Reality, nature, the Universe and everything abhors a contradiction

 People used to say that ‘nature abhors a vacuum’, which is more often than not used metaphorically. Arguably, contradiction avoidance is more fundamental in that you don’t even need a universe for it to be requisite. Many mathematical proofs are premised on the unstated axiom that you can’t have a contradiction - reductio ad absurdum.

However, the study of physics has revealed that nature seems to love paradoxes and the difference between a paradox and a contradiction is often subtle and sometimes inexplicable. So, following that criterion, I believe that reality exists in that sliver of possibility between paradox and contradiction.

 

Clifford A Pickover, who normally writes about mathematics and physics, wrote an entertaining and provocative book, The Paradox of God and the Science of Omniscience. One of the conclusions that I took from that book is that there are rules of logic that even God can’t break. And one of those rules is the rule of contradiction that something can’t ‘be’ and ‘not be’ at the same time. It turns the argument on its head that God created logic. 

 

It’s obvious to anyone who reads this blog that I’m unceasingly fascinated by science and philosophy, and, in particular, where they meet and possibly crossover. So an unerring criterion for me is that you can’t have a contradiction. My recent exposition on the famous twin paradox demonstrates this. It can only be resolved if one accepts that only one twin experiences time dilation. If they both did, you would arrive at a contradiction, both mathematically and conceptually. Specifically, each twin would perceive the other one as younger, which is impossible. 

 

The opposite to contradiction is consistency, and if you look at the mathematical analysis of the twin paradox, you’ll see it’s consistent throughout for both twins.

 

To give another example, physicists tell us that time does not flow (as Paul Davies points out in this presentation, 48.30min mark), yet we all experience time ‘flowing’. Davies and I agree that the sensation we have of time ‘flowing’ is a psychological experience; we disagree on how or why that happens. 

 

Time is a dimension determined by the speed of light. Everything is separated, not only spatially, but also in time, because it takes a finite time for light to travel between events separated in space. This leads to the concept of spacetime, which is invariant for different observers, while space and time (independently) can be ‘measured’ to be different for different observers. Spacetime is effectively an extension of Pythagoras’s theorem into 4 dimensions, only it involves negatives.

Δs² = c²Δt² - Δx² - Δy² - Δz²

So Δs is the ‘interval’ that remains invariant, and cΔt is the time dimension converted into a spatial dimension, otherwise the equation wouldn’t work. But note that it’s c (the constant speed of light) that makes time a dimension, and it’s one of the dimensions of the Universe as a whole. Einstein’s equations work for the entire Universe, which is his greatest legacy.

 

I’ve been reading Brian Greene’s The Fabric of the Cosmos (2004), which I came across while browsing in a bookshop and bought it on impulse – I’m glad I did. It’s a 500 page book, covering all the relevant topics on cosmology, so it’s very ambitious, but also very readable.

 

Theories of gravity started with Newton, and he came up with a thought experiment that was still unresolved when Einstein revolutionised his theory. Greene discusses it in some detail. If you take a bucket of water and hang it from a rope, then turn the bucket many times so that the rope is twisted. When you release the rope the bucket spins and the water surface becomes concave in the bucket due to the centrifugal force. The point is, what is the reference frame that the bucket is spinning to? Is it the Universe as a whole? Newton would have argued that it was spinning relative to absolute space.

 

Now imagine that you could do this experiment in space; only, instead of a bucket of water, you have 2 rocks tied together. You could do it on the space station. As you spin them, you’d expect the rope or cord between them to tension. So again, what are they spinning in reference to? Greene gives a detailed historical account because it involves Mach’s principle. But in the end, when Einstein applied his theories of relativity, he came to the conclusion that they spin relative to spacetime. While we don’t have absolute space and absolute time, we have absolute spacetime, according to Einstein.

 

Why have I taken so much trouble to describe this? Because there is a frame of reference that is used to determine what direction and what speed our solar system travels in the context of the overall Universe. And it’s the Cosmic Microwave Background Radiation. Paul Davies described this in his book, About Time (1995). By measuring the difference in the Doppler effect (for CMBR) in different regions of the sky, we can deduce we are travelling in the direction of the Pisces constellation. Greene also points this out in his book.

 

All physicists that I’ve read, or listened to, argue that ‘now’ is totally dependent on the observer. They will tell you that if you move backwards and forwards here on Earth, then the time changes on some far off constellation will be in the order of hundreds of years because of the change in angle of the time slice across that part of the Universe. Greene himself explains this in a video, as well as in his book. But there is an ‘age’ for the Universe, so you have an implicit contradiction. Greene is the only person I’ve read who actually attempts to address this, though not very satisfactorily (for me).

 

But one doesn’t need to look at far off galaxies, one can look at Einstein’s original thought experiment involving 2 observers: one on a train and one on a platform. The reason physicists argue that there is no objective now is because simultaneity is different according to different observers, and Einstein uses a train as a thought experiment to demonstrate this.

 

If you have a light source in the centre of a moving carriage then a person in the carriage will observe that it gets to both ends at the same time. But a person on the platform will see that the back of the train will receive the light before the front of the train. However, the light source is moving relative to the observer on the platform, so they will see a Doppler shift in the light showing that it is moving relative to them. I contend that only the observer in the same frame of reference as the light source sees the true simultaneity. In other words, I argue that you can have 'true simultaneity' in the same way as you can have ‘true time’. Also, what many people don’t realise, that different observers not only see simultaneity happening at different times but different locations, as this video demonstrates.

 

I’m a subscriber to Quora, mainly because I get to read posts by lots of people in various fields, most of whom are more knowledgeable than me. In fact, I claim my only credential is that I read a lot of books by people much smarter than me. One of the regular contributors to Quora is Viktor T Toth, whom I’ve referenced before, and who calls himself a ‘part-time physicist’. Toth knows a lot about cosmology, QFT (quantum field theory) and black holes. He occasionally shows his considerable mathematical abilities in dealing with a question, but most of the time keeps them in reserve. What I like about Toth, is not just his considerable knowledge, but his no-nonsense approach. He doesn’t pretend or bluff; he has no problem admitting what he doesn’t know and is very respectful to his peers, while not tolerating fools.

 

Toth points out that while 2 observers can experience different durations in time (like the twins in the twin paradox) they agree on the time when they meet again. In other words, there is a time reference (like a space reference) that’s independent of the path they took to get there. As I pointed out in my post explaining relativity based on waves, it’s not only the time duration that 2 observers disagree on, but also the space duration. If someone was able to travel so fast that they could cross the galaxy in years instead of thousands of years, then they would also traverse a much shorter distance (according to them). In other words, not only does time shrink, but so does distance. We don’t tend to think that space can be just as rubbery as time.

 

And this brings me to a point that Toth and Greene seem to disagree on. Toth is adamant that space is not an entity but just the ‘distance’ between physical objects. Regarding the expanding universe, he says ‘space’ does not ‘stretch’ but it’s just that the ‘distance’ between ‘objects’ increases. Greene would probably disagree. Greene argues that wavelengths of light lengthen as space ‘stretches’.

 

What do I think? I tend to side with Greene. I think space is an entity because it has dimensions. John Barrow, in his book, The Constants of Nature, gives an excellent account of how a universe that didn’t exist in 3 dimensions would be virtually unworkable. In particular, the inverse square law for gravity, that keeps planets in stable orbits for hundreds of millions of years, would not work in any other dimensional universe.

 

But also, space can be curved by gravity, or more specifically, spacetime, as Toth readily acknowledges. I’ll return to Toth’s specific commentary on gravity and black holes later.

 

I’ve already mentioned that Greene discussed the age of the Universe. I recently did an online course provided by New Scientist on The Cosmos, and one of the lecturers was Chris Impey, Distinguished Professor, Department of Astronomy, University of Arizona. He made the point that the Universe has an ‘edge in time’, but not an edge in space. Greene expanded on this, by pointing out that everywhere in the Universe all clocks are ‘in synchronicity’, which contradicts the notion that there is no universal now. I’ll quote Greene directly on this, because it’s an important point. According to Greene (but not only Greene) whether an observer is moving away from a distant stellar object, or towards it, determines whether they would see into that object’s distant past or distant future. Mind you, because they are so far away, the object’s future is still in our past.

 

Each angled slice intersects the Universe in a range of different epochs and so the slices are far from uniform. This significantly complicates the description of cosmic history, which is why physicists and astronomers generally don’t contemplate such perspectives. Instead, they usually consider only the perspective of observers moving solely with the cosmic flow...

 

I don’t know the mathematics behind this, but I can think of an analogy that we all observe every day. You know when you walk along a street with the Sun low in the sky, so it seems to be moving with you. It will disappear behind a building then appear on the other side. And of course, another observer in another town will see the Sun in a completely different location with respect to their horizon. Does this mean that the Sun moved thousands of miles while you were walking along? No, of course not. It’s all to do with the angle of projection. In other words, the movement in the sky is an illusion, and we all know this because it happens all the time and it happens in sync with our own movements. I remember once travelling in a car with a passenger and we could see a plane low in the sky through the windscreen. My passenger commented that the plane was travelling really fast, and I pointed out that if we stopped, we’d find that the plane would suddenly slow down to a speed more commensurate with our expectations.

 

I think the phenomenon that Greene describes is a similar illusion, only we conjure it up mathematically. It makes sense to ignore it, as astronomers do (as he points out) because we don’t really expect it happens in actual fact.

 

Back in 2016, I wrote a post on a lecture by Allan Adams as part of MIT Open Courseware (8.04, Spring 2013) titled Lecture 6: Time Evolution and the Schrodinger Equation. This was a lecture for physics students, not for a lay audience. I found this very edifying, not least because it became obvious to me, from Adams’ exposition, that you could have a wave function with superposition as described by Schrodinger’s equation or you could have an observed particle (like an electron) but you couldn’t have both. Then I came across the famous quote by William Lawrence Bragg:

Everything that has already happened is particles, everything in the future is waves. The advancing sieve of time coagulates waves into particles at the moment ‘now’.

 

In that post on Adams’ lecture, I said how people (like Roger Penrose, among others) explained that ‘time’ in the famous time dependent Schrodinger equation exists outside the hypothetical Hilbert space where the wave function hypothetically exists. And it occurred to me that maybe that’s because the wave function exists in the future. And then I came across Freeman Dyson’s lecture and his unorthodox claim:

 

... the “role of the observer” in quantum mechanics is solely to make the distinction between past and future...

What really happens is that the quantum-mechanical description of an event ceases to be meaningful as the observer changes the point of reference from before the event to after it. We do not need a human observer to make quantum mechanics work. All we need is a point of reference, to separate past from future, to separate what has happened from what may happen, to separate facts from probabilities.

The inherent contradictions in attempting to incorporate classical physics into quantum mechanics (QM) disappear, if one is describing all the possible future paths of an event while the other describes what actually happened.

 

Viktor Toth, whom I’ve already mentioned, once made the interesting contention that the wave function is just a ‘mathematical construct’ (his words) and he’s not alone. He also argued that the ‘decoherence’ of the wave function is never observed, which infers that it’s already happened. Toth knows a great deal about QFC (and I don’t) but, if I understand him correctly, the field exists all the time and everywhere in spacetime.

 

Another contributor on Quora, whom I follow, is Mark John Fernee (PhD in physics, University of Queensland), who obviously knows a great deal more than me. He had this to say about ‘wave function collapse’ (or decoherence) which corroborates Toth.

 

The problem is that there is no means to detect the wavefunction, and consequently no way to detect a collapse. The collapse hypothesis is just an inference that can't be experimentally tested.

 

And, in a comment, he made this point:

 

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.

 

And I’ve made this exact same point, that we also get the ‘irreversibility’ or asymmetry between past and future, from QM physics becoming classical physics.

 

Dyson is also contentious when it comes to gravity and QM, arguing that we don’t need to combine them together and that, even if the graviton existed, it’s impossible to detect. Most physicists argue that we need a quantum gravity – that it’s the ‘missing link’ in a TOE (Theory of Everything).

 

It’s occurred to me that maybe the mathematics is telling us something when it appears obstructive to marrying general relativity with QM. Maybe they don’t go together, as Dyson intimated.

 

Again, I think Toth gives the best reasoning on this, as I elaborated on in another post.

 

We can do quantum field theory just fine on the curved spacetime background of general relativity.

Then he adds this caveat:

What we have so far been unable to do in a convincing manner is turn gravity itself into a quantum field theory.

 

Toth explains how and why they are ‘incompatible’, though he loathes that term, because he doesn’t think they’re incompatible at all.

 

Basically, Einstein’s field equations are geometrical, whereby one side of the equation gives the curvature of spacetime as a consequence of the energy, expressed on the other side of the equation. The energy, of course, can be expressed in QM, but the geometry can’t. 

 

Someone else on Quora, Terry Bollinger (retired Chief Scientist), explains this better than me:

 

It all goes back to that earlier point that GR is a purely geometric theory, which in turn means that the gravity force that it describes is also specified purely in terms of geometry. There are no particles in gravity itself, and in fact nothing even slightly quantum. Instead, you assume the existence of a smooth fabric called spacetime, and then start bending it. From that bending emerges the force we know as gravity.

 

Bollinger wrote a lengthy polemic on this, but I will leave you with his conclusion, because it is remarkably similar to Toth’s.

 

Even if you finally figure out a clever way to define a gravity-like quantum force that allows objects in spacetime to attract each other, what are those force particles traveling across?

 

He provides his own answer:

 

Underneath the quantum version, since like all of the other forces in the Standard Model this swarm-like quantum version of a gravity must ride on top of spacetime. (Emphasis in the original)

 

In other words, Bollinger claims you’ll have a redundancy: a quantum field gravity on top of a spacetime gravity. Spacetime provides the ‘background’ to QFT that Toth described, which doesn’t have to be quantum.

 

So what about quantum gravity that is apparently needed to explain black holes?

 

There is an inherent contradiction in relation to a black hole, and I’m not talking about the ‘information paradox’. There is a debate about whether information (meaning quantum information) gets lost in a black hole, which contradicts the conservation of quantum information. I’m not going to get into that as I don’t know enough about it.

 

There is a more fundamental issue: according to Toth (but not only Toth) the event horizon of a black hole is always in an observer’s future. Yet for someone at the event horizon, they could cross over it without even knowing they had done so, especially if it was a really big black hole and the tidal effects at the event horizon weren’t strong enough to spaghettify them. Of course, no one really knows this, because no one has ever been anywhere near a black hole event horizon.

 

The point is that, at the event horizon of a black hole, time stops according to an external observer, which is why, theoretically it’s always in their future. Toth makes this point many times. So, basically, for someone watching something fall into a black hole, it becomes frozen in time (at the event horizon). In fact, the Russian term for a black hole is ‘frozen star’.

 

What we can say is that light from any object gets red-shifted so much that it disappears even before it reaches the event horizon. But what about an observer at or near the event horizon looking back out at the Universe. Now, I don’t see any difference in this scenario to the twin paradox, only it’s in extremis. The observer at the event horizon, or just outside it, will see the whole universe pass by in their lifetime. Because, if they could come back and meet up with their twin, their twin would be a hologram frozen in time, thousands of years old. Now, Toth makes the point, that as far as an observer at or near the event horizon, the speed of light is still constant for them, so how can that be?

 

There is another horizon in the Universe, which is the theoretical and absolute practical limit that we can see. Because the Universe is expanding, there is a part of the Universe that is expanding faster than light, relative to us. Now, you will say, how is that possible? It’s possible because space can travel faster than light. Now Toth will confirm this, even though he claims space is not an entity. Note that some other observer in a completely different location, would see a different horizon, in the same way that sailors in different locations in the same ocean see different horizons.

 

So, a hypothetical observer, at the horizon of the Universe (with respect to us) would still see the speed of light as c relative to their spacetime. Likewise, an observer at the event horizon of a black hole also sees light as c relative to their spacetime.

 

Now most black holes, we assume, are spinning black holes and they drag an accretion disk around with them. They also drag space around with them. Is it possible then that the black hole drags space along with an observer across the event horizon into the black hole? I don’t know, but it would resolve the paradox. According to someone on Quora, Leonard Susskind argues that nothing ever crosses the event horizon, which is how he resolves the quantum information paradox.

 

This is a very lengthy post, even by my standards, but I need to say something quickly about entanglement. There appears to be a contradiction between relativity and entanglement, but not in practical terms. If there is a universal 'now', implicit in the Universe having an ‘edge in time’ (but not in space) and if QM describes the future, then entanglement is not a mystery, because it’s a correlation between events separated in space, but not in time. 

 

Entanglement involves a ‘decoherence’ in the wave function that predicts the state of a decoherence in the particle it’s entangled with, because they share the same wave function. Schrodinger understood this better than anyone else, because he realised that entanglement was an intrinsic consequence of the wave function. He famously said that entanglement was the defining characteristic of quantum mechanics.

 

But there is no conflict with relativity because the entangled particles, whatever they are, can’t be separated at any greater rate than the speed of light. However, when the correlation occurs, it appears to happen instantaneously. But this is no different to a photon always being in the future of whatever it interacts with, even if it crosses the observable universe. However, for someone who detects such a photon, they instantaneously see something in the distant past as if there has been a backward-in-time connection to its source.

 

There is no reason to believe that anything I’ve said is true and correct. I’ve tried to follow a simple dictum that nature abhors a contradiction and apply it to what I know about the Universe, while acknowledging there are lots of people who know a great deal more than me, who probably disagree.

 

I see myself as an observer on the boundary line of the history of ideas. I try to make sense of the Universe by reading and listening to people much cleverer than me, including people I have philosophical differences with.

Addendum 1: I referenced Paul Davies 1995 book, About Time; Einstein's Unfinished Revolution. I mentioned that Earth is travelling relative to the CMBR towards Pisces (at 350 km/s), and according to Davies:

This is about 0.1 percent of the speed of light, and the time-dilation factor is only about one part in a million. Thus, to an excellent approximation, Earth's historical time coincides with cosmic time, so we can recount the history of the universe contemporaneously with the history of the Earth, in spite of the relativity of time. Similar hypothetical clocks could be located everywhere in the universe, in each case in a reference frame where the cosmic background heat radiation looks uniform... we can imagine the clocks out there, and legions of sentient beings dutifully inspecting them. This set of imaginary observers will agree on a common time scale and a common set of dates for major events in the universe, even though they are moving relative to each other as a result of the general expansion of the universe. They could cross-check dates and events by sending each other data by radio; everything would be consistent. So cosmic time as measured by this special set of observers constitutes a type of universal time... It is the existence of this pervasive time scale that enables cosmologists to put dates to events in cosmic history - indeed, to talk meaningfully at all about "the universe" as a single system. (my emphasis)

Addendum 2: This is a PBS video, which gives the conventional physics view on time. I don't know who the presenter is, but it would be fair to say he knows more about this topic than me. He effectively explains Einstein's 'block universe' and why 'now' is considered totally subjective. Remember Einstein's famous words in a letter to the mother of a friend who had died:

We physicists know that the past, present and future is only a stubbornly persistent illusion.

This was a consequence of simultaneity being different for different observers, as I discussed in the main text, and is described in the video. It's important to point out that this does not undermine causality, so it refers to events that are not causally related. The video presenter goes on to point out that different observers will see different pasts and different futures on worlds far far away, dependent on their motion on this world. This infers that all events are predetermined, which is what Einstein believed, and explains why so many physicists claim that the Universe is deterministic. But it contradicts the view, among cosmologists, that the Universe has an 'edge in time but not in space'.

It's certainly worth watching the video. Curiously, his logic leads him to the conclusion that we live in a quantum multiverse (the many worlds interpretation of QM). I agree with him that different observers in different parts of the Universe must have different views of 'Now'. That's just a logical consequence of the finite speed of light. Motion then distorts that further, as he demonstrates. My view is that what we perceive is not necessarily what actually 'is'. If one looks at the clock of a moving observer their time is dilated compared to ours, and likewise they see our clocks showing time dilation compared to them. But logic tells us that they both can't be right. The twin paradox is resolved only if one acknowledges that time dilation is an illusion for one observer but not the other. And that's because one of the twin travels relative to an absolute spacetime if not an absolute space or an absolute time.

Back to the video, my contention is that one observer can't see another observer's future, even though we can see another observer's 'present' in our 'past'; I don't find that contentious at all.

The closest I’ve ever seen to someone explaining my philosophy

 I came across this 8min video of Paul Davies from 5 years ago, where I was surprised to find that he and I had very similar ideas regarding the ‘Purpose’ of the Universe. In more recent videos, he has lighter hair and has lost his moustache, which was a characteristic of his for as long as I’ve followed him.

 

Now, one might think that I shouldn’t be surprised, as I’ve been heavily influenced by Davies over many years (decades even) and read many of his books. But I thought he was a Deist, and maybe he was, because not halfway through he admits he had recently changed his views.

 

But what makes me consider that this video probably comes closest to expressing my own philosophy is when he says that meaning or purpose has evolved and that it’s directly related to the fact that the Universe created the means to understand itself. Both these points I’ve been making for years. In his own words, “We unravel the plot”.

Or to quote John Wheeler (whom Davies admired): “The universe gives birth to consciousness, and consciousness gives meaning to the universe.”

P.S. This is also worth watching: his philosophy on mathematics; to which I would concur. His metaphor of a 'warehouse' is unusual, yet very descriptive and germane in my view.

The Twin paradox, from both sides now (with apologies to Joni)

 I will give an exposition on the twin paradox, using an example I read in a book about 4 decades ago, so I’m relating this from memory.

Imagine that one of the twins goes to visit an extra-terrestrial world 20 light years away in a spaceship that can travel at 4/5 the speed of light. The figures are chosen because they are easy to work with and we assume that acceleration and stopping are instantaneous. We also assume that the twin starts the return journey as soon as they arrive at their destination.

 

From the perspective of the twin on Earth, the trip one-way takes 25 years because the duration is T = s/v, where s = 20 (light years) and v = 4/5c. 

So 5/4 x 20 = 25.

 

From the perspective of the twin on the spaceship, their time is determined by the Lorentz transformation (γ).

 

γ = 1/√(1 – v²/c²)

 

Note v²/c² = (4/5)² = 16/25

So √(1 – v²/c²) = √(9/25) = 3/5

 

Now true time for the space ship (τ) is given by τ = T/γ

So for the spaceship twin, the duration of the trip is 3/5 x 25 = 15

So the Earth twin has aged 25 years and the spaceship twin has aged 15 years.

 

But there is a relativistic Doppler effect, which can be worked out by considering what each twin sees when the spaceship arrives at its destination. 

 

Note that light, or any other signal, takes 20 years to come back from the destination. So the Earth twin will see the space ship arrive 25 + 20 = 45 years after it departed. But they will see that their twin is only 15 years older than when they left. So, from the Earth twin’s perspective, the Doppler effect is a factor of 3. (3 x 15 = 45). So the Doppler effect slowed time down by 3. Note: 45 years has passed but they see their twin has only aged 1/3 of that time.

 

What about the spaceship twin’s perspective? They took 15 years to get there, but the Doppler effect is a factor of 3 for them as well. They’ve been receiving signals from Earth ever since they left so they will see their twin only 5 years older because 15/3 = 5, which is consistent with what their twin saw. In other words, their Earth twin has aged 5 years in 15, or 1/3 of their travel time. 

 

If spaceship twin was to wait another 20 years for the signal to arrive then it would show Earth twin had aged 5 + 20 = 25 years at the time of their arrival. But, of course, they don’t wait, they immediately return home. Note that the twins would actually agree on each other’s age if they allowed for the time it takes light to arrive to their respective locations.

 

So what happens on the return trip? The Lorentz transformation is the same for the spaceship twin on the return trip, so they only age another 15 years, but according to the Earth twin the trip would take another 25 years, so they would have aged 50 years compared to the 30 years of their twin.

 

But what about the Doppler effect? Well, it’s still a factor of 3, only now it works in reverse, speeding time up. For the spaceship twin, their 15 years of observing their Earth twin is factored by 3 and 15 x 3 = 45. And 5 + 45 = 50, which is how much older their twin is when they arrive home.

 

For the Earth twin, their spaceship twin’s round trip is 50 years, so the return trip appears to only take 5 years. And allowing for the same Doppler effect, 3 x 5 = 15.

When the Earth twin adds 15 to the 15 years they saw after 45 years, they deduce the age of their spaceship twin is 30 years more (against their own 50). So both twins are in agreement.

 

Now, the elephant in the room is why do we only apply the Lorentz transformation to the spaceship twin? The usual answer to this question is that the spaceship twin had to accelerate and turn around to come back, so it’s obvious they did the travelling.

 

But I have another answer. The spaceship twin leaves the surface of Earth and even leaves the solar system. It’s obvious that the spaceship didn’t remain stationary while the solar system travelled through the cosmos at 4/5 the speed of light. There is an asymmetry to the scenario which is ultimately governed by the gravitational field created by everything, and dominated by the solar system in this particular case. In other words, the Lorentz transformation only applies to the spaceship twin, even when they only travel one way.

Relativity makes sense if everything is wavelike

 When I first encountered relativity theory, I took an unusual approach. The point is that c can always be constant while the wavelength (λ) and frequency (f ) can change accordingly, because c = λ x f. This is a direct consequence of v = s/t (where v is velocity, s distance and t time). We all know that velocity (or speed) is just distance divided by time. And λ represents distance while f represents 1/t. 

So, here’s the thing: it occurred to me that while wavelength and frequency would change according to the observer’s frame of reference (meaning relative velocity to the source), the number of waves over a specific distance would be the same for both, even though it’s impossible to measure the number of waves. And a logical consequence of the change in wavelength and frequency is that the observers would ‘measure’ different distances and different periods of time.

 

One of the first confirmations of relativity theory was to measure the half-lives of cosmic rays travelling through the Earth’s atmosphere to reach a detector at ground level. Measurements showed that more particles arrived than predicted by their half-life when stationary. However, allowing for relativistic effects (as the particles travelled at high fractional lightspeeds), the number of particles detected corresponded to time dilation (half-life longer, so more particles arrived). This means from the perspective of the observers on the ground, if the particles were waves, then the frequency slowed, which equates to time dilation - clocks slowing down. It also means that the wavelength was longer so the distance they travelled was further. 

 

If the particles travelled slower (or faster), then wavelength and frequency would change accordingly, but the number of waves would be the same. Of course, no one takes this approach - why would you calculate the Lorentz transformation on wavelength and frequency and multiply by the number of waves, when you could just do the same calculation on the overall distance and time.

 

Of course, when it comes to signals of communication, they all travel at c, and changes in frequency and wavelength also occur as a consequence of the Doppler effect. This can create confusion in that some people naively believe that relativity can be explained by the Doppler effect. However, the Doppler effect changes according to the direction something or someone is travelling while relativistic effects are independent of direction. If you come across a decent mathematical analysis of the famous ‘twin paradox’, you’ll find it allows for both the Doppler effect and relativistic effects, so don’t get them confused.

 

Back to the cosmic particles: from their inertial perspective, they are stationary and the Earth with its atmosphere is travelling at high fractional lightspeed relative to them. So the frequency of their internal clock would be the same as if they were stationary, which is higher than what the observers on the ground would have deduced. Using the wave analogy, higher frequency means shorter wavelength, so the particles would ‘experience’ the distance to the Earth’s surface as shorter, but again, the number of waves would be the same for all observers.

 

I’m not saying we should think of all objects as behaving like waves - despite the allusion in the title - but Einstein always referred to clocks and rulers. If one thinks of these clocks and rulers in terms of frequencies and wavelengths, then the mathematical analogy of a constant number of waves is an extension of that. It’s really just a mathematical trick, which allows one to visualise what’s happening.

What is scientism?

 I’m currently reading a book (almost finished, actually) by Hugh Mackay, The Inner Self; The joy of discovering who we really are. Mackay is a psychologist but he writes very philosophically, and the only other book of his I’ve read is Right & Wrong: How to decide for yourself, which I’d recommend. In particular, I liked his chapter titled, The most damaging lies are the ones we tell ourselves.

You may wonder what this has to do with the topic, but I need to provide context. In The Inner Self, Mackay describes 20 ‘hiding places’ (his term) where we hide from our ‘true selves’. It’s all about living a more ‘authentic’ life, which I’d endorse. To give a flavour, hiding places include work, perfectionism, projection, narcissism, victimhood – you get the picture. Another term one could use is ‘obsession’. I recently watched a panel of elite athletes (all Australian) answering a series of public-sourced questions (for an ABC series called, You Can’t Ask That), and one of the take-home messages was that to excel in any field, internationally, you have to be obsessed to the point of self-sacrifice. But this also applies to other fields, like performing arts and scientific research. I’d even say that writing a novel requires an element of obsession. So, obsession is often a necessity for success.

 

With that caveat, I found Mackay’s book very insightful and thought-provoking – It will make you examine yourself, which is no bad thing. I didn’t find any of it terribly contentious until I reached his third-last ‘hiding place’, which was Religion and Science. The fact that he would put them together, in the same category, immediately evoked my dissent. In fact, his elaboration on the topic bordered on relativism, which has led me to write this post in response.

 

Many years ago (over 2 decades) when I studied philosophy, I took a unit that literally taught relativism, though that term was never used. I’m talking epistemological relativism as opposed to moral relativism. It’s effectively the view that no particular discipline or system of knowledge has a privileged or superior position. Yes, that viewpoint can be found in academia (at least, back then).

 

Mackay’s chapter on the topic has the same flavour, which allows him to include ‘scientism’ as effectively a religion. He starts off by pointing out that science has been used to commit atrocities the same as religion has, which is true. Science, at base, is all about knowledge, and knowledge can be used for good or evil, as we all know. But the ethics involved has more to do with politicians, lawmakers and board appointees. There are, of course, ethical arguments about GM foods, vaccinations and the use of animals in research. Regarding the last one, I couldn’t personally do research involving the harming of animals, not that I’ve ever done any form of research.

 

But this isn’t my main contention. He makes an offhand reference at one point about the ‘incompatibility’ of science and religion, as if it’s a pejorative remark that reflects an unjustified prejudice on the part of someone who’d make that comment. Well, to the extent that many religions are mythologically based, including religious texts (like the Bible), I’d say the prejudice is justified. It’s what the evolution versus creation debate is all about in the wealthiest and most technologically advanced nation in the world.

 

I’ve long argued that science is neutral on whether God exists or not. So let me talk about God before I talk about science. I contend that there are 2 different ideas of God that are commonly conflated. One is God as demiurge, and on that I’m an atheist. By which I mean, I don’t believe there is an anthropomorphic super-being who created a universe just for us. So I’m not even agnostic on that, though I’m agnostic about an after-life, because we simply don’t know.

 

The other idea of God is a personal subjective experience which is individually unique, and most likely a projection of an ‘ideal self’, yet feels external. This is very common, across cultures, and on this, I’m a theist. The best example I can think of is the famous mathematician, Srinivasa Ramanujan, who believed that all his mathematical insights and discoveries came directly from the Hindu Goddess, Namagiri Thayar. Ramanujan (pronounced rama-nu-jan) was both a genius and a mystic. His famous ‘notebooks’ are still providing fertile material 100 years later. He traversed cultures in a way that probably wouldn’t happen today.

 

Speaking of mathematics, I wrote a post called Mathematics as religion, based on John Barrow’s book, Pi in the Sky. According to Marcus du Sautoy, Barrow is Christian, though you wouldn’t know it from his popular science books. Einstein claimed he was religious, ‘but not in the conventional sense’. Schrodinger studied the Hindu Upanishads, which he revealed in his short tome, Mind and Matter (compiled with What is Life?).

 

Many scientists have religious beliefs, but the pursuit of science is atheistic by necessity. Once you bring God into science as an explanation for something, you are effectively saying, we can’t explain this and we’ve come to the end of science. It’s commonly called the God-of-the-gaps, but I call it the God of ignorance, because that’s exactly what it represents.

 

I have 2 equations tattooed on my arms, which I describe in detail elsewhere, but they effectively encapsulate my 3 worlds philosophy: the physical, the mental and the mathematical. Mackay doesn’t talk about mathematics specifically, which is not surprising, but it has a special place in epistemology. He does compare science to religion in that scientific theories incorporate ‘beliefs', and religious beliefs are 'the religious equivalent of theories'. However, you can’t compare scientific beliefs with religious faith, because one is contingent on future discoveries and the other is dogma. All scientists worthy of the name know how ignorant we are, but the same can’t be said for religious fundamentalists.

 

However, he's right that scientific theories are regularly superseded, though not in the way he infers. All scientific theories have epistemological limits, and new theories, like quantum mechanics and relativity (as examples), extend old theories, like Newtonian mechanics, into new fields without proving them wrong in the fields they already described. And that’s a major difference to just superseding them outright.

 

But mathematics is different. As Freeman Dyson once pointed out, a mathematical theorem is true for all time. New mathematical discoveries don’t prove old mathematical discoveries untrue. Mathematics has a special place in our system of knowledge.

 

So what is scientism? It’s a pejorative term that trivialises and diminishes science as an epistemological success story.

Is the Universe deterministic?

 I’ve argued previously, and consistently, that the Universe is not deterministic; however, many if not most physicists believe it is. I’ve even been critical of Einstein for arguing that the Universe is deterministic (as per his famous dice-playing-God statement). 

Recently I’ve been watching YouTube videos by theoretical physicist, Sabine Hossenfelder, and I think she’s very good and I highly recommend her. Hossenfelder is quite adamant that the Universe is deterministic, and her video arguing against free will is very compelling and thought-provoking. I say this, because she addresses all the arguments I’ve raised in favour of free will, plus she has supplementary videos to support her arguments.

 

In fact, Hossenfelder states quite unequivocally towards the end of the video that ‘free will is an illusion’ and, in her own words, ‘needs to go into the rubbish bin’. Her principal argument, which she states right at the start, is that it’s ‘incompatible with the laws of nature’. She contends that the Universe is completely deterministic right from the Big Bang. She argues that everything can be described by differential equations, including gravity and quantum mechanics (QM), which she expounds upon in some detail in another video. 

 

My immediate reaction to this: is what about Poincare and chaos theory? Don’t worry, she addresses that as well. In fact, she has a couple of videos on chaos theory (though one is really about weather and climate change), which I’d recommend.

 

The standard definition of chaos is that it’s deterministic but unpredictable, which seems to be an oxymoron. As she points out, chaotic phenomena (which includes the weather and the orbits of the planet, among many other things, like evolution) are dependent on the ‘initial conditions’. An infinitesimal change in the initial conditions will result in a different outcome. The word ‘infinitesimal’ is the key here, because you need to work out the initial conditions to an infinite decimal place to get the answer. That’s why it’s not predictable. As to whether it’s deterministic, I think that’s another matter.

 

To overcome this apparent paradox, I prefer to say it’s indeterminable, which is not contentious. Hossenfelder explains, using a subtly different method, that you can mathematically prove, for any chaotic system, that you can only forecast to a finite time in the future, no matter how detailed your calculation (it’s worth watching her video, just to see this).

 

Because the above definition for chaos seems to lead to a contradiction or, at best, an oxymoron, I prefer another definition that is more pragmatic and is mostly testable (though not always). Basically, if you rerun a chaotic phenomenon, you’ll get a different outcome. The best known example is tossing a coin. It’s well known in probability theory (in fact it’s an axiom) that the result of the next coin toss is independent of all coin tosses that may have gone before. The reason for this is that coin tosses are chaotic. The same principle applies to throwing dice, and Marcus du Sautoy expounds on the chaos of throwing dice in this video. So, tossing coins and throwing dice are considered ‘random’ events in probability theory, but Hossenfelder contends they are totally deterministic; just unpredictable.

 

Basically, she’s arguing that just because we can’t calculate the initial conditions, they still happened and therefore everything that arises from them is deterministic. Du Sautoy (whom I referenced above) in the same video and in his book, What We Cannot Know, cites physicist turned theologian, John Polkinghorne, that chaos provides the perfect opportunity for an interventionist God – a point I’ve made myself (though I’m not arguing for an interventionist God). I’m currently reading Troy by Stephen Fry, an erudite rendition based on Homer’s tale, and it revolves around the premise that one’s destiny is largely predetermined by the Gods. The Hindu epic, Mahabharata, also portrays the notion of destiny that can’t be avoided. Leonard Cohen once remarked upon this in an interview, concerning his song, If It Be Your Will. In fact, I contend that you can’t believe in religious prophecy if you don’t believe in a deterministic universe. My non-belief in a deterministic universe is the basis of my argument against prophecy. And my argument against determinism is based on chaos and QM (which I’ll come to shortly).

 

Of course, one can’t turn back the clock and rerun the Universe, and, as best I can tell, that’s Hossenfelder’s sole argument for a deterministic universe – it can’t be changed and it can’t be predicted. She mentions Laplace’s Demon, who could hypothetically calculate the future of every particle in the Universe. But Laplace’s Demon is no different to the Gods of prophecy – it can do the infinite calculation that we mortals can’t do.

 

I have to concede that Hossenfelder could be right, based on the idea that the initial conditions obviously exist and we can’t rewind the clock to rerun the Universe. However, tossing coins and throwing dice demonstrate unequivocally that chaotic phenomena only become ‘known’ after the event and give different outcomes when rerun. 

 

So, on that basis, I contend that the future is open and unknowable and indeterminable, which leads me to say, it’s also non-deterministic. It’s a philosophical position based on what I know, but so is Hossenfelder’s, even though she claims otherwise: that her position is not philosophical but scientific.

 

Of course, Hossenfelder also brings up QM, and explains it is truly random but it’s also time reversible, which can be demonstrated with Schrodinger’s equation. She makes the valid point that the inherent randomness in QM doesn’t save free will. In fact, she says, ‘everything is either determined or random, neither of which are affected by free will’. However, she makes the claim that all the particles in our brain are quantum mechanically time reversible and therefore deterministic. However, I contend that the wave function that allows this time reversibility only exists in the future, which is why it’s never observed (I acknowledge that’s a personal prejudice). On the other hand, many physicists contend that the wave function is a purely mathematical construct that has no basis in reality.

 

My argument is that it’s only when the wave function ‘collapses’ or ‘decoheres’ that a ‘real’ physical event is observed, which becomes classical physics. Freeman Dyson argued something similar. Like chaotic events, if you were to rerun a quantum phenomenon you’d get a different outcome, which is why one can only deal in probabilities until an ‘observation’ is made. Erwin Schrodinger coined the term ‘statistico-deterministic’ to describe QM, because at a statistical level, quantum phenomena are predictable. He gives the example of radioactive decay, which we can predict holistically very accurately with ‘half-lives’, but you can’t predict the decay of an individual isotope at all. I argue that, both in the case of QM and chaos, you have time asymmetry, which means that if you could hypothetically rewind the clock before the wave function collapse or some initial conditions (whichever the case), you would witness a different outcome.

 

Hossenfelder sums up her entire thesis with the following statement:

 

...how ever you want to define the word [free will], we still cannot select among several possible different futures. This idea makes absolutely no sense if you know anything about physics.

 

Well, I know enough about physics to challenge her inference that there are no ‘possible different futures’. Hossenfelder, herself, knows that alternative futures are built-into QM, which is why the multiple worlds interpretation is so popular. And some adherents of the Copenhagen interpretation claim that you do get to ‘choose’ (though I don’t). If the wave function describes the future, it can have a multitude of future paths, only one of which becomes reality in the past. This derives logically from Dyson’s interpretation of QED.

 

Of course, none of this provides an argument for free will, even if the Universe is not deterministic.

 

Hossenfelder argues that the brain’s software (her term) runs calculations that determine our decisions, while giving the delusion of free will. I thought this was her best argument:

 

Your brain is running a calculation, and while it is going on you do not know the outcome of that calculation. So the impression of free will comes from our ‘awareness’ that we think about what we do, along with our inability to predict the result of what we are thinking.

 

You cannot separate the idea of free will from the experience of consciousness. In another video, Hossenfelder expresses scepticism at all the mathematical attempts to describe or explain consciousness. I’ve argued previously that if we didn’t all experience consciousness, science would tell us that it is an illusion just like free will is. That’s because science can’t explain the experience of consciousness any better than it can explain the intuitive sense of free will that most of us take for granted.

 

Leaving aside the use of the words, ‘calculation’ and ‘software’, which allude to the human brain being a computer, she’s right that much of our thinking occurs subconsciously. All artists are aware of this. As a storyteller, I know that the characters and their interactions I render on the page (or on a computer screen) largely come from my subconscious. But everyone experiences this in dreams. Do you think you have free will in a dream? In a so-called ‘lucid dream’, I’d say, yes.

 

I would like to drop the term, free will, along with all its pseudo-ontological baggage, and adopt another term, ‘agency’. Because it’s agency that we all believe we have, wherever it springs from. We all like to believe we can change our situation or exert some control over it, and I’d call that agency. And it requires a conscious effort – an ability to turn a thought into an action. In fact, I’d say it’s a psychological necessity: without a sense of agency, we might as well be automatons.

 

I will finish with an account of free will in extremis, as told by London bomber survivor, Gill Hicks. Gill Hicks was only one person removed from the bomber in one of the buses, and she lost both her legs. As she tells it, she heard a voice, like we do in a dream, and it was a female voice and it was ‘Death’ and it beckoned to her and it was very inviting; it was not tinged with fear at all. And then she heard another voice, which was male and it was ‘Life’, and it told her that if she chose to live she had a destiny to fulfil. So she had a choice, which is exactly how we define free will and she consciously chose Life. As it turned out, she lost 70% of her blood and she had a hole in the back of her head from a set of keys. In the ambulance, she later learned that she was showing no signs of life – no pulse and she had flatlined – yet she was talking. The ambo told the driver, ‘Dead but talking.’ It was only because she was talking that he continued to attempt to save her life.

 

Now, I’m often sceptical about accounts of ‘near-death experiences’, because they often come across as contrived and preachy. But Gill Hicks comes across as very authentic; down-to-Earth, as we say in Oz. So I believe that what she recalled is what she experienced. I tell her story, because it represents exactly what Hossenfelder claims about free will: it defies a scientific explanation.