The problem with physics

 This title could be easily misconstrued, as it gives the impression that there is only one problem in physics and if we could solve that, everything would be resolved and there would be nothing left to understand or explain. Anyone familiar with this blog will know that I don’t believe that at all, so I need to unpack this before I even start.
 
And you might well ask: if I know there are a number of problems in physics, why didn’t I make that clear in the title? You see, I’ve embedded a question in the title that I want you to ask.
 
I’ve been watching a number of videos over a period of time, many of them on Curt Jaimungal’s channel, Theories of Everything, where he talks to a lot of people, much cleverer than me, some of whom have the wildest theories in science, and physics in particular. If one takes John Wheeler’s metaphor of an island of knowledge in an infinite sea of ignorance, they are all building theories on the shoreline of that island. I like to point out (as a personal ego-boost) that I came up with that metaphor before I knew Wheeler had beaten me to it.
 
To give just one example that seems totally ‘out there’, Emily Adlam proposes her ‘Sudoku universe’ where everything exists at once. She’s not alone, because it’s not dissimilar to Sabine Hossenfelder’s position, though she uses different arguments. Of course, both her and Sabine are far more knowledgeable on these topics than me, so while I disagree, I acknowledge I don’t have the chops to take them on in a proper debate. Another example is Claudia de Rahm, whom I’ve referenced before, who thinks that gravitons may have mass, which would seem to contradict the widely held belief that gravitational waves travel at the speed of light. She has discussions with Curt, that once again, are well above my level of knowledge on this topic. 

Another person he interviews is Avshalom Elitzur, who even makes statements I actually agree with. In this video, he argues that space-time is created when the wave function collapses. It’s a very unorthodox view but it’s consistent with mine and Freeman Dyson’s belief that QM (therefore the wave function) can only describe the future. However, he also has a radical idea that the ‘creation’ of space may be related to the creation of charge, because if the space is created between the particles, they repel, and if it’s created outside, they attract. I admit I have problems with this, even though it took Curt to clarify it. Richard Muller (whose book, NOW, I’ve read) also argues that space may be created along with time. Both of these ideas are consistent with the notion that the Big Bang is still in progress – both time and space are being created as the Universe expands.
 
So there are lots of problems, and the cleverest people on the planet, including many I haven’t mentioned like Roger Penrose and Sean Carroll, all have their own pet theories, all on the shoreline of Wheeler’s metaphorical island.
 
But the island metaphor provides a clue to why the problem exists, and that is that they are all just as philosophical as they are scientific. Sabine attempted to address this in 2 books she wrote: Lost in Math and Existential Physics; both of which I’ve read. But there are 2 levels to this problem when it comes to physics, which are effectively alluded to in the titles of her books. In other words, one level is philosophical and the next level is mathematical.
 
All of the people I mentioned above, along with others I haven’t mentioned, start with a philosophical position, even if they don’t use that term. And all physics theories are dependent on a mathematical model. There is also arguably a third level, which is experimental physics, and that inexorably determines whether the model, and hence the theory, is accurate.
 
But there is a catch: sometimes the experimental physics has proven the ‘theory’ correct, yet the philosophical implications are still open to debate. This is the case with quantum mechanics (QM), and has been for over a century. As Sabine pointed out in a paper she wrote, our dilemmas with QM haven’t really changed since Bohr’s and Einstein’s famous arguments over the Copenhagen interpretation, which are now almost a century old.
 
Some would argue that the most pertinent outstanding ‘problem’ in physics is the irreconcilability of gravity, or Einstein’s general theory of relativity (GR), and QM. Given the problems we have with dark matter and dark energy, which are unknown yet make up 95% of the Universe, I think we are ripe for another Kuhnian revolution in physics. And if that’s true, then we have no idea what it is.

Time again

 This is a topic I’ve written about before, many times, but I’m returning to it on this occasion because of a video I watched by Curt Jaimungal, whom I can recommend. He’s smart and interviews people who are even smarter, and he has a particular penchant for interviewing people with unorthodox ideas, but with the knowledge to support them. He also has the good sense to let them do nearly all of the talking. He rarely interjects and when he does, it’s pertinent and tends to not interrupt the flow. I’ve sometimes been annoyed by interviewers cutting someone off when they were about to say something that I was interested in hearing. I could never accuse Curt of that.
 
In this case he’s interviewing Avshalom Elitzur, whom I’ve also referenced before. He’s a bit of an iconoclast – my favourite type of person, even if I disagree with them. If I’m to be fair, I’d have to include Donald Hoffman in that category, though I’ve been a harsh critic in the past. Having said that, I’ve noticed that Donald has changed his approach over the 8 or so years I’ve been following him. As I’ve said before, it’s important to follow the people you disagree with as well as those you agree with, especially when they have knowledge or expertise that you don’t.
 
Elitzur discusses three or more topics, all related to Einstein’s theories of relativity, but mostly the special theory. He starts off by calling out (my phrase) what he considers a fundamental problem that most physicists, if not all (his phraseology) ignore, which is that time is fundamentally different to space, because time changes in a way that space does not. What’s more we all experience this, with or without a scientific theory to explain it. He gives the example of how another country (say, Japan) still exists even though you don’t experience it (assuming you’re not Japanese). If you are in Japan, make it Australia. On the other hand, another time does not exist in the same way (be it past or present), yet many physicists talk about it as if it does. I discussed this in some depth, when I tackled Sabine Hoffenfelder’s book, Existential Physics; A Scientist’s Guide to Life’s Biggest Questions.
 
Elitzur raises this at both the start and towards the end of the video, because he thinks it’s distorting how physicists perceive the world. Specifically, Einstein’s block-universe, where all directions in time exist simultaneously in the same way that all directions in space exist all at once. He mentions that Penrose challenges this and so did Paul Davies once, but not now. In fact, I challenge Davies’ position in another post I wrote after reading his book, The Demon in the Machine. Elitzur makes the point that challenging this is considered naïve but he also makes another point much more dramatically. He says that for Einstein, the ‘future cut’ in time is ‘already there’ (10.50) and consequently said, ‘…has the same degree of reality as the present cut and the past cut. Are you okay with that?’ His exact words.
 
He recounts the famous letter that Einstein wrote to the family of a good friend who had just passed away, and only 4 weeks before Einstein himself passed away (I didn’t know that before Elitzur told me), from which we have this much quoted extract: ‘The past, present and future is only a stubbornly persistent illusion.’ Davies also used this quote in his abovementioned book.
 
I’m going to talk about last what Elitzur talked about early, if not quite first, which is the famous pole-in-the-barn thought experiment. Elitzur gives a good explanation, if you haven’t come across it before, but I’ll try because I think it’s key to understanding the inherent paradox of special relativity, and also providing an explanation that reconciles with our perception of reality.
 
It's to do with Lorenz-contraction, which is that, for an observer, an object travelling transversely to their field of vision (say horizontally) shortens in the direction of travel. This is one of those Alice and Bob paradoxes, not unlike the twin paradox. Let us assume that Alice is in a space ship who goes through a tunnel with doors at both ends, so that her ship fits snugly inside with no bits hanging out (like when both are stationary). And Bob operates the doors, so that they open when Alice arrives, close when she is inside and open to allow her to leave. From Bob’s perspective, Alice’s spaceship is shorter than the tunnel, so she fits inside, no problem. Also, and this is the key point (highlighted by Elitzur): according to Bob, both doors open and close together – there is no lag.
 
The paradox is resolved by relativity theory (and the associated mathematics), because, from Alice’s perspective, the doors don’t open together but sequentially. The first door opens and then closes after she’s passed through it, and the second door opens slightly later and remains open slightly longer so that the first door closes behind her before she leaves the tunnel. In other words, both doors are closed while she’s in the tunnel, but in such a way that they’re not closed at the same time, therefore her spaceship doesn’t hit either of them. This is a direct consequence of simultaneity being different for Alice. If you find that difficult to follow, watch the video
 
I have my own unorthodox way of resolving this, because, contrary to what everyone says, I think there is a preferred frame of reference, which is provided by ‘absolute spacetime’. You can even calculate the Earth’s velocity relative to the overall spacetime of the entire universe by measuring the Doppler shift of the CMBR (cosmic microwave background radiation). This is not contentious – Penrose and Davies both give good accounts of this. It’s also related to what Tim Maudlin called, the most important experiment in physics, which is Newton spinning a bucket of water and observing the concave surface of the water due to the centrifugal force, and then asking: what is it spinning in reference to? Answer: the entire universe.
 
You might notice that when someone describes or explains the famous twin paradox, they only ever talk about the time difference – they rarely, if ever, talk about the space contraction. Personally, I don’t think space contracts in reality, but time duration does. If you take an extreme example, you could hypothetically travel across the entire galaxy in your lifetime, which means, from your perspective, the distance travelled would be whole orders of magnitude shorter. This can be resolved if it’s the ruler measuring the distance that changes and not the distance. In this case, the clock acts as a ruler. Kip Thorne has commented on this without drawing any conclusions.
 
This same logic could be applied to the spaceship and the tunnel. For Alice, it appears shorter, but she’s the one ‘measuring’ it. If one extends this logic, then I would argue that there is a ‘true simultaneity’, experienced by Bob in this case, because he is in the same frame of reference as the tunnel and the doors. I need to point out that, as far as I know, no one else agrees with me, including Elitzur. However, it’s consistent with my thought experiment about traversing the galaxy: time contracts but space doesn't.
 
I’ve raised this before, but I believe that there is an independent reality to all observers, and this is consistent with Kant’s famous dictum that there is a ‘thing-in-itself’ that we may never perceive. In other words, relativity can only tell us about what we observe, which leaves open the possibility that there is a reality that one observer has a better perception of than another. It’s possible that while ‘time passed’ is observer-dependent, space is not, but only the observer’s perception of it.
 
This is also consistent with Elitzur’s overall thesis and core argument that space and time are different. It’s also consistent with the idea that there is a frame of reference for the entire universe, which I argue is what general relativity (GR) gives us. And in fact, we observe that local frames of reference can actually travel faster than light, which is why the observable universe has a horizon: there are parts of the Universe receding from us faster than light.
 
There is another aspect of this that Elitzur doesn’t bring up, and that is that there is an edge in time for the Universe, but no boundary in space. I find it curious that, if physicists bring this up at all, they tend to gloss over it and not provide a satisfactory resolution. You see, it conflicts with the idea, inherent in the block-universe model, that there is no ‘now’.
 
Curt introduces ‘now’ towards the end of the video, but only in reference to the ‘flow’ of time that we all experience. Again, I’m a heretic in that I believe there is a universal now for the entire universe.
 
And while I don’t think it explains entanglement and non-locality in QM, it’s consistent with it. Entanglement works across space and time independently of relativistic causality, without breaking the relativistic rule that you can’t send information faster than light.
 
As it happens, there is another video by Curt with Tim Maudlin, an American philosopher of science, whom Curt introduces as ‘bringing some sober reality to this realm of quantum confusion and mysticism.’ In particular, Maudlin gives an excellent exposition of Bell’s famous theorem, and debunks the claim that it questions whether there is ‘reality’. In other words, it’s often formulated as: you can accept non-locality or you can accept reality, but you can’t have both. Just to clarify, ‘locality’ means local phenomena that obey SR (special relativity) as I’ve discussed above.
 
Maudlin argues quite cogently that you only need 2 assumptions for Bell’s theorem to make sense and neither of them break reality. The main assumption is that there is ‘statistical independence’, which he explains by giving examples of medical controlled experiments (for example, to test if tobacco causes lung cancer). It just means that random really does mean random, which gives true independence.
 
The only other assumption is that we can have non-locality, which means you can have a connection or relationship between events that is not dependent on special relativity. Numerous experiments have proven this true.
 
Maudlin challenges Sabine’s contention that Bell’s Theorem can only be explained by ‘superdeterminism’, which is another name for Einstein’s block-universe, which started this whole discussion. Sabine is so convinced by superdeterminism, she has argued that one day everyone will agree with her. This of course has implications for free will and is central to Elitzur’s argument that the future does not exist in the same way as the present or even the past, which is fixed. And that’s his point. Sabine’s and most physicist’s view on all this is that what we experience must be an illusion: there is no now, no flow of time, and no free will.

Addendum 1: I came across another video by Curt with Jacob Barandes, that came out after I posted this. Jacob is a Harvard scientist, who has done a series of videos with Curt. It's relevance to this topic is that he talks about space-time in GR and how, unlike Newtonian physics, and even SR, you can't tell which direction time and space have. And this axiomatically creates problems when you try to quantumise it (to coin a term). I think the superposition of a gravitational field creates its own problems (not discussed). He then goes on to conjecture that there should be an intermediate step in trying to derive a quantum field theory of gravity, and that is to do probabilities on gravity. He acknowledges this is a highly speculative idea.

He then goes on to talk about 'expectation values', which is the standard way physicists have tried to model QFT (quantum field theory) on to spacetime, and is called 'semi-classical gravity'. Viktor T Toth (on Quora) says about this: …it is hideously inelegant, essentially an ad-hoc averaging of the equation that is really, really ugly and is not derived from any basic principle that we know. Nevertheless, Toth argues that it 'works'. Barandes goes further and says it's based on a fallacy (watch the video if you want an elaboration). To quote Toth again: We can do quantum field theory just fine on the curved spacetime background of general relativity. What we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.

I tend to agree with Freeman Dyson, who contends that they are not compatible in theory or in nature. In other words, he argues that quantum gravity is a chimera. Dyson also argues that QM can't describe past events; so, if that's true, quantum gravity is attempting to describe spacetime in its future. Arguably, this is what happens the other side of the event horizon of a black hole, where space itself only exists in one's future, which leads to the singularity. 

Addendum 2: Since posting this I've watched a lot of other videos, many of them by Curt, which may become the subject of a future post. But I just wanted to reference this one with Emily Adlam, who has a view completely opposite to the one expressed in my post above. She's developed what she calls the 'Sudoku universe', or the 'all at once' universe. The analogy with Sudoku is that the outcome is already 'known' and you can start anywhere at all - there is no progression from a fixed starting point to a fixed end point. This video is 1hr 19m, and I need to point out that she knows a lot more about this subject than I do, and so does Curt. Curt had obviously read all her papers relevant to this and knew exactly what to ask her. I know that if I was to go one-on-one with her, I could never argue at her level. I intend, at some point, to write another post where I discuss points-of-view of various physicists that are all driven more by philosophy than science.

Is there a cosmic purpose? Is our part in it a chimera?

 I’ve been procrastinating about writing this post for some time, because it comes closest to a ‘theory’ of Life, the Universe and Everything. ‘Theory’ in this context being a philosophical point of view, not a scientifically testable theory in the Karl Popper sense (it can’t be falsified), but using what science we currently know and interpreting it to fit a particular philosophical prejudice, which is what most scientists and philosophers do even when they don’t admit it.
 
I’ve been watching a lot of YouTube videos, some of which attempt to reconcile science and religion, which could be considered a lost cause, mainly because there is a divide going back to the Dark Ages, which the Enlightenment never bridged despite what some people might claim. One of the many videos I watched was a moderated discussion between Richard Dawkins and Jordan Peterson, which remained remarkably civil, especially considering that Peterson really did go off on flights of fancy (from my perspective), comparing so-called religious ‘truths’ with scientific ‘truths’. I thought Dawkins handled it really well, because he went to pains not to ridicule Peterson, while pointing out fundamental problems with such comparisons.
 
I’m already going off on tangents I never intended, but I raise it because Peterson makes the point that science actually arose from the Judea-Christian tradition – a point that Dawkins didn’t directly challenge, but I would have. I always see the modern scientific enterprise, if I can call it that, starting with Copernicus, Galileo and Kepler, but given particular impetus by Newton and his contemporary and rival, Leibniz. It so happens that they all lived in Europe when it was dominated by Christianity, but the real legacy they drew on was from the Ancient Greeks with a detour into Islam where it acquired Hindu influences, which many people conveniently ignore. In particular, we adopted Hindu-Arabic arithmetic, incorporating zero as a decimal place-marker, without which physics would have been stillborn.
 
Christianity did its best to stop the scientific enterprise: for example, when it threatened Galileo with the inquisition and put him under house arrest. Modern science evolved despite Christianity, not because of it. And that’s without mentioning Darwin’s problems, which still has ramifications today in the most advanced technological nation in the world.
 
A lengthy detour, but only slightly off-topic. There is a mystery at the heart of everything on the very edge of our scientific understanding of the world that I believe is best expressed by Paul Davies, but was also taken up by Stephen Hawking, of all people, towards the end of his life. I say, ‘of all people’, because Hawking was famously sceptical of the role of philosophy, yet, according to his last collaborator, Thomas Hertog, he was very interested in the so-called Big Questions, and like Davies, was attracted to John Wheeler’s idea of a cosmic-scale quantum loop that attempts to relate the end result of the Universe to its beginning.
 
Implicit in this idea is that the Universe has a purpose, which has religious connotations. So I want to make that point up front and add that there is No God Required. I agree with Davies that science neither proves nor disproves the existence of God, which is very much a personal belief, independent of any rationalisation one can make.
 
I wrote a lengthy post on Hawking’s book, The Grand Design, back in 2020 (which he cowrote with Leonard Mlodinow). I will quote from that post to highlight the point I raised 2 paragraphs ago: the link between present and past.
 
Hawking contends that the ‘alternative histories’ inherent in Feynman’s mathematical method, not only affect the future but also the past. What he is implying is that when an observation is made it determines the past as well as the future. He talks about a ‘top down’ history in lieu of a ‘bottom up’ history, which is the traditional way of looking at things. In other words, cosmological history is one of many ‘alternative histories’ (his terminology) that evolve from QM.
 
Then I quote directly from Hawking’s text:
 
This leads to a radically different view of cosmology, and the relation between cause and effect. The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us (my emphasis).
 
One can’t contemplate this without considering the nature of time. There are in fact 2 different experiences we have of time, and that has created debate among physicists as well as philosophers. The first experience is simply observational. Every event with a causal relationship that is separated by space is axiomatically also separated by time, and this is a direct consequence of the constant speed of light. If this wasn’t the case, then everything would literally happen at once. So there is an intrinsic relationship between time and light, which Einstein had the genius to see: was not just a fundamental law of the Universe; but changed perceptions of time and space for different observers. Not only that, his mathematical formulations of this inherent attribute, led him to the conclusion that time itself was fluid, dependent on an observer’s motion as well as the gravitational field in which they happened to be.
 
I’m going to make another detour because it’s important and deals with one of the least understood aspects of physics. One of the videos I watched that triggered this very essay was labelled The Single Most Important Experiment in Physics, which is the famous bucket experiment conducted by Newton, which I’ve discussed elsewhere. Without going into details, it basically demonstrates that there is a frame of reference for the entire universe, which Newton called absolute space and Einstein called absolute spacetime. Penrose also discusses the importance of this concept, because it means that all relativistic phenomena take place against a cosmic background. It’s why we can determine the Earth’s velocity with respect to the entire universe by measuring the Doppler shift against the CMBR (cosmic microwave background radiation).
 
Now, anyone with even a rudimentary knowledge of relativity theory knows that it’s not just time that’s fluid but also space. But, as Kip Thorne has pointed out, mathematically we can’t tell if it’s the space that changes in dimension or the ruler used to measure it. I’ve long contended that it’s the ruler, which can be the clock itself. We can use a clock to measure distance and if the clock changes, which relativity tell us it does, then it’s going to measure a different distance to a stationary observer. By stationary, I mean one who is travelling at a lesser speed with respect to the overall CMBR.
 
So what is the other aspect of time that we experience? It’s the very visceral sensation we all have that time ‘flows’, because we all ‘sense’ its ‘passing’. And this is the most disputed aspect of time, that many physicists tell us is an illusion, including Davies. Some, like Sabine Hossenfelder, are proponents of the ‘block universe’, first proposed by Einstein, whereby the future already exists like the past, which is why both Hossenfelder and Einstein believed in what is now called superdeterminism – everything is predetermined in advance – which is one of the reasons that Einstein didn’t like the philosophical ramifications of quantum mechanics (I’ll get to his ‘spooky action at a distance’ later).
 
Davies argues that the experience of time passing is a psychological phenomenon and the answer will be found in neuroscience, not physics. And this finally brings consciousness into the overall scheme of things. I’ve argued elsewhere that, without consciousness, the Universe has no meaning and no purpose. Since that’s the point of this dissertation, it can be summed up with an aphorism from Wheeler.
 
The Universe gave rise to consciousness and consciousness gives the Universe meaning.
 
I like to cite Schrodinger from his lectures on Mind and Matter appended to his tome, What is Life? Consciousness exists in a constant present, and I argue that it’s the only thing that does (the one possible exception is a photon of light, for which time is zero). As I keep pointing out, this is best demonstrated every time someone takes a photo: it freezes time, or more accurately, it creates an image frozen in time; meaning it’s forever in our past, but so is the event that it represents.
 
The flow of time we all experience is a logical consequence of this. In a way, Davies is right: it’s a neurological phenomenon, in as much as consciousness seems to ‘emerge’ from neuronal activity. But I’m not sure Davies would agree with me – in fact, I expect he wouldn’t.
 
Those who have some familiarity with my blog, may see a similarity between these 2 manifestations of time and my thesis on Type A time and Type B time (originally proposed by J.M.E. McTaggart, 1906); the difference between them, in both cases, being the inclusion of consciousness.
 
Now I’m going to formulate a radical idea, which is that in Type B time (the time without consciousness), the flow of time is not experienced but there are chains of causal events. And what if all the possible histories are all potentially there in the same way that future possible histories are, as dictated by Feynman’s model. And what if the one history that we ‘observe’, going all the way back to the pattern in the CMBR (our only remnant relic of the Big Bang), only became manifest when consciousness entered the Universe. And when I say ‘entered’ I mean that it arose out of a process that had evolved. Davies, and also Wheeler before him, speculated that the ‘laws’ of nature we observe have also evolved as part of the process. But what if those laws only became frozen in the past when consciousness finally became manifest. This is the backward-in-time quantum loop that Wheeler hypothesised.
 
I contend that QM can only describe the future (an idea espoused by Feynman’s collaborator, Freeman Dyson), meaning that Schrodinger’s equation can only describe the future, not the past. Once a ‘measurement’ is made, it no longer applies. Penrose explains this best, and has his own argument that the ‘collapse’ of the wave function is created by gravity. Leaving that aside, I argue that the wave function only exists in our future, which is why it’s never observed and why Schrodinger’s equation can’t be applied to events that have already happened. But what if it was consciousness that finally determined which of many past paths became the reality we observe. You can’t get more speculative than that, but it provides a mechanism for Wheeler’s ‘participatory universe’ that both Davies and Hawking found appealing.
 
I’m suggesting that the emergence of consciousness changed the way time works in the Universe, in that the past is now fixed and only the future is still open.
 
Another video I watched also contained a very radical idea, which is that spacetime is created like a web into the future (my imagery). The Universe appears to have an edge in time but not in space, and this is rarely addressed. It’s possible that space is being continually created with the Universe’s expansion – an idea explored by physicist, Richard Muller – but I think it’s more likely that the Universe is Euclidean, meaning flat, but bounded. We may never know.
 
But if the Universe has an edge in time, how does that work? I think the answer is quantum entanglement, though no one else does. Everyone agrees that entanglement is non-local, meaning it’s not restricted by the rules of relativity, and it’s not spatially dependent. I speculate that quantum entanglement is the Universe continually transitioning from a quantum state to a classical physics state. This idea is just as heretical as the one I proposed earlier, and while Einstein would call it ‘spooky action at a distance’, it makes sense, because in quantum cosmology, time mathematically disappears. And it disappears because you can’t ‘see’ the future of the Universe, even in principle.

Addendum 1: This excerpt from a panel discussion shows how this debate is unresolved even among physicists. The first speaker, Avshalom Elitzur (who is also referenced in one of the videos linked in the 2nd last paragraph of the main text) probably comes closest to expressing my viewpoint.

In effect, he describes what I expound on in my post, though I'm sure he wouldn't agree with my more radical ideas - the role of consciousness and that entanglement is intrinsically linked to the edge of time for the whole universe. However, he does say, 'In some profound way the future does not exist'. 

Addendum 2: I came across this article in New Scientist, which you might not be able to access if you're not a subscriber (I have an online subscription). Basically, the author, Karmela Padavic-Callaghan, argues that 'classical time' arises from quantum 'entanglement', citing Alessandro Coppo. To quote:

This may mean that if we perceive the passage of time, then there is some entanglement woven into the physical world. And an observer in a universe devoid of entanglement – as some theories suggest ours was at its very beginning – would have seen nothing change. Everything would be static.

The role of dissonance in art, not to mention science and mathematics

 I was given a book for a birthday present just after the turn of the century, titled A Terrible Beauty; The People and Ideas that Shaped the Modern Mind, by Peter Watson. A couple of things worth noting: it covers the history of the 20th Century, but not geo-politically as you might expect. Instead, he writes about the scientific discoveries alongside the arts and cultural innovations, and he talks about both with equal erudition, which is unusual.
 
The reason I mention this, is because I remember Watson talking about the human tendency to push something to its limits and then beyond. He gave examples in science, mathematics, art and music. A good example in mathematics is the adoption of √-1 (giving us ‘imaginary numbers’), which we are taught is impossible, then suddenly it isn’t. The thing is that it allows us to solve problems that were previously impossible in the same way that negative numbers give solutions to arithmetical subtractions that were previously unanswerable. There were no negative numbers in ancient Greece because their mathematics was driven by geometry, and the idea of a negative volume or area made no sense.
 
But in both cases: negative numbers and imaginary numbers; there is a cognitive dissonance that we have to overcome before we can gain familiarity and confidence in using them, or even understanding what they mean in the ‘real world’, which is the problem the ancient Greeks had. Most people reading this have no problem, conceptually, dealing with negative numbers, because, for a start, they’re an integral aspect of financial transactions – I suspect everyone reading this above a certain age has had experience with debt and loans.
 
On the other hand, I suspect a number of readers struggle with a conceptual appreciation of imaginary numbers. Some mathematicians will tell you that the term is a misnomer, and its origin would tend to back that up. Apparently, Rene Descartes coined the term, disparagingly, because, like the ancient Greek’s problem with negative numbers, he believed they had no relevance to the ‘real world’. And Descartes would have appreciated their usefulness in solving problems previously unsolvable, so I expect it would have been a real cognitive dissonance for him.
 
I’ve written an entire post on imaginary numbers, so I don’t want to go too far down that rabbit hole, but I think it’s a good example of what I’m trying to explicate. Imaginary numbers gave us something called complex algebra and opened up an entire new world of mathematics that is particularly useful in electrical engineering. But anyone who has studied physics in the last century is aware that, without imaginary numbers, an entire field of physics, quantum mechanics, would remain indescribable, let alone be comprehensible. The thing is that, even though most people have little or no understanding of QM, every electronic device you use depends on it. So, in their own way, imaginary numbers are just as important and essential to our lives as negative numbers are.
 
You might wonder how I deal with the cognitive dissonance that imaginary numbers induce. In QM, we have, at its most rudimentary level, something called Schrodinger’s equation, which he proposed in 1926 (“It’s not derived from anything we know,” to quote Richard Feynman) and Schrodinger quickly realised it relied on imaginary numbers – he couldn’t formulate it without them. But here’s the thing: Max Born, a contemporary of Schrodinger, formulated something we now call the Born rule that mathematically gets rid of the imaginary numbers (for the sake of brevity and clarity, I’ll omit the details) and this gives the probability of finding the object (usually an electron) in the real world. In fact, without the Born rule, Schrodinger’s equation is next-to-useless, and would have been consigned to the dustbin of history.
 
And that’s relevant, because prior to observing the particle, it’s in a superposition of states, described by Schrodinger’s equation as a wave function (Ψ), which some claim is a mathematical fiction. In other words, you need to get rid (clumsy phrasing, but accurate) of the imaginary component to make it relevant to the reality we actually see and detect. And the other thing is that once we have done that, the Schrodinger equation no longer applies – there is effectively a dichotomy between QM and classical physics (reality), which is called the 'measurement problem’. Roger Penrose gives a good account in this video interview. So, even in QM, imaginary numbers are associated with what we cannot observe.
 
That was a much longer detour than I intended, but I think it demonstrates the dissonance that seems necessary in science and mathematics, and arguably necessary for its progress; plus it’s a good example of the synergy between them that has been apparent since Newton.
 
My original intention was to talk about dissonance in music, and the trigger for this post was a YouTube video by musicologist, Rick Beato (pronounced be-arto), dissecting the Beatles song, Ticket to Ride, which he called, ‘A strange but perfect song’. In fact, he says, “It’s very strange in many ways: it’s rhythmically strange; it’s melodically strange too”. I’ll return to those specific points later. To call Beato a music nerd is an understatement, and he gives a technical breakdown that quite frankly, I can’t follow. I should point out that I’ve always had a good ‘ear’ that I inherited, and I used to sing, even though I can’t read music (neither could the Beatles). I realised quite young that I can hear things in music that others miss. Not totally relevant, but it might explain some things that I will expound upon later.
 
It's a lengthy, in-depth analysis, but if you go to 4.20-5.20, Beato actually introduces the term ‘dissonance’ after he describes how it applies. In effect, there is a dissonance between the notes that John Lennon sings and the chords he plays (on a 12-string guitar). And the thing is that we, the listener, don’t notice – someone (like Beato) has to point it out. Another quote from 15.00: “One of the reasons the Beatles songs are so memorable, is that they use really unusual dissonant notes at key points in the melody.”
 
The one thing that strikes you when you first hear Ticket to Ride is the unusual drum part. Ringo was very inventive and innovative, and became more adventurous, along with his bandmates, on later recordings. The Ticket to Ride drum part has become iconic: everyone knows it and recognises it. There is a good video where Ringo talks about it, along with another equally famous drum part he created. Beato barely mentions it, though right at the beginning, he specifically refers to the song as being ‘rhythmically strange’.
 
A couple of decades ago, can’t remember exactly when, I went and saw an entire Beatles concert put on by a rock band, augmented by orchestral strings and horn parts. It was in 2 parts with an intermission, and basically the 1st half was pre-Sergeant Pepper and the 2nd half, post. I can still remember that they opened the concert with Magical Mystery Tour and it blew me away. The thing is that they went to a lot of trouble to be faithful to the original recordings, and I realised that it was the first time I’d heard their music live, albeit with a cover band. And what immediately struck me was the unusual harmonics and rhythms they employed. Watching Beato’s detailed technical analysis puts this into context for me.
 
Going from imaginary numbers and quantum mechanics to one of The Beatles most popular songs may seem like a giant leap, but it highlights how dissonance is a universal principle for humans, and intrinsic to progression in both art and science.
 
Going back to Watson’s book that I reference in the introduction, another obvious example that he specifically talks about is Picasso’s cubism.
 
In storytelling, it may not be so obvious, and I think modern fiction has been influenced more by cinema than anything else, where the story needs to be more immediate and it needs to flow with minimal description. There is now an expectation that it puts you in the story – what we call immersion.
 
On another level, I’ve noticed a tendency on my part to create cognitive dissonance in my characters and therefore the reader. More than once, I have combined sexual desire with fear, which some may call perverse. I didn’t do this deliberately – a lot of my fiction contains elements I didn’t foresee. Maybe it says something about my own psyche, but I honestly don’t know.

Mathematics links epistemology to ontology, but it’s not that simple

A recurring theme on this blog is the relationship between mathematics and reality. It started with the Pythagoreans (in Western philosophy) and was famously elaborated upon by Plato. I also think it’s the key element of Kant’s a priori category in his marriage of analytical philosophy and empiricism, though it’s rarely articulated that way.
 
I not-so-recently wrote a post about the tendency to reify mathematical objects into physical objects, and some may validly claim that I am guilty of that. In particular, I found a passage by Freeman Dyson who warns specifically about doing that with Schrodinger’s wave function (Ψ, the Greek letter, psi, pronounced sy). The point is that psi is one of the most fundamental concepts in QM (quantum mechanics), and is famous for the fact that it has never been observed, and specifically can’t be, even in principle. This is related to the equally famous ‘measurement problem’, whereby a quantum event becomes observable, and I would say, becomes ‘classical’, as in classical physics. My argument is that this is because Ψ only exists in the future of whoever (or whatever) is going to observe it (or interact with it). By expressing it specifically in those terms (of an observer), it doesn’t contradict relativity theory, quantum entanglement notwithstanding (another topic).
 
Some argue, like Carlo Rovelli (who knows a lot more about this topic than me), that Schrodinger’s equation and the concept of a wave function has led QM astray, arguing that if we’d just stuck with Heisenberg’s matrices, there wouldn’t have been a problem. Schrodinger himself demonstrated that his wave function approach and Heisenberg’s matrix approach are mathematically equivalent. And this is why we have so many ‘interpretations’ of QM, because they can’t be mathematically delineated. It’s the same with Feynman’s QED and Schwinger’s QFT, which Dyson showed were mathematically equivalent, along with Tomanaga’s approach, which got them all a Nobel prize, except Dyson.
 
As I pointed out on another post, physics is really just mathematical models of reality, and some are more accurate and valid than others. In fact, some have turned out to be completely wrong and misleading, like Ptolemy’s Earth-centric model of the solar system. So Rovelli could be right about the wave function. Speaking of reifying mathematical entities into physical reality, I had an online discussion with Qld Uni physicist, Mark John Fernee, who takes it a lot further than I do, claiming that 3 dimensional space (or 4 dimensional spacetime) is a mathematical abstraction. Yet, I think there really are 3 dimensions of space, because the number of dimensions affects the physics in ways that would be catastrophic in another hypothetical universe (refer John Barrow’s The Constants of Nature). So it’s more than an abstraction. This was a key point of difference I had with Fernee (you can read about it here).
 
All of this is really a preamble, because I think the most demonstrable and arguably most consequential example of the link between mathematics and reality is chaos theory, and it doesn’t involve reification. Having said that, this again led to a point of disagreement between myself and Fermee, but I’ll put that to one side for the moment, so as not to confuse you.
 
A lot of people don’t know that chaos theory started out as purely mathematical, largely due to one man, Henri Poincare. The thing about physical chaotic phenomena is that they are theoretically deterministic yet unpredictable simply because the initial conditions of a specific event can’t be ‘physically’ determined. Now some physicists will tell you that this is a physical limitation of our ability to ‘measure’ the initial conditions, and infer that if we could, it would be ‘problem solved’. Only it wouldn’t, because all chaotic phenomena have a ‘horizon’ beyond which it’s impossible to make accurate predictions, which is why weather predictions can’t go reliably beyond 10 days while being very accurate over a few. Sabine Hossenfelder explains this very well.
 
But here’s the thing: it’s built into the mathematics of chaos. It’s impossible to calculate the initial conditions because you need to do the calculation to infinite decimal places. Paul Davies gives an excellent description and demonstration in his book, The Cosmic Blueprint. (this was my point-of-contention with Fernee, talking about coin-tosses).
 
As I discussed on another post, infinity is a mathematical concept that appears to have little or no relevance to reality. Perhaps the Universe is infinite in space – it isn’t in time – but if it is, we might never know. Infinity avoids empirical confirmation almost by definition. But I think chaos theory is the exception that proves the rule. The reason we can’t determine the exact initial conditions of a chaotic event, is not just physical but mathematical. As Fernee and others have pointed out, you can manipulate a coin-toss to make it totally predictable, but that just means you’ve turned a chaotic event into a non-chaotic event (after all it’s a human-made phenomenon). But most chaotic events are natural, like the orbits of the planets and biological evolution. The creation of the Earth’s moon was almost certainly a chaotic event, without which complex life would almost certainly never have evolved, so they can be profoundly consequential as well as completely unpredictable.
 

What’s inside a black hole?

 The correct answer is no one knows, but I’m going to make a wild, speculative, not fully-informed guess and suggest, possibly nothing. But first, a detour, to provide some context.
 
I came across an interview with very successful, multi-award-winning, Australian-Canadian actor, Pamela Rabe, who is best known (in Australia, at least) for her role in Wentworth (about a fictional female prison). She was interviewed by Benjamin Law in The Age Good Weekend magazine, a few weekends ago, where among many other questions, he asked, Is there a skill you wish you could acquire? She said there were so many, including singing better, speaking more languages and that she wished she was more patient. Many decades ago, I remember someone asking me a similar question, and I can still remember the answer: I said that I wish I was more intelligent, and I think that’s still true.
 
Some people might be surprised by this, and perhaps it’s a good thing I’m not, because I think I would be insufferable. Firstly, I’ve always found myself in the company of people who are much cleverer than me, right from when I started school, and right through my working life. The reason I wish I was more intelligent is that I’ve always been conscious of trying to understand things that are beyond my intellectual abilities. My aspirations don’t match my capabilities.
 
And this brings me to a discussion on black holes, which must, in some respects, represent the limits of what we know about the Universe and maybe what is even possible to know. Not surprisingly, Marcus du Sautoy spent quite a few pages discussing black holes in his excellent book, What We Cannot Know. But there is a short YouTube video by one of the world’s leading exponents on black holes, Kip Thorne, which provides a potted history. I also, not that long ago, read his excellent book, Black Holes and Time Warps; Einstein’s Outrageous Legacy (1994), which gives a very comprehensive history, in which he was not just an observer, but one of the actors.
 
It's worth watching the video because it highlights the role mathematics has played in physics, not only since Galileo, Kepler and Newton, but increasingly so in the 20th Century, following the twin revolutions of quantum mechanics and relativity theory. In fact, relativity theory predicted black holes, yet most scientists (including Einstein, initially) preferred to believe that they couldn’t exist; that Nature wouldn’t allow it.
 
We all suffer from these prejudices, including myself (and even Einstein). I discussed in a recent post how we create mathematical models in an attempt to explain things we observe. But more and more, in physics, we use mathematical models to explain things that we don’t observe, and black holes are the perfect example. If you watch the video interview with Thorne, this becomes obvious, because scientists were gradually won over by the mathematical arguments, before there was any incontrovertible physical evidence that they existed.
 
And since no one can observe what’s inside a black hole, we totally rely on mathematical models to give us a clue. Which brings me to the title of the post. The best known equation in reference to black holes in the Bekenstein-Hawking equation which give us the entropy of a black hole and predicts Hawking radiation. This is yet to be observed, but this is not surprising, as it’s virtually impossible. It’s simply not ‘hot’ enough to distinguish from the CMBR (cosmic microwave background radiation) which permeates the entire universe. 

Here is the formula:

S(BH) = kA/4(lp)^2 

Where S is the entropy of the black hole, A is the surface area of the sphere at the event horizon, and lp is the Planck length given by this formula:

√(Gh/2πc^3) 

Where G is the gravitational constant, h is Planck’s constant and c is the constant for lightspeed.

Hawking liked the idea that it’s the only equation in physics to incorporate the 4 fundamental natural constants: k, G, h and c; in one formula.

So, once again, mathematics predicts something that’s never been observed, yet most scientists believe it to be true. This led to what was called the ‘information paradox’ that all information falling into a black hole would be lost, but what intrigues me is that if a black hole can, in principle, completely evaporate by converting all its mass into radiation, then it infers that the mass is not in fact lost – it must be still there, even if we can’t see it. This means, by inference, that it can’t have disappeared down a wormhole, which is one of the scenarios conjectured.

One of the mathematical models proposed is the 'holographic principle' for black holes, for which I’ll quote directly from Wikipedia, because it specifically references what I’ve already discussed.

The holographic principle was inspired by the Bekenstein bound of black hole thermodynamics, which conjectures that the maximum entropy in any region scales with the radius squared, rather than cubed as might be expected. In the case of a black hole, the insight was that the information content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon. The holographic principle resolves the black hole information paradox within the framework of string theory.

I know this is a long hop to make but what if the horizon not only contains the information but actually contains all the mass. In other words, what if everything is frozen at the event horizon because that’s where time ‘stops’. Most probably not true, and I don’t know enough to make a cogent argument. However, it would mean that the singularity predicted to exist at the centre of a black hole would not include its mass, but only spacetime.

Back in the 70s, I remember reading an article in Scientific American by a philosopher, who effectively argued that a black hole couldn’t exist. Now this was when their purported existence was mostly mathematical, and no one could unequivocally state that they existed physically. I admit I’m hazy about the details but, from what I can remember, he argued that it was self-referencing because it ‘swallowed itself’. Obviously, his argument was much more elaborate than that one-liner suggests. But I do remember thinking his argument flawed and I even wrote a letter to Scientific American challenging it. Basically, I think it’s a case of conflating the language used to describe a phenomenon with the physicality of it.

I only raise it now, because, as a philosopher, I’m just as ignorant of the subject as he was, so I could be completely wrong.

Addendum 1: I was of 2 minds whether to write this, but it kept bugging me - wouldn't leave me alone, so I wrote it down. I've no idea how true it might be, hence all the caveats and qualifications. It's absolutely at the limit of what we can know at this point in time. As I've said before, philosophy exists at the boundary of science and ignorance. It ultimately appealed to my aesthetics and belief in Nature’s aversion to perversity.

Addendum 2: Another reason why I'm most likely wrong is that there is a little known quirk of Newton's theory of gravity that the gravitational 'force' anywhere inside a perfectly symmetrical hollow sphere is zero. So the inside of a black hole exerting zero gravitational force would have to be the ultimate irony, which makes it highly improbable. I've no idea how that relates to the 'holographic principle' for a black hole. But I still don't think all the mass gets sucked into a singularity or down a wormhole. My conjecture is based purely on the idea that 'time' might well become 'zero' at the event horizon, though, from what I've read, no physicist thinks so. From an outsider's perspective, time dilation becomes asymptotically infinite (effective going to zero, but perhaps taking the Universe's lifetime to reach it). In this link, it begs a series of questions that seem to have no definitive answers. The alternative idea is that it's spacetime that 'falls' into a black hole, therefore taking all the mass with it.

Addendum 3: I came across this video by Tibbees (from a year ago), whom I recommend. She cites a book by Carlo Rovelli, White Holes, which is also the title of her video. Now, you can't talk about white holes without talking about black holes; they are just black holes time reversed (as she explicates). We have no evidence they actually exist, unless the Big Bang is a white hole (also mentioned). I have a lot of time for Carlo Rovelli, even though we have philosophical differences (what a surprise). Basically, he argues that, at a fundamental level, time doesn't exist, but it's introduced into the universe as a consequence of entropy (not the current topic). 

Tibbees gives a totally different perspective to my post, which is why I bring it up. Nevertheless, towards the end, she mentions that our view of a hypothetical person (she suggests Rovelli) entering a black hole is that their existence becomes assymptotically infinite. But what, if in this case, what we perceive is what actually happens. Then my scenario makes sense. No one else believes that, so it's probably incorrect.

Addendum 4: Victor T Toth, whom even Mark John Fernee defers to (on Quora), when it comes to cosmology and gravity, has said more than once, that 'the event horizon is always in your future', which infers you never reach it. This seems to contradict the prevailing view among physicists that, while that's true for another 'observer' observing 'you' (assuming you're the one falling into a black hole), from 'your' perspective you could cross the event horizon without knowing you have (see the contradiction). This is the conventional, prevailing view among physicists. To my knowledge, Toth has never addressed this apparent contradiction specifically.

However, if one follows Toth's statement to its logical conclusion, 'you' would approach the event horizon asymptotically, which is what I'm speculating. In which case, everything that falls into a black hole would accumulate at the event horizon. The thing is that gravity determines the 'true time' (τ) for a free falling object, and if τ became zero at the event horizon, then everything I've said makes sense. The thing is I really don't know enough physics to back up my conjecture with mathematics.

Addendum 5: Possibly the most important addendum to this post, in that it provides yet another plausible scenario based on what we currently know, and is rather eruditely expounded upon by someone on Quora calling himself 'The Physics Detective' (John Duffield). Of course, I've heard of the 'Firewall' explanation, without knowing if it's true or not. But I suspect no one does.

Image by W H Freeman and company, publishers of Gravitation

Addendum 6: I don't think I've ever written so many addendums to a post, which demonstrates how equivocal and unconvinced I am by my own arguments. It's symptomatic of our ignorance, and mine in particular, on this subject.

So I'm going to renege and go back to an earlier post I wrote, where I align myself with Kip Thorne, who is an actual expert on this matter.

Addendum 7: This must be a record (for the number of addendums to one post). This is another video by Curt Jaimungal posted some time after I originally wrote this (6 mths), which gives a completely different mathematical theory that effectively argues that the interior of a black hole is 'empty'. It highlights to me, just how up-in-the-air our current knowledge of black holes is. Basically, he argues that there is no singularity and that the black hole is a 'mirror'. You need to watch the video to get a grasp on what he's talking about, because I can't do it justice in this space.

Do we make reality?

 I’ve read 2 articles, one in New Scientist (12 Oct 2024) and one in Philosophy Now (Issue 164, Oct/Nov 2024), which, on the surface, seem unrelated, yet both deal with human exceptionalism (my term) in the context of evolution and the cosmos at large.
 
Staring with New Scientist, there is an interview with theoretical physicist, Daniele Oriti, under the heading, “We have to embrace the fact that we make reality” (quotation marks in the original). In some respects, this continues on with themes I raised in my last post, but with different emphases.
 
This helps to explain the title of the post, but, even if it’s true, there are degrees of possibilities – it’s not all or nothing. Having said that, Donald Hoffman would argue that it is all or nothing, because, according to him, even ‘space and time don’t exist unperceived’. On the other hand, Oriti’s argument is closer to Paul Davies’ ‘participatory universe’ that I referenced in my last post.
 
Where Oriti and I possibly depart, philosophically speaking, is that he calls the idea of an independent reality to us ‘observers’, “naïve realism”. He acknowledges that this is ‘provocative’, but like many provocative ideas it provides food-for-thought. Firstly, I will delineate how his position differs from Hoffman’s, even though he never mentions Hoffman, but I think it’s important.
 
Both Oriti and Hoffman argue that there seems to be something even more fundamental than space and time, and there is even a recent YouTube video where Hoffman claims that he’s shown mathematically that consciousness produces the mathematical components that give rise to spacetime; he has published a paper on this (which I haven’t read). But, in both cases (by Hoffman and Oriti), the something ‘more fundamental’ is mathematical, and one needs to be careful about reifying mathematical expressions, which I once discussed with physicist, Mark John Fernee (Qld University).
 
The main issue I have with Hoffman’s approach is that space-time is dependent on conscious agents creating it, whereas, from my perspective and that of most scientists (although I’m not a scientist), space and time exists external to the mind. There is an exception, of course, and that is when we dream.
 
If I was to meet Hoffman, I would ask him if he’s heard of proprioception, which I’m sure he has. I describe it as the 6th sense we are mostly unaware of, but which we couldn’t live without. Actually, we could, but with great difficulty. Proprioception is the sense that tells us where our body extremities are in space, independently of sight and touch. Why would we need it, if space is created by us? On the other hand, Hoffman talks about a ‘H sapiens interface’, which he likens to ‘desktop icons on a computer screen’. So, somehow our proprioception relates to a ‘spacetime interface’ (his term) that doesn’t exist outside the mind.
 
A detour, but relevant, because space is something we inhabit, along with the rest of the Universe, and so is time. In relativity theory there is absolute space-time, as opposed to absolute space and time separately. It’s called the fabric of the universe, which is more than a metaphor. As Viktor Toth points out, even QFT seems to work ‘just fine’ with spacetime as its background.
 
We can do quantum field theory just fine on the curved spacetime background of general relativity.
 
[However] what we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.
 
And this is where Oriti argues we need to find something deeper. To quote:
 
Modern approaches to quantum gravity say that space-time emerges from something deeper – and this could offer a new foundation for physical laws.
 
He elaborates: I work with quantum gravity models in which you don’t start with a space-time geometry, but from more abstract “atomic” objects described in purely mathematical language. (Quotation marks in the original.)
 
And this is the nub of the argument: all our theories are mathematical models and none of them are complete, in as much as they all have limitations. If one looks at the history of physics, we have uncovered new ‘laws’ and new ‘models’ when we’ve looked beyond the limitations of an existing theory. And some mathematical models even turned out to be incorrect, despite giving answers to what was ‘known’ at the time. The best example being Ptolemy’s Earth-centric model of the solar system. Whether string theory falls into the same category, only future historians will know.
 
In addition, different models work at different scales. As someone pointed out (Mile Gu at the University of Queensland), mathematical models of phenomena at one scale are different to mathematical models at an underlying scale. He gave the example of magnetism, demonstrating that mathematical modelling of the magnetic forces in iron could not predict the pattern of atoms in a 3D lattice as one might expect. In other words, there should be a causal link between individual atoms and the overall effect, but it could not be determined mathematically. To quote Gu: “We were able to find a number of properties that were simply decoupled from the fundamental interactions.” Furthermore, “This result shows that some of the models scientists use to simulate physical systems have properties that cannot be linked to the behaviour of their parts.”
 
This makes me sceptical that we will find an overriding mathematical model that will entail the Universe at all scales, which is what theories of quantum gravity attempt to do. One of the issues that some people raise is that a feature of QM is superposition, and the superposition of a gravitational field seems inherently problematic.
 
Personally, I think superposition only makes sense if it’s describing something that is yet to happen, which is why I agree with Freeman Dyson that QM can only describe the future, which is why it only gives us probabilities.
 
Also, in quantum cosmology, time disappears (according to Paul Davies, among others) and this makes sense (to me), if it’s attempting to describe the entire universe into the future. John Barrow once made a similar point, albeit more eruditely.
 
Getting off track, but one of the points that Oriti makes is whether the laws and the mathematics that describes them are epistemic or ontic. In other words, are they reality or just descriptions of reality. I think it gets blurred, because while they are epistemic by design, there is still an ontology that exists without them, whereas Oriti calls that ‘naïve realism’. He contends that reality doesn’t exist independently of us. This is where I always cite Kant: that we may never know the ‘thing-in-itself,’ but only our perception of it. Where I diverge from Kant is that the mathematical models are part of our perception. Where I depart from Oriti is that I argue there is a reality independently of us.
 
Both QM and relativity theory are observer-dependent, which means they could both be describing an underlying reality that continually eludes us. Whereas Oriti argues that ‘reality is made by our models, not just described by them’, which would make it subjective.
 
As I pointed out in my last post, there is an epistemological loop, whereby the Universe created the means to understand itself, through us. Whether there is also an ontological loop as both Davies and Oriti infer, is another matter: do we determine reality through our quantum mechanical observations? I will park that while I elaborate on the epistemic loop.
 
And this finally brings me to the article in Philosophy Now by James Miles titled, We’re as Smart as the Universe gets. He argues that, from an evolutionary perspective, there is a one-in-one-billion possibility that a species with our cognitive abilities could arise by natural selection, and there is no logical reason why we would evolve further, from an evolutionary standpoint. I have touched on this before, where I pointed out that our cultural evolution has overtaken our biological evolution and that would also happen to any other potential species in the Universe who developed cognitive abilities to the same level. Dawkins coined the term, ‘meme’, to describe cultural traits that have ‘survived’, which now, of course, has currency on social media way beyond its original intention. Basically, Dawkins saw memes as analogous to genes, which get selected; not by a natural process but by a cultural process.
 
I’ve argued elsewhere that mathematical theorems and scientific theories are not inherently memetic. This is because they are chosen because they are successful, whereas memes are successful because they are chosen. Nevertheless, such theorems and theories only exist because a culture has developed over millennia which explores them and builds on them.
 
Miles talks about ‘the high intelligence paradox’, which he associates with Darwin’s ‘highest and most interesting problem’. He then discusses the inherent selection advantage of co-operation, not to mention specialisation. He talks about the role that language has played, which is arguably what really separates us from other species. I’ve argued that it’s our inherent ability to nest concepts within concepts ad-infinitum (which is most obvious in our facility for language, like I’m doing now) that allows us to, not only tell stories, compose symphonies, explore an abstract mathematical landscape, but build motor cars, aeroplanes and fly men to the moon. Are we the only species in the Universe with this super-power? I don’t know, but it’s possible.
 
There are 2 quotes I keep returning to:
 
The most incomprehensible thing about the Universe is that it’s comprehensible. (Einstein)
 
The Universe gave rise to consciousness and consciousness gives meaning to the Universe. (Wheeler)
 
I haven’t elaborated, but Miles makes the point, while referencing historical antecedents, that there appears no evolutionary 'reason’ that a species should make this ‘one-in-one-billion transition’ (his nomenclature). Yet, without this transition, the Universe would have no meaning that could be comprehended. As I say, that’s the epistemic loop.
 
As for an ontic loop, that is harder to argue. Photons exist in zero time, which is why I contend they are always in the future of whatever they interact with, even if they were generated in the CMBR some 13.5 billion years ago. So how do we resolve that paradox? I don’t know, but maybe that’s the link that Davies and Oriti are talking about, though neither of them mention it. But here’s the thing: when you do detect such a photon (for which time is zero) you instantaneously ‘see’ back to 380,000 years after the Universe’s birth.

How scale demonstrates that mathematics is intrinsically entailed in the Universe

 I momentarily contemplated another title: Is the Planck limit an epistemology or an ontology? Because that’s basically the topic of a YouTube video that’s the trigger for this post. I wrote a post some time ago where I discussed whether the Universe is continuous or discrete, and basically concluded that it was continuous. Based on what I’ve learned from this video, I might well change my position. But I should point out that my former opposition was based more on the idea that it could be quantised into ‘bits’ of information, whereas now I’m willing to acknowledge that it could be granular at the Planck scale, which I’ll elaborate on towards the end. I still don’t think that the underlying reality of the Universe is in ‘bits’ of information, therefore potentially created and operated by a computer.
 
Earlier this year, I discussed the problem of reification of mathematics so I want to avoid that if possible. By reification, I mean making a mathematical entity reality. Basically, physics works by formulating mathematical models that we then compare to reality through observations. But as Freeman Dyson pointed out, the wave function (Ψ), for example, is a mathematical entity and not a physical entity, which is sometimes debated. The fact is that if it does exist physically, it’s never observed, and my contention is that it ‘exists’ in the future; a view that is consistent with Dyson’s own philosophical viewpoint that QM can only describe the future and not the past.
 
And this brings me to the video, which has nothing to say about wave functions or reified mathematical entities, but uses high school mathematics to explore such esoteric and exotic topics as black holes and quantum gravity. There is one step involving integral calculus, which is about as esoteric as the maths becomes, and if you allow that 1/∞ = 0, it leads to the formula for the escape velocity from any astronomical body (including Earth). Note that the escape velocity literally allows an object to escape a gravitational field to infinity (∞). And the escape velocity for a black hole is c (the speed of light).
 
All the other mathematics is basic algebra using some basic physics equations, like Newton’s equation for gravity, Planck’s equation for energy, Heisenberg’s Uncertainty Principle using Planck’s Constant (h), Einstein’s famous equation for the equivalence of energy and mass, and the equation for the Coulomb Force between 2 point electric charges (electrons). There is also the equation for the Schwarzschild radius of a black hole, which is far easier to derive than you might imagine (despite the fact that Schwarzschild originally derived it from Einstein’s field equations).
 
Back in May 2019, I wrote a post on the Universe’s natural units, which involves the fundamental natural constants, h, c and G. This was originally done by Planck himself, which I describe in that post, while providing a link to a more detailed exposition. In the video (embedded below), the narrator takes a completely different path to deriving the same Planck units before describing a method that Planck himself would have used. In so doing, he explains how at the Planck level, space and time are not only impossible to observe, even in principle, but may well be impossible to remain continuous in reality. You need to watch the video, as he explains it far better than I can, just using high school mathematics.
 
Regarding the title I chose for this post, Roger Penrose’s Conformal Cyclic Cosmology (CCC) model of the Universe, exploits the fact that a universe without matter (just radiation) is scale invariant, which is essential for the ‘conformal’ part of his theory. However, that all changes when one includes matter. I’ve argued in other posts that different forces become dominant at different scales, from the cosmological to the subatomic. The point made in this video is that at the Planck scale all the forces, including gravity, become comparable. Now, as I pointed out at the beginning, physics is about applying mathematical models and comparing them to reality. We can’t, and quite possibly never will, be able to observe reality at the Planck scale, yet the mathematics tells us that it’s where all the physics we currently know is compatible. It tells me that not only is the physics of the Universe scale-dependent, but it's also mathematically dependent (because scale is inherently mathematical). In essence, the Universe’s dynamics are determined by mathematical parameters at all scales, including the Planck scale.
 
Note that the mathematical relationships in the video use ~ not = which means that they are approximate, not exact. But this doesn’t detract from the significance that 2 different approaches arrive at the same conclusion, which is that the Planck scale coincides with the origin of the Universe incorporating all forces equivalently.
 
 
Addendum: I should point out that Viktor T Toth, who knows a great deal more about this than me, argues that there is, in fact, no limit to what we can measure in principle. Even the narrator in the video frames his conclusion cautiously and with caveats. In other words, we are in the realm of speculative physics. Nevertheless, I find it interesting to contemplate where the maths leads us.

What does physics really tell us about reality?

 A little while ago I got into another discussion with Mark John Fernee (see previous post), but this time dealing with the relationship between ontology and epistemology as determined by physics. It came about in reference to a paper in Physics Today that someone cited, by N. David Nermin, a retired Professor of physics in Ithaca, New York, titled What’s bad about this habit. In particular, he talked about our tendency to ‘reify’ mathematically determined theories into reality. It helps if we have some definitions, which Fernee conveniently provided that were both succinct and precise.

Epistemology - concerning knowledge.

Ontology - concerning reality.

Reify - to think of an idea as real.

It so happens that around the same time I read an article in New Scientist (25 Mar 2024, pp.32-5) Strange but true? by philosopher, Eric Schwitzgebel, which covers similar territory. The title tells you little, but it’s really about how modern theories in physics don’t really tell us what reality is; instead giving us a range of possibilities to choose from.

I will start with Nermin, who spends the first page talking about quantum mechanics (QM), as it’s the most obvious candidate for a mathematical theory that gets reified by almost everyone who encounters it. This selected quote gives a good feel for what he’s talking about.

When I was a graduate student learning quantum field theory, I had a friend who was enchanted by the revelation that quantum fields were the real stuff that makes up the world. He reified quantum fields. But I hope you will agree that you are not a continuous field of operators on an infinite-dimensional Hilbert space. Nor, for that matter, is the page you are reading or the chair you are sitting in. Quantum fields are useful mathematical tools. They enable us to calculate things.

I found another quote by Freeman Dyson (2014), who makes a similar point to Nermin about the wave function (Ψ).

Unfortunately, people writing about quantum mechanics often use the phrase "collapse of the wave-function" to describe what happens when an object is observed. This phrase gives a misleading idea that the wave-function itself is a physical object. A physical object can collapse when it bumps into an obstacle. But a wave-function cannot be a physical object. A wave-function is a description of a probability, and a probability is a statement of ignorance. Ignorance is not a physical object, and neither is a wave-function. When new knowledge displaces ignorance, the wave-function does not collapse; it merely becomes irrelevant.

But Nermin goes on to challenge even the reality of space and time. Arguing that it is a mathematical abstraction. 

What about spacetime itself? Is that real? Spacetime is a (3+1) dimensional mathematical continuum. Even if you are a mathematical Platonist, I would urge you to consider that this continuum is nothing more than an extremely effective way to represent relations between distinct events.

He then goes on to explain that ‘an event… can be represented as a mathematical point in spacetime.’

He elaborates how this has become so reified into ordinary language that we’re no longer aware that it is an abstraction.

So spacetime is an abstract four-dimensional mathematical continuum of points that approximately represent phenomena whose spatial and temporal extension we find it useful or necessary to ignore. The device of spacetime has been so powerful that we often reify that abstract bookkeeping structure, saying that we inhabit a world that is such a four (or, for some of us, ten) dimensional continuum. The reification of abstract time and space is built into the very languages we speak, making it easy to miss the intellectual sleight of hand.

And this is where I start to have issues with his overall thesis, whereas Fernee said, ‘I completely concur with what he has written, and it is well articulated.’ 

When I challenged Fernee specifically on Nermin’s points about space-time, Fernee argued:

His contention was that even events in space-time are an abstraction. We all assume the existence of an objective reality, and I don't know of anyone who would seriously challenge that idea. Yet our descriptions are abstractions. All we ask of them is that they are consistent, describe the observed phenomena, and can be used to make predictions.

I would make an interesting observation on this very point, that distinguishes an AI’s apparent perspective of space and time compared to ours. Even using the word, ‘apparent’, infers there is a difference that we don’t think about.

I’ve made the point in other posts, including one on Kant, that we create a model of space and time in our heads which we use to interact with the physical space and time that exists outside our heads, and so do all living creatures with eyes, ears and touch. In fact, the model is so realistic that we think it is the external reality.

When we throw or catch a ball on the sporting field, we know that our brains don’t work out the quadratic equations that determine where it’s going to land. But imagine an AI controlled artillery device, which would make those calculations and use a 3-dimensional grid to determine where its ordinance was going to hit. Likewise, imagine an AI controlled drone using GPS co-ordinates – in other words, a mathematical abstraction of space and time – to navigate its way to a target. And that demonstrates the fundamental difference that I think Nermin is trying to delineate. The point is that, from our perspective, there is no difference.

This quote gives a clearer description of Nermin’s philosophical point of view.

Space and time and spacetime are not properties of the world we live in but concepts we have invented to help us organize classical events. Notions like dimension or interval, or curvature or geodesics, are properties not of the world we live in but of the abstract geometric constructions we have invented to help us organize events. As Einstein once again put it, “Space and time are modes by which we think, not conditions under which we live.”

Whereas I’d argue that they are both, and the mathematics tells us things about the ‘properties of the world [universe]’ which we can’t directly perceive with our senses – like ‘geodesics’ and the ‘curvature’ of spacetime. Yet they can be measured as well as calculated, which is why we know GR (Einstein’s general theory of relativity) works.

My approach to understanding physics, which may be misguided and would definitely be the wrong approach according to Nermin and Fernee, is to try and visualise the concepts that the maths describes. The concept of a geodesic is a good example. I’ve elaborated on this in another post, but I can remember doing Newtonian-based physics in high school, where gravity made no sense to me. I couldn’t understand why the force of gravity seemed to be self-adjusting so that the acceleration (g) was the same for all objects, irrespective of their mass.

It was only many years later, when I understood the concept of a geodesic using the principle of least action, that it all made sense. The objects don’t experience a force per se, but travel along the path of least action which is also the path of maximum relativistic time. (I’ve described this phenomenon elsewhere.) The point is that, in GR, mass is not in the equations (unlike Newton’s mathematical representation) and the force we all experience is from whatever it is that stops us falling, which could be a chair you’re sitting on or the Earth.

So, the abstract ‘geodesic’ explains what Newton couldn’t, even though Newton gave us the right answers for most purposes.

And this leads me to extend the discussion to include the New Scientist article. The author, Eric Schwitzgebel, ponders 3 areas of scientific inquiry: quantum mechanics (are there many worlds?); consciousness (is it innate in all matter?) and computer simulations (do we live in one?). I’ll address them in reverse order, because that’s easiest.

As Paul Davies pointed out in The Goldilocks Enigma, the so-called computer-simulation hypothesis is a variant on Intelligent Design. If you don’t believe in ID, you shouldn’t believe that the universe is a computer simulation, because some entity had to design it and produce the code.

'Is consciousness innate?' is the same as pansychism, as Schwitzgebel concurs, and I’d say there is no evidence for it, so not worth arguing about. Basically, I don’t want to waste time on these 2 questions, and, to be fair, Schwitzgebel’s not saying he’s an advocate for either of them.

Which brings me to QM, and that’s relevant. Schwitzbegel makes the point that all the scientific interpretations have bizarre or non-common-sensical qualities, of which MWI (many worlds interpretation) is just one. Its relevance to this discussion is that they are all reifications that are independent of the mathematics, because the mathematics doesn’t discern between them. And this gets to the nub of the issue for me. Most physicists would agree that physics, in a nutshell, is about creating mathematical models that are then tested by experimentation and observation, often using extremely high-tech, not-to-mention behemoth instruments, like the LHC and the James Webb telescope.

It needs to be pointed out that, without exception, all these mathematical models have limitations and, historically, some have led us astray. The most obvious being Ptolemy’s model of the solar system involving epicycles. String theory, with its 10 dimensions and 10^500 possible universes, is a potential modern-day contender, but we don’t really know.

Nevertheless, as I explained with my brief discourse on geodesics (above), there are occasions when the mathematics provides an insight we would otherwise be ignorant of.

Basically, I think what Schwitzgebel is really touching on is the boundary between philosophy and science, which I believe has always existed and is an essential dynamic, despite the fact that many scientists are dismissive of its role.

Returning to Nermin, it’s worth quoting his final passage.

Quantum mechanics has brought home to us the necessity of separating that irreducibly real experience from the remarkable, beautiful, and highly abstract super-structure we have found to tie it all together.

The ‘real experience’ includes the flow of time; the universality of now which requires memory for us to know it exists; the subjective experience of free will. All of these are considered ‘illusions’ by many scientists, not least Sabine Hossenfelder in her excellent book, Existential Physics. I tend to agree with another physicist, Richard Muller, that what this tells us is that there is a problem with our theories and not our reality.

In an attempt to reify QM with reality, I like the notion proposed by Freeman Dyson that it’s a mathematical model that describes the future. As he points out, it gives us probabilities, and it provides a logical reason why Feynman’s abstraction of an infinite number of ‘paths’ are never observed.

Curiously, Fernee provides tacit support for the idea that the so-called ‘measurement’ or ‘observation’ provides an ‘abstract’ distinction between past and future in physics, though he doesn’t use those specific words.

In quantum mechanics, the measurement hypothesis, which includes the collapse of the wave function, is an irreversible process. As we perceive the world through measurements, time will naturally seem irreversible to us.

Very similar to something Davies said in another context:

The very act of measurement breaks the time symmetry of quantum mechanics in a process sometimes described as the collapse of the wave function…. the rewind button is destroyed as soon as that measurement is made.

Lastly, I would like to mention magnetism, because, according to SR, it’s mathematically dependent on a moving electric charge. Only it’s not always, as this video explicates. You can get a magnetic field from electric spin, which is an abstraction, as no one suggests that electrons do physically spin, even though they produce measurable magnetic moments.

What most people don’t know is that our most common experience of a magnetic field, which is a bar magnet, is created purely by electron spin and not moving electrons.