Schrödinger's Security Lamp

Yesterday I fitted a new PIR security light above the front door. This is the sort of job that sits in the narrow band of domestic tasks where a man can feel both heroic and competent while standing on a stepladder holding a screwdriver in his teeth. It is not rocket science. It is, at most, mild ladder science, with a short appendix on not touching the brown wire.

The light went up. The wires went in. The breaker went back on. Nothing happened, which was correct, because it was the middle of the afternoon and the light had been designed by people who understand that illuminating a front door at two o'clock on a sunny Athenian Thursday is the act of a lunatic.

And that is where the trouble started. Because I now had a light that I believed worked, and no way of proving it.

 

A Brief Note on How These Things Think

A PIR (passive infrared) sensor is a modest little device with one job. Behind its faceted plastic dome, which is a Fresnel lens chopping the world into a fan of invisible zones, sits a pyroelectric sensor that produces a tiny voltage when the amount of infrared falling on it changes. It does not see you. It sees warmth moving. A warm thing crossing from one zone to the next produces a little blip, the electronics decide the blip is interesting, and on comes the light.

Note the word "moving". A warm thing sitting perfectly still is, to a PIR, indistinguishable from the furniture. This will become important.

Most of these units also carry a second sensor: a photocell that measures the ambient light and vetoes the whole operation if it is too bright outside. There are usually three little dials on the underside, marked something like:

• TIME: how long the light stays on after the last movement
• SENS: how far away and how enthusiastically it detects things
• LUX: how dark it has to be before the PIR is allowed to have an opinion

 

So in daylight the light is, by design, deaf to the world. Which is lovely for the electricity bill, and maddening for anybody who would quite like to know whether they have wired it correctly before going to bed.

 

The Box

My first thought was elegant in its simplicity. If the problem is daylight, remove the daylight. Put a cardboard box over the lamp, and the photocell, finding itself in sudden darkness, would conclude that night had fallen with unusual speed and arm the sensor.

My second thought arrived approximately four seconds later and was less elegant. If the lamp is inside a box, what exactly is going to move in front of it?

Not me. I am outside the box. I am, in fact, the whole reason for the box. A PIR cannot see through cardboard, and it is not much better with glass, which is why waving at your security light from the kitchen window has never once worked and never will.

I briefly considered engineering. A piece of string, threaded through a hole in the side of the box, attached to a cardboard hand on a little pivot. Pull the string, the hand waves, the sensor sees movement, the lamp comes on. I got as far as mentally specifying the hand (five fingers, for realism, although I accept a PIR is unlikely to count) before encountering the obvious flaw. A cardboard hand is the same temperature as the cardboard box it lives in. It is, thermally speaking, a box waving at itself. The PIR would watch this performance with the polite indifference of a cat watching television.

Which is when the better idea arrived.

 

The Better Idea

What I needed was something warm, something that moves of its own accord, and something that would voluntarily get into a cardboard box.

Anybody who has ever owned, met or been ignored by a cat will see where this is going. A cat runs at about 38.5°C, which makes it a superb infrared source. It moves unpredictably. And it has a well documented, scientifically unexplained and frankly compulsive attraction to cardboard boxes. You do not need to persuade a cat into a box. You need only to place a box on the floor and wait, and within a period ranging from eleven seconds to the end of the afternoon, there will be a cat in it. Athens, being a city with roughly one cat per square metre of pavement, presents no supply problem whatsoever.

The protocol was therefore:

1. Place box over lamp, so the photocell believes it is night.
2. Introduce cat.
3. Cat moves. PIR detects warm moving object. Lamp comes on.
4. Declare success. Remove cat. Thank cat. Be ignored by cat.

 

It was at roughly this point, with the stepladder still out and the box still empty, that I realised I had heard all of this somewhere before.

 

The Risk Assessment

A sealed box. A cat. A device that is triggered by an event inside the box which cannot be observed from outside it. And, crucially, a non-trivial chance that when you finally lift the lid, the cat will be dead.

Because let us be honest about the hazards. The box is small and not well ventilated. The lamp, if it is an old halogen, will reach temperatures at which a cat goes from "mildly put out" to "cooked". Even a modern LED fitting is mounted on a backbox full of 230 volts that I have only just persuaded myself I connected correctly, and the whole purpose of the test is that I am not sure. A curious cat, a loose terminal and a sealed box is not an experiment. It is an inquest.

So, before lifting the lid, the cat is in a state that can only be described as both alive and dead. The lamp is both on and off. My wiring is both correct and catastrophically wrong. And I, standing outside on the step with a screwdriver, am in a superposition of competent homeowner and person who will shortly be having a very difficult conversation with the neighbours.

 

The Hypothesis

The orthodox history of physics tells us that in 1935 Erwin Schrödinger proposed his famous thought experiment, in which a cat is sealed in a steel chamber with a radioactive atom, a Geiger counter, a hammer and a flask of poison. If the atom decays, the counter trips, the hammer falls, the flask breaks, and the cat dies. Under the Copenhagen interpretation of quantum mechanics, the atom is in a superposition of decayed and not decayed until observed, and therefore, absurdly, so is the cat.

The orthodox history further tells us that Schrödinger was not endorsing this. He was pointing at it and saying "look how ridiculous this is", which is a thing physicists did a great deal in the 1930s, usually in long letters to Einstein, who generally agreed.

I would like to propose an alternative reading.

Schrödinger was not trying to explain wave function collapse at all. He was trying to fit a security lamp.

Consider the evidence. A man. A box. A cat. A detection device triggered by an event inside the box. A strong suspicion that something might go badly wrong with the electrics. And, most damningly, no satisfactory way of checking the result without opening the box. The radioactive atom, the hammer and the poison are, I submit, later embellishments added to make the paper more publishable. "I put the cat in a box to see if the porch light worked" does not get you into Naturwissenschaften, however good the results.

The obvious objection is that the passive infrared motion sensor would not be commercialised for another forty years or so. I regard this as a detail. Great minds have always been ahead of their time, and some of them were simply ahead of their hardware.

 

The Observer Effect, Demonstrated Domestically

Here is the part that I genuinely did not expect, and which I think would have pleased Schrödinger enormously.

Suppose the experiment works. The cat moves, the PIR fires, the lamp comes on inside the box. How do I know? I have to look. And to look, I have to lift the lid. And the moment I lift the lid, the afternoon sunshine floods in, the photocell detects broad daylight, and the lamp switches itself off.

The act of observation literally collapses the state. The light is on precisely as long as nobody can see it. The instant anyone checks, it is off, and there is a cat looking at you with an expression that suggests this is your fault, which, to be fair, it is.

This is, as far as I am aware, the first macroscopic, domestic, entirely reproducible demonstration of the observer effect, and it can be performed with materials from any branch of a well known Swedish furniture retailer. I am expecting a call from Stockholm, although probably from the furniture people rather than the Nobel committee.

 

The Sleeping Cat Problem

There is one further complication, and it is the one that finally killed the idea (the idea, not the cat).

A PIR detects movement. And what does a cat do when placed in a warm, dark, enclosed cardboard box? It goes to sleep. Instantly, and for about nine hours.

A sleeping cat is warm but stationary, and so to the PIR it is simply part of the scenery. The lamp would stay off. I would lift the lid to find a cat that was very much alive, a lamp that was very much off, and no information whatsoever about my wiring. The experiment would collapse not into "alive" or "dead" but into a third state, familiar to anyone who has ever tried to get a cat to do anything: "asleep, and unwilling to discuss it".

 

What I Actually Did

Nobody comes out of this well, least of all me, because the real answer was printed on a small slip of paper in the bottom of the box the lamp came in.

Turn the LUX dial all the way to the little sun symbol. This tells the photocell to permit operation in full daylight. Turn TIME to minimum. Walk past. The light comes on, stays on for a few seconds, and goes off again. Adjust, walk past again, and when you are satisfied that it works, turn LUX back to the moon symbol so it only operates after dark.

Most PIR fittings have exactly this test mode, because the engineers who design them have presumably also stood on stepladders at two in the afternoon wondering how to proceed. They simply thought of it before they reached the cat stage, which is the difference between an engineer and a physicist.

 

Conclusion

The lamp works. I know this because I walked past it last night, and it came on, and I was able to observe it without anything collapsing other than my enthusiasm for a more interesting method of testing it.

I remain convinced, however, that somewhere in an Oxford garden in the autumn of 1935 there was a man on a stepladder, a cardboard box, and a deeply unimpressed cat. History remembers the paper. History does not remember the porch light. And the cat, as cats always do, has declined to comment.

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