---
title: "Bothe and Geiger ask whether two signals belong together"
description: "When two counters respond, how can we tell whether they recorded the same event?"
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[Detecting a passing particle](https://sandboxphysics.com/stories/particle-evidence/#detectors)

Particles · Experiments · Discovery

# Bothe and Geiger ask whether two signals belong together

When two counters respond, how can we tell whether they recorded the same event?

Sandbox Physics · 2026-10-24

Nobel contribution: 1954-2

1. Record each detector’s signal time
2. Compare a short time interval
3. Estimate accidental pairs
4. Test the common-event interpretation

A coincidence is a time-based selection with a measurable accidental rate.

## A question about each collision

In 1924–1925, Walther Bothe and Hans Geiger at Berlin’s Physikalisch-Technische Reichsanstalt asked whether scattered X-rays and recoil electrons appeared together in individual interactions. Compton’s scattering work had made the transfer of energy between radiation and electrons a pressing question. A competing proposal associated with Bohr, Kramers and Slater allowed conservation to hold statistically across many processes. Bothe and Geiger wanted to test the connection one event at a time.

Measuring an average current could not answer that question. Two detectors might accumulate comparable totals without ever responding to the same interaction. The experiment needed a record of when each detector reacted. One counter registered recoil electrons and another the scattered radiation, detected through the charged particles it produced. Their electrical responses were recorded against a common time reference.

Think of listening for an echo. Counting all shouts and all returning sounds over an hour loses the association. Keep the times and a repeated short delay can connect a sound with its source. Bothe and Geiger looked for signals close together, allowing for the response of the counters. The essential new information was the pairing in time.

Sources: [2] [3]

## The time window can be too generous

A coincidence means that two signals fall within a chosen interval. It does not automatically mean that they share a cause. If two unrelated counters fire often enough, some of their signals will happen to be close. Make the allowed interval wider and more accidental pairs pass. Make it very narrow and true pairs can be lost because the detectors do not respond at perfectly fixed times.

This trade-off can be understood with a simple imagined experiment. Place two independent clickers on a table. Each produces a few pulses per second. A rule accepting pulses within a whole second will call many unrelated clicks a pair. A rule accepting only a tiny fraction of a second will call fewer pairs. The same reasoning applies to radiation counters, even though the time scales and physical signals differ.

Bothe and Geiger compared the excess of near-simultaneous detections with what unrelated events could supply. Their results supported the association of scattered radiation and recoil electrons in individual interactions. The apparatus did not determine every outgoing energy and direction in each event. The observed time connection favoured individual linked interactions over the statistical-only alternative.

Sources: [2] [3]

## A comparison tests the chance-pair explanation

Accidental coincidences depend on the single-counter rates and the width of the accepted interval. If one counter fires more often, there are more opportunities for an unrelated pulse from the other to land nearby. The effect can be tested by changing the time condition or by comparing signals whose timing has deliberately been displaced. A large displacement destroys a prompt physical pairing while leaving independent pulses available to overlap.

The comparison has to preserve the conditions that generate the background. If the source intensity changes during the run, a control assembled from a different time may have a different pulse rate. If one physical background produces both signals, it can survive the coincidence rule too. Timing is powerful because it offers a testable association, and useful because its possible false associations can be measured and studied.

Sources: [3]

## Two counters can also choose a direction

Timing became even more useful when combined with geometry. Put two counters one above the other and require a coincidence: a penetrating particle travelling through both becomes a plausible source of the pair. Place absorbing material between them and ask which coincidences survive. The arrangement begins to test both the direction and the penetrating power of the radiation.

This later use of the method fed into cosmic-ray work and into the counter-controlled cloud chamber. In the latter, the joint electrical signal told a mechanical imaging apparatus when to operate. The counters were fast but gave little spatial detail. The chamber was slower but could preserve a detailed pattern. Combining them made a practical instrument out of strengths that neither part had by itself.

The 1954 Nobel Prize had two distinct shares. Max Born was recognised for the statistical interpretation of the wavefunction; Bothe for the coincidence method and discoveries made with it. A reader can connect those contributions to the same period of quantum physics without merging their experimental claims. Bothe and Geiger’s enduring idea is concrete: preserve timing, measure accidental associations, and use a pair of signals to learn about a single physical event.

Sources: [3] [1]

Continue with the physics

## Try the related models

### [Compare true and accidental pairs](https://sandboxphysics.com/labs/reactor-coincidence/)

Widen the timing window and compare accepted reactor-event pairs.

The model applies coincidence selection to synthetic prompt–delayed antineutrino signals.

## Sources and reading notes

1. [P. M. S. Blackett and G. Occhialini, Photography of penetrating corpuscular radiation (1932)](https://doi.org/10.1038/130363a0)

   Their first report describes two-counter triggering and high-energy tracks on more than 75 percent of the selected photographs.

2. [W. Bothe and H. Geiger, Über das Wesen des Comptoneffekts (1925)](https://doi.org/10.1007/BF01331702)

   The original coincidence experiment tests whether scattered radiation and recoil electrons accompany one another in individual events.

3. [W. Bothe, The coincidence method (1954)](https://www.nobelprize.org/prizes/physics/1954/bothe/lecture/)

   Bothe’s written Nobel lecture recounts the counters, photographic timing and extensions to penetrating radiation.

## Follow the next question

[Blackett and Occhialini let a particle take its own photograph](https://sandboxphysics.com/stories/particle-evidence/blackett-counter-controlled-cloud-chamber/)

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