The 2 publications could hardly have failed to attract attention. One carried the name of Albert Einstein, the other that of Erwin Schrodinger -- 2 of the key players in the development of the theory they now urged their colleagues to reject. But in spite of some discomfort caused by having the weirdness of the quantum world highlighted by Einstein, Schrodinger and a handful of other scientists, physicists continue to stick by the Copenhagen interpretation. But now, perhaps, its time is up.

It was in May 1935 that Einstein, together with Boris Podolsky and Nathan Rosen (then all working at Princeton) published the description of what has ever since been known as the 'EPR paradox', although it is not really a paradox at all (Physical Review, vol 47 p 7777). They wanted to highlight 2 features of the Copenhagen interpretation that they regarded as absurd -- the so-called "collapse of the wave function", and the notion that every part of a quantum system responds instantaneously to a stimulus affecting any part of the system.

You can see what they were worried about in a slightly modified version of the original thought experiment. Imagine an atom which emits 2 photons simultaneously in opposite directions. The quantum rules say that the 2 photons must have opposite polarizations, but that it doesn't matter which one has which polarization. (Polarization is a property of light which gives it a kind of orientation vertically or horizontally across its line of motion.)

According to the Copenhagen interpretation, until somebody measures the polarisation, each photon exists in a superposition of states, a wave function that is a 50:50 mixture of the 2 possibilities, sometimes called a probability wave. But as soon as the photon is measured, the wave function collapses into one of the 2 possible states. Even worse, by measuring one of the photons and forcing it to choose a definite polarization state, you instantaneously force the other photon into the other polarization state, even though by that time the 2 photons may, in principle, be light years apart.

Now, Einstein and his colleagues never dreamed that the experiment would be carried out. They were happy that it demonstrated the logical absurdity of the situation. But as a result of theoretical work by David Bohm, in London, in the '50s and John Bell, at CERN (the European centre for particle and nuclear physics in Switzerland) in the 1960s it became clear that a modified version of the EPR experiment really could be carried out. And in the '80s Alain Aspect and his colleagues, working in Paris, actually did the trick. The real experiment is slightly more complicated than I have described, and involves measuring 3 correlated polarization states of the 2 photons. In essence, measuring property A of photon number 1 and property B of photon number 2 gives you information about property C for each photon. But the bottom line is clear and unambiguous -- the behaviour of real photons in real experiments agrees with the Copenhagen interpretation and the ridiculous predictions of the EPR paper.

What Einstein was most concerned about in all this was the implication, now proved by experiment, that some communication between the 2 photons propagates faster than light, seemingly in violation of the requirements of his own theory of relativity. He called this "spooky action at a distance", and abhorred it. The Aspect experiment shows that the spooky action at a distance is real.

Schrodinger, on the other hand, was more worried about the collapse of the wave function. He invented the most famous quantum thought experiment of them all to demonstrate just now absurd that is.

Imagine a cat locked in a box with a system like the one I described for the simplified EPR experiment. The atom emits its 2 photons, which, for the sake of this agreement, we can imagine bouncing about between a pair of perfectly reflecting mirrors. The box contains an automated device that will kill the cat if the polarization of one of the photons, chosen at random, is measured to be in one of the 2 possible states. If it is found to be in the other state, the cat lives. According to the Copenhagen interpretation, as Schrodinger spelled out in a paper published in three parts in Naturwissenshaften late in 1935 (vol 23 pages 807, 823 and 844), everything in the box, including the cat itself, remains in a superposition of states until the measurement is observed. Only then does the system collapse into one of the two possibilities, containing either a dead cat or a live cat.

How can a cat be in a superposition of states? Does this mean that it is somehow both dead and alive (or neither dead nor alive) until the photon polarization is observed? If it does, does this imply that an intelligent observer has to make the measurement, or will the wave function collapse as soon as a sophisticated computer measures the polarization?

Fortunately for the cat, this experiment has never been attempted, and the puzzle has never, in that sense, been resolved. Most quantum mechanics are untroubled by such hypothetical examples, and are happy that they can use the equations of quantum physics to solve problems involving quantum entities such as photons and electrons (thus enabling them to design computer chips and lasers, and manipulate DNA), without worrying about the philosophical implications. But the bottom line of the EPR experiment, as put into practice by Alain Aspect and his colleagues in Parts, is that the Universe does not work in accordance with 'local reality'.

This means that you can either believe in spooky action at a distance, and have a 'real' Universe in the sense that photons do have a definite polarization even when nobody is looking, and cats are always either dead or alive but not both at once, or you can have a 'local' Universe in which no signals travel faster than light but cats can be literally half dead, in a superposition of states.

The cat in the box experiment has spawned a cottage industry of variations on the basic theme, without ever resolving the issue. Here's my contribution, taking on board the EPR experiment as well.
For this trick, we need 2 kittens, distant descendants of Schrodinger's venerable cat, placed in a box which contains, in duplicate, all the necessities for life, plus the diabolical cat killing device, and which can be divided automatically down the middle to make 2 boxes. The now familiar atom is placed in the middle of the box, and allowed to fire its photons off in opposite directions. The photons are trapped in each of the 2 halves of the box, each of which contains 1 kitten, and the box is separated into its 2 halves. Each half-box, containing 1 kitten and a photon in a superposition of states is carried off to a different distant planet, a journey that may take several years. At some point along the way, an automatic device measures the polarization of the photon, and triggers (or not, as the case may be) the lethal device. But nobody knows whether or not the device has been triggered until the boxes arrive at their destinations. Then, and only then, an intelligent observer opens one of the boxes and looks inside.

According to the strict Copenhagen interpretation then, and only then, the state of the kitten in that particular box collapses into being either alive or dead. And simultaneously, in a galaxy far far away, the state of the other kitten, still sealed inside its box, collapses into the opposite condition, either dead or alive.

You might think that just about any interpretation of quantum theory would make more sense than that, and I wouldn't be inclined to argue. There are at least 6 interpretations which stand up as well as the Copenhagen interpretation, and several more dodgy ones. But there is one that I particularly like, which explains all of the quantum mysteries, and which requires only one tiny adjustment in your image of the Universe -- accepting the reality of signals that travel backwards in time.

This is a highly respectable version of quantum theory, developed by John Cramer, of the University of Washington, Seattle. He pointed out that for 70 years physicists have been ignoring half of the set of equations that they use to describe the quantum world--the wave equation developed by Schrodinger himself, and which bears his name.

Schrodinger's equation describes the behaviour of something like a photon, or an electron (or, in principle, a cat) making its way across the Universe. It's a fairly simple equation describing the propagation of a wave -- a time-dependent wave equation. The probabilities that are so important in quantum physics, and which tell us the likelihood of finding an electron in a particular place, or a photon in a particular polarization state (or, in principle, whether a cat is dead or alive), are obtained by squaring the wave function. But there's one subtlety involved. The Schrodinger equation is complex, in the mathematical sense, and has an imaginary part, with i (the square root of minus one) associated with its time-varying component. The way to square a complex variable is not to multiply it by itself, but to multiply it by its complex conjugate, which is obtained by changing the sign in front of the imaginary part of the variable (see box).

In the case of the Schrodinger equation, that means changing the sign associated with the direction of time for the wave it describes. The Schrodinger equation describes a wage propagating towards in time, while its complex conjugate describes a wave propagation backwards in time. Everybody who has ever used the Schrodinger equation to calculate a quantum probability has implicitly taken account of waves that travel backwards in time.

The way Cramer describes a typical quantum 'transaction' is in terms of a particle 'shaking hands' with another particle somewhere else in space and time. One of the difficulties with any such description in ordinary language is how to treat interactions that are going both ways in time simultaneously, and are therefore occurring instantaneously as far as clocks in the everyday world are concerned. Cramer does this by effectively standing outside of time, and using the semantic device of a description in terms of some kind of pseudotime. This is no more than a semantic device -- but it certainly helps to get the picture straight.
It works like this. When, for example, an electron vibrates, on this picture it attempts to radiate by producing a field which is a time-symmetric mixture of a so-called retarded wave propagating into the future and so-called advanced wave propagation into the past. As a first step in getting a picture of what happens, ignore the advanced wave and follow the story of the retarded wave. This heads off into the future until it encounters an electron which can absorb the energy being carried by the field. The process of absorption involves making the electron that is doing the absorbing vibrate, and this vibration produces a new retarded field which exactly cancels out the first retarded field. So in the future of the absorber, the net effect is that there is no retarded field.

But the absorber also produces a negative energy advanced wave travelling backwards in time to the emitter, down the track of the original retarded wave. At the emitter, this advanced wave is absorbed, making the original electron recoil in such a way that it radiates a second advanced wave back into the past. This 'new' advanced wave exactly cancels out the 'original' advanced wave, so that there is no effective radiation going back in the past before the moment when the original emission occurred. All that is left is a double wave linking the emitter and the absorber, made up half of a retarded wave carrying positive energy into the future and half of an advanced wave carrying negative energy into the past (in the direction of negative time). Because 2 negatives make a positive, this advanced wave adds to the original retarded wave as if it too were a retarded wave travelling from the emitter to the absorber.

In Cramer's words (Reviews of Modern Physics, vol 58 p 647): The emitter can be considered to produce an 'offer' wave which travels to the absorber. The absorber then returns a 'confirmation' wave to the emitter, and the transaction is completed with a 'handshake' across spacetime.

But this is only the sequence of events from the point of view of pseudotime. In reality, the process is atemporali: it happens all at once. This is because, as Einstein explained with his theory of relativity, signals that travel at the speed of light take no time at all to complete any journey -- in effect, for light signals every point in the Universe is next door to every other point in the Universe. Whether the signals are travelling backwards or forwards in time doesn't matter, since they take zero time (in their own frame or reference), and +0 is the same as -0.

So what does this tell us about the fate of Schrodinger's kittens? Instead of anything being in a superposition of states, at the moment the 2 photons are emitted by the atom, they each send an offer wave off into the future. One of these waves makes a handshake with the later observation of the state of the photon, and that automatically makes certain the photon set of from the atom in that state, and never does exist in a superposition of states, while its counterpart happily sets off on its journey in the other possible state. As soon as the photons' polarisations are measured, one cat is killed and the other lives. Neither cat was ever in a superposition of states, either.

Cramer's transactional interpretation is so simple that I can happily leave it up to you to work out how it resolves the EPR paradox and such puzzles as the electron that seems to go both ways at once through a double-slit experiment (hint: the offer wave goes both ways, but the confirmation comes back only through one slit). And the special beauty of it is that all this involves no new mathematical tricks at all -- it is exactly the same as the way physicists have been using the equations for 70 years, but it provides anew insight into the significance of what they are doing. Time, surely, for teachers and text book writers, at least, to take note.

*John Gribbin is a Visiting Fellow in Astronomy at the University of Sussex. His book Schrodinger's Kittens has just been published by Weidenfeld & Nicolson*

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