A friend of mine – someone whom I’d go to for help – leant me a ‘Creation’ magazine to prove that there are creationists who are real scientists. And, I have to admit, my friend was right: the magazine was full of contributors who had degrees in science, including one who has a PhD and honours and works at a run-of-the-mill university; but who wrote the following howler: ‘Cosmology is unscientific because you can’t do an experiment in cosmology.’ I wonder if said writer would be willing to say that to Australian Nobel Prize winner, Brian Schmidt. Only humans can be living contradictions.
Creation science is an epistemological contradiction – there’s no such thing – by definition. Science does not include magic – I can’t imagine anyone who would disagree with that, but I might be wrong. Replacing a scientific theory with supernaturally enhanced magic is anti-science, yet creationists call it science – as the Americans like to say: go figure.
The magazine was enlightening in that the sole criterion for these ‘scientists’ as to the validity of any scientific knowledge was whether or not it agreed with the Bible. If this was literally true, we would still be believing that the Sun goes round the Earth, rather than the other way round. After all, the Book of Joshua tells us how God stopped the Sun moving in the sky. It doesn’t say that God stopped the Earth spinning, which is what he would have had to do.
One contributor to the magazine even allows for ‘evolution’ after ‘creation’, because God programmed ‘subroutines’ into DNA, but was quick to point out that this does ‘not contradict the Bible’. Interesting to note that DNA wouldn’t even have been discovered if all scientists were creationists (like the author).
Why do you think the ‘Dark Ages’ are called the dark ages? Because science, otherwise known as ‘natural philosophy’, was considered pagan, as the Greeks’ neo-Platonist philosophy upon which it was based was pagan. Someone once pointed out that Hypatia’s murder by a Christian mob (around 400AD) signalled the start of the dark ages, which lasted until around 1200, when Fibonacci introduced the West to the Hindu-Arabic system of numbers. In fact, it is the Muslims who kept that knowledge in the interim, otherwise it may well have been lost to us forever.
So science and Christianity have a long history of contention that goes back centuries before Copernicus, Galileo and Darwin. If anything, the gap has got wider, not closer; they’ve only managed to co-exist by staying out of each other’s way.
There are many religious texts in the world, a part of our collective cultural and literary legacy, but none of them are scientific or mathematical texts, which also boast diverse cultural origins. It is an intellectual conceit (even deceit) to substitute religious teaching for scientifically gained knowledge. Of course scientifically gained knowledge is always changing, advancing, being overtaken and is never over. In fact, I would contend that science will never be complete, as history has demonstrated, so there will always be arguments for supernatural intervention, otherwise known as the ‘God-of-the-Gaps’. Godel’s Incompleteness theorem infers that mathematics is a never-ending epistemological mine, and I believe that the same goes for science.
Did I hear someone say: what about Intelligent Design (ID)? Well, it’s still supernatural intervention, isn’t it? Same scenario, different description.
Religion is not an epistemology, it’s a way of life. Whichever way you look at it, it’s completely subjective. Religion is part of your inner world, and that includes God. So the idea that the God you’ve found within yourself is also the Creator of the entire Universe is a non sequitur. Because everyone’s idea of God is unique to them.
Tuesday 2 February 2016
Tuesday 19 January 2016
Is this the God equation?
Yes, this is a bit tongue-in-cheek, but like most things tongue-in-cheek it just might contain an element of truth. I’m not a cosmologist or even a physicist, so this is just me being playful yet serious in as much as anyone can be philosophically serious about the origins of Everything, otherwise known as the Universe.
Now I must make a qualification, lest people think I’m leading them down the garden path. When people think of ‘God’s equation’, they most likely think of some succinct equation or set of equations (like Maxwell’s equations) from which everything we know about the Universe can be derived mathematically. For many people this is a desired outcome, founded on the belief that one day we will have a TOE (Theory Of Everything) – itself a misnomer – which will incorporate all the known laws of the Universe in one succinct theory. Specifically, said theory will unite the Electromagnetic force, the so-called Weak force, the so-called Strong force and Gravity as all being derived from a common ‘field’. Personally, I think that’s a chimera, but I’d be happy to be proven wrong. Many physicists believe some version of String Theory or M Theory will eventually give us that goal. I should point out that the Weak force has already been united with the Electromagnetic force.
So what do I mean by the sobriquet, God’s equation? Last week I watched a lecture by Allan Adams as part of MIT Open Courseware (8.04, Spring 2013) titled Lecture 6: Time Evolution and the Schrodinger Equation, in which Adams made a number of pertinent points that led me to consider that perhaps Schrodinger’s Equation (SE) deserved such a title. Firstly, I need to point out that Adams himself makes no such claim, and I don’t expect many others would concur.
Many of you may already know that I wrote a post on Schrodinger’s Equation nearly 5 years ago and it has become, by far, the most popular post I’ve written. Of course Schrodinger’s Equation is not the last word in quantum mechanics –more like a starting point. By incorporating relativity we have Dirac’s equation, which predicted anti-matter – in fact, it’s a direct consequence of relativity and SE. In fact, Schrodinger himself, followed by Klein-Gordon, also had a go at it and rejected it because it gave answers with negative energy. But Richard Feynman (and independently, Ernst Stuckelberg) pointed out that this was mathematically equivalent to ordinary particles travelling backwards in time. Backwards in time, is not an impossibility in the quantum world, and Feynman even incorporated it into his famous QED (Quantum Electro-Dynamics) which won him a joint Nobel Prize with Julian Schwinger and Sin-Itiro Tomonaga in 1965. QED, by the way, incorporates SE (just read Feynman’s book on the subject).
This allows me to segue back into Adams’ lecture, which, as the title suggests, discusses the role of time in SE and quantum mechanics generally. You see ‘time’ is a bit of an enigma in QM.
Adams’ lecture, in his own words, is to provide a ‘grounding’ so he doesn’t go into details (mathematically) and this suited me. Nevertheless, he throws terms around like eigenstates, operators and wave functions, so familiarity with these terms would be essential to following him. Of those terms, the only one I will use is wave function, because it is the key to SE and arguably the key to all of QM.
Right at the start of the lecture (his Point 1), Adams makes the salient point that the Wave function, Ψ, contains ‘everything you need to know about the system’. Only a little further into his lecture (his Point 6) he asserts that SE is ‘not derived, it’s posited’. Yet it’s completely ‘deterministic’ and experimentally accurate. Now (as discussed by some of the students in the comments) to say it’s ‘deterministic’ is a touch misleading given that it only gives us probabilities which are empirically accurate (more on that later). But it’s a remarkable find that Schrodinger formulated a mathematical expression based on a hunch that all quantum objects, be they light or matter, should obey a wave function.
But it’s at the 50-55min stage (of his 1hr 22min lecture) that Adams delivers his most salient point when he explains so-called ‘stationary states’. Basically, they’re called stationary states because time remains invariant (doesn’t change) for SE which is what gives us ‘superposition’. As Adams points out, the only thing that changes in time in SE is the phase of the wave function, which allows us to derive the probability of finding the particle in ‘classical’ space and time. Classical space and time is the real physical world that we are all familiar with. Now this is what QM is all about, so I will elaborate.
Adams effectively confirmed for me something I had already deduced: superposition (the weird QM property that something can exist simultaneously in various positions prior to being ‘observed’) is a direct consequence of time being invariant or existing ‘outside’ of QM (which is how it’s usually explained). Now Adams makes the specific point that these ‘stationary states’ only exist in QM and never exist in the ‘Real’ world that we all experience. We never experience superposition in ‘classical physics’ (which is the scientific pseudonym for ‘real world’). This highlights for me that QM and the physical world are complementary, not just versions of each other. And this is incorporated in SE, because, as Adams shows on his blackboard, superposition can be derived from SE, and when we make a measurement or observation, superposition and SE both disappear. In other words, the quantum state and the classical state do not co-exist: either you have a wave function in Hilbert space or you have a physical interaction called a ‘wave collapse’ or, as Adams prefers to call it, ‘decoherence’. (Hilbert space is a theoretical space of possibly infinite dimensions where the wave function theoretically exists in its superpositional manifestation.)
Adams calls the so-called Copenhagen interpretation of QM the “Cop Out” interpretation which he wrote on the board and underlined. He prefers ‘decoherence’ which is how he describes the interaction of the QM wave function with the physical world. My own view is that the QM wave function represents all the future possibilities, only one of which will be realised. Therefore the wave function is a description of the future yet to exist, except as probabilities; hence the God equation.
As I’ve expounded in previous posts, the most popular interpretation at present seems to be the so-called ‘many worlds’ interpretation where all superpositional states exist in parallel universes. The most vigorous advocate of this view is David Deutsch, who wrote about it in a not-so-recent issue of New Scientist (3 Oct 2015, pp.30-31). I also reviewed his book, Fabric of Reality, in September 2012. In New Scientist, Deutsch advocated for a non-probabilistic version of QM, because he knows that reconciling the many worlds interpretation with probabilities is troublesome, especially if there are an infinite number of them. However, without probabilities, SE becomes totally ineffective in making predictions about the real world. It was Max Born who postulated the ingenious innovation of squaring the modulus of the wave function (actually multiplying it with its complex conjugate, as I explain here) which provides the probabilities that make SE relevant to the physical world.
As I’ve explained elsewhere, the world is fundamentally indeterministic due to asymmetries in time caused by both QM and chaos theory. Events become irreversible after QM decoherence, and also in chaos theory because the initial conditions are indeterminable. Now Deutsch argues that chaos theory can be explained by his many worlds view of QM, and mathematician, Ian Stewart, suggests that maybe QM can be explained by chaos theory as I expound here. Both these men are intellectual giants compared to me, yet I think they’re both wrong. As I’ve explained above, I think that the quantum world and the classical world are complementary. The logical extension of Deutch’s view, by his own admission, requires the elimination of probabilities, making SE ineffectual. And Stewart’s circuitous argument to explain QM probabilities with chaos theory eliminates superposition, for which we have indirect empirical evidence (using entanglement, which is well researched). Actually, I think superposition is a consequence of the wave function effectively being everywhere at once or 'permeates all of space' (to quote Richard Ewles in MATHS 1001).
If I’m right in stating that QM and classical physics are complementary (and Adams seems to make the same point, albeit not so explicitly) then a TOE may be impossible. In other words, I don't think classical physics is a special case of QM, which is the current orthodoxy among physicists.
Addendum 1: Since writing this, I've come to the conclusion that QM and, therefore, the wave function describe the future - an idea endorsed by non-other than Freeman Dyson, who was instrumental in formulating QED with Richard Feynman.
Addendum 2: I've amended the conclusion in my 2nd last paragraph, discussing Deutch's and Stewart's respective 'theories', and mentioning entanglement in passing. Schrodinger once said (in a missive to Einstein, from memory) that entanglement is what QM is all about. Entanglement effectively challenges Einstein's conclusion that simultaneity is a non sequitur according to his special theory of relativity (and he's right, providing there's no causal relationship between events). I contend that neither Deutch nor Stewart can resolve entanglement with their respective 'alternative' theories, and neither of them address it from what I've read.
Now I must make a qualification, lest people think I’m leading them down the garden path. When people think of ‘God’s equation’, they most likely think of some succinct equation or set of equations (like Maxwell’s equations) from which everything we know about the Universe can be derived mathematically. For many people this is a desired outcome, founded on the belief that one day we will have a TOE (Theory Of Everything) – itself a misnomer – which will incorporate all the known laws of the Universe in one succinct theory. Specifically, said theory will unite the Electromagnetic force, the so-called Weak force, the so-called Strong force and Gravity as all being derived from a common ‘field’. Personally, I think that’s a chimera, but I’d be happy to be proven wrong. Many physicists believe some version of String Theory or M Theory will eventually give us that goal. I should point out that the Weak force has already been united with the Electromagnetic force.
So what do I mean by the sobriquet, God’s equation? Last week I watched a lecture by Allan Adams as part of MIT Open Courseware (8.04, Spring 2013) titled Lecture 6: Time Evolution and the Schrodinger Equation, in which Adams made a number of pertinent points that led me to consider that perhaps Schrodinger’s Equation (SE) deserved such a title. Firstly, I need to point out that Adams himself makes no such claim, and I don’t expect many others would concur.
Many of you may already know that I wrote a post on Schrodinger’s Equation nearly 5 years ago and it has become, by far, the most popular post I’ve written. Of course Schrodinger’s Equation is not the last word in quantum mechanics –more like a starting point. By incorporating relativity we have Dirac’s equation, which predicted anti-matter – in fact, it’s a direct consequence of relativity and SE. In fact, Schrodinger himself, followed by Klein-Gordon, also had a go at it and rejected it because it gave answers with negative energy. But Richard Feynman (and independently, Ernst Stuckelberg) pointed out that this was mathematically equivalent to ordinary particles travelling backwards in time. Backwards in time, is not an impossibility in the quantum world, and Feynman even incorporated it into his famous QED (Quantum Electro-Dynamics) which won him a joint Nobel Prize with Julian Schwinger and Sin-Itiro Tomonaga in 1965. QED, by the way, incorporates SE (just read Feynman’s book on the subject).
This allows me to segue back into Adams’ lecture, which, as the title suggests, discusses the role of time in SE and quantum mechanics generally. You see ‘time’ is a bit of an enigma in QM.
Adams’ lecture, in his own words, is to provide a ‘grounding’ so he doesn’t go into details (mathematically) and this suited me. Nevertheless, he throws terms around like eigenstates, operators and wave functions, so familiarity with these terms would be essential to following him. Of those terms, the only one I will use is wave function, because it is the key to SE and arguably the key to all of QM.
Right at the start of the lecture (his Point 1), Adams makes the salient point that the Wave function, Ψ, contains ‘everything you need to know about the system’. Only a little further into his lecture (his Point 6) he asserts that SE is ‘not derived, it’s posited’. Yet it’s completely ‘deterministic’ and experimentally accurate. Now (as discussed by some of the students in the comments) to say it’s ‘deterministic’ is a touch misleading given that it only gives us probabilities which are empirically accurate (more on that later). But it’s a remarkable find that Schrodinger formulated a mathematical expression based on a hunch that all quantum objects, be they light or matter, should obey a wave function.
But it’s at the 50-55min stage (of his 1hr 22min lecture) that Adams delivers his most salient point when he explains so-called ‘stationary states’. Basically, they’re called stationary states because time remains invariant (doesn’t change) for SE which is what gives us ‘superposition’. As Adams points out, the only thing that changes in time in SE is the phase of the wave function, which allows us to derive the probability of finding the particle in ‘classical’ space and time. Classical space and time is the real physical world that we are all familiar with. Now this is what QM is all about, so I will elaborate.
Adams effectively confirmed for me something I had already deduced: superposition (the weird QM property that something can exist simultaneously in various positions prior to being ‘observed’) is a direct consequence of time being invariant or existing ‘outside’ of QM (which is how it’s usually explained). Now Adams makes the specific point that these ‘stationary states’ only exist in QM and never exist in the ‘Real’ world that we all experience. We never experience superposition in ‘classical physics’ (which is the scientific pseudonym for ‘real world’). This highlights for me that QM and the physical world are complementary, not just versions of each other. And this is incorporated in SE, because, as Adams shows on his blackboard, superposition can be derived from SE, and when we make a measurement or observation, superposition and SE both disappear. In other words, the quantum state and the classical state do not co-exist: either you have a wave function in Hilbert space or you have a physical interaction called a ‘wave collapse’ or, as Adams prefers to call it, ‘decoherence’. (Hilbert space is a theoretical space of possibly infinite dimensions where the wave function theoretically exists in its superpositional manifestation.)
Adams calls the so-called Copenhagen interpretation of QM the “Cop Out” interpretation which he wrote on the board and underlined. He prefers ‘decoherence’ which is how he describes the interaction of the QM wave function with the physical world. My own view is that the QM wave function represents all the future possibilities, only one of which will be realised. Therefore the wave function is a description of the future yet to exist, except as probabilities; hence the God equation.
As I’ve expounded in previous posts, the most popular interpretation at present seems to be the so-called ‘many worlds’ interpretation where all superpositional states exist in parallel universes. The most vigorous advocate of this view is David Deutsch, who wrote about it in a not-so-recent issue of New Scientist (3 Oct 2015, pp.30-31). I also reviewed his book, Fabric of Reality, in September 2012. In New Scientist, Deutsch advocated for a non-probabilistic version of QM, because he knows that reconciling the many worlds interpretation with probabilities is troublesome, especially if there are an infinite number of them. However, without probabilities, SE becomes totally ineffective in making predictions about the real world. It was Max Born who postulated the ingenious innovation of squaring the modulus of the wave function (actually multiplying it with its complex conjugate, as I explain here) which provides the probabilities that make SE relevant to the physical world.
As I’ve explained elsewhere, the world is fundamentally indeterministic due to asymmetries in time caused by both QM and chaos theory. Events become irreversible after QM decoherence, and also in chaos theory because the initial conditions are indeterminable. Now Deutsch argues that chaos theory can be explained by his many worlds view of QM, and mathematician, Ian Stewart, suggests that maybe QM can be explained by chaos theory as I expound here. Both these men are intellectual giants compared to me, yet I think they’re both wrong. As I’ve explained above, I think that the quantum world and the classical world are complementary. The logical extension of Deutch’s view, by his own admission, requires the elimination of probabilities, making SE ineffectual. And Stewart’s circuitous argument to explain QM probabilities with chaos theory eliminates superposition, for which we have indirect empirical evidence (using entanglement, which is well researched). Actually, I think superposition is a consequence of the wave function effectively being everywhere at once or 'permeates all of space' (to quote Richard Ewles in MATHS 1001).
If I’m right in stating that QM and classical physics are complementary (and Adams seems to make the same point, albeit not so explicitly) then a TOE may be impossible. In other words, I don't think classical physics is a special case of QM, which is the current orthodoxy among physicists.
Addendum 1: Since writing this, I've come to the conclusion that QM and, therefore, the wave function describe the future - an idea endorsed by non-other than Freeman Dyson, who was instrumental in formulating QED with Richard Feynman.
Addendum 2: I've amended the conclusion in my 2nd last paragraph, discussing Deutch's and Stewart's respective 'theories', and mentioning entanglement in passing. Schrodinger once said (in a missive to Einstein, from memory) that entanglement is what QM is all about. Entanglement effectively challenges Einstein's conclusion that simultaneity is a non sequitur according to his special theory of relativity (and he's right, providing there's no causal relationship between events). I contend that neither Deutch nor Stewart can resolve entanglement with their respective 'alternative' theories, and neither of them address it from what I've read.
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