Quantum physics is famously weird and difficult to understand. Even Richard Feynman, who won a Nobel Prize for his work in the area, wrote in his book The Character Of Physical Law: “I think I can safely say that nobody understands quantum mechanics.”
Even the most basic features of the theory stretch beyond common sense, with concepts like something being both a particle and a wave at the same time. In fact, more precisely, it behaves as if it is both a particle and a wave, but this distinction is often forgotten.
Then there’s the idea that a particle exists in more than one state (such as decayed or undecayed) at the same time until it is measured, when it ‘collapses’ into one state or the other. That leads to Schrödinger’s cat, the famous thought experiment that supposes that a cat can therefore be both alive and dead at the same time if its life somehow depends on which state the particle is in.
An even more bizarre result is that of quantum entanglement, also known as the Einstein-Podolsky-Rosen (EPR) paradox. Imagine producing two particles, each with a quantity called ‘spin’: one must have spin up and the other down, so that they cancel out. But, until you measure them, which one is which isn’t determined, and both particles have spin up and spin down.
Imagine you fired those particles in opposite directions so that they’re light-years apart, and then measure one. You force this one to decide whether it’s spin up or spin down, which instantly decides for the other particle, too. But that particle is light-years away. So how did your particle influence its twin? Einstein called this “spooky action at a distance”.
These phenomena are not necessarily intrinsic to quantum physics, but result from the way we choose to interpret the equations. This particular way of understanding is called the Copenhagen Interpretation, and it dominates discussion of quantum physics. That’s not to say that it’s the only interpretation, or even that it’s the best.
In the following extract from Six Impossible Things: The ‘Quanta of Solace’ and the Mysteries of the Subatomic World (£9.99, Icon Books), John Gribbin explains why the Copenhagen Interpretation, one of six ‘solaces’ (or interpretations), is not so wonderful as it’s made out to be.
The Not So Wonderful Copenhagen Interpretation
The interpretation of quantum physics that became the standard way of looking at things for decades is based on the idea of waves – and on largely forgetting the caveat ‘as if’. In the 1920s, physicists already knew that the quantum world could be described in either of two mathematical ways. One involved waves, summed up in the Schrödinger equation. The other involved pure numbers, in the form of arrays called matrices, developed from the work of Werner Heisenberg and Paul Dirac.
They gave the same answers, so it was a matter of choice which one to work with; and since most physicists already had some familiarity with wave equations, that was what they chose. In any quantum calculations, however, what you calculate is the relationship between two states of a system, where the system may be an electron, the experiment with two holes, or (in principle) the entire Universe – or anything in between the electron and the Universe. If you have a set of parameters describing the system in state A, you can calculate the probability that it will be in state B after a certain time. But there is nothing which tells you what is going on in between.
Niels Bohr © Getty Images
The archetypal example is an electron in an atom. Electrons can, for some calculations, be thought of as if (that caveat) they are in orbits which correspond to different amounts of energy. When an atom emits energy in the form of light, an electron disappears from one orbit and appears in another orbit closer to the nucleus of the atom. When an atom absorbs light, an electron disappears from one orbit and appears in one further out from the nucleus of the atom. But it does not move from one orbit to the other. First it is here, then it is there. This is known as a quantum jump (or a quantum leap (*contrary to what advertisers think, a quantum leap is a very small change made at random.)).
Schrödinger intended his wave mechanics to explain what happens during the leap, but it didn’t, and he said: ‘If all this damned quantum jumping were really here to stay, I should be sorry I ever got involved with quantum theory.’ Alas for Schrödinger, it was, and is, here to stay. The matrix approach is more honest, since it does not pretend to try to tell us what is happening between state A and state B, but it provides less solace than the Schrödinger equation.
What was for decades the standard way of looking at the quantum world became known as the Copenhagen Interpretation, because it was vigorously promoted by Niels Bohr, a forceful personality who was based in that city. This name (actually given to the package of ideas by Werner Heisenberg) caused considerable irritation to Max Born, who was not a member of Bohr’s team, and did not work in Copenhagen, but whose ideas about probability were an integral part of the interpretation.
Bohr so dominated any discussions about quantum physics at the end of the 1920s that as well as getting his home town recognised in this way he dissed an alternative, completely viable interpretation of quantum mechanics so thoroughly that it was neglected for two decades. I shall present it as Solace 2.
Bohr was essentially a pragmatist who was happy to stick together different bits and pieces of ideas to make a working package without worrying too much about what it all meant. As a result, there is no straightforward, definitive statement of what the Copenhagen Interpretation is, although Bohr came close to such a revelation in a talk he gave at Como, in Italy, in 1927 – long before the interpretation got its name.
The conference at which that talk was given was a landmark moment in physics, because it marked the point where physicists were presented with the tools they would require in order to ‘shut up and calculate’, applying quantum mechanics to the solutions of practical problems involving atoms and molecules (for example, chemistry, lasers, and molecular biology) without having to think about the fundamentals of what it all meant.
Bohr’s pragmatic approach extended to his interpretation. He said that we do not know anything except for the outcomes of experiments. These outcomes depend on what the experiments are designed to measure – on the questions we choose to ask of the quantum world (of nature). These questions are coloured by our everyday experiences of the world, on a scale much larger than atoms and other quantum entities.
So we may guess that electrons are particles, and build an experiment designed to test this in an obvious way by measuring the momentum of an electron, thinking of the electron as a tiny pool ball. When we do so, lo and behold, the experiment measures the momentum of the electron, confirming our notion that electrons are particles. But a friend of ours has a different idea. She thinks that electrons are waves, and designs an experiment to measure the wavelength of an electron. Lo and behold, her experiment gives a measurement of the wavelength, confirming her notion that electrons are waves.
So what, says Bohr. Just because the electron behaves as if it were a particle when you are looking for particles, or as if it were a wave when you are looking for waves, doesn’t mean that it is either, let alone both. What you see is what you get, and what you see depends on what you chose to look for. It is meaningless, according to the Copenhagen Interpretation, to ask what quantum entities such as electrons and atoms are, or what they are doing, when nobody is measuring them – looking at them, if you like.
So far, so pragmatic, and nothing really too alarming. But Bohr quickly takes us into muddy waters. This is where probability comes in. When Schrödinger came up with his wave equation, he thought of it as being a literal description of an electron (or other quantum entity; electrons are the simplest example to use for illustration). To him, an electron was a wave.
But Bohr took Schrödinger’s ball and ran off with it, combining it with Born’s ideas on the role of probability to produce a bizarre and troubling concoction which worked (and still works), as far as quantum calculating was concerned, but makes your head hurt when you stop to think about it. The equation that Schrödinger gave us is, on this new picture, to be thought of as a ‘probability wave’, and the chance of finding an electron at any location is determined by ‘the square of the wave function’, essentially by multiplying the equation that describes the wave by itself, at any point.
When we make a measurement, or observe a quantum entity, the wave function ‘collapses’ to a point, determined by the probabilities. But although some locations are more likely than others, in principle the electron could appear anywhere that the wave function has spread to. A very simple example highlights the oddity of this behaviour.
Think of a single electron trapped in a box. The probability wave spreads out to fill up the box evenly, meaning that there is an equal chance of finding the electron at any location inside the box. Now drop a partition down the middle of the box. Common sense tells us that the electron must now be trapped in one half of the box. But the Copenhagen Interpretation (CI) says that the probability wave still fills each half of the box and the electron might with equal probability be found on either side of the partition. Now divide the box in two down the centre of the partition.
Erwin Schrödinger © Getty Images
Keep one half-box in your laboratory, and put the other one on a rocket which takes it to Mars. Still, according to Bohr, there is a 50:50 chance of the electron popping up in the box in the lab or the one on Mars. Now open the box in your lab. Either you find an electron, or you don’t. But either way, the wave function has collapsed. If your box is empty, the electron is on Mars; if you have the electron, the other box is empty. This is not the same as saying that the electron ‘always was’ in one half of the box or the other; the CI insists that the collapse only happens when the contents of the box in the lab are examined.
This is the kernel of the idea behind the EPR ‘paradox’, and Schrödinger’s famous puzzle involving a dead-and-alive cat. But before going into that story, I want to look at how the Copenhagen Interpretation ‘explains’ the experiment with two holes.
According to the CI, which I was taught as a student, and which too many students are still taught today, as ‘the’ way to ‘understand’ quantum mechanics, an electron is emitted from a source – an electron gun – on one side of the experiment as a particle. It immediately dissolves into a ‘probability wave’ which spreads through the experiment and heads towards the detector screen on the other side.
This wave passes through however many holes are open, interfering with itself or not as appropriate, and arrives at the detector as a pattern of probabilities, higher in some places and lower in others, spread across the screen. At that instant, the wave ‘collapses’ and turns back into a particle, whose position on the screen is chosen at random, but in accordance with the probabilities. This is called ‘the collapse of the wave function’. The electron travels as a wave but arrives as a particle.
The wave, however, carries more than just probabilities. If the quantum entity has a choice of states it can be in, such as an electron which may be spin up or spin down, both states are somehow included in the wave function, the situation called a ‘superposition of states’, and the state the entity settles into at the point of detection, or interaction with another entity, is also determined at the moment the wave function collapses. In a lecture at the University of St Andrews in 1955, Werner Heisenberg said ‘the transition from the “possible” to the “actual” takes place during the act of observation’.
This works as a method of calculating quantum behaviour, as if things like electrons really did behave like this. But it also poses many puzzles. One of the most puzzling is a so-called ‘delayed choice’ experiment, dreamed up by the physicist John Wheeler. He started from the fact that when photons are red one at a time through the experiment with two holes they still build up an interference pattern on the detector screen. But according to the CI, if a device is placed between the two holes and the detector screen to monitor which hole the photon goes through, the interference pattern will vanish, showing that each photon really did go through just one of the holes.
The ‘delayed choice’ comes in because we can decide whether or not to monitor the photons after they have passed the screen with two holes. Of course, human reactions are not fast enough to do this. But experiments have been carried out with automatic monitoring devices to do exactly this, switching the monitors on or off after the photons have passed the holes. They show that the interference pattern does indeed disappear when the photons are monitored, meaning that each photon (or the probability wave) only goes through one hole – even though the decision to monitor the photon was made only after it had passed the holes.
Werner Heisenberg © Getty Images
Wheeler pointed out that you can imagine a similar experiment on a literally cosmic scale. In a phenomenon known as gravitational lensing, light from a distant object, such as a quasar, is focused by the gravity of an intervening object, such as a galaxy, so that it follows two (or more) paths around the gravitational lens. This makes two images of the object in detectors here on Earth. In principle, instead of making those two images it would be possible to merge the light coming different ways around the gravitational lens to make an interference pattern, caused by waves going both ways round the lens. A cosmic version of the experiment with two holes.
But then we could monitor the photons before they get a chance to make the interference pattern to see which way round the lens they have come. In that case, according to the results of the laboratory-scale experiments, the interference pattern would disappear. The quasar might be 10 billion light years away, the galaxy acting as a gravitational lens might be 5 billion light years away. But according to everything we know from experiment, what the photons were doing billions of years ago and billions of light years away is affected by what we choose to measure here and now. What is going on? As Wheeler himself put it, ‘the Copenhagen Interpretation commands us not to ask such things’(*Quoted by Philip Ball). Not so wonderful, then.
In essence, the Copenhagen Interpretation says that a quantum entity does not have a certain property – any property – until it is measured. Which raises all kinds of questions about what constitutes a measurement. Does human intelligence have to be involved? Is the Moon there if nobody is looking at it? Does the Universe only exist because human beings are intelligent enough to notice it? Or does the interaction of a quantum entity with a detector count as a measurement? Or where in between those extremes do you find the boundary between the quantum world and the ‘classical’ world of good old Newtonian physics?
It was this kind of concern that led Schrödinger to come up with his famous puzzle about the cat locked in a room (he used the German word for ‘chamber’, not ‘box’) with a diabolical device that is primed to kill the cat, but is in a 50:50 superposition of states. Updating his example, imagine that a detector in the room measures the spin of the electron. If it is up, the device is triggered and the cat dies. If it is down, the cat is safe.
The electron is in a superposition of states before it is measured. But there is nobody in the room to see what happens when the detector is triggered. So does the wave function collapse, or not? Is the cat also in a superposition of states, both dead and alive, until someone opens the door of the room to look in?
My own development of this idea involves two of the cat’s offspring (assuming it has survived) who I call Schrödinger’s kittens (*particle physicists have taken the name and used it in another context. That is their privilege). These identical twin daughters of Schrödinger’s cat live in identical space capsules, provided with all the necessities of life, and even some toys to play with. The capsules are connected by a tube, and in the middle of the tube there is a box which contains a single electron. The electron wave fills the box evenly. A partition is slid down to divide the box in two and separate the two capsules, each now connected to a box containing half an electron wave. The two capsules are now taken on separate long journeys, in opposite directions at exactly the same speed, until they are a couple of light years apart. Each one has a detector to monitor the presence of an electron.
After a certain time (it doesn’t have to be the same time in each case) the half-box in each capsule is opened by an automatic device. If there is an electron in it, the now grown- up cat dies. If not, the cat lives. But there is no intelligent observer to know what is going on. So are the cats now each in a superposition? An intelligent alien in a passing spaceship captures one of the capsules and looks inside, to see either a dead cat or a live cat. Is it at that point that the wave function in each capsule collapses, so that what the alien sees determines the fate of the other cat two light years away? Yes, according to the not so wonderful Copenhagen Interpretation.
So what is the alternative? There are many, although you may find them just as laughable as the CI, and the first off the rank is the one that started to emerge at the same time as the Copenhagen Interpretation, was nearly smothered at birth by Bohr, but lived to fight another day.
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