What is quantum physics, and why is an electron not a tiny ball?

Each electron produces an individual detection event. If many electrons are recorded after passing through two slits, those events gradually form an interference distribution: some places receive more hits, others fewer. This buildup from individual events was recorded, for example, in Bach and colleagues’ experiment.

Quantum physics describes matter and light using quantum states and rules for calculating measurement outcomes. It predicts probabilities and, for indistinguishable alternatives, includes interference between probability amplitudes. This explains why electron statistics differ from those of ordinary little balls. Feynman: quantum behaviour, §§1–4–1–7.

Individual events are local; their distribution has wave properties

For balls independently travelling through the first or second opening, we can count the two contributions separately and add their probabilities. When two quantum alternatives retain the ability to interfere, that addition is insufficient. In some regions, opening the second path even reduces the number of hits.

The model assigns alternatives probability amplitudes. These mathematical quantities have a magnitude and a phase. Phase describes a relationship within an oscillation: two contributions can reinforce or cancel each other. Amplitudes are added first; probability is then calculated from the result. Adding probabilities immediately is a different operation with a different result.

Water waves offer a useful analogy for reinforcement and cancellation. But an electron detector records separate events, not half a charge smeared between two hits. “Particle” and “wave” describe different features of behaviour here; the electron is not switching between two kinds of matter. Feynman: amplitudes and interference.

Superposition is more than an unknown choice

A superposition is a quantum state formed by combining the amplitudes of other states. For two paths, it retains both their weights and their relative phase. Ordinary ignorance about which preselected path a classical ball takes would not have this phase or the corresponding interference.

To see the difference without a complicated slit image, imagine an ideal interferometer: it creates two equally weighted paths, recombines them, and has outputs A and B. At one setting, amplitudes reinforce at A and cancel at B. Changing the relative phase can redirect the entire ideal output to B while the path weights remain equal. A similar principle is explained in MIT’s course using a Mach–Zehnder interferometer.

Equal path weights, different outcomes after recombination

Ideal model: two equally weighted paths → balanced recombination → outputs A and B.

Coherent paths · phase 0

Output A100%

Output B0%

Coherent paths · phase π/2

Output A50%

Output B50%

Coherent paths · phase π

Output A0%

Output B100%

Fully distinguishable paths · any phase

Output A50%

Output B50%

Calculated probabilities, not measured frequencies or electron trajectories. Equal path weights, ideal recombination, no losses, noise or detector inefficiency. The last row is the overall distribution without selection by the path record. Colour only assists comparison; every value is given in text. The rule and calculation are explained in the article.

The diagram’s numbers are model probabilities, not a promise that every hundred trials will produce exactly those counts. At a probability of 50%, short runs fluctuate. An ideal probability of 0, however, means an outcome excluded at this setting; real noise can spoil that minimum.

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One calculation separates phase from randomness

Under our phase convention, the ideal device’s output amplitudes are:

\begin{aligned} a_A&=\frac{1+e^{i\varphi}}{2},\\ a_B&=\frac{1-e^{i\varphi}}{2}. \end{aligned}

$i$ is the imaginary unit and $\varphi$ the relative phase in radians; amplitudes and probabilities here are dimensionless. Taking the squared magnitude gives:

\begin{aligned} P(A)&=|a_A|^2=\frac{1+\cos\varphi}{2},\\ P(B)&=|a_B|^2=\frac{1-\cos\varphi}{2}. \end{aligned}

At $\varphi=0$ the values are $1$ and $0$ ; at $\varphi=\pi/2$ , $1/2$ and $1/2$ ; at $\varphi=\pi$ , $0$ and $1$ . Their sum is always $1$ , and adding a full turn of $2\pi$ repeats the result. These check normalization and periodicity.

The formulas combine two equally weighted paths in a balanced device; the general rule is the squared magnitude of the sum of amplitudes. If an independent record perfectly marks the path, then without selecting outcomes according to that record, the two output probabilities are $1/2$ regardless of phase. This is a different preparation/interaction, not proof that phase has “ceased to exist” throughout the whole system.

Measurement does not require human consciousness

If a device correlates each path with a physically distinguishable record, interference between those paths disappears from the overall distribution. What matters is the change in the quantum system and its relationship with the apparatus, not whether somebody opens the results file. Partial distinguishability can merely weaken interference; not every interaction eliminates it completely.

A measurement turns “which outcomes are possible?” into a concrete record that can be compared with the prediction. How to interpret the appearance of an individual outcome and the quantum state belongs to interpretations and the measurement problem. But a conscious gaze does not enter the interference calculation. Feynman: what path detection changes, §1–6, MIT: states and measurement outcomes, §4.

Uncertainty and quantization are specific properties of the model

A quantum state specifies distributions of outcomes for different measurements. Position along the $x$ axis and momentum along that same axis obey $\Delta x\,\Delta p_x\geq\hbar/2$ . Here $\Delta$ is the standard deviation, a measure of the width of the corresponding distribution for identically prepared states; $\hbar$ is the reduced Planck constant.

This limit does not vanish when we buy a better instrument. A narrower spatial wave packet requires a wider range of momenta. The spread of outcomes in a state and the error or disturbance introduced by a particular measuring device are different concepts; one cannot replace the other in this formula. Feynman: wave packets, §2–1, Erhart and colleagues: uncertainty versus measurement error.

Another consequence is that certain quantities have separate allowed values. Bound states of a hydrogen atom, for example, form discrete energy levels. Transitions between them involve particular light energies, rather than arbitrary colours. This does not mean every energy in every system belongs to one universal set of packets: a free particle has a different structure of possible energies. NIST: neutral hydrogen levels.

Entanglement links statistics, not faster-than-light mail

In an entangled state, two systems cannot be described simply as two independently specified pure quantum states. Their outcomes have special correlations. Experiments violating Bell inequalities exclude a certain class of local explanations using pre-existing hidden parameters under the test’s assumptions, including independent selection of measurement settings. This does not mean every possible hidden-variable interpretation has been disproved. Hensen and colleagues: an experimental test.

Correlation does not let you choose your own random outcome and encode a message for a distant partner. Comparing records and using them in a transmission protocol requires an ordinary communication channel. IBM: why quantum teleportation cannot send information faster than light.

Quantum physics does not declare that “anything is possible”. It sets strict rules for what is possible, with what probability and under what conditions. Its unusual behaviour becomes clearer when we compare experiments instead of trying to turn an electron into a miniature ball. The next useful foundation is atoms and their parts.