*New Scientist*puts out booklets that contain articles published in their magazine (periodicals) on particular themes and two that I have are on quantum mechanics and cosmology. Both of these areas are at the frontiers of physics and therefore bump up against metaphysics and/or philosophy. So this post is intended to be a discussion of people's beliefs and my beliefs in particular, and how those beliefs affect our perspective(s) on science and reality. It needs to be pointed out that sometimes people argue metaphysical ideas as if they are scientific theories, when, strictly speaking, they're not. They will discuss their particular point of view as if it can't be challenged because (according to them) science has proved them right. I will provide examples as I progress.

Before I start, I need to mention a well-written book with a similar title:

*Why Beliefs Matter; Reflections on the Nature of Science*by E. Brian Davies (Professor of Mathematics at Kings College London and a Fellow of the Royal Society); which I discussed back in February 2011 (twice).

When I studied philosophy at a tertiary institution (which I never completed, I might add), one of the lecturers made a salient point which has stayed with me ever since: there are things you know and things you believe, and what you believe should be contingent on what you know and not the other way round. So, for the sake of consistency, I need to define what I mean by ‘things I know’. Scientific discoveries and theories that have been demonstrated valid through evidence, I call ‘things I know’, whereas philosophical ruminations I would call ‘things I believe’. So, for example, I would contend that evolution is something 'I know' because 150 years of accumulated evidence in a variety of disciplines tells me so, even though I’ve not made any of those discoveries myself nor ever contributed intellectually or otherwise to the discipline of evolutionary biology. It needs to be pointed out that the evidence that demonstrates evolution to be valid could equally demonstrate it to be false – the evidence is not neutral.

Because quantum mechanics and relativity theories both challenge our intuitive ideas of how the world works, they provide grist for philosophical and metaphysical interpretations, some of which border on the absurd. Whether I fit into that category or not, I leave for the reader to draw their own conclusions.

I will start with Einstein’s theories of relativity because they have become the basis of all cosmological theories developed over the last century. It was 100 years on November 2015 that he published his seminal paper on the General Theory of Relativity (the Special Theory of Relativity was published 10 years earlier in 1905). In fact, I attempted an exposition on the General Theory to mark the centenary of its birth. This is one of the ‘things I know’ because the sat-nav in your car, or on your phone, utilises both of these theories to provide accurate locations. Of course, there have been innumerable experiments that have proven Einstein’s theories correct in the 100 years that have past since their inception, so there’s no argument concerning their validity. However, there were beliefs held by Einstein, as a direct consequence of his theory, that have since been proven wrong. A mathematical consequence of his theory was to express time as a 4th dimension along with the 3 dimensions of space, which led to the concept of spacetime. Whereas space and time dimensions can change depending on an observer’s frame of reference and velocity, the combined dimension of spacetime remains unchanged.

One of Einstein’s beliefs was that time is a fixed dimension just like space, so the future is just as fixed as the past. In other words, Einstein believed in a strict determinism, which rules out free will. This strongly held belief led Einstein to dispute one of the fundamental tenets of quantum mechanics: that it was random and its outcomes could only be predicted by probabilities. So how can I claim that Einstein’s specific belief in this instance has been proven wrong? It’s generally acknowledged by physicists that quantum mechanics is one of the most successful theories, if not the most successful theory, in the history of science. And indeterminism is an intrinsic attribute of QM brought about by the collapse of the wave function, called its decoherence (which I’ll elaborate on later). In fact, this has led to a range of widely held beliefs, which I’ve discussed elsewhere.

Only a month ago I wrote a post challenging the beliefs of a correspondent to

*Philosophy Now*, who effectively argued that there is no time without consciousness. And a year ago (Nov 2016), I wrote a post challenging a paper written by a couple of academics in California that consciousness brings objects into ‘reality’ including spacetime, which is ‘impermanent’. And more recently, I came across an article in another

*Philosophy Now*magazine (Issue 93, Nov/Dec 2012) called

*On ‘Known-To-Be-False’ Materialist Philosophies of Mind*by Graham Smetham, a Buddhist philosopher. Yes, that’s the full title with ‘On Known-To-Be-False’ highlighted in red. Smethan argues that materialists (who argue that mind is a consequence of ‘materials’ like neurons and synapses in the brain) are using obsolete classical physics. To quote

*‘…the belief in the existence of solid material stuff which exists completely independent of mind is now about as scientifically acceptable as the phlogiston theory of heat.’*The context of this proclamation was the discovery of the Higgs boson at the Large Hadron Collider, which effectively demonstrates that ‘Mass, and so matter, are derived aspects of an

*insubstantial*process of reality.’ (Italics in the original.) Basically, Smethan adheres to an extreme interpretation of the Copenhagen interpretation of QM that ‘things’ only come into existence when observed by a conscious entity.

All three of these abovementioned ‘beliefs’ - argued as virtually indisputable - border on solipsism, which is the philosophical premise that everything you see and observe is the product of your mind. The problem with solipsism is that there can only be ONE observer, and everyone else is a product of that observer’s observations. To get around this, they would argue that mind came first, and all other minds are a consequence thereof, rather than a consequence of individual brains. Basically, they all argue that we have the causal process in reverse. Consciousness has not arisen out of an evolutionary process that itself arose from a cosmological process, but the entire cosmological process arose from mind, of which we are all a part.

There is a way, however, in which Smethan could be right, which he alludes to in his ‘Conclusions’. John Wheeler, who famously coined the term, black hole, has argued that we and the Universe are the consequence of a cosmic scale quantum time loop. The point is that QM allows for backwards in time possibilities that have been demonstrated experimentally. In the famous double slit experiment, it’s well known that ‘detecting’ which slit a photon will go through destroys the interference pattern that occurs when it goes through both. In other words, when we try and determine which slit a photon will go through it stops being a wave and becomes a particle. Only waves can produce interference, which infers that the photon goes through both slits simultaneously. Wheeler conjectured that if we ‘looked at’ the photon after it had gone through the slit(s) but before it hit the screen, it would have the same effect. This infers that the ‘detection’ works backwards in time. He was proven correct when the technology eventually caught up with his thought experiment.

There is something compelling about the idea that the Universe saw us coming, which would make it teleological and would support the so-called Strong Anthropic Principle. Paul Davies has argued cogently for the Strong Anthropic Principle without calling it by that name. In his book,

*The Goldilocks Enigma*, he looks at all current scenarios and ‘beliefs’ concerning the nature of the Universe, and he concludes that

*‘I have suggested that only self-consistent loops capable of understanding themselves can create themselves, so that only universes with (at least the potential for) life and mind really exist.’*This ‘belief’ is logically consistent with Wheeler’s ‘belief’ and it’s no coincident that Davies dedicated the book to Wheeler, whom he saw as a mentor.

In an earlier book,

*The Mind of God*, Davies expresses the same view in subtly different words:

*I belong to the group of scientists who do not subscribe to a conventional religion but nevertheless deny that the universe is a purposeless accident… I have come to the point of view that mind – i.e., conscious awareness of the world – is not a meaningless and incidental quirk of nature, but an absolute fundamental facet of reality. That is not to say that we are the purpose for which the universe exists. Far from it. I do, however, believe that we human beings are built into the scheme of things in a very basic way.*

I’ve written about this on other posts, and I’ve concluded that the Universe is pseudo-teleological in as much as the natural laws that it obeys allow for complex intelligent life to evolve without a blueprint or a final goal evident. Both QM and chaos theory make a deterministic universe virtually impossible - I will elaborate on this later.

Richard Feynman, who is arguably the most famous physicist in the post-Einstein era was mentored by Wheeler, and took Wheeler’s backwards in time idea and incorporated it into his Nobel Prize winning theory, QED (quantum electrodynamics).

Robbert Dijkgraaf, who is a professor at the Princeton Institute for Advanced Study and calls himself a mathematical physicist, describes in a not-too-esoteric lecture (on string theory) how Richard Feynman, in his Nobel Prize acceptance speech, told the world how he got this idea from Wheeler. Apparently Wheeler rang him up and said, ‘I know why all the electrons are exactly the same. It’s because they are all the same electron.’ So Feynman logically asked him how this could be and Wheeler responded: ‘Because the same electron simply repeats over time.’ If you go to the 19min mark of Dijkgraaf’s lecture, he explains it with images. What Dijkgraaf doesn’t explain is that an anti-particle (which is a positron in the case of an electron) going forward in time is mathematically equivalent to a particle (electron) going backwards in time. In an interview, I saw with Feynman, he said the ‘same electron’ idea he left alone but the ‘backwards in time’ idea he took from Wheeler.

And since we’re talking about time, I would like to reference a podcast someone alerted me to where scientists and philosophers explain how time has been effectively explained away in physics. While this is partly true, I found the discussion a little disingenuous, if not misleading, because they didn’t provide the context nor explain the significance of time in both relativity theory and QM.

To provide context, Carlo Rovelli, who has written a couple of popular science books (recently translated into English) has stated that at a fundamental level in physics, time disappears mathematically. And Paul Davies, whom I referenced above, has also written in

*The Goldilocks Enigma*: [The]

*vanishing of time for the entire universe becomes very explicit in quantum cosmology, where the time variable simply drops out of the quantum description.*To be more specific, John Wheeler and Bryce De-Witt, in the late 1960s, rewrote Einstein’s field equations for general relativity (gravity) in the same form as electromagnetism and time simply disappeared, which became known as the Wheeler-DeWitt equation.

And yet: Einstein’s very successful theories of relativity incorporate time as a 4th dimension into spacetime, which provides the effective structure of the Universe, even if it can be warped by gravity. And one of the most important and seminal equations in QM is the time dependent Schrodinger equation. What’s more, the wave function, which is the centrepiece of the equation, is incorporated into Feynman’s QED where its phase is time variant (as it is in Schrodinger’s original).

For me, this paradox simply underlines my ‘belief’ that time is the fundamental parameter that makes the marriage of general relativity with QM a stumbling block. I’ve written a number of posts on ‘time’ over a number of years, some of which I’ve plundered for this post. In one of the

*New Scientist*articles I referenced at the start of this post, Anil Ananthaswamy explains how the wave function of Schrodinger’s equation, whilst it evolves in time,

*‘…time is itself not part of the Hilbert space where everything else physical sits, but somehow exists outside of it.’*(Hilbert space is the ‘abstract’ space that Schrodinger’s wave function inhabits.)

*‘When we measure the evolution of a quantum state, it is to the beat of an external timepiece of unknown provenance.’*My ‘belief’, which I’ve expressed elsewhere, is that time doesn’t exist in QM (in the sense that Ananthaswamy describes above). I came to this conclusion even before I read Ananthaswamy’s article because it would explain superposition, which is a well known phenomenon in QM.

What’s more, the ‘external timepiece’ could be provided by gravity, since gravity determines the rates of clocks, even to the extent that clocks stop when they reach the event horizon of a black hole. I find this a compelling idea, and compelling ideas have a tendency to become beliefs.

And getting to the nub of the title of this post, it’s beliefs that drive science or scientific breakthroughs. Basically, scientists follow a belief until it’s validated or it’s proven wrong.

I mentioned Carlo Rovelli earlier, who is a proponent of loop quantum gravity theory, and one of his books I’ve read is

*Reality Is Not What It Seems: The Journey to Quantum Gravity*, which is essentially a brief and erudite history of physics going back to the Ancient Greeks. Curiously, he’s dismissive of Schrodinger’s equation, which he relegates to a footnote, and argues that the wave function is a mathematical fiction which has conceptually led people astray from a true understanding of QM. He argues that Heisenberg’s matrix formulation is conceptually superior because there is nothing in between observations – the wave function and Hilbert space simply don’t exist.

In his historical account of QM, Rovelli goes straight from Heisenberg to Dirac’s equation as if Schrodinger played no significant role. In fact, Dirac derived his eponymous equation from Schrodinger's, and therefore contains its own (fictional) wave function. Heisenberg and Schrodinger were rivals, philosophically, professionally and politically (during WW2, Heisenberg worked on the atomic bomb project for the Nazis while Schrodinger went into exile in Ireland). Max Born contributed to both Heisenberg’s matrix formulation and Schrodinger’s wave interpretation (by determining how to derive probabilities from Schrodinger’s eponymous equation). Even though Heisenberg eschewed Schrodinger’s wave function, Schrodinger was able to demonstrate that they were mathematically equivalent once Born’s rule was applied to his equation (by squaring the modulus of the wave function which removes the imaginary component). Dirac applied Einstein’s special theory of relativity to Schrodinger’s equation which provides negative energies (as Schrodinger himself had discovered and abandoned). But Dirac predicted that the negative energies could be interpreted as antiparticle electrons (positrons) and was later proven correct.

Obviously, Rovelli is far more knowledgeable on this topic than me, yet we have different ‘beliefs’, as do many other physicists. Jim Al-Khalili, a physicist at the University of Surrey, has written one of the best introductory books on QM I’ve read, called

*Quantum: A Guide for the Perplexed*. Unlike Rovelli, the wave function is key to his exposition and Schrodinger’s equation is the only equation in the entire book, which he calls 'the most important equation in physics'.

At the time I read Rovelli’s book, I also read Roger Penrose’s latest tome,

*Fashion Faith and Fantasy in the New Physics of the Universe*. I’ve long been a fan of Penrose and we share some ‘beliefs’, though I don’t necessarily share his ‘belief’ of a cyclic universe. Penrose can be delightfully edifying or maddeningly esoteric. This book, however, I found quite accessible, and he put the more challenging aspects of his exposition in an appendix.

I didn’t realise before that Penrose does most of his own illustrations, which are surprisingly good quality for someone not known for his artistic talents. On the back cover is an illustration (credited to Penrose) of a mermaid sitting on a rock with a seashore landscape in the background and the underwater world in the foreground, including the mermaid’s tail. I know from reading the book that this is a metaphor for Penrose’s own ‘beliefs’ regarding QM. The underwater world represents the quantum universe and the seashore represents the classical world of physics, with the water’s surface representing the wave function collapse or decoherence that delineates the two. From what I’ve read and know on this subject, most physicists ignore this dichotomy whereas I ‘believe’ there are 2 worlds that interact and the so-called collapse of Schrodinger’s wave function is the mathematical representation of that interaction.

Penrose ‘believes’ that gravity causes this decoherence and reading one of the

*New Scientist*articles I mentioned, decoherence occurs when superposition can no longer exist. The reason that superposition doesn’t occur on a macro scale, according to Penrose, is that if you get enough particles together they create a gravitational field which in itself can’t be superimposed. It’s well known that clock rates change in a gravitational field, even from your head to your toe. If you have a superposition (of 2) separated far enough then their different clock rates determined by Planck’s

*hf*(or atomically) will cause a decoherence so the particle suddenly becomes 1 in the so-called classical physical world.

In another

*New Scientist*article, Yakir Aharanov, at Chapman University, Orange, California, asked the fundamental question some 50 years ago:

*‘Does time in quantum mechanics have to flow from the past to the present? The answer, at least mathematically, is no.’*Aharanov along with a colleague, Jeff Tollaksen, has been performing experiments to attempt to demonstrate this. I won’t elaborate, but, of course, some argue that the experiments, whilst compelling, can be interpreted in other ways. But Aharanov says the mathematical interpretation of time symmetry is 'very elegant'.

However, the decoherence, which I argue is the interface between the QM and classical physics world, creates a time asymmetry that we are all familiar with: the past is fixed yet the future is open-ended. Once decoherence occurs, the time symmetry that Aharanov ‘believes’ becomes time assymetrical. Schrodinger once pointed out (according to John Gribbin’s biography) that the Born rule, which multiplies the complex component of the wave function by its conjugate to remove the imaginary component and provide a probability, is effectively the same as solving the equation both forwards and backwards in time. As Arthur I Miller points out in Graham Farmelo’s book,

*It Must Be Beautful*:

*‘Born’s aim was nothing less striking than to associate Schrodinger’s wave function with the presence of matter.’*In other words, it was Born’s great insight that gave us a mathematical means to go from the quantum world to the classical world by transforming Schrodinger’s equation into probabilities.

It should be pointed out that Schrodinger’s equation was purely suppositional. As Feynman once pointed out:

*‘No one knows where Schrodinger’s equation came from. It came out of Schrodinger’s head. It can’t be derived from anything we know.’*I’ve jokingly called Schrodinger’s equation God’s equation because it attempts to predict the future via probabilities, and, statistically, it’s proven very accurate.

So what about the mathematical prediction that time disappears in quantum cosmology. I don’t know enough to answer that, but I’ve always found the Hartle-Hawking model of the Universe somewhat compelling. They argue, mathematically, that the time dimension may have originally been a 4th 'spatial' dimension (expressed through complex algebra, therefore imaginary) and this implies that in the beginning there was no time. Now, people will say: How can you have a beginning without time? I don’t know, but I admit that the idea appeals to me.

Is time symmetrical at a macro level, without QM? It’s been argued that Newtonian physics allows for time reversal and it’s only entropy that provides a direction in time. Entropy’s time direction is usually explained by the example of dropping an egg on the floor. If you were to run a film (or video) backwards of the event with the egg coming together and rising from the floor, everyone would know it’s impossible. But entropy doesn’t really provide a direction for time because it’s based on probabilities. To give another example, if you open a bottle of perfume in a room the perfume molecules quickly disperse to all corners of the room, they don’t congregate in one corner. There is an infinitesimal probability that they could all end up in one corner but there is a much higher probability, that increases with time, that they will disperse everywhere.

However, time asymmetry on a macro scale (without QM) is caused by chaos theory. Chaos theory is described as deterministic but unpredictable, which sounds like a contradiction, but it’s dependent on initial conditions; which is why weather forecasts are only predictable short term. A slight change has long term effects, but short term is predictable. This even applies to the orbits of the planets, which, despite appearances, are mathematically chaotic. It’s Earth's position in its orbit that's unpredictable (in the order of 150 million km over 100 million years).

I think that one of the more insightful posts I’ve written for this blog was called What is now? However, one issue I didn’t really address was: Is there a universal now? Towards the end of that post I explained how Einstein’s special theory of relativity made simultaneity impossible to be agreed upon by different observers, pending their relative velocities and positions in spacetime. Einstein concluded that there was no universal 'now' because everyone’s ‘time’ was different.

However, as we’ve already seen, Einstein was not infallible. One of the

*New Scientist*articles I read challenges this particular aspect of Einstein’s relativity. Certainly, people who are in the same ‘frame of reference’ (occupy the same dimensional point of spacetime) would agree on ‘now’. Rovelli, whom I cited earlier, has argued that ‘now’ is the edge of the Big Bang. In my previous post, I made the point that we talk about an ‘age of the Universe’ which infers a universal now and I tend to agree with Rovelli: it’s the edge of the Big Bang which is everywhere in the Universe, including where you are currently standing or sitting. And entanglement, which is a feature of QM that doesn’t exist in classical physics, also infers a universal now. Science fiction writers, like myself, adopt a universal now even though we know we can’t physically send a signal anywhere in the Universe faster than the speed of light. But this contradiction (between relativity and QM) led to a renowned debate between Einstein and Niels Bohr, where Einstein famously called entanglement: ‘spooky action at a distance’. To cut a century long story short, every experiment, which has tested entanglement over relativity, has shown that QM triumphs.

This is a post with no conclusions, just a collection of ‘beliefs’, so I’ll finish with a joke provided by Robbert Dijkgraaf in his aforementioned video (at the 45 min mark).

*What’s the difference between a physicist and a mathematician?*

A physicist studies the laws that God provided nature to obey.

A mathematician studies the laws that God has to obey.

A physicist studies the laws that God provided nature to obey.

A mathematician studies the laws that God has to obey.