Beliefs, prejudices and theories; where is truth?

 During COVID, New Scientist started doing a lot of online events, including courses and ‘talks’ by experts in various fields. I watched one of these talks last week by Claudia De Rahm titled What We Don’t Know About Gravity, which I thought was very good. It was informative and thought-provoking and therefore deserves special mention. Claudia is a young woman, Professor of Physics at Imperial College London, with a distinct Italian accent. She gestures a lot while she’s talking and exudes passion. Sometimes her face appeared childlike, especially at the end when she conveyed her appreciation to the presenter, Martin Davies. She’s won a number of awards and she’s done research in particle physics, gravity and cosmology.

 

One of the first things she told us is that Einstein’s GR (general theory of relativity) comes with its own ‘proof’ of its limitations. She didn’t use the word proof, but she demonstrated what she meant. If one tries to apply QM to Einstein’s mathematical theory you get probabilities of over 100%. I never knew this, but I found it a remarkable revelation. From what I could gather, it happens near the Planck scale where the curvature of spacetime becomes so large the physics breaks down. She pointed out that this doesn’t occur near the event horizon of a black hole, so for everything we can observe, GR is perfectly valid. But I was astounded to learn that GR predicts its own failure at certain scales of the Universe.

 

She also questioned whether GR breaks down at the other extreme of scale, given that there is disagreement on how fast the Universe is expanding to a significant degree (in her own words, ‘the chance of it being a fluke is 1 part in 14,000’). Of course, she also explained how 95% of the Universe is ‘missing’, meaning it can’t be accounted for. Personally, I think we’re ripe for another scientific revolution comparable to the one that occurred 100 years ago, which in turn was comparable to the one created by Copernicus, Galileo, Kepler and Newton.

 

This highlights a point I’ve raised before: the significance of scale in determining which ‘natural laws’ dominate, though they all seem to obey a Lagrangian (based on my limited knowledge of physics). Roger Penrose argues that scale is dependent on mass. If the Universe was all radiation then scale becomes irrelevant. This is essential for his CCC (Conformal Cyclic Cosmology) model of the Universe to work. Penrose also argues that there is no time without mass, because time is always zero for a photon. This creates a paradox, because the photon has an energy dependent on its frequency, which has no meaning without time. I’ve no doubt Penrose can resolve that, but I don’t know how. Perhaps gravity resolves that conundrum. But, as the Universe exists in its current epoch within our range of observations, scale plays a significant, even critical role in determining which mathematical formulations we use to model it.

 

Claudia tip-toed around the argument about whether gravity is a force or not, but gave me the impression she believes it isn’t. She did point out that a gravitational wave effectively creates a force and there are tidal forces, but this is not what people mean when they argue that there is a ‘force of gravity’ in the Newtonian sense. In answer to a question at the end, she pointed out that “gravity is related to the very structure of spacetime; you can never switch it off”.

 

On the subject of GR’s inherent limitations around a singularity inside a black hole, she seemed optimistic that new physics would overcome this eventually. Along with the questions around dark energy and dark matter, that comprise 70% and 25% of the Universe respectively, I think that only a revolution in physics and cosmology will rescue it. Towards the end of the talk, she put up a slide showing all the current theories in the running, without discussing any of them or mentioning any personal favourites she might have. She literally covered the screen with balloons of speculative ideas, demonstrating the burgeoning interest in this field.

 

And this segues into something else she said in answer to a question, where someone asked if all the current theories should be ‘thrown in the rubbish bin’ and replaced with something completely different. She pointed out that the current theories work extremely well, and whatever you replace them with has to, at the very least, account for what we already ‘know’, and you can’t just ‘throw them in the rubbish bin’. This touches on the subject of my last post where people sometimes argue that we really don’t ‘know’ anything and we only have 'beliefs'. In science, all theories have limitations. Truth is cumulative in science; just because we don’t know everything, it doesn’t mean that what we do know is wrong and should be thrown out. Personally, I don’t think there will ever be a TOE (theory of everything) simply because there’s never been one in the past, and people have always ‘believed’ that we know almost everything, which history has proved, repeatedly, is untrue.

 

And this brings me to the subject of pet theories or pet prejudices. If Claudia has her own pet theories she didn’t elaborate, yet I’m sure she has. People much smarter than me have their pet prejudices, some of which differ dramatically, so they can’t all be right, and that also applies to me. But, having said that, I like to think my prejudices are well informed and I acknowledge those who share them, and sometimes those who don’t.

 

I will quickly talk about one that is relevant and that is time. I contend that consciousness exists in a constant present, while everything we observe has already happened, which is why we ‘feel’ like we’re travelling through time. According to relativity theory, we are travelling through time just by standing still. But when we move, we start travelling through space and, as a consequence, we travel through time more slowly – that is, time slows down. In fact, if we could travel through space at the speed of light, we would stop travelling through time altogether. But here’s the thing: that’s only true in our specific frame of reference. There could be another frame of reference, like the horizon of the observable universe where space itself travels at the speed of light. I discussed this in another post.

 

This infers that everything travels through time and not just consciousness. However, while our consciousness remains in a constant present, our thoughts don’t. Our thoughts become memories as soon as we think them, otherwise we wouldn’t even know we think. Consciousness exists on the edge of time and so does the universe itself. I’ve no reason to believe that the edge of time we all experience isn’t concordant with the edge of time for the whole Cosmos. This is considered naive thinking, but it’s one of my pet prejudices.

Symptoms of living in a post-truth world

 I recently had 2 arguments with different people, who took extreme positions on what we mean by truth. One argued that there is no difference between mathematical truths and truths in fiction – in fact, he described mathematics, that is not being ‘applied’, as ‘mathematical fiction’. The other argued that there is no objective truth and everything we claim to know are only ‘beliefs’, including mathematics. When I told her that I know there will always be mathematics that remain unknown, she responded that I ‘believe I know’. I thought that was an oxymoron, but I let it go. The trivial example, that there are an infinite number of primes or an infinite number of digits in pi, should put that to rest, or so one would think. 

Norman Wildberger, whom I’ve cited before, says that he doesn’t ‘believe’ in Real numbers, and neither does he believe in infinity, and he provides compelling arguments. But I feel that he’s redefining what we mean by mathematics, because his sole criterion is that it can be computed. Meanwhile, we have a theorem by Gregory Chaitin who contends that there are infinitely more incomputable Real numbers than computable Real numbers. People will say that mathematics is an abstract product of the mind, so who cares. But, as Paul Davies says, ‘mathematics works’, and it works so well that we can comprehend the Universe from the cosmic scale to the infinitesimal. 

 

Both of my interlocutors, I should point out, were highly intelligent, well-educated and very articulate, and I believe that they really believed in what they were saying. But, if there is no objective truth, then there are no 'true or false' questions that can be answered. To take the example I’ve already mentioned, it’s either true or false that we can’t know everything in mathematics. And if it’s false, then we must know everything. But my interlocutor would say that I claimed we’d never know and I can’t say I know that for sure. 

 

Well, putting aside the trivial example of infinity, there are proofs based on logic that says it’s true and that’s good enough for me. She claimed that logic can be wrong if the inputs are wrong, which is correct. In mathematics, this is dependent on axioms, and mathematics like all other sciences never stands still, so we keep getting new axioms. But it’s the nature of science that it builds on what went before, and, if it’s all ‘belief’, then it’s a house built on sand. And if it's a house built on sand, then all the electronic gadgets we use and the satellite systems we depend on could all crash without warning, but no one really believes that.

 

So that’s one side of the debate and the other side is that truths in art have the same status as truths in science. There are a couple of arguments one can use to counter this, the most obvious being that a work of art, like Beethoven’s 5^th, is unique – no one else created that. But Pythagoras’s theorem could have been discovered by anyone, and in fact, it was discovered by the Chinese some 500 years before Pythagoras. I write fiction, and while I borrow tropes and themes and even plot devices from others, I contend that my stories are unique and so are the characters I create. In fact, my stories are so unique, that they don’t even resemble each other, as at least one reader has told me.

 

But there is another argument and that involves memes, which are cultural ideas, for want of a better definition, that persist and propagate. Now, some argue that virtually everything is a meme, including scientific theories and mathematical theorems. But there is a difference. Cultural memes are successful because they outlive their counterparts, but scientific theories and mathematical theorems outlive their counterparts because they are successful. And that’s a fundamental distinction between truth in mathematics and science, and truth in art.

Addendum: I just came across this video (only posted yesterday) and it’s very apposite to this post. It’s about something called Zero Knowledge Proof, and it effectively proves if someone is lying or not. It’s relevance to my essay is that it applies to true or false questions. You can tell if someone is telling the truth without actually knowing what that truth is. Apparently, it’s used algorithmically as part of blockchain for bitcoin transactions.

 

To give the example that Jade provides in her video, if someone claims that they have a proof of Riemann’s hypothesis, you can tell if they’re lying or not without them having to reveal the actual proof. That’s a very powerful tool, and, as a consequence, it virtually guarantees that a mathematical truth exists for a true or false proposition; in this hypothetical case, Riemann’s hypothesis, because it’s either true or false by definition.

Our eternal fascination with Light and Dark

 Someone on FaceBook posted one of those inane questions: If you could delete one thing in the world what would it be? Obvious answers included war, hate, evil, and the like; so negative emotive states and consequences. My answer was, ‘Be careful what you wish for’.

What I find interesting about this whole issue is the vicarious relationship we have with the ‘dark side’ through the lens of fiction. If one thinks about it, it starts early with fairy tales and Bible stories. Nightmares are common in our childhood where one wakes up and is too scared to go back to sleep. Fear is an emotion we become familiar with early in our lives; I doubt that I was an exception, but it seems to me that everyone tries to keep children innocent these days. I don’t have children, so I might have it wrong.

 

Light and dark exists in the real world, but we try to keep it to the world of fiction – it’s a universal theme found in operas, mythologies and TV serials. I write fiction and I’m no exception. If there was no dark in my stories, they’d have no appeal. You have to have nemeses, figures of various shades of grey to juxtapose the figures of light, even if the light shines through flawed, imperfect glass.

 

In life we are tested, and we judge ourselves accordingly. Sometimes we pass and sometimes we fail. The same thing happens with characters in fiction. When we read a story we become actors, which makes us wonder how we’d behave in the same situation. I contend that the same thing happens in dreams. As an adult, I’ve always seen dreams as what-if scenarios and it’s the same with stories. I’ve long argued that the language of stories is the language of dreams and I think the connection is even stronger than that. I’m not surprised that storytellers will tell you that they dream a lot.

 

In the Judaeo-Christian religion I grew up with, good and evil were stark contrasts, like black and white. You have God, Christ and Satan. When I got older, I thought it a bit perverse that one feared God as much as Satan, which led me to the conclusion that they weren’t really that different. It’s Christ who is the good guy, willing to forgive the people who hate him and want him dead. I’m talking about them as fictional characters, not real people. I’m sure Jesus was a real person but we only have the myth by which to judge him.

 

The only reason I bring all this up, is because they were the template we were given. But fearing someone you are meant to love leads to neurosis, as I learned the hard way. A lot of people of my generation brought up the next generation as atheists, which is not surprising. The idea of a judgemental, schizophrenic father was past its use-by-date.

 

There is currently a conflict in Ukraine, which has grabbed the world’s attention in a way that other wars have not. It’s partly because of our Euro-centric perspective, and the fact that the 2 biggest and world-changing conflicts of the 20^th Century both started in Europe. And the second one, in particular, has similarities, given it started with a dictator invading a neighbour, when he thought the world would look the other way.

 

There is a fundamental flaw in the human psyche that we’ve seen repeated throughout history. We have a tendency to follow charismatic narcissistic leaders, when you think we should know better. They create an army (not necessarily military) of supporters, but for whom they have utter contempt. This was true of Hitler, but also true of Trump and Putin.

 

Ukraine’s leader, Volodymyr Zelenskyy, like Trump, became a TV celebrity, but in a different vein. He was a satirical comedian who sent up the country’s leader, who was a Russian stooge, and then ran for office where he won by 70%. I believe this is the real reason that Putin wants to bring him down. If he’d done the same thing in Russia, he would have been assassinated while still a TV personality. It’s well known that Putin has attempted to assassinate him at least twice since the invasion, but assassinating opponents in a foreign country is a Putin specialty.

 

Zelenskyy and Putin represent, in many Western people’s minds, a modern day parable of good and evil. And, to me, the difference is stark. Putin, like all narcissists, only cares about himself, not the generals that have died in his war, not the barely out of school conscripts he’s sent into battle and certainly not the Russian people who will suffer enormous deprivations if this continues for any length of time. On the other hand, Zelenskyy doesn’t care about his self-preservation, because he would rather die for a principle than live the rest of his life in shame for deserting his country when it needed him most. Zelenskyy is like the fictional hero we believe in but know we couldn’t emulate.

 

It's when we read or watch fiction that the difference between right and wrong seems obvious. We often find ourselves telling a character, ‘don’t do that, don’t make that decision’, because we can see the consequences, but, in real life, we often seem to lose that compass.

 

My father was in a war and I know from what he told me that he didn’t lose that particular compass, but I also know that he once threatened to kill someone who was stealing from the wounded he was caring for. And I’ve no doubt he would have acted on it. So his compass got a bit bent, because he’d already seen enough killing to last several lifetimes.

 

I’ve noticed a theme in my own writing, which is subconscious, not intentional, and that is my protagonists invariably have their loyalty tested and it ends up defining them. My villains are mostly self-serving autocrats who have a hierarchical view of humanity where they logically belong at the top.

 

This is a meandering post, with no conclusion. We each of us have ambitions and desires and flaws. Few of us are ever really tested, so we make assumptions based on what we like to believe. I like something that Socrates said, who’d also been in battle.

 

To live with honour in this world, actually be what you try to appear to be.

What is existentialism?

 A few years back, I wrote a ‘vanity piece’, My philosophy in 24 dot points, which I admit is a touch pretentious. But I’ve been prompted to write something more substantive, in a similar vein, whilst reading Gary Cox’s How to Be an Existentialist; or How to Get Real, Get a Grip and Stop Making Excuses. I bought this tome (the 10^thAnniversary Edition) after reading an article by him on ‘Happiness’ in Philosophy Now (Issue 147, Dec 2021/Jan 2022). Cox is an Honorary Research Fellow at the University of Birmingham, UK. He’s written other books, but this one is written specifically for a general audience, not an academic one. This is revealed in some of the language he uses, like ‘being up shit creek’.

 

I didn’t really learn anything about existentialism until I studied Sartre in an off-campus university course, in my late 40s. I realised that, to all intents and purposes, I was an existentialist, without ever knowing what one was. I did write about existentialism very early in the life of this blog, in the context of my own background. The thing is that one’s philosophical worldview is a product of one’s milieu, upbringing and education, not to mention the age in which one lives. I grew up in a Western culture, post WW2, and I think that made me ripe for existentialist influences without being conscious of it. I lived in the 60s when there was a worldwide zeitgeist of questioning social mores against a background of a religious divide, the Vietnam war and the rise of feminism. 

 

If there is a key word or mantra in existentialism, it’s ‘authenticity’. It’s the key element in my 3 Rules for Humans post, and it’s also the penultimate chapter in Cox’s aforementioned book. The last chapter is on counselling and is like a bookend.

 

As Cox himself points out, existentialism is not a ‘school’ of philosophy in the way ‘analytical philosophy’ or ‘logical positivism’ are. There’s not really a set of rules – it’s more about an attitude and how to live a life without losing your soul or self-respect. It’s not an epistemology, nor an ideology, even though it’s probably associated with a liberal outlook, as I hope will become clear.

 

Many commentators associate existentialism with atheism, the absurd and nihilism. I agree with Cox that it’s actually the opposite of nihilism; if anything, it’s about finding purpose. As I wrote in a post last year:

 

If the Universe has any meaning at all, it’s because it created sentient beings who find meaning against the odds that science tells us are astronomical, both literally and figuratively. Existentialism is about finding purpose in an absurd universe, which is the opposite of nihilism.

 

And that’s the most important lesson of existentialism: if you are to find a purpose, only you can do that; it’s not dependent on anyone else, be they family, a spouse, an employer or a mentor. And logically, one could add, it’s not dependent on God either.

 

Cox doesn’t talk about God at all, but he does talk quite a lot about consciousness and about it being ‘nothing’ (materialistically). He very fleetingly gives mathematics as an example of something else that’s not ‘corporeal’, specifically numbers. Very curious, as I think that both mathematics and consciousness are ‘special’ in that they are distinct, yet intimately connected to the physical world, but that’s another topic.

 

He also talks about consciousness having a special relationship with time. I’ve said that consciousness is the only thing that exists in a constant present, whereas Cox says the opposite, but I believe we mean the same thing. He says consciousness is forever travelling from the past to the future, whereas I say that the future is forever becoming the past while only consciousness exists in the present – the experiential outcome is the same.

 

So how does God enter the picture? God only exists in someone’s consciousness – it’s part of one’s internal state. So, you can be ‘authentic’ and believe in God, but it’s totally an individualistic experience – it can’t be shared. That’s my interpretation, not anyone else’s, I should emphasise.

 

An important, even essential, aspect of all this is a belief in free will. You can’t take control of your life if you don’t have a belief in free will, and I would argue that you can’t be authentic either. And, logically, this has influenced my prejudices in physics and cosmology. To be consistent, I can’t believe we live in a deterministic universe, and have argued strongly on that point, opposing better minds than mine.

 

Existentialism has some things in common with Buddhism, which might explain why Eastern philosophy seemed to have an influence on the 60s zeitgeist. Having said that, I think the commonality is about treating life as a journey that’s transient. Accepting the impermanence and transience of life, I believe, is part of living authentically.

 

And what do I mean by ‘authentic’ in this context? Possibly, I never really appreciated this until I started writing fiction. I think anyone who creates art strives to be authentic, which means leaving your ego out of your work. I try to take the attitude that it’s my characters’ story, not mine. That’s very difficult to explain to anyone who hasn’t experienced it, but I know that actors often say something similar.

 

In my professional life, my integrity was everything to me. I often worked in disputatious environments and it was important to me that people could trust my word and my work. Cox talks about how existentialism intrinsically incorporates our interactions with others. 

 

Freedom is a much-abused, misappropriated term, but in existentialism it has a specific meaning and an interdependent relationship with responsibility – you can’t divorce one from the other. Freedom, in existentialism, means ‘free to choose’, hence the emphasis on free will. It also means, if you invoke the term, that the freedom of others is just as important as your own.

 

One can’t talk about authenticity without talking about its opposite, ‘bad faith’ (mauvaise foi), a term coined by Sartre. Bad faith is something that most of us have experienced, be it working in a job we hate, staying in a destructive relationship or not pursuing a desired goal in lieu of staying in our comfort zone.

 

Of course, sometimes we are in a situation outside our control, so what do we do? Speaking from personal experience, I think one needs to take ownership of one’s response to it; one needs to accept that only YOU can do something about it and not someone else. I’ve never been a prisoner-of-war, but my father was, and he made 3 attempts to escape, because, as he told the Commandant, ‘It’s my job’.

 

I’ve actually explored this in my own fiction. In my last story, two of my characters (independently) find themselves in circumstances of ‘bad faith’. I only analyse this in hindsight – don’t analyse what you write while you’re writing. In fact, one of those characters is attracted to another character who lives authentically, though neither of them ‘think’ in those terms.

Addendum: Someone asked me to come up with a single sentence to describe this. After sleeping on it, I came up with this:

Be responsible for what you are and who you become. That includes being responsible for your failures. (2 sentences)

We are not just numbers, but neither is the Universe

 A few years back I caught up with someone I went to school with, whom I hadn’t seen in decades, and, as it happened, had studied civil engineering like me. I told him I had a philosophy blog where I wrote about science and mathematics, among other things. He made the observation that mathematics and philosophy surely couldn’t be further apart. I pointed out that in Western culture they had a common origin, despite a detour into Islam, where mathematics gained a healthy and pivotal influence from India. 

I was reminded of this brief exchange when I watched this Numberphile video on the subject of numbers, where Prof Edward Frankel (UC Berkeley) briefly mentions the role of free will in our interaction with mathematics.

 

But the main contention of the video is that numbers do not necessarily have the status that we give them in considering reality. In fact, this is probably the most philosophical video I’ve seen on mathematics, even though Frankel is not specifically discussing the philosophy of mathematics.

 

He starts off by addressing the question whether our brain processes are all zeros and ones like a computer, and obviously thinks not. He continues that in another video, which I might return to later. The crux of this video is an in-depth demonstration of how a vector can be represented by a pair of numbers. He points out that the numbers are dependent on the co-ordinate system one uses, which is where ‘free will’ enters the discussion, because someone ‘chooses’ the co-ordinate system. He treats the vector as if it’s an entity unto itself, which he says ‘doesn’t care what co-ordinates you choose’. Brady, who is recording the video, takes him up on this point: that he’s effectively personifying the vector. Frankel acknowledges this, saying that it’s an ‘abstraction within an abstraction.’

 

Now, Einstein used vectors in his general theory of relativity, and one of the most important points was that the vectors are independent of the co-ordinate system. So we have this relationship between a mathematical abstraction and physical reality. People often talk about mistaking the ‘map for the terrain’ and Frankel uses a different metaphor where he says, ‘don’t confuse the menu for the meal’. I agree with all this to a point.

 

My own view is that there are 2 aspects of mathematics that are conflated. There is the language of mathematics, which includes the numbers and the operations we use, and which are ‘invented’ by humans. Then there are the relationships, which this language describes, but which are not prescribed by us. There is a sense that mathematics takes on a life of its own, which is why Frankel can talk about a vector as if it has an independent existence to him. Then there is Einstein who incorporated vectors into his mathematical formulation to describe how gravity is related to spacetime. 

 

Now here’s the thing: the relationship between gravity and spacetime still exists without humans to discover it or describe it. Spacetime is the 3 dimensions of space and 1 of time that, along with gravity, allows planets to maintain orbits over millions of years. But here’s the other thing: without mathematics, we would never know that or be able to describe it. It’s why some claim that mathematics is the language of nature. Whether Frankel agrees or not, I don’t know.

 

In the second video, Brady asks Frankel if he thinks he’s above mathematics, which makes him laugh. What Frankel argues is that there are inner emotional states, like ‘falling in love’, which can’t be described by mathematics. I know that some people would argue that falling in love is a result of biochemical algorithms, nevertheless I agree with Frankel. You can construct a computer model of a hurricane but it doesn’t mean that it becomes one. And it’s the same with the brain. You might, as someone aspired to do, create a computer model of a human brain, but that doesn’t mean it would think like one.

 

This all brings me back to Penrose’s 3 worlds philosophy of the mathematical, the mental and the physical and their intrinsic relationships. In a very real way, numbers allow us to comprehend the physical world, but it is not made of numbers as such. Numbers are the basis of the language we use to access mathematics, because I believe that’s what we do. I’ve pointed out before, that equations that describe the physical world (like Einstein’s) have no meaning outside the Universe, because they talk about physical entities like space and time and energy – things we can measure, in effect.

 

On the other hand, there are mathematical relationships, like Riemann’s hypothesis, for example, that deals with an infinity of primes, which literally can’t be contained by the Universe, by definition. At the end of the 2^ndvideo, Frankel quickly mentions Godel’s Incompleteness Theorem, which he describes in a nutshell by saying that there are truths in mathematics that can’t be formally proven. So there is a limit on what the human mind can know, given a finite universe, yet the human mind is 'not a mathematical machine’, as he so strongly argues.

 

He discusses more than I’ve covered, like his contention that our fixation with the rational is ‘irrational’, and there is no proof for the existence or non-existence of God. So, truly philosophical.

Space and time: still a mystery after all this (time?)

How’s that for a self-referential title, hence the question mark and parentheses. It highlights the fact that time is an everyday phenomenon that literally runs our lives and yet it remains one of the great mysteries of the Universe, still debated among philosophers and scientists. You may think that space is less of a mystery, yet it sparks debate as well, even without Einstein’s revelation that they are cosmologically entwined thanks to the constant speed of light, c.

The problem is with how do we categorise space and time. Are they entities, parameters, dimensions, metrics, mathematical constructions? Perhaps all of the above. I think we can safely say they are not physical objects, yet they determine the relationships between objects everywhere in the Universe, including those that we can’t perceive. In fact, some scientists would argue that time and space are all about relationships and nothing else, which I’ll return to later.

 

But let’s start with one obvious question, which was raised by Kant and still persists today, thanks to Donald Hoffman (refer my last post), and that is: are time and space simply constructs of the mind? To quote Kant from Critique of Pure Reason:

 

But this space and this time, and with them all appearances, are not in themselves things; they are nothing but representations and cannot exist outside our minds.

 

The problem with this viewpoint is that it’s readily believed by almost everyone that space and time existed for billions of years before any ‘mind’ arose in the Universe.

 

Another contentious point is to whether space is an ‘entity’ that ‘expands’ and ‘stretches’ as the Universes itself expands (which is not disputed). Viktor T Toth, a renowned expert on physics on Quora, argues very strongly that it doesn’t and what we witness is the ‘distance’ actually increasing between objects. Proponents against space expanding (like Toth) argue that the space within atoms doesn’t expand. My response is that the size of atoms is determined almost solely by Planck’s constant (h), for which there is no evidence that it changes with the universe’s expansion.

 

However, space can travel faster than light, which suggests it is an entity. This is not disputable, and it’s why there is a horizon to the observable universe (refer my post on the End of the Universe). It’s also why we can incorporate ‘inflation’ into the birth of the Universe. It also has ramifications for black holes, which I’ll come to later. According to Einstein’s theories of relativity, both space and time can change according to the observer and these changes are measurable. In other words, space and time are not ‘fixed’ and they are affected by gravity. In fact, Einstein’s famous formula for his general theory has the curvature of spacetime on one side and the momentum-energy tensor on the other side. In other words, spacetime is curved by energy/matter. To quote John Wheeler: “Spacetime tells matter how to move; matter tells spacetime how to curve.”

 

During this discussion, I’ll cite people who know a lot more than me, like Viktor T Toth and John Wheeler (already cited), even if I disagree with them. But I’m going to attempt the impossible: I’m going to argue ideas that I consider obvious, though not incontrovertible, and I will probably fail, since they will include black holes, quantum mechanics and relativity, all of which I don’t have as much knowledge as I would like. But bear with me, because it’s mostly just logic.

 

I want to point out, right at the start, that I’m not one of those people who think Einstein got it wrong, quite the contrary, but I will point out the limitations of his theory based on what we can actually observe. And that’s a good place to start. A common diagram used to visualise Einstein’s formulation of spacetime is the light cone going both forwards and backwards in time. If you are an observer at the centre of this cone you can only be affected by events from the past within the past light cone, and you can only affect events in the future within the future light cone. Everything else outside these cones can’t be observed or have a causal relationship with you, and this is what I mean when I say relativity has limitations because they are real limitations. Sometimes people will tilt the cones over, indicating movement on your part and the horizontal plane, called the 'hypersurface present', also tilts over. However, there is no causal connection along that 'hypersurface' (through spacetime), according to what I’ve just described.

But this brings one to the subject of simultaneity, because Einstein showed with his famous train and platform thought experiment that 2 observers in different frames of reference could observe different sequences of the same event or perceive a difference in what occurs simultaneously.

 

This is a video that explains this better than I can, including the mathematics involved. Two things worth mentioning: the lecturer includes the spatial Lorenz contraction as well as the time dilation in his calculations; and the observer in the same frame of reference as the source of light sees zero difference and therefore observes a ‘true simultaneity’, though no one calls it that. I’ve long argued that the ‘other observer’ who doesn’t see the simultaneity, observes a difference in the Doppler effect caused by the ‘moving’ frame of reference with the moving light source, which should tell that observer that their observation is incorrect. The Doppler effect tells the observer if the light source is in their frame of reference or a frame of reference moving relative to them. It’s the Doppler effect that tells us that the Universe is expanding uniformly in all directions – it has no centre. It also tells us that we’re moving relative to the CMBR (cosmic microwave background radiation). In other words, we can measure our ‘velocity’ relative to the whole of spacetime, which, of course, is the Universe.

 

I’ve explained elsewhere how different observers in different parts of the Universe literally see different ‘now(s)’. They can literally see events occurring in opposite sequences, as a consequence of the finite speed of light, even without relativistic effects. However, if the events have a causal relationship, then all observers will see them in the same sequence. But this also means that my present will be seen in another observer’s past in their future, but it doesn’t mean the converse: that their future can be seen in my present. In fact, the relationship is reciprocal because I will see their past in my present. Observers can only see another observer’s past, no matter where they are. No observer can see another observer’s future. 

 

To give an example, a hypothetical observer in the Small Magellanic Cloud would see us 210,000 years ago when we were just emerging from Africa. Likewise, we would observe them 210,000 years ago (relative to us) if that was physically possible. Therefore, I don’t hold to the widely held view that we can theoretically see another observer’s future (due to the tilting 'hypersurface' plane in the light cone graphic), which infers that the future must already exist for everyone.

 

We know from the twin paradox thought experiment, as well as data from orbiting satellites, that clocks do literally run at different rates due to gravity as well as motion (your satnav depends on making corrections). Also, the famous muon observations arriving on the Earth’s surface. So both special and general theories of relativity change the rate of time, yet when the clocks are back in the same reference frame, they will show a different time duration while agreeing on where they are in the spacetime co-ordinates of the solar system. In other words, they don’t exist in different ‘now(s)’ just because they measured different durations to arrive at the same destination.

 

We know that different animals see time ‘flow’ at different rates. Many birds and insects see the world in slow-motion compared to us. This means they will see the hands of a clock literally moving slower while telling the same time. As Paul Davies has pointed out, if time was to slow down or speed up, you wouldn’t notice. But you can notice if you compare clocks in relativity. My point is that ‘now’ doesn’t change for these creatures even though they perceive time flowing at a different rate to us.

 

Well, I contend the same is true on a cosmic scale. If you were to go near the event horizon of a black hole, like in the movie, Interstellar, time would slow down for you compared to everyone back on Earth, even though you wouldn’t notice it. My argument is that this is no different, perceptually, to the bird observing time going slower. If you were to use the Doppler effect of receding galaxies as a clock, they would actually appear to be going faster (assuming you could take accurate enough measurements) compared to what Earthlings observed, and when you returned, you would agree on what ‘now’ is, compared to these distant cosmic clocks, though you would be considerably younger than your counterparts, if they were still alive, but more likely you would be meeting their subsequent generations.

 

And this is true even on Earth, where clocks run infinitesimally faster on mountaintops compared to sea level. But you don’t see an accumulated difference in ‘now’ over millions of years of the Earth’s rotation. All the while, the clocks are in the same ‘present’ while they are measuring different rates of time passing.

 

Carlo Rovelli gave a talk at the Royal Institute on ‘time’, where he argues that there is no ‘universal time’. But during the 15min question time (shown in another video), he contends that we arrive at a cosmic time for the Universe by taking an ‘average’. Brian Greene, in his book, The Fabric of the Universe, said something similar. However, if you lived on a planet orbiting near a black hole, surely the age of the Universe would be much less than what we observe, because any clock would be measuring time passing at a much slower rate than what we measure on Earth. Like the clocks on top of the mountains on Earth, I don’t believe hypothetical observers orbiting close to a black hole, perceive a ‘now’ that progressively gets out of step with the ‘now’ Earthlings observe over the course of their lives in the Universe, even if they measured a different age. In other words, I contend that you can have a universal now for the whole universe even if different clocks measure different rates of time dependent on where they are located.

 

Another video, which is an interview with loop quantum gravity theorist, Lee Smolin, describes time and space as being separate, which is both heretical and interesting. I think he has a point when you consider that, on a cosmic scale, time is finite and space is possibly infinite. Space could also be finite but perceptually infinite, like a hyperbolic universe, but, as Marcus du Sautoy pointed out in his book, What We Cannot Know, if the Universe is truly spatially infinite, we might never know. Smolin conjectures that space could be a consequence of ‘causal relationships’ between physical objects, which he doesn’t elaborate on, but which I find difficult to conceptualise. Causation is determined by the speed of light, otherwise everything would happen at once (Caspar Henderson, A New Map of Wonders). Smolin also contends that time might be an ‘emergent’ property (also without elaborating). The point is that causality requires time axiomatically. The thing about both space and time is that they are dimensions and if you add light (c) into the mix, you get a 4-dimensional universe that is fundamental for it to function in the way it does. With more than 3 spatial dimensions, planets would not have stable orbits, and if there was more than 1 dimension of time you would get time loops. If you have 2 spatial dimensions you would literally fall apart. Also, more than 3 spatial dimensions causes light waves to travel inconsistently. Our universe has the ideal time-space dimensional combination for its goldilocks existence.

 

In the same video, Smolin explains how the event horizon of a black hole breaks causality. This can be seen mathematically by Schwarzchild’s equation for a static black hole, which is described in this video. As the presenter explains, the +ve and -ve signs of the equation change when you cross the event horizon, which breaks causality. Causality is caused by the space dimension being less than the (negative) time dimension, and they are reversed on the other side of the event horizon (watch the video). It should be pointed out that Einstein was initially sceptical about the existence of black holes, even though Schwarzchild derived his equation from Einstein’s tensor.

 

There is a paradox inherent in a black hole (more than one, actually) but the most fundamental one is that time theoretically stops at the event horizon because time is related to light, and light can’t escape a black hole by definition. Viktor T Toth says that ‘the event horizon is always in an observer’s future’, so how can anyone (or anything) fall into a black hole? In a previous post, I speculated that maybe ‘space’ itself ‘falls’ into the black hole and that’s exactly what the guy in the video says. This is only possible because space can travel faster than light, as I described earlier.

 

This is already a lengthy post but I can’t talk about time without mentioning quantum mechanics. The same guy (who talks about black holes), gives a very good summary explanation of Richard Feynman’s path integral formulation of QED (quantum electrodynamics) in this video. It should be pointed out that Julian Schwinger’s ‘field’ interpretation called QFT (quantum field theory) is now more popular, if that’s the right word. In QFT, particles are seen as ‘excitations’ of a quantum field which is everywhere in the Universe. Someone on Quora even suggested that the word ‘particle’ should be erased from every physics text book, because they just don’t exist. Curiously, Feynman, in his book, QED, argued that everything is ‘particles’, but that was in the context of whether quantum phenomena are ‘waves’ or ‘particles’ in the Bohr tradition. I like Freeman Dyson’s view that it depends on whether an event is in an observer’s future or past, but I’m getting ahead of myself.

 

A good place to start with QM is Schrodinger’s equation. Carlo Rovelli, whom I cited earlier, in one of his books, is almost dismissive of Schrodinger’s equation and argues that the wave function (ψ) has misled us in our understanding of QM. But Schrodinger’s wave function is the basis of Feynman’s QED, so that’s where I’ll start.

 

Schrodinger’s equation encapsulates all the characteristics of QM which make it weird: superposition, entanglement and the uncertainty principle. The wave function also incorporates time-reversal symmetry, which is an inherent feature of QM. It doesn’t incorporate relativity, but I’ll come to that later.

 

The thing about Schrodinger’s equation, which is rarely mentioned, is that it describes the future – it makes predictions about where something will be in time. It was Dirac who derived the Lagrangian for QM, and Feynman adopted that for his ‘sum over histories’ or ‘path integral’ formulation, because it calculates the path of ‘least action’, which dictates what something does. (This also applies in a gravitational field, by the way, but I don’t want to confuse you.) Feynman used the proper time (τ) in place of t (that Schrodinger used) which automatically allows for special relativity (as explained in the video).

 

As someone on Quora once explained (David Moore, who is a Sydney based GP), a probability of ONE exists in the past, after the event. In the future, the probability is always less than one. This is what happens when the wave function ‘collapses’, for want of a better word, and neatly incorporates Freeman Dyson’s view that QM describes the future while classical physics describes the past. Feynman’s formulation has an infinity of possible future paths, that he integrates (hence the ‘integral’ in path integral) and also gives the path of least action. There is an element of teleology in this, but I don’t believe it makes the universe deterministic, though others disagree. On a large enough scale, as Schrodinger himself pointed out, you get a statistical deterministic effect, which he coined ‘statistico-deterministic’. But it can’t predict individual events, like when a radioactive isotope will decay, which is the crucial component in his eponymous cat thought experiment.

 

In regard to photons being the ‘particle’ nature of light, Mark John Fernee (physicist at Queensland University and regular Quora contributor) made the point in one of his posts, that if we didn’t observe light as photons, we would not be able to see many of the distant stars that we do. If light was purely a wave, then it would be so dispersed over the massive sphere of its influence it would be too faint to see. But, as a photon, it can arrive in just one point in space, where we happen to observe it.

 

I will leave the last word to Paul Davies. Even though he’s talking about QM in reference to black holes and Hawking radiation, the principle he describes is universal.

 

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.

Addendum: This video gives a more detailed and accurate explanation of black holes. It's more complex than my exposition would suggest.