The Serial Quantum

The paradox of superposed states

In November 1935 physicist Erwin Schrödinger published his famous cat paradox. It arose out of a conversation with Einstein. A quantum wave function describes all the possibilities that might be observed. In this sense the wave represents a superposition of all possible states in which it could exist. Neither of them was happy about the implications of this. Einstein drily remarked that if a barrel of unstable gunpowder were left unobserved, according to the quantum view it would eventually exist in both exploded and unexploded states simultaneously.

To make the case even more vividly, Schrödinger imagined an experiment in which a cat was the subject of a superposition. It would be enclosed in a box along with a radioactive atom, a detector, a hammer and a vial of poison. There is no knowing exactly when a radioactive atom will decay, so at first it exists in a quantum state of having both decayed and not decayed. When Schrödinger's atom did finally decay it would emit a flash of radiation which would trigger the detector, release the hammer, smash the vial and poison the cat. After a certain time there was an even chance that the source would have decayed – the possibilities that it had or had not were equally likely. According to the quantum formulation, the cat now existed in a superposition of states, being alive and dead at the same time. At this point Schrödinger would open the box and observe the cat to be either alive or dead, but not both, making an absurdity of the quantum picture.

The paradox of the dual-state observer

There is a potential regress in the experiment in the fact that one living being is observing another, but it was not given rigorous form until 1961. Eugene P. Wigner published a variation in which his friend waited a fixed length of time for a random flash of light, much as the cat had awaited its radioactive decay. At that point the friend knew fully whether the light had flashed or not. But Wigner did not know. In quantum terms he still understood the flash as both having happened and not happened, with his friend being in a superposition of having both seen and not seen it. In this version the friend is unarguably another sentient observer. The quantum formulation is different for each observer, implying that they have each observed different versions of reality.

Subsequent commentators have pointed out that if another friend were to then appear on the scene intending to ask Wigner what the result was, Wigner himself would appear to be in a superposition of both a knowing-that-his-first-friend-said-yes and a knowing-that-his-first-friend-said-no state. Each of the three scientist now sees a different reality. And so on in an open-ended regress.

Schrödinger’s cat created a furore which continues to this day and the fundamental paradox remains unresolved. Wigner’s friends only rub salt in the wound. However it is essentially a philosophical question rather than scientific. As Einstein among others has noted, physicists tend to make poor philosophers (The reverse is often also true, but at least philosophers are more honest with themselves about their ignorance of the othert discipline).

Quantum regresses ad nauseam

The paradox of the observer is not the only endless regress in quantum physics, far from it. Some more enlightened modern physicists have bemoaned the seemingly endless list of them; those discussed here are far from exhaustive.

One of the first to become apparent is that of phase spaces, created by each and every quantum wave to propagate through independently of all the others; the quantum only returns to reality when it is observed.

In the later Everett many-worlds hypothesis there are multiple universes created following each and every quantum event; the cat and Wigner exist in multiple parallel universes, with each universe offering a different experimental outcome. Some observations, such as exactly where a particular dot of light appears on a screen, may have millions of possible outcomes. Thus, the universe clones itself in a relentless cascade of branching serial regresses, reminiscent of Borges' "garden of forking paths", which puts Dunne's timid little linear regress in stark perspective.

Some regresses are more overtly mathematical in nature. The technique of renormalisation is designed to sidestep a regressive approximation to infinite field strengths. The projective spaces used to flatten out a Calabi-Yau manifold in modern string theory also regress into ever higher dimensions, though these are of space rather than time. Many of these examples are most likely mathematical awkwardnesses to be worked around, with the hope that one day our maths will improve and we will be able to recast our equations without any pesky infinities.


Where Dunne acknowledged nonlocality in time but baulked at nonlocality in space (his theory in that direction was flawed and never published), physicists have been apt to do the reverse. However certain weird phenomena of the quantum deeps have recently been leading the more adventurous to question the forward flow in time of cause-and-effect, with what they call retrocausality providing the simplest explanation.

Dunne and the serial quantum

Such paradoxes of quantum reality and the role of the observer pursue us with as much if not more impenetrability than ever and, setting aside Dunne's obsolete particle-realist interpretation (shared by many leading physicists at the time), the old arguments against him have largely been undermined by our modern understanding (or, equally, our lack of it).

Dunne's regresses of time and the observer were the first to be offered to the physics community. At that time, any such regress was regarded as proof of a logical flaw. His ideas also came laden with metaphysical baggage of dream precognition and life after death. Most commentators dismissed all infinite regresses on principle, not to mention anything which threatened atheistic materialism in its crusade against religious dogma and folk superstition. And the plain truth was, he was a lousy physicist and his cod mathematics did not stand up to scrutiny. For all these reasons, he received short shrift. But he was right, or at least was far from wrong, about some things and many criticisms of him were unjustified.

He noted the regressive phase spaces, endlessly following the creation and annihilation of every quantum wave. He remarked acidly on the hypocrisy of the prevailing view that, while this regress was entirely acceptable, his own was not to be allowed even in principle.

He does not appear to have noticed the close parallel between his own serial observer and Schrödinger cat. He had already published The Serial Universe the year before, but when he put out a new and radically rewritten edition in 1942, he wholly missed the opportunity. To be sure, Schrödinger's victim was only a cat. And his regress was of a superficially different character; he described a single multi-level observer in multi-dimensional time whereas Schrödinger implied a multitude of independent observers in one-dimensional time. But under the skin it is the same logical regress of observers, just packaged differently. Moreover, where Schrödinger’s paradox left Wigner and others with a gross regress from one individual to another, Dunne’s was cleaner in that it resolved all the observers the cat needs into a single regressive mind who, depending on your beliefs about sentience in animals, is either the cat itself or Schrödinger. But by the time Wigner and his friends came along, physicists had all but forgotten Dunne.

As for all the regresses that arose from the mathematics, Dunne faced very similar issues, especially those put to him by JB Priestley. He came to acknowledge that his regresses might not represent reality but be artefacts of the model our minds construct for themselves, and which he had modelled mathematically. He accepted that Priestley's recasting of his model might well be right, however he always maintained that our current understanding led directly to the regresses and only a radical advance in knowledge could avoid them. The parallel with all those other quantum regresses is striking.

If modern physicists remember Dunne at all, it is only enough to condemn his serial regresses. Bizarrely, many of them still subscribe to Everett's towering regress while at the same time dismissing Dunne because the whole idea of a regress is decalred untenable. Their blatant intellectual dishonesty and hypocrisy is lost on them. Sorry folks, physicists make lousy philosophers – Einstein said so. Worse than that, you have let your rubbish philosophy bias your physics. Dunne may not have been right, but he was a lot less wrong than you like to imagine and you have a lot to learn from him still.

Updated 10 Jun 2021