**By **Robert M. Hazen, Ph.D.**, **George Mason University

## Most of the time, quanta don’t really matter. But at the atomic level and the subatomic scale, they’re vitally important. The quantization of the atomic world carries with it the remarkable property that every measurement must change the object that’s being measured. Someone can’t measure something without changing it while they’re measuring it.

**R**equirements for Every Measurement at Every Scale

Every measurement at every scale requires three things. First of all, there has to be a sample or a piece of matter. It can be a single electron or an entire galaxy or the Earth. Then there is a need for a source of energy. That source can be light or heat or kinetic energy. Someone has to do something to interact with that sample, and they can’t interact with a sample without having some kind of energy in the process. A detector is the third thing needed to do measurements.

When people go to the grocery store, they do this kind of measurement all the time. For example, people go to the grocery store, and they want to buy a piece of fruit like melon. And what do they do? They take the melon—that’s the sample. They’re trying to decide its physical properties. Is this the melon they want to buy? So they might smell the melon or tap on it and listen to it.

They have got to apply energy to the sample. And they have to have a detector, which then will determine the interaction of the energy with the sample. And that gives them information about the object they’re trying to study. It happens all the time in people’s day-to-day lives. It also happens at the largest scale of the most expensive laboratories in the world. So, in principle, every measurement is the same way.

This is a transcript from the video seriesThe Joy of Science.Watch it now, on Wondrium.

### The Measurement Process at the Subatomic Scale

For this measurement process at the scale of an atom, the smallest increment of energy one can imagine is a photon, a single wavelength of light, a single piece of light that hits an atom. If the atom absorbs that photon and interacts with it, the atom somehow should be changed in the process. This situation is rather analogous to trying to find a bowling ball in an empty dark room.

There’s a bowling ball someplace in an empty dark room. And the only way to find that bowling ball is to take a second bowling ball and roll it into the room and listen for the clunk. Once the bowling ball is located, one would have no idea where it was after the measurement because the very process of measuring the bowling ball moves it.

### Heisenberg’s Uncertainty Principle

German physicist Werner Heisenberg, 1901-1976, expressed this dilemma—this quantum scale dilemma—in an elegant mathematical form. This expression is noted as the Heisenberg Uncertainty Principle.

Eventually, Werner was made director of the Max Planck Institute for Physics in Munich. Heisenberg’s great insight was the realization that someone can’t know the exact position and the exact velocity of an object in a subatomic realm at exactly the same time.

In fact, the uncertainty in position, he said, times the uncertainty in velocity must be greater than Planck’s constant divided by the mass. And that can be expressed as an equation, [Uposition×Uvelocity>h/mass]. The uncertainty in position, sometimes called delta position, times the uncertainty in velocity, or delta velocity, must be greater than Planck’s constant, h, divided by mass.

Learn more about nuclear fission and fusion reactions.

### Uncertainty in Velocity According to Heisenberg

According to Heisenberg, if the mass is large, the uncertainty in position and velocity are going to be small because the mass is the denominator of that fraction. But if there is a very small mass like an electron—an electron weighs only nine times 10^{-31} kilograms—and if one wants to know the position of that electron, one says that electron is in an atom, and an atom is only about 10^{-10} across.

Then those numbers are plugged into the constant, and then the result is something very, very different indeed. Now, the position is determined, so what’s the uncertainty in velocity?

Well, Planck’s constant, 6.63 times 10^{34} joule-seconds, is plugged in. The mass of the electron, nine times 10^{-31} kilograms is plugged in. And the distance—it’s known that the electron’s within the atom, that’s 10^{-10} meters.

And the result is that the uncertainty in velocity is about seven times 106. That’s seven million meters per second uncertainty in the velocity. Seven million meters per second is a very large uncertainty.

Learn more about semiconductors and modern microelectronics.

### Relationship between Position and Velocity at the Subatomic Scale

Someone can know either the position or the velocity to any arbitrary precision, but the more they pin down one—the better they know the position, the less they know about velocity. Or the more they know about the velocity, the less they know about the position.

For a large object like a baseball, this isn’t a problem because the mass is so large it swamps all the other effects. But for an electron, it introduces very large uncertainties in what is known about the subatomic world.

The uncertainty principle means that the quantum world can’t be talked about in an absolute deterministic way. Instead, it is necessary to use probabilities and use a probabilistic treatment of any quantum-scale event. This need to resort to probabilities profoundly disturbed Albert Einstein. It’s one of the reasons why he really didn’t like quantum mechanics.

### Common Questions about the Importance of Quanta at the Subatomic Scale

**Q: What are the requirements for every measurement at a subatomic scale?**There are three requirements for every measurement, not only at a subatomic scale but also at every scale. The first requirement is the sample, the second is the source of energy, and the third is the need for a detector.

**Q: What happens to the atom when its measured at the subatomic scale?**A photon is the smallest increment of energy. It is a single wavelength and piece of light that hits an atom. When a single atom absorbs that small increment it will be changed in the measuring process.

**Q: What’s the relationship between position and velocity at a subatomic scale?**German physicist Werner Heisenberg’s great insight was the realization that someone can’t know the exact position and the exact velocity of an object in a subatomic realm at exactly the same time. He expressed this dilemma in mathematical form as the Heisenberg Uncertainty Principle.