Shortly after Newton proposed his new mechanics, the "shut up and calculate" approach
of Newton, Halley and others produced the first astonishing results.
However, it did not take long until the foundational debate about the interpretation of the new physics began.
In particular, the true meaning of the position coordinates x(t) was heavily discussed.
The x(t) were of course projections onto a holonomic basis in the 3-dimensional
Euclidean vector space. But how exactly would they be determined in a measurement process?
It came down to measuring distances between point masses (1). But how does one actually measure
such a distance? Suppose we use a ruler in the simplest case (2). We have then only replaced one
distance measurement with two distance measurements, because instead of measuring the distance
between two mass points we need to measure now the distance of each mass point to the markings on the ruler (3).
Now we could use another two rulers to measure those distances etc. - an infinite regress. (Notice the superposition of rulers at 3!)
There were soon two main groups of opinion. The first was known as realists, assuming that the x(t) represented
the real position of a mass point, and even if human beings had a problem to comprehend the infinite regress
of the measurement process, the omniscient God would necessarily know it.
A small subgroup proposed that the infinite regress is the position, but could not really explain what this means.
The other group insisted that the x(t) were only a subjective description of reality but not part of reality itself.
They emphasized the important role of the conscious observer who would terminate the otherwise infinite regress
of the measurement process; This introduced the issue of subjective uncertainty into the debate.
Careful analysis showed that x(t) was only known with finite uncertainty dx and in general this
uncertainty would increase with time. Astronomers noticed that the dx for some planets was larger than the whole Earth!
The realists assumed that there was still one true x(t), even if we do not know it,
while Sir Everett 1st proposed the stunning interpretation that *all* positions within dx were equally real, rejecting the
idea of random measurement errors. The world was really a multitude of infinitely many worlds and the infinite regress of the measurement problem reflected this multitude!
Subsequently, this type of analysis became known as decoherence program: The position of a mass point can be determined only
if the mass point interacts with other mass points. But this means that in order to reduce the uncertainty dx, one necessarily
increases the uncertainty of the position of all mass points in the environment.
While it was not clear if decoherence really helped to solve the foundational problems, the complicated calculations were
certainly very interesting.
In a devilish thought experiment, a cat was put in a large box and then the lid closed. Obviously the cat would move around
inside the box (some would even suggest that the cat moved around randomly, since no law was known that could determine the
movement of the cat!), but one could not observe it.
The stunning question was, and still is, if the cat had a position x(t) if one waited long enough.
The realists again insisted that the position of the cat was a real property of the cat, even if it was unknown to everybody.
But others insisted that it made no sense to assign a position, since the rays emitted by the eyes of the observer were not
able to reach the cat; Furthermore, the animal itself has no conscious soul and thus cannot determine its own position.
While the "shut up and calculate" approach celebrated many more successes, the foundational issues of the new physics were never resolved.