There are many works of fiction featuring battles between ‘Good’ and ‘Evil’, yet it would not be distorting the truth to say that we are witnessing one now, though I think it is largely misconstrued by those of us who are on the sidelines. We see it as a conflict between Islam and the West, when it’s actually within Islam itself. This came home to me when I recently saw the biographical movie, He Named Me Malala (pronounce Ma-la-li, by the way).
Malala is well known as the 14 year old Pakistani school girl, shot in the head on a school bus by the Taliban for her outspoken views on education for girls in Pakistan. Now 18 years old (when the film was made) she has since won the Nobel Peace Prize and spoken in the United Nations, as well as having audiences with world leaders, like Barak Obama. In a recent interview with Emma Watson (on Emma’s Facebook page) she appeared much wiser than her years. In the movie, amongst her family, she behaves like an ordinary teenager with ‘crushes’ on famous sports stars. In effect, her personal battle with the Taliban represents in microcosm a much wider battle between past and future that is occurring on the world stage within Islam. A battle for the hearts and minds of Muslims all over the world.
IS or ISIS or Daesh has arisen out of conflicts between Shiites and Sunnis in both Iraq and Syria, but the declaration of a Caliphate has led to a much more serious, even sinister, connotation, because its followers believe they are fulfilling a prophecy which will only be resolved with the biblical end of the world. I’m not an Islamic scholar, so I’m quoting from Audrey Borowski, currently doing a PhD at the University of London, who holds a MSt (Masters degree) in Islamic Studies from Oxford University. She asserts: ‘…one of the Prophet Muhammad’s earliest hadith (sayings) locates the fateful showdown between Christians and Muslims that heralds the apocalypse in the city of Dabiq in Syria.’
“The Hour will not be established until the Romans (Christians) land at Dabiq. Then an army from Medina of the best people on the earth at that time… will fight them.”
She wrote an article of some length in Philosophy Now (Issue 111, Dec. 2015/Jan. 2016) titled Al Qaeda and ISIS; From Revolution to Apocalypse.
The point is that if someone believes they are in a fight for the end of the world, then destroying entire populations and cities is not off the table. They could resort to any tactic, like contaminating water supplies of entire cities or destroying food crops on a large scale. I alluded in the introduction that this apocalyptic ideology, in a fictional context, represents a classic contest between good and evil. From where I (and most people reading this blog) stand, anyone intent on destroying civilization as we know it, would be considered the ultimate evil.
What is most difficult for us to comprehend is that the perpetrators, the people ‘on the other side’ would see the roles reversed. Earlier this year (April 2015), I wrote a post titled Morality is totally in the eye of the beholder, where I explained how two different cultures in the same country (India) could have completely opposing views concerning a crime against a young woman, who was raped and murdered on a bus returning from seeing a movie with her boyfriend. One view was that the girl was the victim of a crime and the other view was that the girl was responsible for her own fate.
Many people have trouble believing that otherwise ordinary people, who commit evil acts in the form of atrocities, would see themselves as not being evil. We have an enormous capacity to justify to ourselves the most heinous acts, and no where is this more evident, than when one believes they are performing the ‘Will of God’. This is certainly the case with IS and their followers.
Unfortunately, this has led to a backlash in the West against all Muslims. In particular, we see both in social media and mainstream media, and even amongst mainstream politicians, a sentiment that Islam is fundamentally flawed and needs to be reformed. It seems to me that they are unaware that there is already a battle happening within Islam, where militant bodies like IS and Boko Haram and the Taliban represent the worse and a young schoolgirl from Pakistan represents the best.
Ayaan Hirsi Ali (whom I wrote about in March 2011), said when she was in Australia many years ago, that Islam was not compatible with a secular society, which is certainly true if Islamists wish to establish a religious-based government. There is a group, Hizb ut-Tahrir, who is banned in most Western countries, but not UK or Australia, and whose stated aim is to form a caliphate and whose political agenda, including the introduction of Sharia law, would clearly conflict with Australian law. But the truth is that there are many Muslims living an active and productive life in Australia, whilst still practising their religion. A secular society is not an atheistic society, yet is religiously nondependent by definition. In other words, there is room for variety in religious practice and that is what we see. Extremists of any religious persuasion are generally not well received in a pluralist multicultural society, yet that is the fear that is driving the debate in many secular societies.
Over a year ago (Aug 2014) I wrote a post titled Don’t judge all Muslims the same, based on another article I read in Philosophy Now (Issue 104, May/Jun 2014) by Terri Murray (Master of Theology, Heythrop College, London) who made a very salient point differentiating cultural values and ideals from individual ones. In particular, she asserted that an individual’s rights overrules the so-called rights of a culture or a community. Therefore, misogynistic issues like female genital mutilation, honour killings, child marriage, all of which are illegal in Australia, are abuses of individual rights that may be condoned, even considered normal practice, in some cultures.
Getting back to my original subject matter, like the case of the Indian girl (a medical graduate) who was murdered for going on a date, this really is a battle between past and future. IS and the Taliban and their variant Islamic ideologies represent a desire to regain a past that has no relevance in the 21st Century – it’s mediaeval, not only in concept but also in practice. One of the consequences of the Internet is that it has become a vehicle for both sides. So young women in far off countries are learning that there is another world where education can lead to a better life. And this is the key: education of women, as Malala has brought to the world’s attention, is the only true way forward. It’s curious that women are what these regimes seem to fear most, including IS, whose greatest fear is to be killed by a female Kurdish warrior, because then they won’t get to Paradise.
Tuesday 15 December 2015
Tuesday 1 December 2015
Why narcissists are a danger to themselves and others
I expect everyone has met a narcissist, though, like all personality disorders, there are degrees of severity, from the generally harmless egotistical know-it-all to the megalomaniac, who takes control of an entire nation. In between those extremes is the person who somehow self-destructs while claiming it’s everyone else’s fault. They’re the ones who are captain of the ship and totally in control, even when it runs aground, but suddenly claim it’s no longer their fault. I’m talking metaphorically, but this happened quite literally and spectacularly, a couple of years back, as most of you will remember.
The major problem with narcissists is not their self-aggrandisement and over-inflated opinion of their own worth, but their distorted view of reality.
Narcissists have a tendency to self-destruct, not on purpose, but because their view of reality, based on their overblown sense of self-justification, becomes so distorted that they lose perspective and then control, even though everyone around them can see the truth, but are generally powerless to intervene.
They are particularly disastrous in politics but are likely to rise to power when things are going badly, because they are charismatic and their self-belief becomes contagious. Someone said (I don’t know who) that when things are going badly society turns on itself – they were referring to the European witch hunts, which coincided with economic and environmental tribulations. The recent GFC creates ripe conditions for charismatic leaders to feed a population’s paranoia and promise miracle solutions with no basis in rationality. Look at what happened in Europe following the Great Depression of the 20th Century: World War 2. And who started it? Probably the most famous narcissist in recent history. The key element that they have in common with the aforementioned witch-hunters is that they can find someone to blame and, frighteningly, they are believed.
Narcissists make excellent villains as I’ve demonstrated in my own fiction. But one must be careful of whom we demonise lest we become as spiteful and destructive as those we wish not to emulate. Seriously, we should not take them seriously; then all their self-importance and self-aggrandisement becomes comical. Unfortunately, they tend to divide society between those who see themselves as victims and those who see the purported culprits as the victims. In other words, they divide nations when they should be uniting them.
But there are exceptions. Having read Steve Jobs’ biography (by Walter Isaacson) I would say he had narcissistic tendencies, yet he was eminently successful. Many people have commented on his ‘reality-distortion field’, which I’ve already argued is a narcissistic trait, and he could be very egotistical at times, according to anecdotal evidence. Yet he could form deep relationships despite being very contrary in his dealings with his colleagues – building them up one moment and tearing them down the next. But Jobs was driven to strive for perfection, both aesthetically and functionally, and he sought out people who had the same aspiration. He was, of course, extraordinarily charismatic, intelligent and somewhat eccentric. He was a Buddhist, which may have tempered his narcissistic tendencies; but I’m just speculating – I never met him or worked with him – I just used and admired his products like many others. Anyway, I would cite Jobs as an example of a narcissist who broke the mould – he didn’t self-destruct, quite the opposite, in fact.
Addendum: When I wrote this I had recently read Isaacson's biography of Steve Jobs, but I've since seen a documentary and he came perilously close to self-destruction. He was called before a Senate Committee under charges of fraud. He was giving his employees backdated shares (I think that was the charge, from memory). Anyway, according to the documentary, he only avoided prison because it would have destroyed the share price of Apple, which was the biggest company on the share market at the time. I don't know how true this is, but it rings true.
The major problem with narcissists is not their self-aggrandisement and over-inflated opinion of their own worth, but their distorted view of reality.
Narcissists have a tendency to self-destruct, not on purpose, but because their view of reality, based on their overblown sense of self-justification, becomes so distorted that they lose perspective and then control, even though everyone around them can see the truth, but are generally powerless to intervene.
They are particularly disastrous in politics but are likely to rise to power when things are going badly, because they are charismatic and their self-belief becomes contagious. Someone said (I don’t know who) that when things are going badly society turns on itself – they were referring to the European witch hunts, which coincided with economic and environmental tribulations. The recent GFC creates ripe conditions for charismatic leaders to feed a population’s paranoia and promise miracle solutions with no basis in rationality. Look at what happened in Europe following the Great Depression of the 20th Century: World War 2. And who started it? Probably the most famous narcissist in recent history. The key element that they have in common with the aforementioned witch-hunters is that they can find someone to blame and, frighteningly, they are believed.
Narcissists make excellent villains as I’ve demonstrated in my own fiction. But one must be careful of whom we demonise lest we become as spiteful and destructive as those we wish not to emulate. Seriously, we should not take them seriously; then all their self-importance and self-aggrandisement becomes comical. Unfortunately, they tend to divide society between those who see themselves as victims and those who see the purported culprits as the victims. In other words, they divide nations when they should be uniting them.
But there are exceptions. Having read Steve Jobs’ biography (by Walter Isaacson) I would say he had narcissistic tendencies, yet he was eminently successful. Many people have commented on his ‘reality-distortion field’, which I’ve already argued is a narcissistic trait, and he could be very egotistical at times, according to anecdotal evidence. Yet he could form deep relationships despite being very contrary in his dealings with his colleagues – building them up one moment and tearing them down the next. But Jobs was driven to strive for perfection, both aesthetically and functionally, and he sought out people who had the same aspiration. He was, of course, extraordinarily charismatic, intelligent and somewhat eccentric. He was a Buddhist, which may have tempered his narcissistic tendencies; but I’m just speculating – I never met him or worked with him – I just used and admired his products like many others. Anyway, I would cite Jobs as an example of a narcissist who broke the mould – he didn’t self-destruct, quite the opposite, in fact.
Addendum: When I wrote this I had recently read Isaacson's biography of Steve Jobs, but I've since seen a documentary and he came perilously close to self-destruction. He was called before a Senate Committee under charges of fraud. He was giving his employees backdated shares (I think that was the charge, from memory). Anyway, according to the documentary, he only avoided prison because it would have destroyed the share price of Apple, which was the biggest company on the share market at the time. I don't know how true this is, but it rings true.
Tuesday 24 November 2015
The Centenary of Einstein’s General Theory of Relativity
This month (November 2015) marks 100 years since Albert Einstein published his milestone paper on the General Theory of Relativity, which not only eclipsed Newton’s equally revolutionary Theory of Universal Gravitation, but is still the cornerstone of every cosmological theory that has been developed and disseminated since.
It needs to be pointed out that Einstein’s ‘annus mirabilis’ (miraculous year), as it’s been called, occurred 10 years earlier in 1905, when he published 3 groundbreaking papers that elevated him from a patent clerk in Bern to a candidate for the Nobel Prize (eventually realised of course). The 3 papers were his Special Theory of Relativity, his explanation of the photo-electric effect using the newly coined concept, photon of light, and a statistical analysis of Brownian motion, which effectively proved that molecules made of atoms really exist and were not just a convenient theoretical concept.
Given the anniversary, it seemed appropriate that I should write something on the topic, despite my limited knowledge and despite the plethora of books that have been published to recognise the feat. The best I’ve read is The Road to Relativity; The History and Meaning of Einstein’s “The Foundation of General Relativity” (the original title of his paper) by Hanoch Gutfreund and Jurgen Renn. They have managed to include an annotated copy of Einstein’s original handwritten manuscript with a page by page exposition. But more than that, they take us on Einstein’s mental journey and, in particular, how he found the mathematical language to portray the intuitive ideas in his head and yet work within the constraints he believed were necessary for it to work.
The constraints were not inconsiderable and include: the equivalence of inertial and gravitational mass; the conservation of energy and momentum under transformation between frames of reference both in rotational and linear motion; and the ability to reduce his theory mathematically to Newton’s theory when relativistic effects were negligible.
Einstein’s epiphany, that led him down the particular path he took, was the realisation that one experienced no force when one was in free fall, contrary to Newton’s theory and contrary to our belief that gravity is a force. Free fall subjectively feels no different to being in orbit around a planet. The aptly named ‘vomit comet’ is an aeroplane that goes into free fall in order to create the momentary sense of weightlessness that one would experience in space.
Einstein learnt from his study of Maxwell’s equations for electromagnetic radiation, that mathematics could sometimes provide a counter-intuitive insight, like the constant speed of light.
In fact, Einstein had to learn new mathematics (for him) and engaged the help of his close friend, Marcel Grossman, who led him through the technical travails of tensor calculus using Riemann geometry. It would seem, from what I can understand of his mental journey, that it was the mathematics, as much as any other insight, that led Einstein to realise that space-time is curved and not Euclidean as we all generally believe. To quote Gutfreund and Renn:
[Einstein] realised that the four-dimensional spacetime of general relativity no longer fitted the framework of Euclidean geometry… The geometrization of general relativity and the understanding of gravity as being due to the curvature of spacetime is a result of the further development and not a presupposition of Einstein’s formulation of the theory.
By Euclidean, one means space is flat and light travels in perfectly straight lines. One of the confirmations of Einstein’s theory was that he predicted that light passing close to the Sun would be literally bent and so a star in the background would appear to shift as the Sun approached the same line of sight for an observer on Earth as for the star. This could only be seen during an eclipse and was duly observed by Arthur Eddington in 1919 on the island of Principe near Africa.
Einstein’s formulations led him to postulate that it’s the geometry of space that gives us gravity and the geometry, which is curved, is caused by massive objects. In other words, it’s mass that curves space and it’s the curvature of space that causes mass to move, as John Wheeler famously and succinctly expounded.
It may sound back-to-front, but, for me, Einstein’s Special Theory of Relativity only makes sense in the context of his General Theory, even though they were formulated in the reverse order. To understand what I’m talking about, I need to explain geodesics.
When you fly long distance on a plane, the path projected onto a flat map looks curved. You may have noticed this when they show the path on a screen in the cabin while you’re in flight. The point is that when you fly long distance you are travelling over a curved surface, because, obviously, the Earth is a sphere, and the shortest distance between 2 points (cities) lies on what’s called a great circle. A great circle is the one circle that goes through both points that is the largest circle possible. Now, I know that sounds paradoxical, but the largest circle provides the shortest distance over the surface (we are not talking about tunnels) that one can travel and there is only one, therefore there is one shortest path. This shortest path is called the geodesic that connects those 2 points.
A geodesic in gravitation is the shortest distance in spacetime between 2 points and that is what one follows when one is in free fall. At the risk of information overload, I’m going to introduce another concept which is essential for understanding the physics of a geodesic in gravity.
One of the most fundamental principles discovered in physics is the principle of least action (formulated mathematically as a Lagrangian which is the difference between kinetic and potential energy). The most commonly experienced example would be refraction of light through glass or water, because light travels at different velocities in air, water and glass (slower through glass or water than air). The extremely gifted 17th Century amateur mathematician, Pierre de Fermat (actually a lawyer) conjectured that the light travels the shortest path, meaning it takes the least time, and the refractive index (Snell’s law) can be deduced mathematically from this principle. In the 20th Century, Richard Feynman developed his path integral method of quantum mechanics from the least action principle, and, in effect, confirmed Fermat’s principle.
Now, when one applies the principle of least action to a projectile in a gravitational field (like a thrown ball) one finds that it too takes the shortest path, but paradoxically this is the path of longest relativistic time (not unlike the paradox of the largest circle described earlier).
Richard Feynman gives a worked example in his excellent book, Six Not-So-Easy Pieces. In relativity, time can be subjective, so that a moving clock always appears to be running slow compared to a stationary clock, but, because motion is relative, the perception is reversed for the other clock. However, as Feynman points out:
The time measured by a moving clock is called its “proper time”. In free fall, the trajectory makes the proper time of an object a maximum.
In other words, the geodesic is the trajectory or path of longest relativistic time. Any variant from the geodesic will result in the clock’s proper time being shorter, which means time literally slows down. So special relativity is not symmetrical in a gravitational field and there is a gravitational field everywhere in space. As Gutfreund and Renn point out, Einstein himself acknowledged that he had effectively replaced the fictional aether with gravity.
This is most apparent when one considers a black hole. Every massive body has an escape velocity which is the velocity a projectile must achieve to become free of a body’s gravitational field. Obviously, the escape velocity for Earth is larger than the escape velocity for the moon and considerably less than the escape velocity of the Sun. Not so obvious, although logical from what we know, the escape velocity is independent of the projectile’s mass and therefore also applies to light (photons). We know that all body’s fall at exactly the same rate in a gravitational field. In other words, a geodesic applies equally to all bodies irrespective of their mass. In the case of a black hole, the escape velocity exceeds the speed of light, and, in fact, becomes the speed of light at its event horizon. At the event horizon time stops for an external observer because the light is red-shifted to infinity. One of the consequences of Einstein’s theory is that clocks travel slower in a stronger gravitational field, and, at the event horizon, gravity is so strong the clock stops.
To appreciate why clocks slow down and rods become shorter (in the direction of motion), with respect to an observer, one must understand the consequences of the speed of light being constant. If light is a wave then the equation for a wave is very fundamental:
v = f λ , where v is velocity, f is the frequency and λ is the wavelength.
In the case of light the equation becomes c = f λ , where c is the speed of light.
One can see that if c stays constant then f and λ can change to accommodate it. Frequency measures time and wavelength measures distance. One can see how frequency can become stretched or compressed by motion if c remains constant, depending whether an observer is travelling away from a source of radiation or towards it. This is called the Doppler effect, and on a cosmic scale it tells us that the Universe is expanding, because virtually all galaxies in all directions are travelling away from us. If a geodesic is the path of maximum proper time, we have a reference for determining relativistic effects, and we can use the Doppler effect to determine if a light source is moving relative to an observer, even though the speed of light is always c.
I won’t go into it here, but the famous twin paradox can be explained by taking into account both relativistic and Doppler effects for both parties – the one travelling and the one left at home.
It needs to be pointed out that Einstein’s ‘annus mirabilis’ (miraculous year), as it’s been called, occurred 10 years earlier in 1905, when he published 3 groundbreaking papers that elevated him from a patent clerk in Bern to a candidate for the Nobel Prize (eventually realised of course). The 3 papers were his Special Theory of Relativity, his explanation of the photo-electric effect using the newly coined concept, photon of light, and a statistical analysis of Brownian motion, which effectively proved that molecules made of atoms really exist and were not just a convenient theoretical concept.
Given the anniversary, it seemed appropriate that I should write something on the topic, despite my limited knowledge and despite the plethora of books that have been published to recognise the feat. The best I’ve read is The Road to Relativity; The History and Meaning of Einstein’s “The Foundation of General Relativity” (the original title of his paper) by Hanoch Gutfreund and Jurgen Renn. They have managed to include an annotated copy of Einstein’s original handwritten manuscript with a page by page exposition. But more than that, they take us on Einstein’s mental journey and, in particular, how he found the mathematical language to portray the intuitive ideas in his head and yet work within the constraints he believed were necessary for it to work.
The constraints were not inconsiderable and include: the equivalence of inertial and gravitational mass; the conservation of energy and momentum under transformation between frames of reference both in rotational and linear motion; and the ability to reduce his theory mathematically to Newton’s theory when relativistic effects were negligible.
Einstein’s epiphany, that led him down the particular path he took, was the realisation that one experienced no force when one was in free fall, contrary to Newton’s theory and contrary to our belief that gravity is a force. Free fall subjectively feels no different to being in orbit around a planet. The aptly named ‘vomit comet’ is an aeroplane that goes into free fall in order to create the momentary sense of weightlessness that one would experience in space.
Einstein learnt from his study of Maxwell’s equations for electromagnetic radiation, that mathematics could sometimes provide a counter-intuitive insight, like the constant speed of light.
In fact, Einstein had to learn new mathematics (for him) and engaged the help of his close friend, Marcel Grossman, who led him through the technical travails of tensor calculus using Riemann geometry. It would seem, from what I can understand of his mental journey, that it was the mathematics, as much as any other insight, that led Einstein to realise that space-time is curved and not Euclidean as we all generally believe. To quote Gutfreund and Renn:
[Einstein] realised that the four-dimensional spacetime of general relativity no longer fitted the framework of Euclidean geometry… The geometrization of general relativity and the understanding of gravity as being due to the curvature of spacetime is a result of the further development and not a presupposition of Einstein’s formulation of the theory.
By Euclidean, one means space is flat and light travels in perfectly straight lines. One of the confirmations of Einstein’s theory was that he predicted that light passing close to the Sun would be literally bent and so a star in the background would appear to shift as the Sun approached the same line of sight for an observer on Earth as for the star. This could only be seen during an eclipse and was duly observed by Arthur Eddington in 1919 on the island of Principe near Africa.
Einstein’s formulations led him to postulate that it’s the geometry of space that gives us gravity and the geometry, which is curved, is caused by massive objects. In other words, it’s mass that curves space and it’s the curvature of space that causes mass to move, as John Wheeler famously and succinctly expounded.
It may sound back-to-front, but, for me, Einstein’s Special Theory of Relativity only makes sense in the context of his General Theory, even though they were formulated in the reverse order. To understand what I’m talking about, I need to explain geodesics.
When you fly long distance on a plane, the path projected onto a flat map looks curved. You may have noticed this when they show the path on a screen in the cabin while you’re in flight. The point is that when you fly long distance you are travelling over a curved surface, because, obviously, the Earth is a sphere, and the shortest distance between 2 points (cities) lies on what’s called a great circle. A great circle is the one circle that goes through both points that is the largest circle possible. Now, I know that sounds paradoxical, but the largest circle provides the shortest distance over the surface (we are not talking about tunnels) that one can travel and there is only one, therefore there is one shortest path. This shortest path is called the geodesic that connects those 2 points.
A geodesic in gravitation is the shortest distance in spacetime between 2 points and that is what one follows when one is in free fall. At the risk of information overload, I’m going to introduce another concept which is essential for understanding the physics of a geodesic in gravity.
One of the most fundamental principles discovered in physics is the principle of least action (formulated mathematically as a Lagrangian which is the difference between kinetic and potential energy). The most commonly experienced example would be refraction of light through glass or water, because light travels at different velocities in air, water and glass (slower through glass or water than air). The extremely gifted 17th Century amateur mathematician, Pierre de Fermat (actually a lawyer) conjectured that the light travels the shortest path, meaning it takes the least time, and the refractive index (Snell’s law) can be deduced mathematically from this principle. In the 20th Century, Richard Feynman developed his path integral method of quantum mechanics from the least action principle, and, in effect, confirmed Fermat’s principle.
Now, when one applies the principle of least action to a projectile in a gravitational field (like a thrown ball) one finds that it too takes the shortest path, but paradoxically this is the path of longest relativistic time (not unlike the paradox of the largest circle described earlier).
Richard Feynman gives a worked example in his excellent book, Six Not-So-Easy Pieces. In relativity, time can be subjective, so that a moving clock always appears to be running slow compared to a stationary clock, but, because motion is relative, the perception is reversed for the other clock. However, as Feynman points out:
The time measured by a moving clock is called its “proper time”. In free fall, the trajectory makes the proper time of an object a maximum.
In other words, the geodesic is the trajectory or path of longest relativistic time. Any variant from the geodesic will result in the clock’s proper time being shorter, which means time literally slows down. So special relativity is not symmetrical in a gravitational field and there is a gravitational field everywhere in space. As Gutfreund and Renn point out, Einstein himself acknowledged that he had effectively replaced the fictional aether with gravity.
This is most apparent when one considers a black hole. Every massive body has an escape velocity which is the velocity a projectile must achieve to become free of a body’s gravitational field. Obviously, the escape velocity for Earth is larger than the escape velocity for the moon and considerably less than the escape velocity of the Sun. Not so obvious, although logical from what we know, the escape velocity is independent of the projectile’s mass and therefore also applies to light (photons). We know that all body’s fall at exactly the same rate in a gravitational field. In other words, a geodesic applies equally to all bodies irrespective of their mass. In the case of a black hole, the escape velocity exceeds the speed of light, and, in fact, becomes the speed of light at its event horizon. At the event horizon time stops for an external observer because the light is red-shifted to infinity. One of the consequences of Einstein’s theory is that clocks travel slower in a stronger gravitational field, and, at the event horizon, gravity is so strong the clock stops.
To appreciate why clocks slow down and rods become shorter (in the direction of motion), with respect to an observer, one must understand the consequences of the speed of light being constant. If light is a wave then the equation for a wave is very fundamental:
v = f λ , where v is velocity, f is the frequency and λ is the wavelength.
In the case of light the equation becomes c = f λ , where c is the speed of light.
One can see that if c stays constant then f and λ can change to accommodate it. Frequency measures time and wavelength measures distance. One can see how frequency can become stretched or compressed by motion if c remains constant, depending whether an observer is travelling away from a source of radiation or towards it. This is called the Doppler effect, and on a cosmic scale it tells us that the Universe is expanding, because virtually all galaxies in all directions are travelling away from us. If a geodesic is the path of maximum proper time, we have a reference for determining relativistic effects, and we can use the Doppler effect to determine if a light source is moving relative to an observer, even though the speed of light is always c.
I won’t go into it here, but the famous twin paradox can be explained by taking into account both relativistic and Doppler effects for both parties – the one travelling and the one left at home.
This is an exposition I wrote on the twin paradox.
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