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.
Saturday 14 November 2015
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 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 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).
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