Schrödinger’s cat and exam results

A large group of my students sat an exam last Saturday. This was for the Chartered Financial Analyst (CFA®) Program, which has exams with a reputation for being somewhat challenging, to say the least. The pass rates have been between 34 and 46% for a number of years, providing success only to those who commit themselves for a number of months prior to the exam.

For the most part, it is fairly straightforward for us, as classroom tutors, to tell prior to the exam which of our students are likely to succeed and which ones won’t, for the simple reason that with 240 multiple choice questions, there is remarkably little luck involved (a statement that would be highly disputed by many students I know!).

However, at what point has a successful student passed and an unsuccessful one failed? On the day of results, or earlier?

Exam results nerves

People of my tender age will remember O-level and A-level exam results arriving at home in a small brown envelope, back in the days when next-day postal deliveries were guaranteed. The envelope was always addressed in my own handwriting, the address being written with extreme care, given my calligraphically-challenged reputation. But when were my exam results decided? When I opened the envelope? Surely earlier than that. When the envelope was posted? When the results slip was put inside? When the exam was marked? As soon as I had walked out of the exam hall? Or even earlier, maybe when I walked into the exam hall?

Most people would agree that the result is determined at some point between the start of the exam and the results becoming known to the candidate.

Let’s consider a point in time just before results are published – these days via the internet. It seems clear that the examiner has already decided results, but is checking the database and the computer system before pressing SEND.

The majority of candidates are unsure whether they have passed or failed. A confident student may feel they have an 80% chance of success. But how does probability come into it, when the result has already been determined?

Schrödinger’s Cat

Without going into the details of quantum mechanics, let me summarise the fate of Schrödinger’s Cat. Austrian physicist Erwin Schrödinger proposed a hypothetical experiment in 1935 in which a cat was placed in a perfectly sealed container. In with the cat was a radioactive device that, with a specified probability, say 50%, would trigger the release of a poison that would kill the cat *.

Because the container is perfectly sealed, no noise, or in fact any information, can travel from the inside to the outside (one must assume a sufficient oxygen supply for the poor, albeit hypothetical, creature). Hence at the specified moment in time, the cat could be either alive or dead.

Schrödinger suggests that the cat is not “either alive or dead” – rather, it is both alive and dead simultaneously. The cat is potentially in two separate overlapping existences at the same time.

It is only when the box is opened that one of these two states is crystallised, and the other vanishes from our own field of view.

The cat and the exam

Now we can apply the analogy of Schrödinger’s Cat to exam results.

Immediately prior to opening the envelope / logging on, one can consider the results as being in two simultaneous states with two probabilities. Each candidate will have different probabilities, depending on their perceived performance.

I use the word “perceived” because the more information that is available, the more skewed the probabilities are. A candidate may think she has a fair chance, say 60%, of passing. As a tutor I may have observed several months of hard work, bringing the probability up maybe to 80%. A theoretical snapshot of her exam paper, and knowledge of how the pass score is determined (I suppose the equivalent of having a secret camera in the container with the cat), may bring the probability up to 100%. Of course, it might instead reduce it to 0%!

Our students are now relaxing, hard work over, and starting an eight-week period of blissful ignorance before the dreaded results arrive. However unsure they may be of what will be inside the little brown envelope, one thing is clear: uncertainty doesn’t come into it.


* No animals were harmed in the creation of this blog entry.