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.
Tuesday, 1 December 2015
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.
Saturday, 14 November 2015
The Unreasonable Effectiveness of Mathematics
I originally called this post: Two miracles that are fundamental to the Universe and our place in it. The miracles I’m referring to will not be found in any scripture and God is not a necessary participant, with the emphasis on necessary. I am one of those rare dabblers in philosophy who argues that science is neutral on the subject of God. A definition of miracle is required, so for the purpose of this discussion, I call a miracle something that can’t be explained, yet has profound and far-reaching consequences. ‘Something’, in this context, could be described as a concordance of unexpected relationships in completely different realms.
This is one of those posts that will upset people on both sides of the religious divide, I’m sure, but it’s been rattling around in my head ever since I re-read Eugene P. Wigner’s seminal essay, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. I came across it (again) in a collection of essays under the collective title, Math Angst, contained in a volume called The World Treasury of Physics, Astronomy and Mathematics edited by Timothy Ferris (1991). This is a collection of essays and excerpts by some of the greatest minds in physics, mathematics and cosmology in the 20th Century.
Back to Wigner, in discussing the significance of complex numbers in quantum mechanics, specifically Hilbert’s space, he remarks:
‘…complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers in this case is not a calculated trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics.’
It is well known, among physicists, that in the language of mathematics, quantum mechanics not only makes perfect sense but is one of the most successful physical theories ever. But in ordinary language it is hard to make sense of it in any way that ordinary people would comprehend it.
It is in this context that Wigner makes the following statement in the next paragraph following the quote above:
‘It is difficult to avoid the impression that a miracle confronts us here… or the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.’
Hence the 2 miracles I refer to in my introduction. The key that links the 2 miracles is mathematics. A number of physicists: Paul Davies, Roger Penrose, John Barrow (they’re just the ones I’ve read); have commented on the inordinate correspondence we find between mathematics and regularities found in natural phenomena that have been dubbed ‘laws of nature’.
The first miracle is that mathematics seems to underpin everything we know and learn about the Universe, including ourselves. As Barrow has pointed out, mathematics allows us to predict the makeup of fundamental elements in the first 3 minutes of the Universe. It provides us with the field equations of Einstein’s general theory of relativity, Maxwell’s equations for electromagnetic radiation, Schrodinger’s wave function in quantum mechanics and the four digit software code for all biological life we call DNA.
The second miracle is that the human mind is uniquely evolved to access mathematics to an extraordinarily deep and meaningful degree that has nothing to do with our everyday prosaic survival but everything to do with our ability to comprehend the Universe in all the facets I listed above.
The 2 miracles combined give us the greatest mystery of the Universe, which I’ve stated many times on this blog: It created the means to understand itself, through us.
So where does God fit into this? Interestingly, I would argue that when it comes to mathematics, God has no choice. Einstein once asked the rhetorical question, in correspondence with his friend, Paul Ehrenfest (if I recall it correctly): did God have any choice in determining the laws of the Universe? This question is probably unanswerable, but when it comes to mathematics, I would answer in the negative. If one looks at prime numbers (there are other examples, but primes are fundamental) it’s self-evident that they are self-selected by their very definition – God didn’t choose them.
The interesting thing about primes is that they are the ‘atoms’ of mathematics because all the other ‘natural’ numbers can be determined from all the primes, all the way to infinity. The other interesting thing is that Riemann’s hypothesis indicates that primes have a deep and unexpected relationship with some of the most esoteric areas of mathematics. So, if one was a religious person, one might suggest that this is surely the handiwork of God, yet God can’t even affect the fundamentals upon which all this rests.
Addendum: I changed the title to reflect the title of Wigner's essay, for web-search purposes.
This is one of those posts that will upset people on both sides of the religious divide, I’m sure, but it’s been rattling around in my head ever since I re-read Eugene P. Wigner’s seminal essay, The Unreasonable Effectiveness of Mathematics in the Natural Sciences. I came across it (again) in a collection of essays under the collective title, Math Angst, contained in a volume called The World Treasury of Physics, Astronomy and Mathematics edited by Timothy Ferris (1991). This is a collection of essays and excerpts by some of the greatest minds in physics, mathematics and cosmology in the 20th Century.
Back to Wigner, in discussing the significance of complex numbers in quantum mechanics, specifically Hilbert’s space, he remarks:
‘…complex numbers are far from natural or simple and they cannot be suggested by physical observations. Furthermore, the use of complex numbers in this case is not a calculated trick of applied mathematics but comes close to being a necessity in the formulation of the laws of quantum mechanics.’
It is well known, among physicists, that in the language of mathematics, quantum mechanics not only makes perfect sense but is one of the most successful physical theories ever. But in ordinary language it is hard to make sense of it in any way that ordinary people would comprehend it.
It is in this context that Wigner makes the following statement in the next paragraph following the quote above:
‘It is difficult to avoid the impression that a miracle confronts us here… or the two miracles of the existence of laws of nature and of the human mind’s capacity to divine them.’
Hence the 2 miracles I refer to in my introduction. The key that links the 2 miracles is mathematics. A number of physicists: Paul Davies, Roger Penrose, John Barrow (they’re just the ones I’ve read); have commented on the inordinate correspondence we find between mathematics and regularities found in natural phenomena that have been dubbed ‘laws of nature’.
The first miracle is that mathematics seems to underpin everything we know and learn about the Universe, including ourselves. As Barrow has pointed out, mathematics allows us to predict the makeup of fundamental elements in the first 3 minutes of the Universe. It provides us with the field equations of Einstein’s general theory of relativity, Maxwell’s equations for electromagnetic radiation, Schrodinger’s wave function in quantum mechanics and the four digit software code for all biological life we call DNA.
The second miracle is that the human mind is uniquely evolved to access mathematics to an extraordinarily deep and meaningful degree that has nothing to do with our everyday prosaic survival but everything to do with our ability to comprehend the Universe in all the facets I listed above.
The 2 miracles combined give us the greatest mystery of the Universe, which I’ve stated many times on this blog: It created the means to understand itself, through us.
So where does God fit into this? Interestingly, I would argue that when it comes to mathematics, God has no choice. Einstein once asked the rhetorical question, in correspondence with his friend, Paul Ehrenfest (if I recall it correctly): did God have any choice in determining the laws of the Universe? This question is probably unanswerable, but when it comes to mathematics, I would answer in the negative. If one looks at prime numbers (there are other examples, but primes are fundamental) it’s self-evident that they are self-selected by their very definition – God didn’t choose them.
The interesting thing about primes is that they are the ‘atoms’ of mathematics because all the other ‘natural’ numbers can be determined from all the primes, all the way to infinity. The other interesting thing is that Riemann’s hypothesis indicates that primes have a deep and unexpected relationship with some of the most esoteric areas of mathematics. So, if one was a religious person, one might suggest that this is surely the handiwork of God, yet God can’t even affect the fundamentals upon which all this rests.
Addendum: I changed the title to reflect the title of Wigner's essay, for web-search purposes.
Friday, 23 October 2015
Freedom; a moral imperative
I wrote something about freedom recently, in answer to a question posed in Philosophy Now (Issue 108, Jun/Jul 2015) regarding What's The More Important: Freedom, Justice, Happiness, Truth? My sequence of importance starting at the top was Truth, Justice, Freedom and Happiness based on the argued premise that each was dependent on its predecessor. But this post is about something else: the relevance of John Stuart Mill’s arguments on ‘liberty’ in the 21st Century.
Once again, this has been triggered by Philosophy Now, but Issue 110 (Oct/Nov 2015) though the context is quite different. Philosophy Now is a periodical and they always have a theme, and the theme for this issue is ‘Liberty & Equality’ so it’s not surprising to find articles on freedom. In particular, there are 2 articles: Mill, Liberty & Euthanasia by Simon Clarke and The Paradox of Liberalism by Francisco Mejia Uribe.
I haven’t read Mill’s book, On Liberty, which is cited in both of the aforementioned articles, but I’ve read his book, Utilitarianism, and what struck me was that he was a man ahead of his time. Not only is utilitarian philosophy effectively the default position in Western democracies (at least, in theory) but he seemed to predict findings in social psychology like the fact that one’s conscience is a product of social norms and not God whispering in one’s ear, and that social norms can be changed, like attitudes towards smoking, for example. I’ve written a post on utilitarian moral philosophy elsewhere, so I won’t dwell on it here.
The first essay by Clarke (cited above) deals with the apparent conflict between freedom to pursue one’s potential and the freedom to end one’s life through euthanasia, which is not the subject of this post either. It’s Clarke’s reference to Mill’s fundamental philosophy of individual freedom that struck a chord with me.
An objectively good life, on Mill’s (Aristotelian) view, is one where a person has reached her potential, realizing the powers and abilities she possesses. According to Mill, the chief essential requirement for personal well-being is the development of individuality. By this he meant the development of a person’s unique powers, abilities, and talents, to their fullest potential.
I’ve long believed that the ideal society allows this type of individualism: that each of us has the opportunity, through education, mentoring and talent-driven programmes to pursue the goals best suited to our abilities. Unfortunately, the world is not an equitable place and many people - the vast majority - don’t have this opportunity.
The second essay (cited above), by Uribe, deals with the paradox that arises when liberal political and societal ideals meet fundamentalism. One may ask: what paradox? The paradox is that liberal attitudes towards freedom of expression, religious and cultural norms allows the rise of fundamentalist ideals that actually wish to curtail such freedoms. In the current age, fundamentalism is associated with Islamic fundamentalism manifested by various ideologies all over the globe, which has led to a backlash in the form of Islamophobia. Some, like IS (Islamic State) and Boko Haram (in Nigeria) have extreme, intolerant views that they enforce on entire populations in the most brutal and violent manner imaginable. In other words, they could not be further from Mill’s ideal of freedom and liberation (Uribe, by the way, makes no reference to Islam).
In Western societies, there is a widely held fear, exploited by many right-winged and nationalist movements, that Islamic fundamentalism will overthrow our Western democratic systems of government and replace it with a religious totalitarian one. The reports of extreme human rights violations (including genocide, slavery and internet posted executions) in far-off politically unstable countries, only adds to this paranoia.
There are caveats to Mill’s manifesto (my term) on individual freedom, as pointed out by Clarke: ‘Excepting children and the insane, for whom intervention for their own sake is permissible…’ and ‘Freedom for the sake of individuality does not allow the harming of others, because that would damage the individuality of others.’
It’s this last point: ‘that would damage the individuality of others’; that I would argue, goes to the crux of the issue. Totalitarianism and fundamentalist ideologies should and can be opposed on this moral principle – political and social structures that inhibit unfairly the ability for individuals to pursue happiness should not be supported. This seems self-evident, yet it’s at the core of the current gay-marriage debate that is happening in many Western countries, including Australia (where I live). It’s also the reason that many Muslims oppose Islam extremists as they affect their own individualism.
On another, freedom-related issue, Australia has for the past 15 years pursued a ruthless, not-to-mention contentious, policy of so-called ‘border protection’ against refugees arriving by boat. Both sides of the political spectrum in Australia pursue this policy because our politics have become almost completely poll-driven, and any change of policy by either side, would immediately damage them in the polls, due to the paranoid nature of our society at large. This is related to the issue of Islamophobia I mentioned earlier, because a large portion of these refugees are from the unstable countries where atrocities are being committed. Not surprisingly, it’s the right-wing elements who exploit this issue as well. But it’s hard to imagine an issue that more strongly evokes Mill’s demand for individual freedom and liberty (except, possibly, the abolition of slavery).
As I said in an earlier post (the one I reference above), freedom and hope are partners. It’s the deliberate elimination of hope that drives my government’s policy, and the fact that this has serious mental health consequences is not surprising, yet it’s ignored.
Imprisonment is the most widely employed method of punishment for criminals because it eliminates freedom, though not necessarily hope. The Australian government’s rationalisation behind their extremely tough policy on asylum seekers is that they are ‘illegals’ and therefore deserve to be punished in this manner. However, the punishment is much worse than what we dispense to convicted criminals under our justice system. It’s a sad indictment on our society that we have neither the political will nor the moral courage to reverse this situation.
Once again, this has been triggered by Philosophy Now, but Issue 110 (Oct/Nov 2015) though the context is quite different. Philosophy Now is a periodical and they always have a theme, and the theme for this issue is ‘Liberty & Equality’ so it’s not surprising to find articles on freedom. In particular, there are 2 articles: Mill, Liberty & Euthanasia by Simon Clarke and The Paradox of Liberalism by Francisco Mejia Uribe.
I haven’t read Mill’s book, On Liberty, which is cited in both of the aforementioned articles, but I’ve read his book, Utilitarianism, and what struck me was that he was a man ahead of his time. Not only is utilitarian philosophy effectively the default position in Western democracies (at least, in theory) but he seemed to predict findings in social psychology like the fact that one’s conscience is a product of social norms and not God whispering in one’s ear, and that social norms can be changed, like attitudes towards smoking, for example. I’ve written a post on utilitarian moral philosophy elsewhere, so I won’t dwell on it here.
The first essay by Clarke (cited above) deals with the apparent conflict between freedom to pursue one’s potential and the freedom to end one’s life through euthanasia, which is not the subject of this post either. It’s Clarke’s reference to Mill’s fundamental philosophy of individual freedom that struck a chord with me.
An objectively good life, on Mill’s (Aristotelian) view, is one where a person has reached her potential, realizing the powers and abilities she possesses. According to Mill, the chief essential requirement for personal well-being is the development of individuality. By this he meant the development of a person’s unique powers, abilities, and talents, to their fullest potential.
I’ve long believed that the ideal society allows this type of individualism: that each of us has the opportunity, through education, mentoring and talent-driven programmes to pursue the goals best suited to our abilities. Unfortunately, the world is not an equitable place and many people - the vast majority - don’t have this opportunity.
The second essay (cited above), by Uribe, deals with the paradox that arises when liberal political and societal ideals meet fundamentalism. One may ask: what paradox? The paradox is that liberal attitudes towards freedom of expression, religious and cultural norms allows the rise of fundamentalist ideals that actually wish to curtail such freedoms. In the current age, fundamentalism is associated with Islamic fundamentalism manifested by various ideologies all over the globe, which has led to a backlash in the form of Islamophobia. Some, like IS (Islamic State) and Boko Haram (in Nigeria) have extreme, intolerant views that they enforce on entire populations in the most brutal and violent manner imaginable. In other words, they could not be further from Mill’s ideal of freedom and liberation (Uribe, by the way, makes no reference to Islam).
In Western societies, there is a widely held fear, exploited by many right-winged and nationalist movements, that Islamic fundamentalism will overthrow our Western democratic systems of government and replace it with a religious totalitarian one. The reports of extreme human rights violations (including genocide, slavery and internet posted executions) in far-off politically unstable countries, only adds to this paranoia.
There are caveats to Mill’s manifesto (my term) on individual freedom, as pointed out by Clarke: ‘Excepting children and the insane, for whom intervention for their own sake is permissible…’ and ‘Freedom for the sake of individuality does not allow the harming of others, because that would damage the individuality of others.’
It’s this last point: ‘that would damage the individuality of others’; that I would argue, goes to the crux of the issue. Totalitarianism and fundamentalist ideologies should and can be opposed on this moral principle – political and social structures that inhibit unfairly the ability for individuals to pursue happiness should not be supported. This seems self-evident, yet it’s at the core of the current gay-marriage debate that is happening in many Western countries, including Australia (where I live). It’s also the reason that many Muslims oppose Islam extremists as they affect their own individualism.
On another, freedom-related issue, Australia has for the past 15 years pursued a ruthless, not-to-mention contentious, policy of so-called ‘border protection’ against refugees arriving by boat. Both sides of the political spectrum in Australia pursue this policy because our politics have become almost completely poll-driven, and any change of policy by either side, would immediately damage them in the polls, due to the paranoid nature of our society at large. This is related to the issue of Islamophobia I mentioned earlier, because a large portion of these refugees are from the unstable countries where atrocities are being committed. Not surprisingly, it’s the right-wing elements who exploit this issue as well. But it’s hard to imagine an issue that more strongly evokes Mill’s demand for individual freedom and liberty (except, possibly, the abolition of slavery).
As I said in an earlier post (the one I reference above), freedom and hope are partners. It’s the deliberate elimination of hope that drives my government’s policy, and the fact that this has serious mental health consequences is not surprising, yet it’s ignored.
Imprisonment is the most widely employed method of punishment for criminals because it eliminates freedom, though not necessarily hope. The Australian government’s rationalisation behind their extremely tough policy on asylum seekers is that they are ‘illegals’ and therefore deserve to be punished in this manner. However, the punishment is much worse than what we dispense to convicted criminals under our justice system. It’s a sad indictment on our society that we have neither the political will nor the moral courage to reverse this situation.
Thursday, 24 September 2015
What is now?
Notice I ask what and not when, because ‘now’, as we experience it, is the most ephemeral of all experiences. As I’ve explained in another post: to record anything at all requires a duration – there is no instantaneous moment in time – except in mathematical calculus where a sleight-of-hand makes an infinitesimal disappear completely. It’s one of the most deceptive tricks in mathematics, but in mathematics you can have points with zero dimensions in space, so time with zero dimensions is just another idealism that allows one to perform calculations that would otherwise be impossible.
But another consequence of ‘now’ is that without memory we would not even know we have consciousness. Think about it: ‘now’ has no duration and consciousness exists in a continuous present so no memory would mean no experience of consciousness, or ‘now’ for that matter, because once it occurs it’s already in the past. Therefore memory is required to experience it at all.
But this post is not about calculus or consciousness per se; it arose from a quote I came across attributed to William Lawrence Bragg:
Everything that has already happened is particles, everything in the future is waves. The advancing sieve of time coagulates waves into particles at the moment ‘now’.
For those who don’t know, Sir William Lawrence Bragg was son of Sir William Henry Bragg, whom, as far as I know, were the only father and son to be jointly awarded a Nobel Prize in physics, for their work on X-ray diffraction in crystals. Henry was born in England and Lawrence was born in Australia. I heard about them at school, naturally, but I only came across this quote earlier in the week. They were among the first to exploit short wave photons (X-rays) to find the atomic-scale dimensions of crystal lattices, thus pioneering the discipline of crystallography.
In the same week, I came across this quote from Freeman Dyson recalling a conversation he had with Richard Feynman:
Thirty-one years ago Dick Feynman told me about his ‘sum over histories’ version of quantum mechanics. ‘The electron does anything it likes’, he said. ‘It goes in any direction at any speed, forward and backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function.’ I said, ‘You’re crazy.’ But he wasn’t.
I’ve discussed in some detail the mathematical formulation of the ‘wave-function’ known as Schrodinger’s equation, in another post, but what’s significant, in regard to the 2 quotes I’ve cited, is that the wave function effectively disappears or becomes irrelevant once an ‘observation’ or experimental ‘measurement’ occurs. In other words, the wave function ‘permeates all space’ (according to Richard Elwes in MATHS 1001) before it becomes part of the ‘classical physics’ real world. So Bragg’s quote makes perfect sense that the wave function represents the future and the particle ‘observation’, be it a photon or electron or whatever, represents the past with the interface being ‘now’.
As I’ve explicated in my last post, the default interpretation of Feyman’s ‘sum over histories’ or ‘path integrals’ mathematical description of quantum mechanics, is that all ‘histories’ occur in parallel universes, but I would argue that it’s a consequence of the irreversibility of time once the particle is ‘observed’. Now ‘observed’, in this context, means that the particle becomes part of the real world, or at least, that’s my prosaic interpretation. There is an extreme interpretation that it does require a ‘conscious observation’ in order to become real, but the fact that the Universe existed many billions of years prior to consciousness evolving, makes this interpretation logically implausible to say the least.
Brian Cox, in one of his BBC TV programmes (on ‘Time’) points out that one of the problems that Einstein had with quantum mechanics is that, according to its ‘rules’, the future was indeterminate. Einstein’s mathematical formulation of space-time, which became fundamental to his General Theory of Relativity (albeit was a consequence of his Special Theory) was that time could literally be treated like a dimension of space. This meant that the future was just as ‘real’ as the past. In other words, Einstein firmly believed that the universe, and therefore our lives, are completely deterministic – there was no place for free will in Einstein’s universe. Interestingly, this was a topic in a not-so-recent issue of Philosophy Now, though the author of the article didn’t explain that Einstein’s strict position on this was a logical consequence of his interpretation of space-time: the future was just as fixed as the past.
But, even without quantum mechanics, we know that chaos theory also contributes to the irreversibility of time, although Einstein was unaware of chaos theory in his lifetime. Paul Davies explains this better than most in his book on chaos theory, The Cosmic Blueprint.
The point is that, both in chaos theory and Feynman’s multiple histories, there are many possibilities that can happen in the ‘future’, but the ‘past’ is only one path and it can’t be remade. According to David Deutsch and Max Tegmark, all the future possibilities occur both in quantum mechanics and at a macro level. In fact, Deutsch has argued that chaotic phenomena are a consequence of the quantum mechanics' many worlds interpretation. In effect, they disassemble the asymmetry between the future and the past. According to their world-view, the future is just as inevitable as the past, because no matter which path is chosen, they all become reality somewhere in some universe; all of which bar one, we can’t see. From my perspective, this is not an argument in support of the many worlds interpretation, but an argument against it.
In my last post but one, I discussed at length Paul Davies’ book, The Mind of God. One of his more significant insights was that the Universe allows evolvement without dictating its end. In other words, it’s because of both chaos and quantum phenomena that there are many possible outcomes yet they all arise from a fixed past and this is a continuing process - it’s deterministic yet unpredictable.
One could make the same argument for free will. At many points in our lives we make choices based on a past that is fixed whilst conscious of a future that has many possibilities. I agree with Carlo Rovelli that free will is not a consequence of quantum mechanics, but the irreversibility of time applies to us as individual conscious agents in exactly the same way it applies to the dynamics of the Universe at both quantum and macro levels.
There is just one problem with this interpretation of the world, and that is, according to Einstein’s theories, there is no universal ‘now’. If there is no simultaneity, which is a fundamental outcome of the Special Theory of Relativity, then it’s difficult to imagine that people separated in space-time could agree on a ‘now’. And yet, the fact that we give the Universe an age and a timeline, effectively insists that there must be a ‘now’ for the Universe at large. I confess I don’t know enough physics to answer this, but quantum entanglement reintroduces simultaneity by stealth, even if we can’t use it to send messages. One of the features of the Universe is causality. Despite the implications of both quantum mechanics and relativity theory on the physics of time, neither of them interfere with causality, despite what some may argue (and that includes entanglement). But causality requires the speed of light to separate causal events, which is why the ‘now’ we experience sees stars in the firmament up to billions of years old. So space-time makes ‘now’ a subjective experience, even to the extent that at the event horizon of a black hole ‘now’ can become frozen to an outside observer.
Addendum: I actually believe there is a universal 'now', which I've addressed in a later post (towards the end).
But another consequence of ‘now’ is that without memory we would not even know we have consciousness. Think about it: ‘now’ has no duration and consciousness exists in a continuous present so no memory would mean no experience of consciousness, or ‘now’ for that matter, because once it occurs it’s already in the past. Therefore memory is required to experience it at all.
But this post is not about calculus or consciousness per se; it arose from a quote I came across attributed to William Lawrence Bragg:
Everything that has already happened is particles, everything in the future is waves. The advancing sieve of time coagulates waves into particles at the moment ‘now’.
For those who don’t know, Sir William Lawrence Bragg was son of Sir William Henry Bragg, whom, as far as I know, were the only father and son to be jointly awarded a Nobel Prize in physics, for their work on X-ray diffraction in crystals. Henry was born in England and Lawrence was born in Australia. I heard about them at school, naturally, but I only came across this quote earlier in the week. They were among the first to exploit short wave photons (X-rays) to find the atomic-scale dimensions of crystal lattices, thus pioneering the discipline of crystallography.
In the same week, I came across this quote from Freeman Dyson recalling a conversation he had with Richard Feynman:
Thirty-one years ago Dick Feynman told me about his ‘sum over histories’ version of quantum mechanics. ‘The electron does anything it likes’, he said. ‘It goes in any direction at any speed, forward and backward in time, however it likes, and then you add up the amplitudes and it gives you the wave-function.’ I said, ‘You’re crazy.’ But he wasn’t.
I’ve discussed in some detail the mathematical formulation of the ‘wave-function’ known as Schrodinger’s equation, in another post, but what’s significant, in regard to the 2 quotes I’ve cited, is that the wave function effectively disappears or becomes irrelevant once an ‘observation’ or experimental ‘measurement’ occurs. In other words, the wave function ‘permeates all space’ (according to Richard Elwes in MATHS 1001) before it becomes part of the ‘classical physics’ real world. So Bragg’s quote makes perfect sense that the wave function represents the future and the particle ‘observation’, be it a photon or electron or whatever, represents the past with the interface being ‘now’.
As I’ve explicated in my last post, the default interpretation of Feyman’s ‘sum over histories’ or ‘path integrals’ mathematical description of quantum mechanics, is that all ‘histories’ occur in parallel universes, but I would argue that it’s a consequence of the irreversibility of time once the particle is ‘observed’. Now ‘observed’, in this context, means that the particle becomes part of the real world, or at least, that’s my prosaic interpretation. There is an extreme interpretation that it does require a ‘conscious observation’ in order to become real, but the fact that the Universe existed many billions of years prior to consciousness evolving, makes this interpretation logically implausible to say the least.
Brian Cox, in one of his BBC TV programmes (on ‘Time’) points out that one of the problems that Einstein had with quantum mechanics is that, according to its ‘rules’, the future was indeterminate. Einstein’s mathematical formulation of space-time, which became fundamental to his General Theory of Relativity (albeit was a consequence of his Special Theory) was that time could literally be treated like a dimension of space. This meant that the future was just as ‘real’ as the past. In other words, Einstein firmly believed that the universe, and therefore our lives, are completely deterministic – there was no place for free will in Einstein’s universe. Interestingly, this was a topic in a not-so-recent issue of Philosophy Now, though the author of the article didn’t explain that Einstein’s strict position on this was a logical consequence of his interpretation of space-time: the future was just as fixed as the past.
But, even without quantum mechanics, we know that chaos theory also contributes to the irreversibility of time, although Einstein was unaware of chaos theory in his lifetime. Paul Davies explains this better than most in his book on chaos theory, The Cosmic Blueprint.
The point is that, both in chaos theory and Feynman’s multiple histories, there are many possibilities that can happen in the ‘future’, but the ‘past’ is only one path and it can’t be remade. According to David Deutsch and Max Tegmark, all the future possibilities occur both in quantum mechanics and at a macro level. In fact, Deutsch has argued that chaotic phenomena are a consequence of the quantum mechanics' many worlds interpretation. In effect, they disassemble the asymmetry between the future and the past. According to their world-view, the future is just as inevitable as the past, because no matter which path is chosen, they all become reality somewhere in some universe; all of which bar one, we can’t see. From my perspective, this is not an argument in support of the many worlds interpretation, but an argument against it.
In my last post but one, I discussed at length Paul Davies’ book, The Mind of God. One of his more significant insights was that the Universe allows evolvement without dictating its end. In other words, it’s because of both chaos and quantum phenomena that there are many possible outcomes yet they all arise from a fixed past and this is a continuing process - it’s deterministic yet unpredictable.
One could make the same argument for free will. At many points in our lives we make choices based on a past that is fixed whilst conscious of a future that has many possibilities. I agree with Carlo Rovelli that free will is not a consequence of quantum mechanics, but the irreversibility of time applies to us as individual conscious agents in exactly the same way it applies to the dynamics of the Universe at both quantum and macro levels.
There is just one problem with this interpretation of the world, and that is, according to Einstein’s theories, there is no universal ‘now’. If there is no simultaneity, which is a fundamental outcome of the Special Theory of Relativity, then it’s difficult to imagine that people separated in space-time could agree on a ‘now’. And yet, the fact that we give the Universe an age and a timeline, effectively insists that there must be a ‘now’ for the Universe at large. I confess I don’t know enough physics to answer this, but quantum entanglement reintroduces simultaneity by stealth, even if we can’t use it to send messages. One of the features of the Universe is causality. Despite the implications of both quantum mechanics and relativity theory on the physics of time, neither of them interfere with causality, despite what some may argue (and that includes entanglement). But causality requires the speed of light to separate causal events, which is why the ‘now’ we experience sees stars in the firmament up to billions of years old. So space-time makes ‘now’ a subjective experience, even to the extent that at the event horizon of a black hole ‘now’ can become frozen to an outside observer.
Addendum: I actually believe there is a universal 'now', which I've addressed in a later post (towards the end).
Tuesday, 15 September 2015
Are Multiverses the solution or the problem?
Notice I use the plural for something that represents a collection of universes. That’s because there are multiple versions of them; according to Max Tegmark there are 3 levels of multiverses.
I’m about to do something that I criticise others for doing: I’m going to challenge the collective wisdom of those who are much smarter and more knowledgeable than me. I’m not a physicist, let alone a cosmologist, and I’m not an academic in any field – I’m just a blogger. My only credentials are that I read a lot, especially about physics by authors who are eminently qualified in their fields. But even that does not give me any genuine qualification for what I’m about to say. Nevertheless, I feel compelled to point out something that few others are willing to cognise.
This occurred to me after I wrote my last post. In the 2 books I reference by Paul Davies (The Mind of God and The Goldilocks Enigma) he discusses and effectively dismisses the multiverse paradigm, yet I don’t mention it. Partly, that was because the post was getting too lengthy as it was, and, partly, because I didn’t need to discuss it to make the point I wished to make.
But the truth is that the multiverse is by far the most popular paradigm in both quantum physics and cosmology, and this is a relatively recent trend. What I find interesting is that it has become the default position, epistemologically, to explain what we don’t know at both of the extreme ends of physics: quantum mechanics and the cosmos.
Davies makes the point, in Mind of God (and he’s not the only one to do so), that for many scientists there seems to be a choice between accepting the multiverse or accepting some higher metaphysical explanation that many people call God. In other words, it’s a default position in cosmology because it avoids trying to explain why our universe is so special for life to emerge. Basically, it’s not special if there are an infinite number of them.
In quantum mechanics, the multiverse (or many words interpretation, as it’s called) has become the most favoured interpretation following the so-called Copenhagen interpretation championed by Niels Bohr. It’s based on the assumption that the wave function, which describes a quantum particle in Hilbert space doesn’t disappear when someone observes something or takes a measurement, but continues on in a parallel universe. So a bifurcation occurs for every electron and every photon every time it hits something. What’s more, Max Tegmark argues that if you have a car crash and die, in another universe you will continue to live. And likewise, if you have a near miss (as he did, apparently) in this universe, then in another parallel universe you died.
In both cases, cosmology and quantum mechanics, the multiverse has become the ‘easy’ explanation for events or phenomena that we don’t really understand. Basically, they are signposts for the boundaries or limits of scientific knowledge as it currently stands. String Theory or M Theory, is the most favoured cosmological model, but not only does it predict 10 spatial dimensions (as a minimum, I believe) it also predicts 10500 universes.
Now, I’m sure many will say that since the multiverse crops up in so many different places: caused by cosmological inflation, caused by string theory, caused by quantum mechanics; at least one of these multiverses must exist, right? Well no, they don’t have to exist – they’re just speculative, albeit consistent with everything we currently know about this universe, the one we actually live in.
Science, as best I understand it, historically, has always homed in on things. In particle physics it homed in on electrons, protons and neutrons, then neutrinos and quarks in all their varieties. In biology, we had evolution by natural selection then we discovered genes and then DNA, which underpinned it all. In mechanics, we had Galileo, Kepler and Newton, who finally gave us an equation for gravity, then Einstein gave us relativity theory that equated energy with mass in the most famous equation in the world, plus the curvature of space-time giving a completely geometric account of gravity that also provided a theoretical foundation for cosmology. Faraday, followed by Maxwell showed us that electricity and magnetism are inherently related and again Einstein took it further and gave an explanation of the photo-electric effect by proposing that light came in photons.
What I’m trying to say is that we made advances in science by either finding more specific events and therefore particles or by finding common elements that tied together apparently different phenomena. Kepler found the mathematical formulation that told us that planets travel in ellipses, Newton told us that gravity’s inverse square law made this possible and Einstein told us that it’s the curvature of space-time that explains gravity. Darwin and Wallace gave us a theory of evolution by natural selection, but Mendel gave us genes that explained how the inheritance happened and Francis and Crick and Franklin gave us the DNA helix that is the key ingredient for all of life.
My point is that the multiverse explanation for virtually everything we don’t know is going in the opposite direction. Now the explanation for something happening, whether it be a quantum event or the entire universe, is that every possible variation or physical manifestation is happening but we can only see the one we are witnessing. I don’t see this as an explanation for anything; I only see it as a manifestation of our ignorance.
Addendum: This is Max Tegmark providing a very cogent counterargument to mine. I think his argument from inflation is the most valid and his argument from QM multiple worlds, the most unlikely. Quantum computers won't prove parallel universes, because they are dependent on entanglement (as I understand it) which is not the same thing as multiple copies. Philip Ball makes this exact point in Beyond Weird, where he explains that so-called multiple particles only exist as probabilities; only one of which becomes 'real'.
I’m about to do something that I criticise others for doing: I’m going to challenge the collective wisdom of those who are much smarter and more knowledgeable than me. I’m not a physicist, let alone a cosmologist, and I’m not an academic in any field – I’m just a blogger. My only credentials are that I read a lot, especially about physics by authors who are eminently qualified in their fields. But even that does not give me any genuine qualification for what I’m about to say. Nevertheless, I feel compelled to point out something that few others are willing to cognise.
This occurred to me after I wrote my last post. In the 2 books I reference by Paul Davies (The Mind of God and The Goldilocks Enigma) he discusses and effectively dismisses the multiverse paradigm, yet I don’t mention it. Partly, that was because the post was getting too lengthy as it was, and, partly, because I didn’t need to discuss it to make the point I wished to make.
But the truth is that the multiverse is by far the most popular paradigm in both quantum physics and cosmology, and this is a relatively recent trend. What I find interesting is that it has become the default position, epistemologically, to explain what we don’t know at both of the extreme ends of physics: quantum mechanics and the cosmos.
Davies makes the point, in Mind of God (and he’s not the only one to do so), that for many scientists there seems to be a choice between accepting the multiverse or accepting some higher metaphysical explanation that many people call God. In other words, it’s a default position in cosmology because it avoids trying to explain why our universe is so special for life to emerge. Basically, it’s not special if there are an infinite number of them.
In quantum mechanics, the multiverse (or many words interpretation, as it’s called) has become the most favoured interpretation following the so-called Copenhagen interpretation championed by Niels Bohr. It’s based on the assumption that the wave function, which describes a quantum particle in Hilbert space doesn’t disappear when someone observes something or takes a measurement, but continues on in a parallel universe. So a bifurcation occurs for every electron and every photon every time it hits something. What’s more, Max Tegmark argues that if you have a car crash and die, in another universe you will continue to live. And likewise, if you have a near miss (as he did, apparently) in this universe, then in another parallel universe you died.
In both cases, cosmology and quantum mechanics, the multiverse has become the ‘easy’ explanation for events or phenomena that we don’t really understand. Basically, they are signposts for the boundaries or limits of scientific knowledge as it currently stands. String Theory or M Theory, is the most favoured cosmological model, but not only does it predict 10 spatial dimensions (as a minimum, I believe) it also predicts 10500 universes.
Now, I’m sure many will say that since the multiverse crops up in so many different places: caused by cosmological inflation, caused by string theory, caused by quantum mechanics; at least one of these multiverses must exist, right? Well no, they don’t have to exist – they’re just speculative, albeit consistent with everything we currently know about this universe, the one we actually live in.
Science, as best I understand it, historically, has always homed in on things. In particle physics it homed in on electrons, protons and neutrons, then neutrinos and quarks in all their varieties. In biology, we had evolution by natural selection then we discovered genes and then DNA, which underpinned it all. In mechanics, we had Galileo, Kepler and Newton, who finally gave us an equation for gravity, then Einstein gave us relativity theory that equated energy with mass in the most famous equation in the world, plus the curvature of space-time giving a completely geometric account of gravity that also provided a theoretical foundation for cosmology. Faraday, followed by Maxwell showed us that electricity and magnetism are inherently related and again Einstein took it further and gave an explanation of the photo-electric effect by proposing that light came in photons.
What I’m trying to say is that we made advances in science by either finding more specific events and therefore particles or by finding common elements that tied together apparently different phenomena. Kepler found the mathematical formulation that told us that planets travel in ellipses, Newton told us that gravity’s inverse square law made this possible and Einstein told us that it’s the curvature of space-time that explains gravity. Darwin and Wallace gave us a theory of evolution by natural selection, but Mendel gave us genes that explained how the inheritance happened and Francis and Crick and Franklin gave us the DNA helix that is the key ingredient for all of life.
My point is that the multiverse explanation for virtually everything we don’t know is going in the opposite direction. Now the explanation for something happening, whether it be a quantum event or the entire universe, is that every possible variation or physical manifestation is happening but we can only see the one we are witnessing. I don’t see this as an explanation for anything; I only see it as a manifestation of our ignorance.
Addendum: This is Max Tegmark providing a very cogent counterargument to mine. I think his argument from inflation is the most valid and his argument from QM multiple worlds, the most unlikely. Quantum computers won't prove parallel universes, because they are dependent on entanglement (as I understand it) which is not the same thing as multiple copies. Philip Ball makes this exact point in Beyond Weird, where he explains that so-called multiple particles only exist as probabilities; only one of which becomes 'real'.
Subscribe to:
Posts (Atom)