I was pondering Schrödinger’s Cat while watching “Deal or No Deal”. Now, it occurs to me at this point that the readers of this journal are more likely to need an explanation of what “Deal or No Deal” is, rather than any enlightenment as to the mysteries of Schrödinger. Nonetheless, I intend to assume the reader has intrinsic knowledge of both topics – go ‘Google’ if you don’t!
My ponderings lay not with the misguided folk who are convinced they have a plan to ‘beat the banker’ because the box they have bears the same number as their birthday, but rather with the possible complexities of what I will call Schrödinger’s Cash.
So, let us imagine the way things happen at the moment. Before the show just one person is responsible for putting the monetary values, from 1p to £250,000 (substitute your own currency depending on where you live) into the boxes numbered 1 to 22. At this point he is the only person in the universe who knows which value is in which box – and of course during game play selecting the box and accepting the bankers deal is simply statistics. Box ‘n’ has always, and will always, contain value ‘x’ and every contestant has a 1 in 22 chance of having any particular value in their box. It doesn’t matter in which order the boxes are opened, these facts will never change and the value ‘y’ in the contestants box will always be the value ‘y’.
Now imagine, if before the show, the 22 boxes do not have a number in their initial state (this may be the case, I don’t know – but I doubt it) so all the boxes are identical, blank and indistinguishable from one another. The boxes are lined up on a long shelf, in a sealed room where only one person at a time is permitted to enter. The first person still has the responsibility to put monetary values into the boxes at random and then seal each box. Once this is done, he leaves the room and a second person enters. Then, at random, the second person randomly allocates each box a number so the boxes now have numbers from 1 – 22.
In my view, all these boxes now have Schrödinger’s Cash inside them. No one in the universe now knows which value (state) any numbered box contains until the box is opened.
However, this now takes my (very) limited understanding of Erwin Schrödinger’s hypothesis beyond breaking point. But that’s just me I hope. Undoubtedly someone reading this has far superior understanding and can offer further comment on the following points.
Firstly, each box has 22 possible states – and by thought experiment this logic can be extended to an infinite amount of possible states in an infinite amount of boxes were used. However, once one box is opened and its value (state) ascertained the other states do not change (as with Schrödinger’s Cat) because there are an infinite number of boxes – as infinity minus 1 is still infinity. Even with a less than infinite number of boxes (lets say 22) once one box is opened the other boxes still have unknown (albeit diminished optional) states.
Now lets consider a variation. None of the boxes have to be opened in order to change all of their states to a known value. All that needs to happen is that ‘person one’ talks to ‘person two’ and says “I put the values in the boxes left to right along the shelf in this order…..” whereby ‘person two’ says “I put the numbers on the boxes left to right in the this order….”. Now, so long as neither were lying, person one and person two both know the state of every box but none have been opened. And to get round the possibility of either person being a scallywag, each person video tapes their time in the sealed room with the boxes so that it clearly shows what they did, but they do not show this recording until they want to collapse the possible states of each box to a known value.
Finally, does this new method of loading the boxes with Schrödinger’s Cash change the statistics of the game? I doubt it, but does it make me wonder how you would explain to Noel Edmonds (substitute your country’s quizmaster) that the final two boxes both contained (say) 10p and £250,000.
