Solid things, blurry parts
A table is made of atoms and electrons. So are you. Tables and people are solidly here, not smeared across the room in probabilities. Yet, in this course’s reading, solid things are built from parts that have no sharp place at all. How the one comes from the other is a question for Lesson 4; this lesson walks through the rules those parts obey.
Energy in steps
Picture a particle trapped in a box, bouncing between two walls. As a wave, it can only take shapes that fit neatly inside the box, like a guitar string that can vibrate in one hump, or two, or three, but nothing in between. Each shape has its own energy. So the particle’s energy can’t be just anything. It comes in a ladder of allowed steps. That is what quantized means. Confinement makes the steps: a free particle can have any energy at all.
An intuitive picture helps. In the lowest step, you are most likely to find the particle near the middle of the box. Higher steps have more humps, with places between them where it is never found. Only at very high energies do the humps blur into an even spread, as a bouncing ball would give.
Atoms work the same way. Their electrons can occupy only certain energy levels, and when an electron drops from one level to a lower one, it emits a photon of exactly the energy difference. That is why each element glows with its own sharp colors, the red of a neon sign, the yellow of an old sodium streetlight, and why astronomers can tell what distant stars are made of. In 1913 the Danish physicist Niels Bohr used this idea to explain hydrogen’s four visible colors, which a Basel schoolteacher, Johann Balmer, had fitted with a formula in 1885. Bohr’s circling orbits were a stepping stone, but the ladder of levels stands.
Steps are not only for the invisibly small. In 1984 and 1985 at Berkeley, John Clarke, Michel Devoret, and John Martinis showed that a circuit on a chip about a centimeter across, cooled near absolute zero, absorbs microwaves only at certain frequencies, like an atom. They shared the 2025 Nobel Prize in Physics.
From idea to tool
The Berkeley circuit did not stay a laboratory curiosity. A circuit with atom-like energy steps is the ancestor of the superconducting qubit, the quantum bit inside one leading kind of quantum computer. Two of the three prizewinners went on to build such machines. As of October 2025, Michel Devoret was chief scientist for quantum hardware at Google Quantum AI, and John Martinis was chief technology officer of Qolab, a start-up he co-founded in 2022 with Alan Ho and Robert McDermott. The path is a common one in physics: a basic question (do quantum rules reach things big enough to hold?), a careful experiment, and decades later, companies built on the answer.
Two states at once
A quantum system can also be in a superposition, a combination of two basic states at once, weighted so that a measurement finds the first 40 percent of the time and the second 60 percent. Measure it, and you always get one state or the other, never a 40–60 blend. So where do the numbers show up? Only when you prepare the same superposition afresh many times and measure it each time. About 40 percent of the measurements will find the first state and 60 percent the second.
Measure a superposition
Prepare a system in a superposition of two states, A and B, with the chances you choose. Each measurement gives only A or B. Measure many times and see the chances emerge.
In this course’s reading, that is the most remarkable feature of all. In Newton’s universe the observer was irrelevant. In quantum theory, whether a measurement is made decides whether the superposition “collapses,” so observing is back inside physics. But a measurement needs no person, only an interaction that leaves a record, in a detector or on a stray photon.
The uncertainty principle
The next example is a speeding ticket. A traffic camera records both where you were and how fast you were going, precisely enough to fine you. But pin things down finely enough and you hit a wall. Werner Heisenberg showed in 1927 that a particle’s position and its momentum, its mass times its velocity, cannot both be sharp at the same time. Pin down one, and the other spreads out. Place an electron at one toll booth, to within a meter, and its speed can still be known to a fraction of a millimeter per second. But squeeze an electron into the width of an atom, and its speed is uncertain by about 600 kilometers a second. That is why an electron in an atom has no orbit.
This isn’t a problem of clumsy instruments. As Earle Kennard proved in 1927, the limit belongs to the particle’s state itself: an electron does not have an exact position and momentum to know. In this course’s comparison, it is as firm a limit as the speed of light. It is also different from chaos, which you met in Course 4. Chaos is uncertainty in a system whose laws are completely fixed, where tiny disturbances grow over time. Quantum uncertainty is in the system itself from the start. Einstein never accepted this. “He does not throw dice,” he wrote of God in 1926, in a letter to the physicist Max Born.
Walking through walls
Send a particle at a thick wall it doesn’t have enough energy to climb over, and it bounces back. Now make the wall thinner and thinner. At some point a detector behind the wall begins to register particles, even though the wall is still there. The thinner the wall, the more get through; the chance rises steeply, exponentially, as the wall thins. This is tunneling: because a particle is spread out as a wave, a little of the wave leaks through a thin barrier, and so there’s a chance of finding the particle on the other side. The whole Berkeley circuit tunneled too, out of a trapped state, as if it were one particle.
Tunneling made possible one of the most remarkable instruments ever built. In 1981 Gerd Binnig and Heinrich Rohrer, at IBM’s laboratory near Zurich, brought an extremely sharp metal tip so close to a surface that electrons tunneled across the gap. The current changes about tenfold for every tenth of a nanometer of distance, so sweeping the tip across the surface maps it atom by atom. Their scanning tunneling microscope won half of the 1986 Nobel Prize in Physics.
Seeing without seeing
Physicists now work at such scales every day. In 2017 a team at NIST in Boulder, Colorado, used light to cool a tiny aluminum drum, 20 micrometers across and 100 nanometers thick, that beats about ten million times a second. Its thickness is below what an ordinary light microscope can make out, about two hundred nanometers. A scanning electron microscope sweeps a fine beam of electrons across the sample and builds the picture point by point from the electrons it knocks loose, though even it cannot show single atoms.
That changes what “observation” means, in this course’s reading. First people looked with their eyes; then with telescopes and microscopes. Now physicists detect effects they cannot see or feel and use trusted physical laws to work backward to their causes. In 2007 a team at Yale showed a superconducting circuit whose signal splits into separate peaks, one for each photon stored in it. No one has seen those photons. But because the laws that link peaks and photons are trusted, physicists are confident they are there.
How is quantum uncertainty different from chaos?
Closer to home
Quantum rules run your daily life. The flash memory in your phone and in every USB drive stores data by making electrons tunnel through a thin insulating layer. Lasers, which read many barcodes and carry fiber-optic internet, depend on quantized energy levels. In 1989 the IBM physicist Don Eigler and his colleague Erhard Schweizer used a scanning tunneling microscope in San Jose to spell out “IBM” with 35 individual xenon atoms, 17 nanometers wide. In 2013 IBM researchers made a short film, A Boy and His Atom, by moving carbon monoxide molecules, two atoms each, one frame at a time. And in 1988 Bai Chunli (白春礼), back from Caltech, led the Beijing team that built China’s first computer-controlled tunneling microscope.
Another view
Einstein’s objection didn’t go away. In 1935, with Boris Podolsky and Nathan Rosen, he argued that quantum mechanics must be incomplete, and that particles that have interacted must already carry properties the theory leaves out. That year Erwin Schrödinger named the link between such particles entanglement, “the characteristic trait” of quantum mechanics. In 1964 John Bell showed how to test the idea. Experiments by John Clauser in California, Alain Aspect in France, and Anton Zeilinger in Austria found that nature violates Bell’s limit, as quantum mechanics predicts; the three shared the 2022 Nobel Prize in Physics. In 2015 teams in Delft, Vienna, and Boulder ran the first tests that closed the main loopholes together. None of this sends a message faster than light: each side’s results look random until the two lists are compared. The local, definite world Einstein hoped for is ruled out; what lies underneath instead is still argued.
What to keep
- Confined particles, from electrons in atoms to a centimeter-sized circuit, can have only certain energies. That is why atoms emit sharp colors.
- A quantum system can be in a superposition of states. Each measurement gives one result; the probabilities show up only over many measurements. A measurement needs a record, not a person.
- Position and momentum can’t both be sharp at once. This is built into nature, not into instruments, and unlike chaos.
- Particles can tunnel through thin barriers, the principle behind the scanning tunneling microscope and flash memory.
Think it over
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Sources and further reading
- Niels Bohr, “On the Constitution of Atoms and Molecules,” Philosophical Magazine 26 (1913), Parts I–III (Project Gutenberg); MacTutor History of Mathematics, biography of Johann Balmer.
- Royal Swedish Academy of Sciences, “The Nobel Prize in Physics 2025” (kva.se), with the laureates’ affiliations; J. M. Martinis, M. H. Devoret, and J. Clarke, Physical Review Letters 55, 1543 (1985); University of Wisconsin–Madison news, October 21, 2025, and UCSB and KEYT reports on Qolab.
- Max Born, Zeitschrift für Physik 37, 863 (1926); Werner Heisenberg, Zeitschrift für Physik 43, 172–198 (1927); Stanford Encyclopedia of Philosophy, “The Uncertainty Principle” (on Kennard’s 1927 inequality); Albert Einstein to Max Born, December 4, 1926, in The Born–Einstein Letters, trans. Irene Born, 1971.
- Werner Heisenberg, Physics and Philosophy, Harper, 1958.
- Gerd Binnig and Heinrich Rohrer, “Scanning Tunneling Microscopy: From Birth to Adolescence,” Nobel lecture, 1986; IBM, history of the scanning tunneling microscope (ibm.com/history); D. M. Eigler and E. K. Schweizer, Nature 344, 524 (1990); Chinese Academy of Sciences, Institute of Chemistry, on Bai Chunli and China’s first STM.
- NIST, “NIST Physicists ‘Squeeze’ Light to Cool Microscopic Drum below Quantum Limit,” January 11, 2017; D. I. Schuster et al., Nature 445, 515 (2007).
- A. Einstein, B. Podolsky, and N. Rosen, Physical Review 47, 777 (1935); E. Schrödinger, Proceedings of the Cambridge Philosophical Society 31 (1935); J. S. Bell, Physics Physique Физика 1, 195 (1964); L. K. Shalm et al., Physical Review Letters 115, 250402 (2015); Royal Swedish Academy of Sciences, “The Nobel Prize in Physics 2022.”
- Anil Ananthaswamy, Through Two Doors at Once, Dutton, 2018.
- Philip Ball, Beyond Weird, University of Chicago Press, 2018.