by Tim James
An electron’s magnetism must be due to some mysterious property they possess in addition to charge, but by the time we realised this everyone was already imagining electrons rotating, so we stuck with the name and called this mysterious property, rather unhelpfully, ‘electron spin’. It does not literally mean an electron is spinning on an axis, it is just the word we use to refer to the electron’s magnetic nature.
In order to probe what was going on with this ‘spin’ property, the German duo Otto Stern and Walther Gerlach decided to measure the spin of particles by firing them through a gateway with a magnetic field stretched across it, slightly stronger at one end to engender an overall force on the particle (rather than cancelling out on both sides).
As a magnetic particle was fired through this gateway and passed through the magnetic field, it should have been deflected at an angle, depending on how much it happened to be ‘spinning’ at that moment. Again, we knew it was not literally the particle whirling round, but whatever spin was it should come at lots of different values with particles deflecting all over the place.
What Stern and Gerlach found instead was that the particles flew in two directions only. Spin (whatever it is) is always the same size but either goes in the same direction as a magnetic field or against it. There were no in between values which means spin, just like energy, is another quantised property.1
At this point, it would have made sense to stop using the word spin and refer to it as magnetic charge or something. But everyone clung stubbornly to spin and, just to be super-extra helpful, rather than calling the two types clockwise and anticlockwise, Stern and Gerlach called them up-spin and down-spin (see Appendix I for a slightly more detailed discussion of spin and magnetism).
The Schrödinger equation was then duly modified by the physicist Wolfgang Pauli to take spin into account, giving us the Pauli equation.
Pauli had a reputation for lab incompetence even worse than Heisenberg’s, so much so that his colleagues referred to the spontaneous malfunctioning of equipment when he entered a room as ‘the Pauli effect’. But, like Heisenberg, he was a theoretical physicist par excellence and his equation was a fantastic modification.
Schrödinger’s equation tells us the probable location of a particle when we measure it and Pauli’s version tells us its probable spin. Our definition of ‘wavefunction’ should really be expanded to mean a list of all a particle’s probable properties including spin, energy, momentum, location, favourite film and whatever else we want to know about it.
ELECTRON’S CHOICE
So, we’ve split our electrons into two beams based on their spin using a Stern–Gerlach gateway and got them emerging in a fifty/fifty ratio. Some electrons have an up-spin property and some have a down-spin. Now, imagine taking just the beam of up-electrons and sending it through a second gateway. For fun.
Every electron in this beam carries on through the gateway in a straight line, just as expected. We’re sending up-spin electrons through, so naturally they all come out in the upward direction only. But now suppose we rotate the second gateway by ninety degrees. The beam of up-electrons splits in two, this time flying left or right.
Spin is apparently determined along whichever axis we are looking at, so obviously if we set our magnets horizontally we should get left and right beams emerging.
We have now separated all our electrons into up or down categories and then subdivided the up-electrons into left and right.
Let’s now take the up-left electron beam and put it through yet another gateway, this time set vertically like the first one. We have got a stream of up-left electrons going through a vertical gate so we should clearly get a single beam of ‘up’ electrons coming out the other side. We do not: 50 per cent of the electrons go down.
NEVER LET THEM GET YOU DOWN
Imagine we had a group of people and we sent them through a hospital clinic for blood testing. First, we send them through a triage that separates A-type from B-type blood. Then we take the A-type people and send them through a second clinic to distinguish A+ from A−. Once that’s done we take the A+ people and send them back through the first clinic, only to discover that some of them have spontaneously transformed their blood into B-type. This is what electrons are apparently doing with their spin. But how can this be so?
Well, we assumed that when we sent our up-electrons through the left/right gateway they came out with their up-ness intact. But that would not explain what we actually see. Technically, when we fire up-electrons through a left/right gateway, all we know for definite on the other side is their left/right spin. We do not know what their up/down spin is any more, so there is no reason to assume it is still there. It looks as though measuring the left/right spin of an electron makes it forget about its up/down spin.
This presents us with a new Heisenberg uncertainty relationship: we can never know two axes of spin for a particle simultaneously. The vertical and horizontal spin can be measured individually but measuring one erases the other, just as measuring a particle’s location erases its momentum. But there is something even stranger going on.
A particle’s properties get erased if we are measuring its complementary property, which would imply that the very act of measuring itself somehow causes a particle to adopt properties in the first place.
The Stern–Gerlach experiment shows that the spin property we are not measuring gets lost and we can only get it back by measuring it again. Apparently, a particle’s properties are literally not there when we are not looking. Which means Empedocles’s ancient idea that our eyes are what make an object have an appearance may contain a shaving of truth after all.
ARE YOU WATCHING CLOSELY?
Looking back at the double-slit experiment, we have to wonder if we understood it correctly. We assumed the particle had a definite location when it went through the double slit but maybe it did not. Maybe the double-slit result arises because the electron is not an electron at all and exists in some freaky-deaky ghost state, only becoming a particle with clearly defined properties when we measure it at the detector screen.
Schrödinger’s wave equation lets us calculate the probability of a particular outcome, but until we actually measure for that outcome, nothing is decided. The particle does not go through either slit because it is not a particle with any properties yet.
What we really ought to do is put some kind of tiny camera next to each slit and watch what the particle does at the moment of decision. If the particle is really there we should be able to see it making its choice. Seems sort of obvious now that we say it.
All right, confession. The experiment concerned does not really put a small camera beside the slits but getting into the specifics of slit measurement is quite tedious, so let’s just imagine for now that it really is done with miniature camera crews.
Prior to Stern and Gerlach’s results we would have expected to record footage of a particle going through both slits at once. What actually happens is one of the most peculiar results in physics. With a camera filming the slits, electrons suddenly go through one at a time like classic particles and the quantum zebra-stripes vanish.
Putting a camera on the slits is a form of measurement and that somehow causes a particle to become a particle. When we do not film them, particles do wave stuff but the instant we switch on a camera they go back to behaving normally. We expect that sort of behaviour from politicians but not from particles. I mean how in the name of Max Planck’s light-bulb-munching ghost does a particle know if our camera is switched on or not?
This is known as the ‘measurement problem’ for self-evident reasons. When we are not observing a particle its momentum, energy, spin and even location are wobbling about in some non-decided nothingness we never see directly. Measuring them somehow forces them to adopt properties in the real world. Particles apparently care if we’re paying attention.
CHAPTER SIX The Box and the Pussycat
THE DANISH WAY
As the observations poured in and the eq
uations solidified, two camps began to emerge, each with its own view on how to move forward with the weirdness.
In one camp were the philosophers who wanted to understand the true nature of quantum mechanics. People such as Einstein, Schrödinger and de Broglie.
In the other camp were the number crunchers who wanted to use quantum mechanics without worrying about what it all meant, the most prominent of which were Bohr and Heisenberg, working out of Copenhagen.
In 1930 Heisenberg wrote a book called The Physical Principles of the Quantum Theory in which he summarised the view he and Bohr had been cooking up over the years. He referred to their vision as ‘das Copenhagen giest’, which literally translates to ‘the Copenhagen ghost’, although a word such as soul or spirit is more in line with his meaning. I’m afraid quantum mechanics does not quite prove ghosts are real, although it does make a pretty good case for the undead (stay tuned).
The ‘Copenhagen interpretation of quantum mechanics is a pragmatic perspective which says the deep laws of physics are too removed from human experience so we will never understand them.
It argues that just as colours can mix to form white, properties of a particle can mix to form a ‘superposition state’ in which it spins neither up nor down and exists neither here nor there. It is everything and nothing at the same time.
In Heisenberg’s own words, ‘particles themselves are not real; they form a world of potentialities or possibilities rather than one of things or facts’.1
Particles do not care whether they make sense to us and are not going to bend to our human limits, so we have no choice but to take them at face value. You either fall in love with what you see or run away screaming. Wavefunctions ripple in a partly real, partly imaginary way, measurement changes them and there is nothing more to say on the matter. End of discussion.
SUMMARISED
Annoyingly, Bohr and Heisenberg never specified all the minute details of their belief in full. You could sometimes pin them down to specific answers but, like the quantum particles themselves, they kept things nebulous if they could help it. Here, however, is a rough summary of what they believed.
When not being measured, nature exists in a plural of states (or an absence of them) called a superposition, but when we take a measurement we swat this superposition down like a fly against a wall, forcing it to become one thing.
Schrödinger’s equation tells us the probable outcome of the measurement but nothing is decided until it actually happens and we say the superposition ‘collapses’ into one state like a bubble being popped. What remains is the ordinary version of a particle, sometimes called the particle’s eigenstate. This is what we work with in classical physics, but before we take the measurement we have to use probability waves instead.
It is also impossible to tell which eigenstate a particle’s wavefunction will collapse into, because the universe herself has not decided. We just take the measurement and see what happens. That’s how Bohr and Heisenberg slept at night.
The Copenhagen interpretation is, to a lot of people, a dirty, stinking cheat. It explains nothing and says you just have to be satisfied with ignorance. Critics have nicknamed it the ‘shut up and calculate’ interpretation2 because it sidesteps intuition and flatly tells you to use the equations blindly, which does not feel right somehow. The questions that arise from the Copenhagen interpretation are pretty deep too:
1) How can a particle exist in multiple states or no states?
2) Why does measurement trap a particle in one eigenstate?
3) Why is this outcome random?
4) Why can we not know all the properties at the same time?
5) Why does the everyday world follow simple classical laws if its particles do not?
The Copenhagen interpretation answers all five by shrugging its shoulders and saying, ‘That’s the way it is, pardner.’ Which did not work for some people, least of all Einstein.
ENOUGH IS ENOUGH!
Einstein and Bohr had a complicated bromance. They respected one another’s intellect, but disagreed vehemently about quantum mechanics. At every conference they attended an argument would ignite and they wrote scores of letters privately and publicly about how mistaken the other was. Had Twitter been invented, their verbal sparring would have rivalled such infamous feuds as Selena Gomez vs Justin Bieber or Kanye West vs the entire internet.
In one famous letter to Max Born, Einstein said he could not accept a theory that made nature random and finished it by saying, ‘The theory says a lot but does not really bring us any closer to the secret of the old one. I, at any rate, am convinced he does not throw dice.’3 The ‘old one’ referred to here was Einstein’s codeword for an impersonal God.
According to Heisenberg, who was good friends with both men, when Bohr heard of Einstein insisting God was not playing dice he responded with, ‘It is not our business to prescribe to God how He should run the world.’4 #Burn.
THE MOON, BEAUTIFUL
Einstein’s chief objection to the Copenhagen interpretation was that the purpose of physics is to find out how things work. Nature was telling us something through quantum mechanics, and we had to figure out what. As he saw it, Bohr was giving up just when things were getting interesting.
In one heated exchange with the Copenhagen supporter Abraham Pais, Einstein picked on the silliness of the measurement problem and asked if Pais believed the moon stopped existing when he was not looking at it.5 In the Copenhagen interpretation things do not have defined properties until measured, so if nobody observes the moon its wavefunction is technically in a superposition, existing in all sorts of places and states at once.
The snag is that this is an objection of gut feeling rather than evidence. Just because we like to believe the moon has existence when unobserved does not prove it does. Why shouldn’t the moon disappear when nobody is measuring it? Can you prove it does not?
From Bohr’s perspective, human minds evolved for the purpose of foraging for berries on the plains of Africa, not doing advanced physics. Sooner or later we were bound to run into some kind of wall. A human trying to understand quantum mechanics would be like a household thermostat trying to understand the plot of the James Bond movie Quantum of Solace. Come to think of it, it would be like an actual human trying to understand the plot of Quantum of Solace. It is simply not possible.
The picture of these debates that filtered through to the public consciousness was that Einstein was over the hill and Bohr was cautiously hailed triumphant. In some accounts Einstein is uncharitably portrayed as a once-great man no longer at the cutting edge of physics, ranting about how science was better in his day.
This probably gives people a sense of satisfaction because it is nice to know Einstein had limits, but in reality he grasped quantum mechanics perfectly. That is why he tried so hard to find a fault with it – he knew what it really was.
SCHRöDINGER’S INFAMOUS ZOMBIE CAT
Einstein’s godly dice and jumping moon were shrugged off by Bohr as emotional objections that made no difference to scientific fact. It was Schrödinger who then decided to have a go at fighting the Copenhagen juggernaut.
I like to imagine him straightening his bow tie, rolling his sleeves up and tag-teaming Einstein out of the wrestling ring, saying something like, ‘Step back, Alby, ya boi Schrödinger’s got this,’ supported by a small harem of cheerleaders on the sidelines. Five of them pregnant with his children.
Schrödinger decided to go a different route and attacked superposition rather than measurement. In the November 1935 edition of Naturwissenschaft, he published an essay that should, he argued, cripple the Copenhagen interpretation for good; it relayed what has now become known as the Schrödinger’s cat paradox.
Imagine a cat sealed inside a steel chamber and left for one hour. Inside the chamber, a radioactive material is placed next to a Geiger counter, which will detect whether a particle has been emitted from it or not. It’s impossible to predict whether an emission will take place by the e
nd of an hour but we can chose a material whose wavefunction gives a probability of 50 per cent likelihood after this time.
The particle’s location is 50 per cent likely to be inside the nucleus and 50 per cent likely to have tunnelled out and hit the detector. But here’s where it gets interesting. The Geiger counter is rigged to a fiendish device that trips a hammer and shatters a flask of hydrocyanic acid next to the cat.
The Copenhagen interpretation says the particle takes both options, existing in a superposition of location inside the nucleus and outside it, so the hammer is simultaneously tripped and not. This means the acid flask is simultaneously shattered and left alone, and the cat is simultaneously dead and alive. If you take the Copenhagen view seriously, you have to accept something absurd. Superposition had to be wrong.
I do not know why Schrödinger did not just make it a dart or something which would execute the cat painlessly, but he chose to slowly corrode the cat over the course of several minutes via an acid bath. Schrödinger was an odd guy.
It’s also not clear why he chose a cat. He definitely owned a dog named Burschie6 and there are some claims that he owned a cat named Milton,7 but they may be apocryphal. Perhaps he was writing his essay one morning when Milton thought it would be a good time to defecate on his desk and Schrödinger immortalised him for ever. Who knows?
Sometimes the Schrödinger’s cat experiment is misrepresented as ‘you do not know if the cat is alive or dead so you have to imagine it both ways’. But that is missing the point.
The Copenhagen interpretation literally says a particle can be in a superposition, which means anything interacting with it can be in a superposition too. When you open the box you are collapsing the wave-function of the cat into a dead or alive eigenstate with 50 per cent likelihood, but until then it is both simultaneously.