Could time-travel subvert Fermi’s paradox?

It’s a little tongue-in-cheek, but I don’t find it totally out-of-the-question either. This post is a confluence of a few things, only two of which are mentioned in the title.

The best exposition of Fermi’s paradox I’ve come across, is by Prof Brian Cox. In fact, he provides a very good succinct definition in the first 2m of his video.

 

Notwithstanding the fact that there has been billions of years on billions of worlds for civilisations to arise, we see no evidence of any of them in the Galaxy at all. So the paradox is, Why?

 

He then uses the remaining 20+ minutes of the video, providing expositions on various reasons why this is the case. Firstly, he gives a history lesson, explaining how life on Earth took close to 4 billion years to evolve to its present state. He doesn’t mention that humans (homo sapiens) only arose in the last 3-400,000 years of that, so the last 0.01% or thereabouts, and it’s only in the last century of that 300k+ years that we developed very rudimentary extra-terrestrial space exploration capabilities (my point, not his). So a blink-of-an-eye in the context of our evolutionary history.

 

He goes on to give various scenarios why the Fermi paradox exists but the one most pertinent to this post (around 7m) is that the distance between worlds that could have the same properties as our solar system, in being able to create a stable environment over tens of billions of years for life to evolve, are at least thousands of lightyears away (in our galaxy), and therefore beyond the ability to travel here in the timeframe that such distances dictate. He points out that even the time required for receiving radio transmissions are commensurate with the distance to be traversed. Which is why searching for ‘artificial’ signals is the most efficient method to look for extra-terrestrial civilisations.

 

One of his best arguments involves Von Neumann machines or ‘replicators’, which are self-replicating robots, which could colonise a galaxy within 100s of millions of years (his estimate). He contends that the fact we’ve never seen any, is the best indicator we have that a spacefaring civilisation doesn’t exist in our galaxy.

 

I won’t elaborate on any of the other scenarios Cox expounds upon, but I recommend watching the full 23m, because it’s very stimulating and informative. He also talks about the ‘Great Filter’ (~10m), which is a scary yet totally plausible scenario, although not relevant to this post. Basically, he says that civilisations like us, who can create the technology for space-travel, also have the technology to destroy ourselves, and may lack the wisdom to do one over the other. In his own words, we’re brought undone by our ‘stupidity’.

 

His best argument he left to last, which I’ve reported on before, but based on Nick Lane’s excellent book, Life Ascending; The Ten Great Inventions of Evolution. Basically, Cox argues there was 4B years of life before complex life arose, and it’s such a rare possibility that maybe it’s never happened anywhere else. Note: this doesn’t rule out simple life being prolific throughout the galaxy. He cites John Barrow's and Frank Kipler’s book, The Anthropic Principle, which he explains, he grew up with, as supporting that particular view. I read that book and reference it here.

 

That took longer than I intended, so now I will address the other part of my question, which is time-travel. Another physicist, Jim Al-Khalili, who wrote an excellent book called Paradox (which I’ve read) has a video titled provocatively, Could I Travel Back in Time? where he explores various time-travel scenarios.

 

Naturally, he starts with the well known grandfather paradox, whereby you travel back in time to kill your grandfather before he met your grandmother, thus breaking the causal chain for your own existence. This idea was exploited in the original Terminator movie. In fact, it’s hard to talk about time-travel without referencing science fiction examples.

 

He then uses the scenario of having found instructions to build a time machine, actually builds it, which takes him 10 years, then travels back 10 years in time to drop the instructions on his desk. Al-Khalili points out a couple of issues: it defeats free will because if the scientist ‘chooses’ not to travel back in time, it can’t happen at all; and the instructions are never actually created in the first place, so causality is overturned. He also mentions the problem of having 2 versions of the scientist existing at the same time, therefore breaking the first law of thermodynamics: conservation of energy.

 

He then talks about how travelling into the future is physically possible according to Einstein’s theories of relativity, either by travelling close to the speed of light, as per the famous twin paradox thought experiment, or spending time in a strong gravitational field, as per the movie, Interstellar. A version of the last one, I’ve used in my own science fiction.

 

Al-Khalili draws a spacetime diagram showing the future and past light cones, which features strongly in my way of viewing this. But without getting ahead of myself, he points out that, according to GR (Einstein’s general theory of relativity), if you could curve spacetime strongly enough you could create a time-loop. In fact, this would be a feature of a rotating universe, as pointed out by Einstein’s friend, Kurt Godel, as well as a possibility for a rapidly spinning black hole. There is good reason to believe we don’t live in a rotating universe, but rotating black holes, one assumes, are quite common. Could one get stuck in a time-loop at the event horizon of a spinning black hole? I don’t know.

 

Al-Khalili cites Russian astrophysicist, Igor Novikov, who proposed his own rule, regarding CTCs (Closed-Timelike-Curves): ‘Only “logically self-consistent” solutions are allowed’.

 

Al-Khalili then introduces us to Dr Fabio Costa, who has published a paper where he talks about taking time-slices, where cause-and-effects create boundary conditions, which neither he nor Al-Khalili explain in detail. But Costa concludes by saying, “Nature is smart enough to prevent such paradoxes” (referring to the grandfather paradox, specifically). My takeaway, which admittedly is rather simplistic, even superficial, is that cause-and-effect is such a fundamental principle in physics, that any scenario that sidesteps it, needs to be treated with extreme caution. I should point out that there are scientists and philosophers (like Donald Hoffman) who think that causality, as a principle, is past its use-by date.

 

As Al-Khalili sums up, Fabio Costa argues that “time paradoxes disappear, not because they’re logically inconsistent, but because they’re physically not allowed.”

 

Al-Khalili also refers to the Many Worlds Interpretation (MWI) of quantum mechanics, as providing another loophole, for want of a better expression, to allow time-travel without creating paradoxes. In fact, this is the scenario invoked in the Back to the Future movie franchise. When Marty McFly goes back to the past and intervenes, he subsequently finds himself in a different universe when he returns to the present. Al-Khalili explains how this resolves the grandfather paradox very neatly (similar to the Marty McFly scenario), but like me, he has issues with MWI as a reality.

 

Lastly, Al-Khalili talks to Dr Lorenzo Gavassino at the Department of Mathematics, Vanderbilt University, Nashville, Tennessee, who took a serious look at the Groundhog Day scenario, but proposes that the individual was in a closed box that underwent a time loop. Specifically, he looked at how this is impacted by the 2^nd Law of Thermodynamics or entropy, because when the individual went back in time their entropy would decrease and their memories would be erased. Again, I might be simplifying it for the sake of explication, but it’s what I expect a time loop would create. The way Gavassino describes it, including his literal handwaving, the time loop has 2 nodes, where at one node the entropy is at its lowest and at the other node, entropy is highest. And effectively, the individual oscillates between these two extremes.

 

Right at the end, Al-Khalili makes the point that I’ve heard before, which is that if someone did invent a time machine, it could never go back to earlier than the time it was invented, which is why we’ve never seen one.

 

Again, I spent much longer on this than I intended but I’m now going to reference yet another video that talks about the edge of time for the entire universe. In essence, I’m going to discuss a video by Curt Jaimungal who discusses an aspect of Einstein’s GR that I’d never heard about before. Curt often discusses very esoteric topics, but I’m confident he knows what he’s talking about, because I’ve seen him hold his own with such luminaries as Stephen Wolfram, Gregory Chaitin, Sir Roger Penrose and Sabine Hossenfelder. In fact, I watched a 2hr video conversation he had with her after he sent me a link, and they were very chatty and friendly.

 

I had to watch this more than once to get my head around it, and I’ll rely heavily on quotes to get my points across. As a side-issue, he addresses a conundrum I’ve raised many times before, which is that the Universe has an edge in time, but not space (as best we can tell), yet relativity theory tells us that there is no universal now. I’ll get to that, but first I’ll address what the video is primarily about.

 

What the video is about, contrary to what everyone seems to believe, including Einstein himself, based on what I know, is that his GR equations don’t provide for a deterministic universe at the very limit or edge of the Universe in time. In fact, Curt contends that it is even less deterministic than quantum mechanics with an infinity of possibilities. At one point, he quips, “God does not even play dice, He just shrugs.”

 

But what I want to focus on, is what Curt calls a ‘Cauchy surface,’ which, if I understand him correctly, is the hypersurface that we are all familiar with in the spacetime diagram that Al-Khalili referred to in his video, which also shows the past and future light cones for any observer at time, t.

Significantly, Curt distinguishes between local determinism and global determinism, because he argues that GR allows for one and not the other, and this is also relevant to determining what ‘now’ means. Significantly, global determinism "determines the future of the entire universe", whereas local determinism refers to "what happens in the immediate future of that region [of space]".

 

Curt defines a ‘Cauchy surface’ as “a spacelike slice, that every causal curve hits exactly once.” He emphasises this with beats of his hand for every single word. An obvious consequence of this is that there can be no time loops.

 

He then asks the obvious question: can you extrapolate local determinism to global determinism? His answer is very informative in that he contends that in flat spacetime this is ‘trivial’ because you can, but not in curved spacetime, which is what GR describes. I think this is also relevant in attempting to understand what a universal now means.

 

In fact, Curt says, specifically, “There are solutions to the field equations of Einstein [in GR] where you literally can’t define a moment of time across the entire universe.” He then emphasises the point, by saying: “In general relativity, there may not be a way to slice spacetime in all of space at time t.” Note, this is a consequence of spacetime curvature and not SR (special theory of relativity) as most arguments claim.

 

And there’s a term for this, which is ‘global hyperbolicity’, and that’s where he introduces his definition of a Cauchy surface which I referenced earlier. So the spacelike slice where every ‘causal curve’ only crosses once, applies to the entire universe.

 

Then, in an apparent contradiction to what he told us before, he says “the Cauchy surface is like a snapshot of the universe at one time.” He then emphasises again that “every world line [for a particle] and every light ray; they all cross the surface exactly once.” He then says, “This is what even allows you to say, the state of the Universe at time t.” And I think this is the closest you will get to the idea of a universal now. But there is a caveat, which is that “not all solutions to Einstein’s equations are globally hyperbolic.”

 

He then provides examples which mostly include black holes, including rotating black holes, which I mentioned in reference to Al-Khalili’s video. He also mentions Godel’s rotating universe, which I think we can confidently say, we don’t inhabit.

 

Curt has an understanding of this topic that makes me realise how little I really know. What I do know is that clocks measure time at different rates depending on gravity, so if you happened to live near a black hole, you would measure the age of the Universe as younger than someone on Earth, so you would axiomatically get a different t.

 

What Curt doesn’t describe is the possibility that there is a wavefunction for the entire universe, which some scientists believe (like Sean Carroll, for example), and, if it describes the future, as Freeman Dyson believed, then maybe entanglement provides an edge in time for the entire universe. But I’m speculating way beyond the limits of my knowledge.

 

This post has already become too long with detours down various rabbit holes, but there is one more video I want to reference, which has specific relevance to the title.

 

I grew up in a small rural town in Australia, and I’m old enough to remember when TV arrived, though we didn’t own a set until I was 16. The saving grace for me were books, including both the primary school and high school libraries, which I devoured. So it was around 16 years of age that I read a book called The Truth About Flying Saucers by Aime Michel, first published in 1956 (I looked it up), and I admit to being profoundly influenced by it. (I’m not sure you’d find a book on flying saucers in a modern high school in Australia.) It so happened that I had a science teacher who was also interested in UFOs – he was a very good science teacher, by the way, and I’m not the only one who would say that.

 

I’ve since become more sceptical about the whole UFO scene, as I’ve developed what I believe is a healthy scepticism towards conspiracy theories of any ilk. So it’s in that context that I reference an episode of Australian Story on ABC TV, where a group of people from a small town in Australia recollect a particular ‘incident’ from their childhood, involving phenomena that couldn’t be explained at the time, or even now.

 

When I watched this and listened to their testimony, I thought that one explanation, which is even more out-there than the possibility of visitors from outer space, is the possibility that some ultra-advanced technological species has learned how to travel through time from the future. Perhaps only a sci-fi writer would even consider that.

 

But there is another possibility, which I thought of when I watched Brian Cox’s video. If you look at the spacetime diagram depicting past and future light cones, it’s obvious that most of the events in the so-called ‘observable’ universe are ‘unobservable.’ It’s possible, therefore, that there are civilisations billions of light years away, who have developed technologies that exceed ours, which we can’t possibly know about using radio waves, Von Neumann machines or whatever. Unless, that is, they’ve developed the technology to travel through time as well as space.

 

The thing is that if someone (or some object) was able to visit us from outside our past or future light cones, it wouldn’t create a causal loop, unlike all the examples that Al-Khalili provided in his video (except MWI).

 

My conjecture, if I can call it that, which is admittedly more sci-fi than science reality, is: What if a technologically advanced enough extra-terrestrial species developed the ability to ride the hyperplane on the Cauchy surface, while avoiding black holes, and was able to visit our world line? As Brian Cox said at the end of his video, a scientist has to be able to admit they’re wrong, but it would require a visitor in a flying saucer to convince him.

 

Footnote: The last video I referenced, Australian Story, is very good reporting, and I recommend you watch it so you can make your own judgement.

Should you believe me?

Note how prefacing the question with ‘why’ would change its focus if not its intent. I’ll return to this point at the end. I was originally going to write a post on time travel and UFOs, but I got sidetracked in my 'research'. In particular, I watched a talk given by famous sceptic, Michael Shermer (executive director of The Skeptics Society) and I remember reading his column in Scientific American in the 70s or 80s when I was a regular reader. He’s only slightly younger than me.

 

He gives a number of challenges in his talk, which are insightful in themselves, and I would gladly take them up. Basically, he’s making the point that when you challenge someone to explain why they believe something, they mostly can’t. He gives the examples of climate change and evolution, which he says are positions based on political beliefs rather than whether or not they understand the science behind them. I fall into this category, even though I’ve read books and accounts on these topics that most people wouldn’t bother, despite holding very passionate views on them.

 

Regarding evolutionary theory, I’d recommend Nick Lane’s excellent book, Life Ascending; The Ten Great Inventions of Evolution, which I’ve written about before. But I have another argument, which I’ve also presented before. Since Darwin and Wallace independently proposed their theories of evolution by natural selection over 160 years ago (1859 to be precise), we’ve made extraordinary discoveries that they could never have dreamed about, specifically in palaeontology and genetics. But here’s the thing: all the evidence discovered in the interim is not neutral; what has proven them right could just as readily have proven them wrong.

 

Regarding anthropomorphic climate change, I know of the role of greenhouse gases like carbon dioxide (CO2) and methane, without knowing the details, and I know that ultimately it’s caused by the difference in heat that can escape our atmosphere and the heat that’s trapped, which can’t be measured directly. However, NASA has data that is publicly available on their website, which combines historical ice-core data with atmospheric data collected at Mauna Loa in Hawaii, and they show how the 2 sources of data are complementary and seamlessly connected.

 

But I have a subsidiary argument, which is that we need to trust the expertise of people who work in climatology, because the rest of us don’t have it. I learned this from spending over 4 decades in engineering, where I constantly relied on expertise by people in various fields from structural and civil engineering to architecture to mechanical and electrical engineering to process engineering to software design and automation. The problem is, with the internet, you can always find an ‘expert’ to provide the evidence that supports your view, which was very prominently exhibited during the not-so-recent COVID pandemic.

 

But, in the case of climate change, nearly all the arguments I’ve come across (that question it) are that it’s a hoax and/or a global conspiracy to keep climatologists in a job. I admit I don’t take those arguments seriously. However, there is someone I know who was a geologist and had spent a very successful career in mining, who put up a technical argument based on the tonnes of CO2 in the atmosphere and how, as a percentage, it contradicted the official reporting, including that provided by NASA. NASA’s data is in ppm (parts per million), and I pointed out that to convert the weight into ppm you had to allow for the molecular weight of CO2, which brings it back in line with the reported results. He knew I was right and he didn't respond. But as Shermer would have pointed out, he was on the Right of politics and I’m on the Left, which axiomatically creates the divide. I’ve long argued that climate change should never have been politicised. But having said that, you’ll find people on the other side of the argument who will say exactly the same thing.

 

Shermer added a couple of other challenges to demonstrate how much we don’t know or take for granted. He asked, ‘Can you explain how a zipper works?’ No, but I can draw a diagram. Engineers often draw a picture when explaining something. He also asked, ‘Can you draw a bicycle?’ and explained how many people get it wrong. Well, actually, I can. I stopped the video to prove it to myself, though I had to raise the handlebars when I finished it. Mind you, I started drawing before I could write.

 

However, Shermer made me question myself, which is why I’m writing this post. You see I write about topics where I’m not an expert, specifically physics and cosmology. I’m not even a proper philosopher – I don’t even have a degree let alone a PhD. My only defence is that I’m well read and pay attention to people who know a lot more than me, even if I disagree with them. And what I’ve found from watching panel discussions on YouTube is that even experts can’t agree.

 

To give an example, I watched a panel discussion between 2 prominent philosophers of science and a theoretical physicist: Tim Maudlin, Hilary Lawson and Sabine Hossenfelder respectively; on whether there are particles or fields. Tim Maudlin appeared to be the odd one out, yet I found I was more in agreement with him, which might just be a reflection of my own ignorance. Basically, he argued that the ‘field’ in quantum mechanics is the wavefunction of the particle which doesn’t even exist in spacetime (it exists in Hilbert space with potentially infinite dimensions) and can’t be measured. It’s possible that Lawson and Hossenfelder were talking about something different – I don’t know enough to comment – but Hossenfelder said you can have different mathematical models that describe the same phenomenon. Maudlin quoted John Bell as saying we effectively don’t have a particle until it creates a spot on a screen or a photographic emulsion. Which is why I think it exists in the past and the wavefunction exists in the future, compatible with Freeman Dyson’s viewpoint.

 

Speaking of Bell, I watched another video with Neil deGrasse Tyson talking to Jana Levin about entanglement which is one of the best discussions I’ve seen on the topic. The point that I think needs to be emphasised is that entanglement introduces instantaneity, which to me, only makes sense if there is a universal 'now'. Tyson focused the discussion on the ramifications for cryptology, where they both agreed that it can’t be used to send a message faster-than-light, though I do it in my science fiction (I readily acknowledge I break the known laws of physics in my sci-fi).

 

I think there is an inherent contradiction or conundrum in physics and cosmology that the Universe has an edge in time but not space, whereas relativity theory tells us there is only spacetime (they are not separate) and ‘now’ is a purely subjective experience – there is no universal, objective now. This has led to physicists arguing that our experience of time ‘flowing’ is an illusion. Paul Davies believes that this experience will ultimately be 'explained by neuroscience, not physics'. Sabine Hossenfelder argues that there is no ‘now’ – it’s an illusion. Everyone knows that I greatly admire both of these scientists, both of whom know a lot more than me, yet I also think that postulating something that’s so outside our everyday experience, requires better explanations than we currently have. To me, it’s a sign that there is something wrong with our current theories rather than a sign that we all suffer from the same illusion that there is a past, present and future.

 

Getting back to Shermer and the role of expertise (though he doesn’t mention it, but I do): what I’ve found is that if you watch a discussion on a topic like evolution or climate change, especially when it’s combative, and you have someone present who is more knowledgeable and more experienced, they will invariably win the argument. And to extend that to my position, I imagine that if I was to have a discussion with Sabine, she would win hands down, and I would have to defer to her greater expertise, while not necessarily agreeing with her.

 

I once wrote a post where I critiqued her position on determinism and free will. It so happened I referenced this post to someone I met online, and to my surprise they said it was ‘very balanced’. I didn’t think it was balanced at all, given my prejudices, but I took it as a compliment.

 

So, addressing the question at the head of this post, the answer is, No. You shouldn’t simply believe what I say or argue; instead, you should do your own research and draw your own conclusions.

Mathematics, language and reality

I recently read an online article with Quanta Magazine, titled How Writing Changes Mathematical Thought, featuring David E Dunning, ‘a historian of mathematics at the Smithsonian’s National Museum of American History’, who was interviewed by John Pavlus.

 

In particular, Dunning pointed out how the notation we use affects the way we explore mathematics and even comprehend it. The most significant innovation was the introduction of Hindu-Arabic numerals, along with its corresponding arithmetic, which we owe to Fibonacci (of Fibonacci numbers fame) in the 12^th Century. Tibees gives a good summary in this short video. The thing is that we would really struggle to do modern mathematics using Roman numerals, and it would be impossible for computers.

 

Dunning gives the example of the difference between Newton’s and Leibniz’s notation for calculus and how “Leibniz’s calculus got used a lot more in continental Europe, and it just grew and was fertile in a way that Newton’s wasn’t.” Which is why we all use Leibniz’s notation today.

 

But there is a more fundamental point, I believe, that Dunning doesn’t discuss. And that is the Wittgensteinian (new word) principle that the language we use limits what we can think about, because we all think in a language. And also, it’s the language of mathematics that I believe resolves the argument going back to Plato and Aristotle, whether mathematics is invented or discovered. On that last point, we invent the language but the relationships that the language describes are discovered. I contend there is a tendency to conflate the language of mathematics with mathematical formulations, because we learn them in tandem.

 

I pointed out in a much earlier post that there is also a tendency to treat mathematics as just another language, like the ones we think in, which takes the conflation I mention above to another level. The fact is that we still use the language we think in to describe mathematical notation and relationships. In other words, we absorb the language we use to do mathematics into our thinking language as a subset thereof. And this brings me back to Wittgenstein’s point, because we keep expanding our language to capture new concepts and ideas, otherwise we cognitively stagnate. And I see mathematical language as such an expansion, otherwise we can’t understand the concepts it’s describing. And perhaps this is why so many people struggle with mathematics in school, but that’s another topic.

 

One of Pavlus’s questions was: Why don’t we teach people to do math with, say, a more pictorial or visual kind of notation?

 

This is what led Dunning to talk about Newton’s and Leibniz’s respective calculus notation, but it got me thinking in a different direction.

 

Specifically, how we are visual creatures, and how I try to visualise mathematical concepts as much as possible. A graph can tell you so much more than the written equation can, and makes some concepts very easy to grasp. The best example that most people would be familiar with is a sine wave. You can see where the wave is zero and where it’s 1 and -1, and everything in between, and how it cycles in periods of 2π radians. It also shows just by looking at the graph how the cosine of an angle is 90 degrees (π/2 radians) out of phase with the corresponding sine wave, just by depicting them on the same graph.

 

Another example most of us are familiar with is a parabola being the graphical representation of a quadratic equation. The zeros (or square roots) are where the graph crosses the x axis, which can’t be greater than 2, so can have 2 square roots. However, you can have one square root if the parabola kisses the x axis and no roots if it doesn’t touch it. Though we all know we can have imaginary roots (√-1), but you need another graph which includes an imaginary axis along with the real axis.

 

In fact, complex algebra is a lot easier to understand if it’s depicted graphically. I’m a little annoyed that it wasn’t taught to me that way when I first encountered it. By depicting it on an Argand diagram, where the imaginary (i) axis replaces the y axis in a Cartesian diagram, and using polar co-ordinates, you can see how multiplication requires adding the angles, and multiplying a complex number by i means rotating everything anticlockwise by 90 degrees.

 

Even esoteric topics like Riemann’s hypothesis becomes amenable to comprehension by mortals when it’s demonstrated graphically, as this video demonstrates quite effectively.

 

Calculus is taught using graphs: the tangent of a curve being found by differentiation and the area under a curve being found by integration. Why one is the inverse function of the other, I’m not sure anyone can tell you. Differential calculus allows one to grasp the concept of instantaneity, which doesn’t physically exist, but it’s an idealism that is more than useful. Likewise, it’s almost incomprehensible that an infinite number of infinitesimal strips can give you a finite area under a curve, but it works. Calculus is like magic.

 

But I extend this visualisation into physics, where everything is depicted in the language of mathematics.

 

I never understood Einstein’s General Theory of Relativity (GR), which is a theory of gravity, until I grasped the concept of a geodesic, which can be visualised. And I can thank Richard Feynman for explaining it relatively succinctly, including mathematical formulations, in his excellent book, Six Not-So-Easy Pieces. A geodesic is the shortest distance between 2 points, and on a sphere, it’s always a great circle. Intercontinental aircraft fly along geodesics for that very reason, though they appear curved when the map is projected onto a flat surface.

 

But here’s the thing, as pointed out by Feynman: “In a uniform gravitational field the trajectory with maximum proper time for a fixed elapsed time is a parabola.” I’ll describe what he means by ‘maximum proper time’ in a moment, because that’s the key to understanding it. But we all learned that a projectile travels through the air following a parabolic curve in high school physics, without knowing anything about GR. We did it using Newton’s equations. But Einstein gives us the same result, assuming the object is not travelling at relativistic speeds.

 

And here’s why, again quoting Feynman: An object always moves from one place to another so that a clock carried on it gives a longer time than any other trajectory (italics in the original). In his words, The time measured by a moving clock is called its “proper time” (τ). In free fall, the trajectory makes the proper time of an object a maximum. And that’s what’s called a geodesic in GR.

 

And that paragraph allowed me to finally comprehend General Relativity. Any deviation of an object from free fall in a gravitational field (from its geodesic), and remember there is a gravitational field everywhere in the Universe, means its clock will slow down which is what SR (special theory of relativity) tells us. I’ve always believed that SR is dependent on GR and not the other way round, and Feynman indirectly confirmed this for me.

 

But visualisations can be misleading, and I think the wavefunction (Ψ) in Schrodinger’s equation is a case-in-point, because it’s not a physical wave. It exists in Hilbert space which, in principle, can have infinite dimensions. There is another way of expressing the same quantum mechanical (QM) phenomena and that is with Heisenberg’s matrix formulation. In fact, Heisenberg’s formulation preceded Schrodinger’s but they are mathematically equivalent. And this brings me back to Dunning’s point that the language we mathematically express something in, will give an intuitively different picture.

 

I recently read an article on Heisenberg’s revolutionary discoveries in Philosophy Now (Issue 172, Feb/Mar 2026, by Dr Kanan Purkayastha), which made the point that ‘Heisenberg attempted to calculate the behaviour of electrons around atoms using quantities we can observe’, so basically an epistemological approach. On the other hand, Schrodinger started with a principle postulated by De Broglie that an electron’s momentum could be formulated as a wave, similar to a photon, which I would call an ontological approach. Philip Ball in his book, Beyond Weird, made a similar point: that Heisenberg’s matrix approach is ‘epistemic’ and Schrodinger’s wave function approach is ‘ontic’ (his terms).

 

Many people originally thought that the famous Heisenberg Uncertainty Principle was an epistemological one, including Einstein, who said it was “just an expression of the limits of what can be determined by measurements. Or in philosophers’ terms, the nature of uncertainty would be an epistemic one.”

 

However, it falls out of Schrodinger’s equation by using a Fourier transform, so it is a mathematical restraint, not just a physical one. Schrodinger’s wavefunction also entails superposition and entanglement, which led Schrodinger to state that entanglement is the defining feature of quantum mechanics, meaning it’s what separates it from classical physics. The other thing about Schrodinger’s equation is that it can only give us probabilities, and following an observation, it no longer applies. This leads me to argue that the wavefunction exists in the future; as far as I know, an idea not shared by anyone else except Freeman Dyson (who is no longer with us).

 

Probabilities were the subject of a recent post, but the thing is we only apply probabilities to things that are yet to happen. After something has happened its probability is no longer relevant; it effectively becomes 1. And this is what happens in QM, as described above. To quote from another online article by Phys Org:

The results showed that the photon's physical presence was distributed across both paths simultaneously, demonstrating that the particle is truly delocalized until a detector forces it into a single location.

 

This is identical to a description provided by Alain Aspect that I reported in a not-so-recent post. But, as Freeman Dyson explains, it corresponds to a change in perspective by the observer from the future to the past, which occurs at the time of ‘detection’.

 

I’d like to make a point about the fact that probabilities exist, not only in QM but classical physics – after all, the entire gambling industry is based on probabilities. I contend that it means the Universe is not deterministic. Simplistic, yes, but I can’t think of a better argument. It’s also my argument against claims of so-called prophecy. You either believe in free will or you believe in prophecy, but you can’t believe in both.

 

I could imagine having a discussion (argument) with a physicist on this issue, where they claim that probabilities are a statistical outcome, as a consequence of what we cannot know. Therefore, the outcome of a coin toss, for example, could be deterministic and the probability is a consequence of our ignorance, not the event. In fact, I had this discussion (over coin tosses) with physicist, Mark John Fernee (Qld Uni). Chaos theory mathematically ensures it can never be known definitively, which is an epistemological argument. However, I argue that chaos occurs ontologically as well, and that the entire universe’s evolvement is dependent on this principle.

 

Just as in the case with Heisenberg’s Uncertainty Principle and people thinking it was a consequence of what we can't physically measure, many physicists argue that chaos theory is a consequence of our limitations of observation. However, I argue that in both cases, the limitation is built into the mathematics, which makes it a feature of the Universe.

 

So, I’ve gone way off track, but while we need a language to understand and express the mathematics we discover, nature is already determined by the rules that mathematics dictates.