The Heisenberg Uncertainty Principle is applied to all types of matter. One of the "controversies" in the early Star Trek series involved these uncertainties. Some Trekkies claimed that the Uncertainty Principle means that transporters would not be feasible. The uncertainties meant that the transporter would never be able to measure the location of the matter in people well enough. So they could not be beamed elsewhere.
Maybe these uncertainties are so small that they are unimportant in the transporter. Suppose a gnat is flying around in the transporter room. When it flies over the transporter pad, we measure its position and momentum. Then try to transport it to a location near somebody's compost pile. We measure the gnat's position only fairly accurately.
The uncertainty of its position is within one millimeter (10 -3 m). According to Heisenberg's Uncertainty Principle, what would be the minimum uncertainty in the gnat's momentum (Dp)?
So, the gnat's uncertainty position and its momentum are rather small. We could conclude that the Uncertainty Principle is not a problem. But, the transporter does not "work" by beaming whole objects. Instead it measures the locations of all atoms (maybe even all protons, neutrons, and electrons). Then, it disassembles the object and reassembles it elsewhere. Review your uncertainty calculation for an electron. How likely is it that the gnat can even be reassembled intact? Explain.
How would the Uncertainty Principle affect our ability to transport objects even larger than gnats? (They will have many more atoms.)
The Star Trek writers worked around this problem with a component they called a "Heisenberg compensator." This device somehow allows precise measurement of both position and momentum. They admit that they don't know how such a device would work. However, they recognize that it is needed to overcome these limitations of quantum physics. Its failure also makes for interesting stories. It should be noted that the Star Trek writers have also been insightful and creative enough to invent "subspace." This spatial continuum is hidden within our own, familiar three-dimensional space. It allows the transporter to "beam" people and objects instantaneously from one site to another since, in subspace, travel is not restricted to speeds below the speed of light. Fortunately, fiction is not restricted by the concepts of physics.
Today we lack the technology to construct "Heisenberg compensators." But, we cannot rule out the possibility that something similar may one day be developed. Talk of trans-porters may sound fantastic, but some current research indicates that "quantum teleportation" (as it is known to scientists) may actually be possible with individual atoms. Researchers at IBM have shown that teleportation of one atom is theoretically possible, but only if the original is destroyed. One atom is far from a person (or even a gnat) and many problems are involved in scaling up. But, it is fun to think about it.
Perhaps the most important aspect of the Uncertainty Principle is its philosophical implications. It states that humans cannot know everything about an object. Even if we try to imagine the "perfect" measuring instruments, we cannot determine the exact position and exact momentum simultaneously. Such a device can never be built. Thus, the Uncertainty Principle places limitations on humankind's knowledge of everything.
This limitation on our knowledge is inherent in nature. We observe the spectra of atoms. To explain them we conclude that matter behaves as waves. If this description is effective, it must describe individual electrons. This description leads to the Heisenberg Uncertainty Principle. Then, we find we cannot know everything precisely, even if we had perfect measuring instruments.
This lack of ability to know is a major departure from the physics of Newton. In 1787 Pierre Simon LaPlace, a mathematician, considered Newton's Laws carefully. If he knew the initial position and velocity, and the forces on an object, he could measure these variables for every object in the universe. Then suppose he could calculate really fast. He could know all of the future because he knows Newton's Laws. The only thing stopping him is good measurements and slow computers.
Quantum mechanics (particularly the Heisenberg Uncertainty Principle) says, "not true." Even with perfect measuring instruments we cannot know enough. The nature of matter, not of measurement limits our knowledge.