller in the past – since the universe is expanding – it would logically imply that it was hotter and the pull stronger. How is it that in that macroscopic parameter consisting of a hot and dense environment instead was smooth and cool? This does not make sense since the early universe was in a state of equilibrium which, given the calculations above, must uphold the thermal law of being in a state of high entropy. In addition, temporal asymmetry works in contradiction to the second law of thermodynamics; motion cannot function without time, it would be like matter frozen in a dimensionless space or swallowed in a blink beyond the event horizon. Time’ arrow works in a manner that directs motion forward, evolutionary of sorts and adapts to the processes within its environment in an attempt to find a state of equilibrium.

In classic thermodynamics, the joule [free] expansion – where within an adiabatic container enclosed with monatomic gas molecules and no energy or thermal properties – the gas densely kept to one side of the container with a closed partition between another empty container that has been vacuumed of any properties at all and therefore completely empty,[13] when the partition is opened and consequently the gas in one container increases in volume and expands into the other, the pressure of the gas that had been densely kept in the other compartment diminishes [like blowing up a balloon with helium gas and then letting it go; the gas is released from the balloon with the rubber shell flying about the place in an awkwardly loud and flatulent manner]. There is no pressure or work, ΔU = q + w = 0 but nevertheless there were changes [in consideration of ideal gas][14] in temperature and therefore PV=nRT whereby the pressure and volume equates to a constant of the gas and the temperature, so the first law regarding the conservation of energy in thermodynamics remains valid. The ergodic hypothesis by Boltzmann was formulated to prove in principle the determination of the distribution of gas molecules and their kinetic speeds in his equipartition theorem, which is mathematically ascertaining the energy of any given physical system through the distribution of generalised coordinates and momenta. The second law of thermodynamics contains the interesting problem vis-à-vis this very blog post, that the law governs the exchange of thermal contact and gradual arrangement toward a fixed equilibrium; that is, the natural evolution of any given system is determined to a state of equilibrium. Once the partition is open and the gases are dispersed, they spontaneously find a state of equilibrium and do not randomly paste themselves to the ceiling of the container etc &c. How can a hot cup of tea become lukewarm as it cools to room temperature and thus asymmetric as it reaches a state of equilibrium with its environment? Or is that a deductive fallacy? Could travel back in time? One of my favourite paradoxes from All You Zombies[15] is as follows:

A baby girl is mysteriously dropped off at an orphanage in Cleveland in 1945. “Jane” grows up lonely and dejected, not knowing who her parents are, until one day in 1963 she is strangely attracted to a drifter. She falls in love with him. But just when things are finally looking up for Jane, a series of disasters strike. First, she becomes pregnant by the drifter, who then disappears. Second, during the complicated delivery, doctors find that Jane has both sets of sex organs, and to save her life, they are forced to surgically convert “her” to a “him.” Finally, a mysterious stranger kidnaps her baby from the delivery room.

Reeling from these disasters, rejected by society, scorned by fate, “he” becomes a drunkard and drifter. Not only has Jane lost her parents and her lover, but he has lost his only child as well. Years later, in 1970, he stumbles into a lonely bar, called Pop’s Place, and spills out his pathetic story to an elderly bartender. The sympathetic bartender offers the drifter the chance to avenge the stranger who left her pregnant and abandoned, on the condition that he join the “time travelers corps.” Both of them enter a time machine, and the bartender drops off the drifter in 1963. The drifter is strangely attracted to a young orphan woman, who subsequently becomes pregnant.

The bartender then goes forward 9 months, kidnaps the baby girl from the hospital, and drops off the baby in an orphanage back in 1945. Then the bartender drops off the thoroughly confused drifter in 1985, to enlist in the time travelers corps. The drifter eventually gets his life together, becomes a respected and elderly member of the time travelers corps, and then disguises himself as a bartender and has his most difficult mission: a date with destiny, meeting a certain drifter at Pop’s Place in 1970.

The question is: Who is Jane’s mother, father, grandfather, grand mother, son, daughter, granddaughter, and grandson? The girl, the drifter, and the bartender, of course, are all the same person. These paradoxes can made your head spin, especially if you try to untangle Jane’s twisted parentage. If we draw Jane’s family tree, we find that all the branches are curled inward back on themselves, as in a circle. We come to the astonishing conclusion that she is her own mother and father! She is an entire family tree unto herself.

Quantum entanglement is an interesting method of understanding the arrow of time in this context. The uncertainty principle in quantum mechanics[16] asserts that measuring the position of a particle and its momentum is never accurate, furthered in confusion with evidence that sometimes interaction between two particles merge or entangle to form a ‘oneness’ that dictates the momentum and position one to the other that they are no longer two separate particles – though physically it is so –nevertheless communicating invisibly one to the other as a combined force. It is of interest to me where the interaction prior to the amalgam between the particles peaked at a derivative equal to zero, namely the very point where particles enjoin to become a state where they can no longer be classified as autonomous. Reaching this balance of connectivity between particles from a pure particle state to a combined oneness in perfect equilibrium as it relaxes into its new and unchanging form is the real parameter that works comparatively to the notion of thermal equilibrium and thus the evaluation of thermodynamic properties.

It appears that no matter where I am in the universe, I will still get the same answers to the same equations and the physical world would appear to me, well, to be the same in every direction. That is, the symmetry of the expansion rate is homogenous confirmed to a degree through Hubble’s Law, which is the velocity between two galaxies being equal to the Hubble parameter times the distance V=Hod and verifies that objects would appear to be expanding outward relative to the observer; the measurement of the radial velocity determined by the redshift. Thus galaxies are moving away and galaxies even further still at a much faster rate explained by the fact that should both the source and the observer be stationary, there would be no time differentiation or delays viz., the time for the wavelength to reach the observer, hence the Doppler effect. When thinking about the cosmological redshift, whereby light that has been emitted from a distant galaxy reaches us on earth, calculations of the spectral features of photons namely λ =h/p requires attentiveness on how the light itself will shift from the frequency it had when emitted to the frequency we measure when receiving it, that is, the momentum and time it takes for the wavelength to reach the observer, the evolution of this process changes as the photons are stretched. Physicists have thus determined that the universe is not only expanding but also accelerating.

It would seem that the universe is expanding whilst galaxies themselves remain static. When photons emitted from a distant galaxy reach us the observer, the distance and velocity of the wavelength with the time it takes to us from the source is quantified by the Hubble constant times the distance between galaxies. The asymptotic nature of ∆t would purport that the atomic properties in space and thermal energy interact with time in a manner that will continuously interfere in the process of reaching absolute zero, and as stated previously, even a vacuum state still contains energy even though extremely low. Measuring time during the inflationary epoch remains questionable, even with the capacity to measure the smallest possible unit of time through Planck [5.39 × 10^-44 s] whereby probabilities are the only reality attributed to the questionable state of time. Perhaps the total entropy in the universe is already infinite, in which case it was always infinite.

How we experience time remains an unexplained phenomenon. If, indeed, time must move both forward and backward, perhaps the equilibrium that I experience in ‘now’ is really both past and future working in perfect uniformity rather than some random existential fluctuation. Perhaps my past can speak to my future and that is the mystical experience of prophesy? That there is no ‘beginning’ or ‘end’ except this singularity itself, namely God who is ‘alpha and omega’? Or maybe the universe is simply a brain!


[1] Don S. Lemons, A Student’s Guide to Entropy, Cambridge University Press (2013) 72
[2] See Lucretius’ cosmology and use of the Principle of Plentitude briefly explained in Michael J. White, Agency and Integrality: Philosophical Themes in the Ancient Discussions of Determinism and Responsibility, Springer Science & Business Media (2012) 4
[3] Philip de May, Lucretius: Poet and Epicurean, Cambridge University Press (2009) 27
[4] Clement John Adkins Equilibrium Thermodynamics, Cambridge University Press (1983) 162
[5] Peter Atkins, Julio de Paula, Ronald Friedman, Physical Chemistry: Quanta, Matter, and Change, OUP Oxford (2013) 576
[6] David Darling, The Universal Book of Mathematics: From Abracadabra to Zeno’s Paradoxes, John Wiley & Sons (2004) 139. See Robert Heinlein’ All You Zombies
[7] K.V.S.Gnaneswara Rao, Engineering Physics, S. Chand Publishing (2008) 38


Gravitational Repulsion: Is Zero Building An Eternally Expanding Universe?

Non-inflationary theories of the genesis of the universe or what we know as the big bang effectively only discuss the hydrogen and helium particles etc &c., that fill the universe or what occurred after the birth of the universe, and now that evidence has been shown[1] that the universe is actually expanding, it has led to questions of what could have been prior to the bang in a much more sophisticated manner. And there are multiple theories, such as Brane collision or the collision of two dimensions or that the universe is formed from within a black hole, all of which are interesting particularly with new areas of thought viz., superstrings and the cyclic universe model, but certainly not as persuasive as cosmic inflation and the multiverse theory.

It is a theory that the universe is constantly expanding, while the density remains at a constant and during the process of decay, pockets of new universes form making our universe one of multiple universes in an eternal stretch of fields. The idea of the cosmological constant λ was formulated by Einstein in his theory of general relativity to describe a static universe prior to Hubble’ discovery that the universe was actually expanding and at the time he himself even rejected this equation, however it appears that the answer for cosmic inflation and the uniformity of the universe can unexpectedly be explained by it. How? According to Alan Guth it can be explained through repulsive gravity, namely that negative pressure can push exponential expansion far greater than its capacity for decay.

At this point where I found myself throwing whatever it was in my hand, cursing and walking briskly around the room for no apparent reason other than sheer excitement. How can zero build an eternally expanding universe? At elementary level, the underpinning of the cosmological constant is that gravity is not always attractive and can behave repulsively,[2] a necessary formulation to counter the problem with a static universe and the big crunch [collapse of the universe]; the negative pressure will provide the force that pushes things apart while the positive three-dimensional field will keep it together as they work in uniformity and subsequently expand. Whilst Einstein’ depiction of the universe may have been incorrect and why the theory was abandoned, the equations nevertheless remained functional with the laws of general relativity, hence its revival particularly within particle physics.

Gravitational repulsion requires a negative pressure, the latter along with energy density can produce cosmic gravitational fields.[3] In Newtonian physics, gravity is an attractive force and yet in the absence of pressure [pressure is a form of gravity] produces deceleration, even with gravitational fields having negative energy. As a comparative analogy, Coulomb’s inverse-square law in proportion to two charges divided by the square of the distance between them[4] (viz. gravity), the constant in the law is that the force between two positive charges is proportional to the product of their charges (like how two positive charges repel one another) and to calculate the energy density in an electrostatic field, more charge would induce more electric force that it no longer depends on the quantity of the charge, thus the two cancel each other out. In gravitational energy terms, not everything is positive and there are negative energies, with positive energy inflating or getting larger as long as there is an accompaniment of increasing quantity of negative energy, thus both offset each other and you have expansion locked at an exponential rate. In order for inflation to begin, a portion of this negative pressure is required for the existence of the early universe, namely that within the context of the grand unification theory – the merging of strong and weak nuclear forces along with gravitation and electromagnetism into a singular interaction – and the energy of the electromagnetic forces interact to form a unified energy value. This very portion of what becomes the big bang and the universe as we know it would be about the size of 10^-28cm (assuming energies being at 10^16 GeV – the problem of thermodynamic arrow relates to inhomogeneity[5] in that anything larger or smaller would make the universe blow apart or suck away galaxies into black holes, an important algorithm vis-à-vis temporal asymmetry where the time-dependence of Ω-1 changes, of which I will discuss later). It then grows at an exponential rate to build what we know as the universe and the mass density does not decrease, namely that it expands at a constant density. Where does the energy – that is constant per volume during growth – come from? As energy equals to positive matter and negative gravity, they cancel one another out in perfect harmony and thus the total energy levels for the universe can be measured at zero.

The universe has no energy? *Quizzical look

Acceleration? This is where the concept of ‘dark energy’ [what I call the ‘will’ of the universe] which makes up about ¾ of the universe comes to the fore or what is known as vacuum energy, considered to be empty [although in cosmology whilst the structure is fundamental to empty space nonetheless contains an energy density, namely the conservation of energy can occur at zero]. The total energy at the beginning of the universe must be at zero with the negative contribution to the energy of the cosmic gravitational field cancelling the energy of matter. Inflation as a constant and eternal is only possible at 0 where matter is being created by the inflation but controlled by the non-uniformity in perfect harmony. The repulsive gravity that drives inflation nevertheless decays [t=10^-33 seconds after the big bang] but the inflation itself remains eternal because the growth of the volume is faster – hence the importance of the thermodynamic arrow of time – than the metastable rate of the decay; the material formed during this process thus becomes the particles required to produce the very same material that forms another universe, ad infinitum (radiation density during this time redshifts away – again I will discuss later in addition to how dark energy appeases the early specialness issue by smoothening the inflationary transition). States of equilibrium can nonetheless be achieved in unstable, disordered environments, such as balancing a spinning basketball on an index finger where for a brief moment in time is in perfect equilibrium but certainly not at a stable one. Inflation is really the physics of scalar fields φ and matter; the particles that make up the universe that form the stuff following the initial phase of inflation leading to the big bang are merely the quantum representation of the (Higgs) fields. In particle physics, the nonzero Higgs field – which is responsible for the emergence of elementary particle masses – contains both positive and negative contributions and has a constant value at every space time point. Observable quantum density fluctuations and tensor perturbations in scalar fields can explain the source of temperature anisotropies (along with universal isotropy, its massive size and relative homogeneity) in the cosmic microwave background (CMB) radiation.[6] As the expansion of the universe is accelerating rather than slowing down under the influence of gravity, it indicates that vacuum energy is simply the energy of empty space and though empty has a mass density (which would mean that it is not actually empty).

Nevertheless, there are a plethora of issues raised at this point. The confusion or controversy really boils down to the concept of disorder and the cosmological epoch. Namely, is the universe a n-dimensional De Sitter space dSn, is it a 3-manifold Poincaré dodecahedral space, the flatness problem where Euclidian geometry applies only at a large scale; is it three-dimensional, four-dimensional, or nine-dimensional squished into three as string theorists propose? The other and perhaps more interesting one is the problem of entropy potentially being extremely low at this point. Whilst warm inflation – modelled on the standard or ‘cold’ inflationary theory[7] – purports a small portion of the vacuum energy density is converted to radiation, whereby the radiation density stabilises during the process of coupling [between inflation and radiation fields], during the decay phase, the scalar field oscillates to become radiation particles that slowly reheats the universe and when this occurs [reheating and inflation together] they become coupled into a unified process. The connection between the flatness problem and entropy is a complex one, particularly related to whether the early universe was adiabatic and why spatially the conditions at the beginning were flat. When inflation begins, the energy stored in the gravitational field as it expands increases whilst the energy density remains constant, thus the gravitational field itself has a repulsive energy density as it expands in volume, with the total energy being very close to 0 without violating the conservation of energy. It may mean that inflation requires a non-adiabatic, extremely low entropy to occur, entropy being the measure of randomness and low entropy itself considered perfectly ordered. If inflation increases entropy, it appears that at the point of inflation, the entropy had to be smaller and the uniformity of the energy density during inflation becomes responsible for the low entropy conditions. What is currently in debate is namely why – in the past – did the universe begin with low entropy and yet the product being the second law of thermodynamics?

I want to maintain that the observable universe (and one should note the keyword here being ‘observable’) would imply that the universe is flat (k=0) or that inflation is pushing Ω to 1 with Ω being the mass density divided by critical mass density, thus the asymptotic curvature of the universe is being exponentially flattened by the expansion at 10^35 seconds after the bang. What that means is that should Ω=1 the curvature must equal to 0 (or be extremely close to it) and the effect would be infinite expansion. Thinking about that model, such expansion could causally be the precise reason we have an arrow of time fixed in perfect and irremediable harmony, although no theory of randomness can explain the arrow of time and the problem of low entropy during the early phase of the universe and the successive phase transition of expansion and cooling. When assessing temporal asymmetry, however, the concept of low entropy during the beginning phases of the universe – whilst objectionable or perhaps superfluous – is nevertheless useful when ascertaining the thermodynamic arrow.

The second law of thermodynamics purports that the time flows in a linear direction as we know it, namely from past to present to future. The question here is that as the universe expands and progresses over this time, from an ordered state – namely that of low-entropy – it is moving toward a high-entropy disordered universe. Entanglement in ordinary quantum mechanics, which can perhaps work as a correlation in that the measurements of the relationship between two particles relies on contact sometime in the past, the interaction or exchange following even when these particles are at a far distance and in a disordered state from one another remain organised and can even affect one another’ quantum state. As a consequence, while separate their properties can only be measured as one. There is an invisible but an active link between the particles. In quantum field theory, entanglement entropy rather than being a correlation contains causality under the assumption that symmetry of a pure state that has ergodic properties.

The total energy at the beginning of the universe started at very close to zero and the negative contribution to the energy of the gravitational field cancels the energy of matter and thus repulsive gravity drives inflation with the growth volume faster than the decay, allowing the physical universe to expand exponentially. We are able to confirm relative homogeneity and isotropy through the fluctuations imprinted in the anisotropy of the cosmic microwave background and gives light to the conditions of the early universe, which was once filled with plasma but where photons themselves – whilst moving at the speed of light – remained immobile in the density and so velocity stood at zero. As the universe expanded, the plasma cooled and became a gas and as such cosmologists began to question thermal equilibrium, the second law of thermodynamics and entropy, the latter allegedly being low during the early epoch of the universe. Thus in continuation, the problem we face here is that as the universe expands and progresses over this time, from an ordered state – namely that of low-entropy – toward a disordered high-entropy, the latter itself dependent on the arrow of time, how exactly can the early universe in the past, where it was hotter and denser and had a stronger gravitation pull, be perfectly smooth?

Hubble expansion, which is about 70km per megaparsec, is the expansion rate that we see at present with the inflationary epoch ending 10^-32 seconds after the big bang to expand at the rate of the Hubble constant.[8] If the universe was thus once condensed to a very small size until it expanded at a factor of 10^26 due to inflation and eventually ending that lead to a fixed or steady expansion as we know is now taking place, the process itself nevertheless preserves the subatomic smoothness that the initial conditions held. This is particularly coherent when assuming that we are a part of a multiverse. In Einstein’ GR field equations, he applied the cosmological constant Λ in an attempt to explain a static universe prior to Hubble’ expanding one and thus later rejected it, however for both inflation and dark energy, the ubiquitous Λ becomes a necessary algorithm that binds the theory together as the energy density of the latter in particular causally drives expansion and a flat universe that can expand infinitely. With Riemannian geometry, cosmological observations of the CMB radiation through the Wilkinson Microwave Anisotropy Probe (WMAP) have measured angles that add to exactly 180 degrees, which in a Euclidean space purports a universe that is k=0 or flat[9] and as its density remains constant as it expands, dark energy or the energy of empty space itself plays a vital role. The horizon problem also shows that the temperatures at different directions of the CMB radiation are uniform to almost 1 part in 10^4 [accounting a minor electric dipole] or 1 part in 10,000 and therefore almost the same – something that should not actually be possible – purporting that the only solution to this thermal equilibrium is inflation. That is, for example, regions billions of light years in opposite directions must communicate or interact in some manner to reach this symmetry and the explanation is that they – at one point in time – were interacting and the process of inflation has stretched them out into altered directions, thus favouring the model of an isotropic and homogenous universe.

As there is an arrow of time and as the universe is expanding, in the past the universe would have been infinitesimally smaller particularly as we reach the beginning of time. As such, the density and heat would have been higher – something clearly attributable to the CMB radiation – and the fact that perfection or a state of low-entropy is requisite should we adhere to thermodynamic laws and the direction of time, the conditions of the big bang becomes formidable. In addition, if the initial conditions were not perfectly ordered and smooth, it would have fizzled away. As mentioned, assuming the universe is geometrically flat because of the ratio between the mass density and the critical mass density being very close to Ω =1 and stabilised through the force of repulsive gravity as illustrated by the cosmological constant, is the fabric of the universe smoothing as it expands. I will write more about the Arrow of Time and Thermodynamics in my next post.

[1] Stephen T. Thornton and Andrew Rex, Modern Physics for Scientists and Engineers, Cengage Learning (2012) 578
[2] Behram N. Kursunogammalu, Stephan L. Mintz, Arnold Perlmutter, The Role of Neutrinos, Strings, Gravity, and Variable Cosmological Constant in Elementary Particle Physics, Springer Science & Business Media (2007) 182
[3] Maurizio Gasperini, The Universe Before the Big Bang: Cosmology and String Theory, 160
[4] John Gribbin, Mary Gribbin, Jonathan Gribbin, Q is for Quantum: An Encyclopedia of Particle Physics, Simon and Schuster (2000) 92
[5] Murray Gell-Mann and James B. Hartle, Time Symmetry and Asymmetry in Quantum Mechanics and Quantum Cosmology,  (February, 2008)
[6] Alejandro Gangui, Cosmic Microwave Background Anisotropies and Theories of the Early Universe, SISSA-International School for Advanced Studies (1995)
[7] Mar Bastero-Gil, Arjun Berera, Ian G. Moss, Rudnei O. Ramos, Theory of non-Gaussianity in warm inflation (Dec 2014)
[8] Cesare Emiliani, Planet Earth: Cosmology, Geology, and the Evolution of Life and Environment, Cambridge University Press (1992) 68
[9] Carlos I. Calle, Einstein For Dummies, Wiley (2005) 309
[10] Don S. Lemons, A Student’s Guide to Entropy, Cambridge University Press (2013) 72

A History of the Eclipse: The Birth of Science

A solar eclipse is a clear demonstration of celestial mechanics as the position of the moon and the sun temporarily shadows the sunlight on earth, and indeed for centuries has led to a number of mythologies that attempt to explain the geometry of the unknown universe and where civilisations and formidable historical figures came to greatly influence the study of science and astronomy as we know of it today. The ancient Babylonians, Egyptians and Chinese were so entrenched in these myths that they formed methodical processes aimed at calculating and predicting occurrences and did so with great accuracy that led to the development of the necessary instruments to aid in their observational techniques. For instance, the Babylonians believed that the solar eclipse could potentially be a bad omen that would predict the death of the King and this fear evoked constant study that soon thereafter established the 223 month Saros cycle of eclipses, something that we still use today. Have eclipses prompted astronomers and philosophers to theorise celestial geometry and planetary motion that ultimately enhanced scientific tools prior to the invention of the telescope by Hans Lippershey in 1608 and led to what is known as science?

Several shadows are formed between the earth and the moon that occurs during both lunar and solar eclipses, the latter a result when the moons’ shadow hits the earth, though the sun is four hundred times larger than the moon. During a total solar eclipse, this shadow is called an Umbra,[1] whereby the very center of the shadow’ core is blocked by the moon as it eclipses the sunlight and as this ends, the shadow becomes an Antumbra that forms the lighter section of this shadow. During an annular solar eclipse, when the light source contains a larger diameter due to the distance of the moon during an Apogee (when the moon is at its farthest distance on the elliptical from the earth), the moon appears smaller and thus silhouettes the heat of the outer edge of the sun, forming a visible ‘ring of fire’.[2] When the moon’ distance from the earth is at a Perigree and therefore at its closest range, it enables a total eclipse as the diameter roughly matches and covers the entire sun.[3] It is estimated that a total solar eclipse in a location only occurs once every several hundred years and being an exceedingly rare phenomenon and difficult to predict only added to the mysteries of the heavens.[4]

Prior to the use of the telescope, astronomers recorded their observations using a number of tools, once such being the Armillary Sphere or the Spherical Astrolabe that was used both as a teaching tool and to aid observations. Aristotle, notwithstanding his vast array of knowledge on a number of subjects, included in his curriculum vitae the title of amateur astronomer and authored On the Heavens that observed the material nature of the cosmos through concentric celestial spheres. For Aristotle, the world is both celestial and terrestrial, with the latter sphere composed of changing and chaotic elements of fire, water, earth and air that is surrounded within a perfect and unchanging celestial universe. His theories of motion and cosmology dominated the subject for centuries and remained similar to that of Eudoxus (c 337 BC) who stated that with the earth being the center of the universe, rotating spheres on individual axis moved at various speeds and angles around the earth.[5] As the earth is spherical in shape, it remains stationary as the sun, moon and planets rotated around the earth and the motions of these spheres carried all celestial activity including the fixed stars and ecliptic rotations. As Aristotle’ work survived and being highly influential unlike many of his predecessors, his cosmological views remained dominant until Ptolemy wrote Almagest, a voluminous encyclopedia of astronomy that summarised all knowledge of astronomy available at the time. He also had his own version of a planetary system that was based on the notion of spheres but instead adopted a preference for circular eccentricity or a circular shape of the ellipse (equant) that rotates at various speeds.[6] Accordingly, his system also abandoned Earth’ positon as the center of the system and thus changed the centuries-old influence of Aristotle.

However, prior to Aristotle’ astronomical accounts the Ionian philosophers perhaps beginning with Thales of Miletus (c624 BC) who is said to have predicted the solar eclipse of the 585 BC[7] became highly influential in the development of natural philosophy. According to Herodotus, this solar eclipse had such a powerful influence that the war between the Lydians and the Medes came to an end when they viewed the eclipse as a sign and a warning from the gods.[8] While the Egyptians and Babylonians had already formed extensive observations of the night sky, the latter in particular employing the Saros that determines periodicity of eclipses governed by a repetitive cycle spanning 18 years, 11 days and 8 hours and enabled them with the skill to predict eclipses,[9] they were restricted by the superstitions and myths formed in their pagan rituals that viewed these eclipses as bad omens, particularly for the ruling class. The Greek philosophers were empowered with more intellectual maneuverability that established a better scientific approach to astronomy that was instead viewed to be governed by natural laws; what made up the universe was material rather than supernatural and the Armillary Sphere exemplified this as a teaching tool. Thales studied geometry in Egypt and this mathematical knowledge was brought back to Greece as he soon thereafter became credited to developing a number of advancements in the subject that attempted to explain unknown astronomical concepts. The earth, for instance, was a large mass floating on water and earthquakes were evidence of oceanic turbulence. Thales stated that the material that formed the universe was water (our dark matter) and is the fundamental element that all the material world. Cosmological theories continued with his followers such as Anaximander and Anaximenes that questioned the origin of the universe. Anaximenes took it one step further, purporting that the element that forms water – air – is the building block of all material things and water is merely the compressed form of this element.

Anaximander was far more interesting as he purported that the universe was formed by a chaos of infinite opposites (such as hot and cold) and his cosmological model of the universe was intriguing to say the least, suggesting a cylindrical earth surrounded by wheels of fire from the sun that we are able to see through holes that rotate past us. This period is clearly marked a great many discussions on the physics of the universe that attempted to explain the appearances of celestial objects, when things are static or dynamic, constant or eternal. Hipparchus (c190 BC) discovered the precession of the equinoxes by using the solar eclipse by estimating the distance of the moon from the earth.[10] The Armillary Sphere were devices that enabled a demonstration of the rings that represented the celestial spheres and attached to them were fixed globes set to an elliptical axis and were “sometimes mounted on handles, but often were set like globes into cradles so that the sphere could be adjusted to represent the heavens as seen from any latitude.”[11] A number of spheres continued to be developed and adjusted from Ptolemy to Copernicus as an instrument to explain and observe equatorial coordinates and through Aristotle moved into the Islamic world.

The cosmological and astronomical theories during this period nevertheless contained the practice of supernatural and mystical influences that viewed the heavens as practical tools for predicting events throughout the passage of time. While methods of observations and the tools that strengthened how they recorded data steadily advanced, the observations continued to be shrouded by such celestial mysteries that evoked a sense of fear and awe. In China, for instance, the Emperor had control of the heavens and therefore predicting eclipses and other activities (lifa) along with the study of astronomical phenomena (tianwen) played a powerful role in his position as supreme leader.[12] Without an orderly understanding of astronomical event, it was viewed as a bad omen and a sign of problems ahead. China is attributed as having the first record of a solar eclipse (c. 2134 BC).[13] Like the ancient Hellenistic astronomers, China also used their own version of an ancillary sphere and took it even one step further by developing a mechanically powered globe using a sophisticated haudralic system during the Han Dynasty.[14] However, Shen Kuo (c1095) who is said to have developed the magnetic-needle compass did so following his observations of planetary motions and by using the models of solar eclipses was able to verify that celestial objects were in fact round.[15]

While such celestial activity was during the time of the Egyptians and Babylonians shrouded with pagan mysticism, astronomy soon thereafter through Saint Thomas Aquinas enabled the world to view Aristotelian cosmology through a Christian lens, one clearly visible when Copernicus’ model that the earth revolves around the sun was met with denunciation by the dominant Catholic influences of the time. Scholastic astronomy was introduced to medieval Europe from the Islamic Golden Age following the decline of the Roman Empire and the new Ottoman Empire steadily controlling the Middle East and North Africa attained access to the library of Alexandria and thus the work of the ancient Greeks, translating them into Arabic and improving a number of astronomical models that advanced an understanding of the elliptical movements of planets and the moon. Translations of the Arabic to Latin enabled Aristotelian and all scientific writing to move into Europe when the Christians conquered the Moors in Spain and Aquinas successfully incorporated Aristotelian philosophy into Christendom. Thinkers such as Casanus began to combine theological influences to cosmological theories, purporting that the universe is infinite and that there was no specific location of space, instead space was everywhere. The subject of eclipses developed intense interest during the Islamic Golden Age as Islam required a sophisticated approach to prayer that required the correct direction toward Mecca during important periods of sunrise and sunset together with the calendrical system of the moon that inevitably enhanced the study and the equipment thereof including sundials and quadrants.[16] However, it is the Equatorium that was developed by Ibn al-Samh and al-Zarqali and translated in Castille under the patronage of King Alfonso X[17] in the book Libros Del Saber De Astronomia (Books of the knowledge of astronomy)[18] that assisted with astronomical calculations.

It is clear that studies of the solar eclipse prior to the development of the telescope have led to a great many developments in the study of astronomy and science as a whole. As the ancient Hellenistic community of philosophers approached the subject with more freedom of religious constraint, natural philosophy contributed vastly to the subject that even included mathematical advancements, such as the Pythagorean Theorem where the square of the hypotenuse is equal to the sum of the square of the remaining sides of a triangle. Pythagoras himself believed that reality is formed through numbers or that the material world can be reduced to simple numbers and by bringing with him the knowledge from the Babylonians that the earth is spherical in shape, visible during a curved shadow on the moon during eclipses, changed the study of astronomy and ultimately influenced the development of the study of science as we know today.

When I first heard of the eclipse in the United States in 2017 as I was in Hawaii, I never really thought that this celestial phenomenon could have had such a profound historical influence on the study of science. While the subject evoked many mythologies, mythologies even present today with theories of biblical Armageddon that the eclipse has stirred, there is no doubt that the motion of the moon around the earth, the sun and planetary models that attempted to explain geometric orbits from spheres to water, mathematical to theological, changed the face of history and enabled the beginning of the study of western science. While the origin of the universe continues to remain impossible to answer – I myself am controversially of the opinion that the origin of the universe is in God – the material world that we experience nevertheless can be scientifically explained without it being shrouded by theological superstition and bad omens. I think we can use science to quite easily predict that if Armageddon were coming, it is likely because of the United States along with many other countries that are ruining the earth without needing the book of revelations to tell us that.


[1] Martin Mobberley, Total Solar Eclipses and How to Observe Them, Springer Science & Business Media (2007) 38
[2] Nicholas Nigro, Knack Night Sky: Decoding the Solar System, from Constellations to Black Holes, Rowman & Littlefield (2010) 206
[3] Op. Cit., Mobberley, 39
[4] Michael Borgia, Human Vision and The Night Sky: How to Improve Your Observing Skills, Springer Science & Business Media (2006) 112. It is good to note that total solar eclipses occur regularly (every 18 months) but in one given location will span over 300 years.
[5] Richard Jones, The Medieval Natural World, Routledge (2013) 30
[6] Michael Zeilik, Astronomy: The Evolving Universe, Cambridge University Press (2002) 34
[7] Lisa Rezende, Chronology of Science, Infobase Publishing (2006) 21
[8] William Hales, Chronology and Geography, C.J.G. & F. Rivington, (1830) 71
[10] Lloyd Motz and Jefferson Hane Weaver, The Story of Astronomy, Springer (2013) 45
[11] John Lankford, History of Astronomy: An Encyclopedia, Taylor & Francis (1997) 34
[12] Frances Wood, Great Books of China (2017) in Almanac or Tongshu (c 1000 – c 600 BCE)
[13] Aaron Millar, The 50 Greatest Wonders of the World, Icon Books (2016)
[14] Joseph Needham, Science and Civilisation in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth, Cambridge University Press (1959) 458
[15] Ancient China’s Technology and Science: Compiled by the Institute of the History of Natural Sciences, Chinese Academy of Sciences. Foreign Languages Press (1983) 153
[16] Ludwig W. Adamec, Historical Dictionary of Islam, Rowman & Littlefield (2016) 393
[17] Roshdi Rashed, Encyclopedia of the History of Arabic Science, Routledge (2002) 256
[18] Belén Bistué, Collaborative Translation and Multi-Version Texts in Early Modern Europe, Routledge (2016) 65

Alice in Wonderland: Inside a Black Hole

After a long morning on a charity walk before spending the afternoon fixing up my backyard, I decided that I would share the evening with a movie and well deserved dinner. ‘Event Horizon’ looked interesting, indeed it had the beloved Morpheus (Laurence Fishburne) as the main actor and certainly watching an action movie when your mind is incapable of processing anything can always work as a treat. But alas, the movie was rather tedious at best and I regretted not adhering to the temptation of re-watching Aliens with Sigourney Weaver who, admittingly, I have a huge girl-crush on. It would seem that the most mysterious in our universe tends to evoke the most interest, and indeed incredible levels of absurdity. The mystery of the existence of black holes is clearly one of them, from those who downright deny its existence to numerous suggestions about what happens to space and time when we enter a black hole that I felt compelled to ameliorate some details about black holes in this post and to hopefully reduce the likelihood of turning the science into a state of wild farcicality.

Stellar evolution is primarily about the mass and luminosity of stars that over time evolves until it reaches the end of its life cycle with millions of years passing during this process. Initially forming from the nuclear reactions or stellar ignition within a nebulae where gravity pulls the clouds of gas and dust into dense and hot ‘cores’ until the collapse reaches a nuclear fusion, the star is finally born and as the temperature during this fusion increases, it provides the energy that enables continuous emission of light or luminosity. Depending on the size, such as our own sun, the star will quietly settle on the Main Sequence for most of its life as thermonuclear fusion is enabled by the temperature  (10mk) to thus burn hydrogen into helium until the former is completely depleted. To burn helium requires a greater temperature and this is enabled by the force of gravity following the end of nuclear fusion as it contracts and therefore becomes hotter that hydrogen burning is thus ignited as the outer layers expand to form into a red dwarf or giant. The helium nuclei fuse to convert into carbon and oxygen in this rather tumultuous and highly energetic process until helium has completely converted but if the size of the star is not large enough, the contraction at the core does not heat up to the high temperatures needed to burn carbon. The Chandrasekhar Limit is a limit of 1.4 solar masses that categorises the mass of white dwarfs, which are the final result of low mass stars that are held together through electron degeneracy pressure. The density and pressure is enough to prevent further gravitational collapse, however stellar remnants that exceeds this limit will continue to collapse further until it forms into a neutron star which, again, is held together by the neutron degeneracy pressure. To form a black hole, the force of gravity overwhelms the neutron degeneracy pressure and therefore there is nothing left in space that would prevent the continued collapse of the star and thus the continuous singularity where therein contains no volume and infinite density becomes a black hole.

So what would happen if we found ourselves falling into a black hole? The mathematical concept of escape velocity was the first introduction to the theoretical concept and force of a black hole by amateur astronomer Reverend John Mitchell in 1783, whereby equating the universal gravitational constant 6.67 × 10-11 N m2 kg-2 with the mass of the body creating the gravitational field and distance between the body and an object escaping the gravitational field – thus the gravitational potential energy and kinetic energy – one could calculate the required velocity an object would require in an attempt to escape the gravitational pull of the field it is near. Accordingly, the size and radius of this body would then mean that,“all light emitted from such a body would be made to return towards it” and therefore such density would mean that light could never escape. The boundary or radius of the region surrounding the black hole that would enable some form of ‘escape’ is called the event horizon and the distance between the black hole and the event horizon is called the Schwarzschild radius Rwhich is calculated by the escape velocity as equal to the speed of light:

$$R_s = \frac{2GM}{c^2}$$

Whatever falls inside the event horizon will never escape. So what would happen if one passed the event horizon and fell into a black hole? A plethora of postulations have been made, one of them being time dilation, whereby the person travelling into the black hole would experience time as we know it, however outside of the black hole we would never be able to see her cross into the event horizon because time is much slower and what would be a few minutes for the person within could be thousands of years for the observer. That is, as one approaches the event horizon, gravitational redshift would make us see increases in speed of the moving object and anything with strong gravitational fields or compact objects causes an increase in the wavelength while at the same time decreasing the energy output. Spaghettification is yet another, where the tidal force of the gravity would stretch the object as it gets pulled in and the friction would cause it to heat to an incredible temperature.

Steven Hawking has recently purported that it is possible to travel to an alternate universe through a black hole; that is a black hole has ‘soft hair’ or extremely low energy quanta and what passes and event horizon does not disappear into oblivion but can actually come back out, only it will no longer be the same place. It is assumed that a black hole contains only several properties and the ‘no hair theorem’ first expressed by John Wheeler is that whatever falls beyond the event horizon is permanently inaccessible. The speculation is that the conservation of time within the black hole is caused by low-energy quantum excitations or ‘soft hair’ that when a black hole captures information by the material entering it, it also releases this information back out as it evaporates. But with time dilation, the information that is released is released perhaps into somewhere billions of years into the future or even a completely different universe. Hawking studied the emission of thermal energy or blackbody radiation (Hawking Radiation), which is indicative that quantum matter must be entering the black hole and that the source of its parameters would also eventually dissipate. According to quantum theory, this is caused by subatomic particles that exist for a moment as two separate (positive and negative) charged particles before reunited into one another and annihilating that momentary separation, as though their existence relies on the other in a perpetuity and these particle/anti-particles are present all over space. If they separate at the time of reaching a black hole, the positive would have the necessary charge to escape – effectively becoming the blackbody radiation that we observe – while the negative is doomed to fall in and as such the black hole will lose mass. This changes the classical conversation laws as the state of the particles changes at quantum level.

There are a number of methods currently being used to observe the existence of black holes, some indirectly particularly through binary systems – where a star is orbiting a black hole – and thus the emission of X-ray sources is stronger from the accretion disk’s spectrum, since it would imply that the star is orbiting a very dense object and thus a black hole. There are stellar black holes and then there are supermassive black holes, the latter containing millions and even a billion times more mass than its stellar counterpart. Supermassive black holes are said to be at the centre of our Milky Way and most large galaxies and observations of distant quasars that radiates incredible energy have enabled astronomers to conclude that the astounding levels of energy is only possible by a supermassive black hole. The formation of a supermassive black hole is unknown, though it is believed that the early stages of the universe assisted in their formation and as it consumed material over billions of years grew to its astounding size and power. It is also said that the supermassive black holes are the cause of active galactic nuclei that emit non-thermal energy such as quasars as well as galactic jets.

In 2014, NASA’ two telescopes detected an X-ray Flare from a supermassive black hole – Markarian 335 – that gave insight to astronomers about shifting coronas to an X-ray flare. The corona is a mysterious source of highly energetic particles or radiation found near the black hole accretion disk and they emit X-ray light, however details relating to their form and location of the black hole – since an event like a flare released near the event horizon would change our understanding of black holes including how fast it is spinning. There are two proposed suggestions of the position of the corona, with the first being Lamp Post Model where the corona is positioned on the axis above the rotating black hole, or the Sandwich Model where the corona is spread above and below the disc but the results suggest the former LP Model is likely. The disk around the black hole glows from the hot gas that is drawn around it and emits X-rays and as the material in the corona contracts as they are drawn closer together and the pressure launches the material out of the corona as it forms into a jet at ~20% speed of light. The brightness from the Doppler boosting or relativistic beaming where the concentration of superluminal motion of the jets remains somewhat mysterious.

The recent observation of the supermassive black hole Markarian 335 by NASA’ Nuclear Spectroscopic Telescope Array (NuSTAR) as well as the Swift Gamma-Ray Telescope – Markarian 335 being 324 million light years away – observed a large pulse of X-ray energy following the release of the corona away from the black hole. The observation enabled scientists to understand that the flare involves a process of release, that is a high-speed “launch” of the corona directly from the Black Hole that then causes the flare itself. The accretion disk of the black hole is incredibly hot where materials such as gas and space dust that has not yet been absorbed by the black spin around the event horizon and produce a glow in ultraviolet light. There are some explanations of the X-ray signals that NASA has detected, suggesting that as the heat around the accretion disk from the material glows ultraviolet and scatter above the disk which is further illuminated by X-ray energy that reflects off the disk, but there is also the theory that clouds block the visualisation of the mouth of the black hole and that shapes the X-ray spectrum that the detectors obtain with recent observations from the Gemini South Telescope in Chile that was able to measure the motions of gas around a supermassive black hole and zoomed in 10x closer to the galaxy core of NGC1097 and detected gas clouds ten light years from the nucleus. While flares are still mysterious, astronomers are taking steps closer toward understanding them.

Michael A. Seeds, Dana Backman, Stars and Galaxies, Cenage Learning (2015) 309
Michal Dovciak, An XSPEC model to explore spectral features from black-hole sources – II. The relativistic iron line in the lamp-post geometry, arXiv:1412.8627  [astro-ph.HE]
Supermassive black hole corona and flare. A&G 2015; 56 (6): 6.5. doi: 10.1093/astrogeo/atv180
The Anatomy of a Black Hole,
Gary T. Horowitz, Viewpoint: Black Holes Have Soft Quantum Hair, University of California, (June 6, 2016) Physics 9, 62
S. W. Hawking, M. J. Perry, and A. Strominger, “Soft Hair on Black Holes,” Phys. Rev. Lett. 116, 231301 (2016).