Before we discuss why the choice of measurement matters, let us imagine that you are tasked with the complicated problem of writing the laws of movement for ants on the floor in the presence of a jar of honey. Since this is a complex problem, you create three different teams, that you call C, Q and R, in the feeble hope that you will maximize your chances of finding the correct solution.

Team C observes individual ants for a long time, and notices that they seems attracted to the honey. “Everything happens”, they postulate, “as if there is some invisible rubber band dragging the ant towards the honey jar”. They decide to call the invisible rubber band a “force”. Apparently, an ant goes towards the jar faster if the jar is closer, so they deduce that the “force” is something like “inversely proportional to the distance to the jar”. In most cases, the predictions of team C work pretty well.

Team Q take a very different approach to the problem. They lay on the floor a sheet of graph paper, and plot where they find ants at various times. They observe that on average, the ants seems to be found much more often near the jar of honey than away from it. So they establish a probability distribution predicting the chances of finding an ant at any particular location. The probability is high near the jar, and much lower far away from the jar. In most cases, the predictions of team Q work pretty well.

Team R, finally, takes yet another approach. They observed ants in the wild, and they tend to walk straight, at least for short periods of time. Why would an ant change its behavior simply because of a jar of honey? Maybe it does not, maybe it keeps trying to walk straight, but the floor around the jar of honey is subtly inclined and curved, guiding the ant towards the jar. In most cases, the predictions of team R work pretty well.

 

This is where we stand today. As you have probably guessed, team C is an analogy for so-called “classical physics”, which is the physics of everyday things; team Q is an analogy for “quantum mechanics”, presently the best theory for the physics of very small things; and team R is an analogy for “relativity”, presently the best theory for the physics of very large things where gravitation dominates.