Let There Be Light!

The binary system V404-Cygni 8,000 light years from earth is a microquasar that contains a black hole more than nine times the mass of our own sun. The best evidence of the existence of black holes comes from binary systems where visible stars orbit an unknown mass, and a recent find has shown V404-Cygni rapidly rotating and pulling gas from the nearby star and ejecting the spiralling plasma in different directions back out into space rather than straight along the axis.

It has been suggested that this new find could be applied to systems much larger than V404-Cygni and particularly how these black holes can affect time and space, especially when the ejected plasma reaches the speed of light that then channels into much larger regions of space. But, how can the governing gravitational and kinetic energy transfer – as seen similarly with astrophysical jets spewing out from the centre of galaxies -communicate the relativistic effects on physics at a large-scale? Read More

Saolré: The Cycle of Life

As I prepare for my trip to beautiful, mythical Ireland in a few months, I am excited about visiting Newgrange (Gaelic sí an bhrú), which is a prehistoric 6,000 year old megalithic in County Meath. What is unique about this monument is that during the Winter Solstice, the sun rises over Boyne Valley and the beams of light strike into the passage chamber. It has been suggested that it was designed to observe solar and lunar cycles as well as that of Venus, but the attachment to astronomical and calendrical cycles with ancient mythological lore is clear, such as Aengus and Caer (I will be writing more about Irish myths and legends at a later date). What is more obvious is the understanding of the importance of cycles that exist in nature and our universe. Read More

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

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, https://www.nasa.gov/image-feature/jpl/pia20051/the-anatomy-of-a-black-hole-flare
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).