Fundamental

by Tim James

  This is why carrying out the experiment for real would be pointless. Schrödinger’s cat would never be observed in a superposition because that’s the point of Copenhagen – you measure the eigenstate a superposition randomly collapses into, never the superposition itself. Opening the box in the real world will not present you with the dead/alive superposition but a classic eigenstate of either a living kitty or a mess and a guilty conscience.

  CHAPTER SEVEN The World is an Illusion

  NOW YOU SEE ME, NOW YOU DO NOT

  The Disney/Pixar movie Toy Story and its sequels are really about quantum mechanics. The main characters are toys who, when being observed by their owner Andy, behave like ordinary toys, but when he stops looking they come to life.

  Andy never sees the toys in their live state and only ever observes their classical behaviour. He also never seems to notice that they shift position in between each playtime (as kind-hearted as he is, he ain’t the most observant kid). But if he were to watch closely he might notice that each time he observes his toys, they are in a slightly different location.

  Particles are similar. When we look away from them they seem to be doing something very different to when we are watching. We can make guesses about where they are likely to wind up by using the Schrödinger equation, but we can never predict exactly what is going to happen each time we walk into the room.

  Suppose Andy began keeping a close tally of where each toy shows up and what state it is in each time. He might begin to notice that he can only describe their observed state using probability. For instance, there could be a 90 per cent probability Woody will be where Andy left him last time, but it is conceivable (the probability is not zero) that Woody is now on the other side of the room, or even outside the building somewhere.

  If Andy was a Copenhagenist he would come up with a neat mathematical explanation for what was happening. His toys exist in all locations simultaneously, arranged in every possible configuration, until he enters the room, at which point their superpositions collapse into something classical. But here is the infinity and beyond question: what is it about Andy’s presence in the room that triggers the toys’ wavefunctions to change?

  There’s a scene in the first Toy Story where Woody explains to a group of other toys that they are going to have to break the ‘rules’ of being a toy, but what exactly are these rules and who decides them?

  If we set up a camera in Andy’s bedroom, would the toys come to life? What if they are being watched from behind and do not know about it? Why do they stay in their living state when another toy observes them? Why does the dog Buster not count? What about an artificially intelligent robot? Would a chimpanzee trigger a collapse? What about the bit where the evil child Sid sees Woody talking and has a nervous breakdown, causing him to give up on school and choose to work for the refuse collection services by Toy Story 3? (Keep an eye out, it’s definitely Sid in a cameo.)

  Trying to figure out the philosophical implications of measurement in the Toy Story universe is a nightmare, but that is what we have to do in quantum mechanics. The measurement problem is not just counterintuitive, it raises serious questions about what makes reality real.

  Sometimes the measurement problem is muddled up with the Heisenberg uncertainty principle but they are not quite the same. The measurement problem says a particle chooses what state to be in when observed, the uncertainty principle says that even when we make that observation, we are forced to abandon all other information about it.

  An analogy for Heisenberg uncertainty would be something like Andy having an eye problem and needing specially tinted glasses to see. When he looks at his toys without these glasses he can tell what colour they are, but the image is blurred. He has certainty of colour but not shape. If he puts his glasses on, the toys become sharp but he is looking through coloured glass and cannot tell what colour they are any more. He can choose to measure colour or shape but never both.

  YOU’VE GOT A FRIEND IN ME

  In 1932 the physicist John von Neumann decided to break the double-slit experiment down and analyse every aspect mathematically to discover which stage was responsible for causing the collapse of the wavefunction. Some aspect of the measurement process had to be special.

  He studied the particle being generated, he studied it leaving the emitter, touching the slits, moving through them, emerging on the other side and so on, calculating the relevant wavefunctions as he went. At the end, to his great annoyance, he found that none of the stages were special. Every part of a quantum mechanical experiment is physically equivalent to every other.1

  This is pretty damaging for the Copenhagen interpretation because if nothing could be shown to cause wavefunction collapse, why is it collapsing in the first place? Bohr and Heisenberg shrugged their shoulders, Einstein scratched his ruffled hair and Schrödinger had his bedroom door closed. It’s best we do not ask what was going on inside.

  The most widely discussed (and poorly represented) solution to the measurement problem was eventually posed by the Hungarian physicist Eugene Wigner, who extended the Schrödinger cat experiment to include the scientist running it herself.

  We have a cat sealed inside a box, existing in a dead-live superposition and when the scientist opens the box, she finds it collapsed into one eigenstate or the other. Fifty/fifty probability either way. But suppose the experiment is being done in a closed room while Wigner is waiting outside.

  If we take the Copenhagen interpretation seriously then the particle both triggers and does not trigger the detector, killing the cat and not killing it at the same time. From Wigner’s perspective, his scientist friend would thus open the box and simultaneously discover a dead cat and living cat. Wigner’s friend would be in a superposition of relief that the cat was alive but also in a state of horror, looking for the scrubbing brush and spatula. It is only when Wigner opens the door to the lab and finds out what is going on that the wavefunction of his friend collapses.2

  But this is preposterous. Wigner’s friend could not be in a superposition because human minds have never been observed doing that. At no point do humans simultaneously observe and not observe something. Conscious awareness is something that always exists in eigenstates. Therefore, said Wigner, consciousness must be the thing collapsing wavefunctions.

  According to Wigner, when we talk about measurement we are literally talking about a sentient mind making an observation and since a mind cannot exist in superposition, the particles it observes cannot either.

  To be clear, Wigner was not some lightweight yahoo with an internet diploma in quantum-avocado studies. He had a Nobel Prize to his name and a reputation as a hard-nosed physicist. Introducing consciousness to the debate was not something he relished doing but he saw no alternative.

  BE CAUTIOUS HERE

  Consciousness was and still is a mystery, but since every other part of the experimental chain can be described, wavefunction collapse had to occur inside a conscious mind, the one place we did not fully understand.

  Wigner’s interpretation implies a few seriously surreal things though. For starters, it would mean the mind has an effect on particles rather than the other way around.

  Second, it would imply that the entire universe was in a state of superposition for billions of years until conscious creatures evolved to observe it. Surely at some point early in human history when the population was small and less spread out, there must have been moments when nobody was watching the moon. Did it jump on these occasions? If so, why did the Earth not lose its stable position in orbit around the Sun and go careening off into oblivion?

  Is something always looking at the moon to stop this happening? Could there be a supreme mind consciously observing the universe at all times, keeping it in check when nobody else is observing?

  To that end, here is a provocative limerick allegedly penned by the philosopher and theologian. Ronald Knox on the subject of observation:

  There was a young man who said ‘God

  Must find i
t exceedingly odd

  To think that a tree

  Should continue to be

  When there’s no one about in the quad.’

  Reply:

  ‘Dear Sir: Your astonishment’s odd;

  I am always about in the quad.

  And that’s why the tree

  Will continue to be

  Since observed by, Yours faithfully, God.’

  THE MAGICAL MIND

  Wigner’s consciousness idea was plucky but naturally it has been misinterpreted, particularly by certain members of the New Age movement. You may not have come across so-called ‘quantum spirituality’ teachings but I can brief you.

  When you look up quantum mechanics on the internet you will come across, along with genuine articles about the science, articles about crystals, exercise, left-wing politics. Buddhism, Hinduism, vegetarianism, yoga, self-identity and meditation. All of these are interesting topics worthy of discussion, but they are not related to quantum mechanics in any significant way.

  Quantum spiritualism is where ‘aspirational philosophy’ gets involved because many spiritual teachers claim that since consciousness impacts reality, you can make things happen by thinking about them. I am paraphrasing their teachings a little here, but that is what they do with quantum mechanics so I think it is fair game.

  I need to make it plain at this point that spirituality is an important topic, which everyone needs to address in their lives at some point. Indeed, many of the founders of quantum mechanics were deeply spiritual people (especially Schrödinger and Pauli). But we have to draw a line at what is and is not true.

  Observing something might trigger wavefunction collapse but it does not determine which eigenstate we end up with. That is still random.

  Each possible eigenstate has a ‘probability amplitude’ associated with it in the Schrödinger equation, which tells us the likelihood of it coming to fruition and the final state is determined by that, not the measurement.

  While it might be acceptable to say consciousness causes an eigenstate to materialise, anything that says you can influence how it does so is immediately wrong. You are an observer of reality, but you do not influence its form in a quantum sense. If you want to make the world a better place, then I am afraid you have to go the old-fashioned way and be a good person.

  Wigner’s version of the Copenhagen interpretation has, in the past, been an interesting part of the debate and it solves the cat paradox nicely since the cat’s consciousness is what collapses its own wavefunction. But if we are honest this is still a cheat.

  It says we do not know how a wavefunction collapses or what consciousness is, but these two intangible things somehow collaborate to present us with our world. It is once again pushing the mystery into a dark cave and saying, ‘This is where the answer happens, no peeking!’

  The brain is mysterious but mysterious does not mean ‘outside the laws of nature’: it just means we do not know the details yet. There are no reasons to invoke the supernatural when accounting for quantum observation and quite a few good reasons to ignore it.

  CHAPTER EIGHT Quantum Must Die

  ALBERT EINSTEIN ATTACKS QUANTUM THEORY!

  That was the New York Times headline on 4 May 1935 when the greatest physicist in the world, then fifty-six, turned against his own creation like Frankenstein abandoning his monster. Einstein always had misgivings about quantum mechanics, of course, and by 1935 he was dedicating all his time to its demise, with the help of his young assistant, Nathan Rosen.

  After years of blood, sweat, tears and a little help from a Russian physicist named Boris Podolsky, they finally found a chink in Bohr’s armour, which has since become known as the Einstein–Podolsky–Rosen problem, or EPR for short.1

  DOES THE CAT HAVE TO BE EXECUTED?

  The Schrödinger equation describes a particle as a list of square-rooted probable properties that change over time – a wavefunction – and there is no reason we have to limit this to one particle.

  A helium atom has two electrons occupying orbitals around its nucleus. Since wavefunctions can mix, the wavefunctions of both electrons can be combined to form a single ‘two-electron wavefunction’. It is more complicated to handle mathematically but it presents no problem in terms of the physics.

  We can go even further and add our electron-pair wavefunction to the proton and neutron wavefunctions in the nucleus, giving a wavefunction for a whole atom. In practice, doing such calculations is difficult and we usually have to take shortcuts (see Appendix II), but in theory we can calculate the wavefunction of anything we want, no matter how many particles it contains.

  Let us start with two electrons whose wavefunctions we combine. Every value we calculate on that wavefunction is now dealing with the pair as a single unit, rather than the individual electrons.

  A wavefunction for a pair of electrons can tell us that one of them is up-spin and the other is down-spin, but it cannot specify which is which until measurement. Because their wavefunctions are combined we have to describe the ensemble rather than the members.

  Schrödinger referred to two particles linked in this way as ‘entangled’ since we treat their properties as knotted together and cannot predict which particle will emerge with which property when the measurement happens.2

  We could think of an analogy by once again taking Schrödinger’s box but sealing two cats inside. Classically the two cats will be distinct. Mittens is a ginger cat with shaggy fur and long whiskers, while Boots is a black cat with coarse fur and short whiskers. But in quantum mechanics all we can say is that inside the box there exists the state of ‘ginger cat’ and ‘black cat’, along with the state ‘coarse hair’, ‘shaggy hair’, ‘stubby whiskers’ and ‘long whiskers’.

  We might open the box to find one of the cats is black with shaggy fur and stubby whiskers while the other is now ginger with coarse fur and long whiskers. It is impossible to say which was originally Mittens.

  Mittens does not exist any more because the features that defined her are no longer one thing, they are muddled up with Boots. So I am afraid the cat does have to cease existing, but it can get hybridised with another cat via entanglement.

  DIVIDE AND CONFUSE

  Suppose you have a particle in an unmeasured state, i.e. its spin is a superposition of up and down simultaneously. Now split it in two (do not worry how, just suppose you can) to form two daughter particles from your original. The wavefunction of the original parent particle has been splintered, but all its information is still there. The daughter particles have the combined properties of the parent but it is still not possible to say which has which.

  Using classical common sense we would conclude one of the particles is up-spin and the other is down-spin. But quantum mechanics says properties of particles are not determined until measurement. The pair exists in an overall up/down state and neither has decided which way it is going to be yet.

  Of course, if we now measure one of these particles it has to pick an eigenstate. Let’s say it picks up. The wavefunction for the pair is still up/down overall, and since one of the particles has chosen to be up, the unmeasured one has to become down at the same instant.

  The unmeasured particle is not allowed to stay in a superposition state because the overall wavefunction, according to Schrödinger, is up/down at all times. If we measure one of our particles into an eigenstate, the other has to take the corresponding eigenstate.

  In order for the unmeasured particle to collapse into the down state, however, the one which did get measured has to let it know. A message would have to pass between them saying something like, ‘I’ve collapsed into up-spin, you’d better collapse into down-spin now!’

  It would not matter how far apart the particles were either. We could do this On opposite sides of a room or opposite sides of a planet and the outcome would be the same. Quantum mechanics predicts that an entangled pair of particles must transfer information between them in zero time and this is where the EPR paradox arises. A signal c
annot go this fast because it violates the theory of special relativity.

  RELATIVELY SIMPLE

  Quantum mechanics was a team effort. Planck was the manager, Einstein was the captain, Bohr was goalkeeper (the actual position he played), de Broglie, Born, Sommerfeld and Pauli were midfield, then Heisenberg and Schrödinger were strikers with Stern and Gerlach in defence. Although typically Schrödinger was usually off to one side flirting with the other footballers’ wives. Oh, and their mascot was a cat. Obviously.

  Over thirty Nobel Prizes have been awarded for the development of quantum mechanics and while Einstein was a key figure, he was one among many. The theory of special relativity on the other hand was pretty much Einstein all the way.

  There are two theories of relativity: the general theory he came up with in 1916 and the special theory in 1905. We will be talking about general relativity towards the end of the book, but the EPR paradox is all about special relativity so let’s get familiar.

  The theory of special relativity states two things:

  1) Nobody’s perspective is special when taking measurements.

  2) The speed of light is the same for everyone, no matter how they are moving.

  The first postulate means nobody can truly say their measurements are objective. For example, you probably think you are sitting still right now. You are not. You are orbiting the Sun and your body is now 90 kilometres away from where it was when you started reading this sentence. This means your velocity will be different depending on who is holding the speedometer. From your perspective your velocity is 0 km/s but from the Sun’s point of view you are moving around it at 30 km/s. Special relativity says that both answers are valid, they are just relative to different surroundings.