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).

Book Review: Ethical Writings of Maimonides

For centuries, from Aristotle to Confucius, Aquinas and Thoreau, moral philosophers have endorsed the idea that a balanced, moderate regularity of character is an important step towards genuine happiness, that excess or deficiency of any sort and the failure to attain a principled attitude toward guiding and cultivating the self toward this mean will lead to the reverse. Thus, one who leads a life attempting to walk down this dutiful path toward a balanced and constant frame of mind is demonstrative of a noble and even a superior person. As said by Socrates, “with his eyes fixed on the nature of his soul, naming the worse life that which will tend to make it more unjust and the better that which will make it more just… all other considerations he will dismiss, for we have seen that this is the best choice.”[i] This choice to lead a life of virtue and justice and abandoning all that is vulgar, vulgarity being interpreted as “the masses and the most vulgar seem – not unreasonably – to believe that the good or happiness is pleasure. Accordingly they ask for nothing better than the life of enjoyment,”[ii] will allow one to adopt a standard that will link them closer to what is beautiful, namely love and honesty.

So what constitutes perfect virtue? Is it defined by the strength of individual will? Is it how one determines right from wrong, the capacity to overcome the influence of a defective ego, the intelligence and the confidence to be autonomous by engaging independently with the world around them? Is it to identify and distinguish the kind of moral values that are functional, valuable and aesthetical, of what is prohibited, useful and authentic, to be capable of ascertaining intent and to act on and maximise moral principles? It is simply the strength of will, the capacity to overcome the proclivity of the ego and the wayward pleasures of our instinctual drives, to recognise the scope of the activity of leading a morally virtuous life by searching for the golden mean. It is to be courageous enough to deliberately abandon a false environment and find the veracity and sense of honour to pursue a life of virtue, to maintain and personify it. “True virtue can only be grafted onto principles, such that the more general they are, the more sublime and noble they become,”[iii] thus distinguishing between the subjective aesthetic toward a universal aesthetic, the former having the possible inclination to waywardness as it remains dependant on the moral disposition of the individual.

It is for this reason that the disposition of the individual and obtaining the correct character traits necessary to reach true virtue is indispensable. Moses Maimonides discussed in detail the importance of this mean in several of his works including Hilkhot De’ot or the Laws Concerning Character Traits and Eight Chapters aside from his more famed work in Guide of the Perplexed. All of which can be found in the Ethical Writings of Maimonides (Moses ben Maimon), edited by Raymond L. Weiss with Charles Butterworth. Maimonides (1138 – 1204) was born in Cordoba, during the short-lived Moorish Almoravid Dynasty that ruled over present-day Morocco and Spain. Known as Rambam, he trained as a physician that later enabled him to become court physician to the Sultan Saladin and was well versed in medicine both in reading and in writing. His writings stretched out to include Rabbinic Law and Jewish Philosophy and his influence as a scholar has maintained his place as authoritative figure in Jewish law and ethics. His metaphysical and epistemological writings are included in his prolific repertoire but his studies on ethics and virtue exemplify the type of obedience and dedication required to preserve the divine wisdom and the t’amei ha-mitzvot that explained the reasons for the commandments.

According to Maimonides, there exists two types of moral standards in an individual, namely those that are pious and those that attempt to find the golden mean, the former considered to be obligatory since such a characteristic is required to encourage the subjective poise required to engage in the middle way.[iv] In his Laws Concerning Character Traits (27-59), he traverses through eleven commandments that attempt to direct one toward the equilibrium required to reach a state of moral virtue that epitomises the ‘right way’ or as said by Solomon, “Ponder the path of thy feet, and let all thy ways be established.”[v] All people have different character traits, different personalities and dispositions, whereby one person may have the calm that another may not as they become intensely angered and impatient. One can be lazy and gluttonous while another ascetic by nature. Maimonides writes about eleven commandments that include 1. to imitate God, 2. to cleave to those who know of God, 3. to love your neighbours, 4. to love converts to God, 5. not to hate brothers, 6. to rebuke, 7. not to put (anyone) to shame, 8. not to afflict the distressed, 9. not to go about as a talebearer, 10. not to take revenge, 11. not to bear a grudge. “The right way is the mean in every single one of a man’s character traits” (29). The golden mean is to find the balance toward establishing a good character indicated by the way they conduct their affairs, by being humble and loving. It is to reach for ‘wisdom’ by finding the mean between the extremes of our character traits before sensibly and continuously practicing until it becomes firmly established.

For Maimonides, it is wisdom to walk in the way of God, to seek the path that leads to God and therefore replicate the virtues or commandments and test your obedience to God as exemplified in the Old Testament. To become “slow to anger and abundant in loving-kindness, just and righteous, perfect, powerful and strong… and a man is obliged to train himself to follow them and to imitate according to his strength.”[vi] It is to uproot the flaws that one may have and ‘cure’ the ailment of immorality by training oneself to understand opposites. If one is wealthy and has a conceited attitude, he should clothe himself in worn-out, shabby garments that will endure him with much degradation until the haughtiness has left him and he is humbled. Whatever the problem may be that causes one to lose the way of this required balance, the individual should move themselves toward the other end of the same extreme until reaching that unaffected balance. As said by David Hume, “[t]he richest genius, like the most fertile soil, when uncultivated, shoots up into the rankest weeds.”[vii]

Although he discusses aspects of one’s personal conduct, including the way that one may eat or drink, sleep and have sexual intercourse, there is one particular aspect that merits further discussion and that was his view on cleaving to those who lead the way of wisdom. “[A] man needs to associate with the just and be with the wise continually in order to learn [from] their actions,”[viii] and by associating with fools one will ultimately enable evil to prosper within. Accordingly, evil is living without adequate care or thought to this measure of behaviour. The human being, says Kant, is aware of the moral law but has failed to incorporate it into his or her maxim, and is thus fundamentally evil.[ix] Regarding the conduct of ones affairs and perfecting eating habits, the way he or she engages with body and desires, and the consistent consciousness to dedicate oneself to moral well being is not simply for the happiness that it enables but also as a way to keep his or her body healthy and strong. There misery therewith when surrounded by the wrong people will prevent one from conducting their affairs correctly. In On the Management of Health (105-113), any such undesirable people and overindulgence leads to excessive mental and physical health issues where strength is spent and “his life and eyes dimmed”[x] or conversely, improving his character traits by cleaving to those who are wise, modest and righteous, his soul ultimately becomes tranquil.[xi] In similar vein, Confucius states that one should, “make conscientiousness and sincerity your leading principles. Have no friends inferior to yourself. And when in the wrong, do not hesitate to amend.”[xii] But it is not merely the afflictions physically, but the afflictions of the soul and the impact of the misery, anxiety and despair that befall people. The remedy is to enable the soul to eliminate the passions and learn to compose oneself ethically and morally by becoming subservient to what is righteous and good. “Thus the passions will diminish, [obsessive] thoughts will disappear, apprehension will be removed, and the soul will be cheerful in whatever condition a man happens to be” [109].

While it is possible that the ego could choose the wrong people to have and thus misconstrue what it means to be surrounded by the right people, the general rule of propriety is that self-development and dedicating oneself to a life of wisdom would enable the faculty accurately observe right and wrong conduct in others and ourselves. The propriety of character and how people conduct themselves and their affairs is a matter of observation and since depravity of character is expressed through impropriety and the product of their behaviour seen by the fruits they produce, the clarity of choice becomes simplified. Those who embody moral virtue and right or wrong behaviour, who – as Mencius expounds – feels a sense of shame[xiii] and is reverently careful in his conduct and affairs is clearly one of right character and mind. This standard establishes a virtuous culture or environment where members equally possess the same will to moral virtue that enjoin to equally share in the development of principles, a formula known as the Kingdom of Ends.[xiv] For Maimonides, “Certain actions necessarily stem from one soul and other actions from another soul” that therefore exemplify the importance of relations with our fellow community.

In Eight Chapters (59-105), Maimonides critically explores piety and the discipline that encompasses morality. Good moral habits initiates the formation of ethics; by obtaining good moral habits, it becomes that very connection between moral virtue and the social and political. Written as an introduction to Pirqei Avot (Chapters of the Fathers), he attempts to isolate the permissible and erroneous and the relevance of been rational as n instrument to become empowered to control the appetitive desires. The soul has the power but disobedience through transgressions and the highly imaginative fails to enable the will to become subservient to moral virtues. “For example, moderation, liberality, justice, gentleness, humility, contentment, courage, and others.” (65) This disobedience becomes a disease to the soul that is seen externally in the body, taking pleasure in things that are not good for the body and the mind and never reaching physical excellence. His references to statements made by Solomon enables clarity on his combined efforts to involve Biblical connections to his ethical and medicinal approaches.

And the reason for living a life dedicated to finding the Golden Mean? Virtue – which is mental health – and the golden mean are necessary for a healthy life. In his Letter to Joseph (113-129), that he writes to his disciple Joseph Ibn Aknin, it is to lead by example and develop a pattern of excellent. The chapter provides some extraordinary insights into the man himself, about his vision and his enormous commitment to his moral objective. “In sum, if you are indeed my disciple, I want you to train yourself to follow my moral habits” (120). His affection and criticisms shed an amazing light on his dedication to justice and his love of knowledge, or as St. Thomas Aquinas states, “Love takes up where knowledge leaves off.”[xvii] Love is the unity formed through knowledge and establishes a state of happiness resides, making knowledge fundamental to this development. Through Rabbinical law and adherence to the commandments along with the dedication to attain a balance of mind will the adherent become suffused with love. It is not simply the mean itself that supplies the individual with the tranquillity required to be happy, but the righteous ability to discern the right time and way to think and behave, to rationally approach ones own emotions.

By improving your character and reaching a state of clarity in mind and reason, one will enable the qualities necessary to reach the balanced standard that Mainmonides expects. In the Guide of the Perplexed (129-155), which is one of his most famous works, is to guide those possessing positive character traits by learning to understand God. The work is addressed to Joseph ben Judah and elucidates ways of overcoming the disillusionment and existential angst of philosophy and law by understanding the differences between the practical and the subjective or speculative. Having strong theoretical foundations and thus continuously ameliorating knowledge, one can uncover the mental capacity necessary to acquire to attain a solid understanding of themselves and the world around them. That laws are not natural but necessary to manage the natural. “The Law as a whole aims at two things: the well-being of the soul and the well-being of the body. As for the well-being of the soul, it consists in the multitude’s acquiring correct opinions corresponding to their respective capacity” (139). The final chapters, Treatise on the Art of Logic (155-165) and The Days of the Messiah (165-177) continue along with the same themes. By distinguishing biblical themes such as the world to come, formulations that deal with immorality and the benefits of the laws particularly the coming messianic era will provide one with an understanding of repentance. “It has become known that the life of the world-to-come is the reward for performing the commandments and is the good that we merit if we have kept the way of the old referred to in the Torah” (169). Discussing the instrument of logic as a necessary condition of the mind in order to appreciate the correct approach of practical reasoning and to think and behave correctly remains an important aspect to the power of rational thought.

I was compelled to his work for my love of history whether it is ancient or medieval, in this case the latter. I have a strong appreciation for literature such as the Ethical Writings of Maimonides that promotes the value of ethics and the moral concerns relating to our conduct and behaviour. His criticism is harsh, views absolute and his beliefs that the actions of our soul, our intent, the choices that we want to make and whether we are thinking correctly formulate the groundwork necessary to compel the right choices that we act out in reality. The book provides additional insight into rabbinical literature and the significance of moral laws that authoritatively posit the necessity of moral conduct. By finding the golden mean and teaching oneself to discover a proper balance of thought and behaviour, compelled by our desire to lead a virtuous life, Maimonides believes that we can reach both physically and mentally excellence in health and in moral virtue.

[i] Plato, Republic [618e]
[ii] Aristotle, Nichomachean Ethics from I.M.N. Al-Jubouri’ History of Islamic Philosophy, (2004) 74
[iii] Immanuel Kant, Observations on the Feeling of the Beautiful and Sublime, 2:217
[iv] Raymond L. Weiss, Ethical Writings of Maimonides, Dover Publications New York (1975), 7
[v] Proverbs 4:26
[vi] Weiss and Butterworth, op. cit., 30
[vii] David Hume, Moral and Political Philosophy, Simon and Schuster (2010)
[viii] Weiss and Butterworth, op. cit., 46
[ix] Immanuel Kant, Religion within the Bounds of Mere Reason, 6:32
[x] Weiss and Butterworth, op. cit., 40
[xi] Ibid., 43
[xii] Confucius, The Analects, Chapter XXIV
[xiii] Menicius, Bk. vii., pti., c.vii., v i.
[xiv] Immanuel Kant, Groundwork of the Metaphysic of Morals, 4:439