SCHRÖDINGER'S CLOWN

From a tale of quantum mechanics.
© Paolo Bolzoni, 19 July 2022

In quantum mechanics, Erwin Schrödinger's cat is a thought experiment that illustrates a paradox of quantum superposition. In the thought experiment, a hypothetical cat may be considered simultaneously both alive and dead as a result of its fate being linked to a random subatomic event that may or may not occur.

Let’s make a thought experiment, err, a VERY REALISTIC EXPERIMENT!
The scenario is often featured in debates in the Commons on the interpretations of quantum mechanics, particularly in situations involving a clown who lives in Downing Street 10.

In layman’s terms, Boris remains PM until the October Conservative Party Conference, or he is kicked out before.
 
One can even set up quite ridiculous cases. Boris the clown is locked up in a steel cage, along with the following device (which must be secured against direct interference by the clown): in the corridor, there is a tiny bit of rebelling Conservative MP’S, so small, that perhaps in the course of the entire term only one MP rushes into the clown’s cage to kick him out.
But also, with equal probability, perhaps none dares.

If it happened, the rebelling MP rage discharges and through a relay releases a hammer that shatters a small flask with the freedom bell in it.
If one has left this entire system to itself for an entire term, one would say that the clown is still the PM, provided no rebelling MP rushed in.
The first rebelling MP who rushed in would have rang the freedom bell. The psi-function, Ψ, of the entire Cabinet of Fools would express this by having the clown in the cage AND the kicked out clown mixed or smeared out in equal catastrophic consequences for Britain.

It is typical of these cases that an indeterminacy originally restricted to Parliament, becomes transformed into macroscopic endless mess for Britain, which can then be only resolved by early elections.
That prevents us from so naïvely accepting as valid a "blurred model" for representing reality. In itself, it would not embody anything unclear or contradictory.
There is a difference between a shaky or out-of-focus Cabinet and a snapshot of a dead Brexit.

Often the result of the experiment is presented in the following terms. After an interval equal to the half-term, the clown may or may not be there with the same probability, so it is in a superposition of the two states: in Dirac’s notation, the state of the clown is:

| A ⟩ = 1/√ 2 ( | clown still there ⟩ + | clown kicked out ⟩ ).

But since the MP in the corridor determines the fate of the clown, it should be considered both sitting in Downing 10 and kicked out:

| G ⟩ = 1/√ 2 ( | clown kicked out ⟩ + | clown still there ⟩ ).

at least until an observation is made by opening the clown’s cage.

P.S.
The apparent paradox arises from the fact that in quantum mechanics it is not possible to describe objects classically, and a probabilistic representation is used: to show the fact that a particle can be placed in different positions, for example, it is described as if it were simultaneously in all the positions it can take. To every possible position corresponds the probability that, observing the particle, it is in that position. The observation operation, however, irremediably modifies the system since once observed in a position the particle definitively assumes that position (i.e. it has the probability 1 of being there) and therefore it is no longer in a "superposition of states".

Returning to the case of Boris the clown, however, it must be pointed out that the above description is incorrect.
The same conclusion by Schrödinger, who nevertheless never uses the term "paradox", is expressed in very different terms: Schrödinger refers to the "wave function of the whole system", not to that of the clown. In fact, quantum theory states that the PM + clown system is described by the quantum correlation state.

| A, G⟩ = 1 / √ 2 (| rebelling MP rushed in, clown kicked out⟩ + | rebelling MP did not rush in, clown still PM⟩).
It is therefore not correct to say that Boris the clown is in a superposition of two states, because the superposition affects the whole system.
The fundamental difference is that the two subsystems, namely the clown is still PM and the clown kicked out taken individually, are rather described by a statistical mixture.
The uncertainty about the fate of Boris the clown is "classic": he is still PM or kicked out with a probability of 50%, without any interference between the two different states.