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Asaf Pe'er

## Why does matter have well defined boundaries as opposed to a pobablistic mess, like the positions of quantum particles such as electrons?

This is a simple matter of scaling.

It's somewhat similar to walking on the beach, and ask what is the boundary of the sea. If you are 100 meters inland, or 100 meters inside the water, you are certain where you are. But on the beach there are waves, and the boundaries constantly change...

One of the fundamental differences between the quantum and classical world is Heisenberg's uncertainty principle. According to this principle, there is a maximum accuracy which can be achieved when measuring certain quantities. One example is the position and the momentum: we can measure both the position and the momentum of a particle, but we can never obtain a result that is better than Planck's constant, which is a fundamental constant of nature. In math lingo, we write dx * dp >=h.

Planck's constant (denoted by h) is in fact tiny, and is many orders of magnitude smaller than quantities we encounter on everyday life. Thus, when we measure big (macroscopic) things, we cannot get any remotely close to the upper accuracy limit. For example, if we measure the higher of a person using everyday ruler, the accuracy we can reach is typically no better than, say a millimetre. And if we measure a momentum (which is the velocity times the mass) our accuracy of measurement say in mass can be milligrams, and in velocity maybe millimetres/second. Thus, our accuracy in measuring dx*dp will be around 0.001 [m] * 0.001 [kg] * 0.001[m/s] ~ 10-10 [m2 kg / s]. This accuracy can be compared to Planck's constant, which is h ~ 6 *10-34 [m2 kg / s], which is 24 orders of magnitude smaller than that !.

So, in our everyday measures, our accuracy is many orders of magnitude coarser than the physical limit (like being 100's of kilometres into the sea... there is no question that you are inside the sea!). On an atomic level, though, things are very different. The masses and typical sizes are much smaller, implying that any measurement is subject to the restrictions given by Heisenberg's uncertainty principle. The same would be for big bodies: if we were able to measure the height of a person to an accuracy of the size of an electron, we would also obtain an uncertain value due to Heisenberg's uncertainty principle... Our standard tools simply cannot reach this limit !.