One step to a different answer about smallness started to take shape in the early 1900s. Werner Heisenberg, while investigating ideas in the development of quantum physics, proposed that there are fundamentally paired physical quantities known as conjugate variables. Examples of these paired quantities are position and momentum, or energy and time.
All of these physically measurable quantities are central to an everyday description of the motion and behavior of objects in our universe. Ideally, we want to know the exact values these physical parameters have to completely understand the behavior of, say, a planet. But, Heisenberg proved that we are inherently unable to exactly determine both of the quantities in one of these pairings simultaneously! Further, the more accurately we know one quantity, the less we can really know about the other.
Here is part of what Heisenberg said:
"The concepts of velocity, energy, etc., have been developed from simple experiments with common objects, in which the mechanical behavior of macroscopic bodies can be described by the use of such words. These same concepts have then been carried over to the electron, since in certain fundamental experiments electrons show a mechanical behavior like that of the objects of common experience. Since it is known, however, that this similarity exists only in a certain limited region of phenomena, the applicability of the corpuscular theory must be limited in a corresponding way. According to Bohr, this restriction may be deduced from the principle that the processes of atomic physics can be visualized equally well in terms of waves or particles. Thus the statement that the position of an electron is known to within a certain accuracy Δx at the time t can be visualized by the picture of a wave packet in the proper position with an approximate extension Δx. By "wave packet" is meant a wavelike disturbance whose amplitude is appreciably different from zero only in a bounded region. This region is, in general, in motion, and also changes its size and shape, i.e., the disturbance spreads. The velocity of the electron corresponds to that of the wave packet, but this latter cannot be exactly defined, because of the diffusion which takes place. This indeterminateness is to be considered as an essential characteristic of the electron, and not as evidence of the inapplicability of the wave picture. . . ."
(The Physical Principles of the Quantum Theory, Werner Heisenberg, Dover Publications, 1949, pp. 13-14)
This property of our universe is called the Heisenberg uncertainty
principle. For the position-momentum and energy-time pairings, the minimum,
simultaneous uncertainties in observable values are related as ΔpxΔx≥h/4π,
where h is a universal physical constant known as Planck's constant.
Its value is about 6.63x10-34Joule-second,
which is a very small number on the scale of our everyday experiences.
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