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### It may be possible to both understand and not understand Schrödinger's Cat at the same time

The danger of referring to a quantum mechanics thought experiment like Schrödinger's Cat, as I did in a recent post, is that readers then expect you to be able to explain quantum mechanics. I can't, obviously.

But then physicist and Nobel laureate Richard Feynman said, "I think I can safely say that nobody understands quantum mechanics." This, presumably, includes himself, the world's foremost authority on quantum mechanics at the time, so I think I'm off the hook.

##### An unscientific approach to quantum mechanics

That said, my fundamental inability to understand quantum mechanics has not stopped me from reading and thinking about it. In this post I set out what are my completely un-scientific musings on the subject, as well as on what appear to be the related topics of consciousness and free will.

It relates to investing only in so far as forcing yourself out of your comfort zone - whether away from the comfort of being part of the investing herd or into territories in which you feel intellectually at sea - is, I believe, always a good idea.

Feel free to hurl abuse at me for even thinking that I could and should write about these complex and specialist topics. Or to send me contact details of a shrink. On the other hand, you may be where I was a decade or two ago - yearning to learn, but having little idea where to start - and therefore be supportive. Or, of course, you are ahead of me, very possibly considerably so, in which case you will be able to tell me where I am getting this wrong.

Amateurs and non-specialists are always at a disadvantage when it comes to understanding specialist subjects. Quantum mechanics must be the granddaddy in that regard, given that mathematicians and physicists have built a complex mathematical language/framework to describe, per Feynman's remark, the incomprehensible.

##### Schrödinger's equation and the hidden world of the wave function

The centrepiece of this framework is Schrödinger's equation which, as far as I can tell, says that the nature of reality changes - from being quantum/weird to Newtonian/mechanical/not weird - when it is observed or measured. Moreover, the existence of the two worlds was demonstrated empirically by the so-called double slit experiment in which light behaved like a wave until it was observed whereupon it behaved like a particle. Hmmm.

Beneath the world we consciously experience/observe is a hidden quantum world described by a so-called wave function that represents an infinite range of possibilities. When we observe/experience/interact with this hidden - quantum - world, the wave function collapses into one of its infinite number of possibilities i.e., into an observed outcome. This realm of observed outcomes is the mechanical/non-quantum/Newtonian world that we experience, know and love.

How on earth can us non-specialists even begin to understand what it means to say that the nature of reality changes when it is observed? By analogy, perhaps. One that has helped me involves tossing a certain number of coins at the same time.

##### An analogy to help understand the quantum and non-quantum worlds

Before the coins are tossed, the various outcomes in terms of number of heads and tails can be described by a so-called probability density function, PDF. The probability of getting k heads, P(X=k), is a function of the probability of getting a head, p(h), the number of coins, n, and the required number of heads, k.

(I won't bother writing the formula here as I do not want to complicate things any further, but if you are interested you can read about it here.)

When three coins are tossed, one of the possible outcomes is realised: two heads and one tail, for example. All possible outcomes were described by the PDF - no heads/three tails, one head/two tails, two heads/one tail, three heads/no tails - but only one of them was realised: two heads/one tail*.

(*The probability of this particular outcome is 37.5pct.)

So, the PDF that describes the probabilities of the various coin toss outcomes is analogous to the wave function of the quantum world. The specific outcome of two tails and one head is akin to the Newtonian/non-quantum/mechanical world that we experience/perceive. Tossing the coins collapses the probability density function into a specific outcome, analogous to the wave function of the quantum world collapsing into a specific reality that we perceive as our familiar world of everyday experience, time, and space.

In other words, what we see in our everyday experience are the equivalent of a whole load of coins, a whole load of heads and tails. It's just that we have no grasp, no understanding, of how they got there, of what it means to toss a coin - it was some mysterious being that tossed the coins, name beginning with G perhaps. Quantum mechanics seems to say that we know there must be a process by which time and space arise from a hidden world, we just don't understand what it is.

##### Plato's Cave and Edwin Abbott Abbott's novella, Flatland

Of further help may be Plato's Cave and Edwin Abbott Abbott's novella, Flatland. These are both allegories that describe hidden worlds beyond our comprehension.

The former tells of prisoners hanging in a cave facing the back wall. All they ever see on the wall are the shadows of people passing back and forth in front of the cave entrance. They cannot see their features - which are hidden, out of reach - just their shadows.

Flatland is similar in that it describes a flat - 2D - world inhabited by 2D shapes that move around, change shape etc. The inhabitants have no way of understanding that they are in fact shadows cast on their 2D world by 3D objects passing through it - a sphere passing through Flatland would look like one of them: a circle appearing, getting bigger, then smaller, then disappearing. How on earth could a circle perceive a sphere?

To put these analogies in their intended context, if what we call reality - space, time, etc. - is the equivalent of the 2D shadow/circle - but almost infinitely more complex than it - then pondering its 3D version is likely to give you the mother of all migraines!

##### A rather terrifying thought experiment

Now, if you can, try to imagine that all your senses suddenly cease to work - your sight, hearing, smell, taste, touch. Pause to think about that for a moment if you need to - it's not easy. All that you are left with are your thoughts, your consciousness. Nothing else.

(I find this experiment rather terrifying, as might you, but you can get reasonably close to the experience in an isolation tank - there is a good reason why they have panic buttons.)

At least at first, you have a clear memory of the reality - the world - that you previously were able to experience with your senses: the people, the buildings, the smells, sounds etc. In fact, you can still picture that world in your mind, as you often did before. You may therefore continue to believe that you are still inhabiting the same physical, objective world, it's just that you can no longer perceive it with your senses.

After a while, however, your memories of that physical, objective world fade, get distorted, disappear, and you struggle to picture it. Indeed, because the only things that exist for you in any real sense are your thoughts, you might start to think that you had it the wrong way round all along. That you in fact did not exist in some external, objective reality but that it existed internally in you, in your consciousness.

##### Reality is a figment of our imagination

In other words, it is our consciousness that is fundamental, not the physical world of objects that we feel is out there. What we call reality is subjective - a function of our unique conscious perception aka you - not objective i.e, external/out there/outside of you.

This perspective now makes complete sense to me, but before you call me a loony, know that it is the one that is central to Buddhism, to a major branch of philosophy, and increasingly is being studied by scientists, many of them computer scientists.

Once one accepts that reality is subjective not objective, another paradox rears its ugly head. Namely, if we all experience reality subjectively, how can we all agree on the same - i.e., objective - laws of physics and other mathematical constructs? Kepler's and Newton's equations describing motion work for everyone, not some, nor just you.

And how can both you be in my consciousness and I be in yours simultaneously? If we stand facing each other, I'm watching you watching me watching you watching me watching you watching...arghhh! It's like being taped to a Möbius strip inside/outside a Klein bottle going up/down one of Escher's impossible staircases! Help! Get me out of here!

##### Everything is maths

But then, of course, if consciousness is all there is, then it is fundamental, objective. Whilst it is impossible for boxes to be inside each other in a mechanical world of objects, it makes complete sense if all there is is consciousness. Newton's, Kepler's, and other mathematical equations work necessarily because consciousness itself is mathematical. Force equals mass times acceleration because force equals mass times acceleration.

Maths does not describe the world we experience, it is the world we experience. Only in some unfathomably complicated way that we can at best only glimpse. Moreover, that the so-called real world does not exist outside of us does not preclude physicists and mathematicians from trying to understand it further and finding new formulae to describe it. If the maths works, it doesn't matter where reality exists!

As for the study of consciousness, despite many scientists dedicating their lives to it, it seems that the goal of understanding it will necessarily be always and tantalisingly out of reach. Why? Because we are using our consciousness to try to understand consciousness, which is like a brick trying to understand a brick i.e., absurd.

Of course, using our consciousness to understand or consider a brick is a conceptually consistent notion and indeed is what we do when we think about bricks. It also makes sense that we use our consciousness to try to understand the brain. The brain after all is like the brick - just another perceived object. It is not the same as consciousness. Indeed, they are as different as it is possible to be.

##### How is free will possible?

Which brings us to free will, the familiar feeling that we are able to make choices.

In a deterministic, mechanical world made up of lifeless fundamental subatomic particles analogous to billiard balls that are on unambiguous, predetermined paths, free will is impossible. Indeed, mathematicians John Conway and Simon Kochen proved in their Free Will Theorem that if we have free will, then so too must fundamental particles.

In other words, our mechanical model of the subatomic world, of the fabric of reality, must be wrong. But then if, as alluded to earlier, the physical world is just a figment of our imagination, and thus there can be no mechanical explanation of consciousness, then free will can start to make sense.

(By the way, you may be intrigued by this series of lectures in which Conway and Kochen explain their theorem. I tried to watch them, but they lost me, and I gave up).

##### What is Schrödinger's Cat?

Schrödinger's Cat is a thought experiment in which a live cat is placed in a box along with a glass vial of lethal gas, a hammer, a trigger mechanism, and some radioactive material. The cat dies if the radioactive material decays, emits a particle, triggering the hammer, which breaks the glass vial, releasing the lethal gas.

Since you are outside the box, you cannot know whether the radioactive material has decayed and thus whether the cat is dead - you cannot open the box to see, because you could be exposed to the lethal gas. If the cat can only be either alive or dead, and you cannot know which, it is deemed to be both alive and dead at the same time. After all, this viewpoint doesn't change anything, and seems conceptually more consistent than dunno.

In other words, Schrödinger's Cat is an analogy that helps explain the notion that there exists a hidden - quantum - world, one in which there are multiple/infinite possibilities - in the case of the cat, two - but one which we can never see/understand. The quantum world, consciousness, free will, are analogous to the passers by in Plato's Cave, to the 3D beings in Flatland, and to Escher's staircases. The landed coins and the shadows in The Cave and Flatland to our everyday experience, what we call reality.

At least that's my take. I could also, of course, be completely wrong.

The views expressed in this communication are those of Peter Elston at the time of writing and are subject to change without notice. They do not constitute investment advice and whilst all reasonable efforts have been used to ensure the accuracy of the information contained in this communication, the reliability, completeness or accuracy of the content cannot be guaranteed. This communication provides information for professional use only and should not be relied upon by retail investors as the sole basis for investment.

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