"I won't get into whether that is even physically possible in practice."

In this thread, I will try to approach this question in the deepest possible way. Does it even make sense to talk about the "actual length" of a desk in a room?

To ease visualization and discussion, we will replace the desk with a tiny bar of copper. The bar will be in the shape of a perfect cylinder, with the diameter being roughly the size of the ink cartridge in a ballpoint pen. The length of the cylinder will be nearly 1 centimeter (at least measured crudely with a ruler). I will further stipulate that the crystalline structure of the cylinder is perfectly machined, so that the molecular grid is a perfect lattice with no imperfections or impurities. For the rest of this article, I will be discussing how or even if, we would assign a true length to this tiny copper bar.

The far ends of the bar are determined by the locations of two copper molecules -- one sitting the farthest left extent of the bar, and the other at the farthest right end. If the bar is at room temperature, we expect that those ending molecules would be shaking around from thermal fluctuations within the bar. (see phonons https://en.wikipedia.org/wiki/Phonon#Thermodynamics )

Going back to the decimal length, we would consider the farthest righthand digits of the significand. Given in meters, we have almost exactly 1 centimeter.

1.000001018283839 x 10

^{-2}m

As time progresses in our lab we continue to measure the length of the copper bar using the finest laser measuring device. Due to thermal fluctuations we expect that the last three digits of this number will change over time, bouncing between various values seemingly at random.

1.000001018283653 x 10

^{-2}m

1.000001018283113 x 10

^{-2}m

1.000001018283608 x 10

^{-2}m

1.000001018283345 x 10

^{-2}m

1.000001018283915 x 10

^{-2}m

1.000001018283821 x 10

^{-2}m

We could cool the copper bar cryogenically, getting its temperature down to (perhaps) milli-kelvins. We repeat our measurements as before and then note that while the far end molecules fluctuate in position, the measurements tend to gravitate around a 'true' value that is the center of a gaussian distribution.

As long as there is any heat in the bar at all, we will never get a true measurement of its length, so we can try harder. We could decrease the bar's temperature down to nanokelvin, say 50 nK. We expect that the true "end" of the bar would be the widest that an electron would fly out in its orbit around a single nucleus of copper atom. We expect that this must be a particular, point-like location in space. Nanokelvin temperatures allows us to gain additional stable digits of precision, but we are left with the problem of the true length.

1.000001018283674815675915 x 10

^{-2}m

1.000001018283674815675821 x 10

^{-2}m

There are still fluctuating values on the far righthand digits of the significand, even after we have removed all thermal heat from the bar. Worse, these fluctuations don't follow a gaussian at all. They are not a product of error in our measuring device, nor are they the product of heat energy. So what is that fluctuating?

At these distances we must relent on achieving our original mission. We could never know the "true length" of this copper bar, because electrons cannot have a position beyond what would be allowed by the Heisenberg Uncertainty Principle. The wiggling decimal digits at the end of the measurement are the product of quantum fluctuations, which persist in ultra-cold solids , well after all the wiggling due to heat energy is removed. We could never remove these quantum fluctuations, because they are an intrinsic property of matter itself.

... and that dovetails with this thread : viewtopic.php?f=2&t=33307