---
title: "Quantum physics: reading the evidence"
description: "From thermal radiation and precision spectra to quantum control and Bell tests: read the observations and their limits."
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/"
last_modified: "2026-10-24"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Quantum physics: reading the evidence

Sandbox Physics · 2026-10-18

From thermal radiation and precision spectra to quantum control and Bell tests: read the observations and their limits.

Start with what each apparatus measured. Then ask which interpretation the data justify, which alternatives they constrain and what is still untested. The articles compare thermal radiation, charge measurement, photon recoil and atomic excitation; follow matter waves, probability and how quantum mechanics took shape; then move from magnetic moments and precision spectra to trapping, cooling, coherence and photon-information experiments. Related Labs are linked where their models make a useful comparison.

## Count photons without absorbing them; slow atoms before probing them

Compare dispersive cavity probes with atomic-beam slowing. Each teaching instrument states how it is prepared and calibrated and what physics it leaves out. Its simulated data are kept apart from historical observations.

- [Cavity Photon Counting & Feedback](https://sandboxphysics.com/labs/cavity-photon-qnd-feedback/)
- [Zeeman Atomic-beam Slower](https://sandboxphysics.com/labs/zeeman-atomic-beam-slower/)

## Readout through a second system

An auxiliary ion reads out a spectrum, and three analyzer stations read out a joint parity. Both protocols keep the detector outcomes and state what their statistics cannot prove.

[Two-Ion Quantum Logic Spectroscopy](https://sandboxphysics.com/labs/two-ion-quantum-logic-spectroscopy/)

[Three-Photon GHZ Correlation Bench](https://sandboxphysics.com/labs/three-photon-ghz-correlations/)

## Two ways to read a magnetic moment

One method watches frequency jumps of a single trapped electron; the other measures how a beam of neutral hydrogen molecules deflects at each velocity. Each has its own apparatus, simulated data and calibration limits.

[Single-Electron Penning Trap & Spin Readout](https://sandboxphysics.com/labs/penning-electron-spin-readout/)

[Molecular-Beam Proton Magnetic Moment](https://sandboxphysics.com/labs/molecular-beam-proton-moment/)

## Read a line’s position, then its width

Two simulated counting experiments separate the effects of finite nuclear mass, thermal motion and instrumental blur. The historical evidence and the real Balmer multiplets have limits of their own.

[Hydrogen–Deuterium Isotope Spectrometer](https://sandboxphysics.com/labs/hydrogen-deuterium-isotope-spectrometer/)

[Two-Isotope Doppler Thermometer](https://sandboxphysics.com/labs/two-isotope-doppler-thermometer/)

## Photon recoil: angle, energy and coincidence

Two simulated instruments link the photopeak measured at each angle with the energy balance in an active target. The historical evidence is covered in a separate article.

[Compton Angular Spectrometer](https://sandboxphysics.com/labs/compton-angular-spectrometer/)

[Compton Coincidence Energy Analyzer](https://sandboxphysics.com/labs/compton-coincidence-energy/)

## Keep driving: absorption, dispersion and saturation

Step a balanced RF bridge through resonance, then compare a scan of the drive amplitude. These are homogeneous, steady-state teaching models with simulated voltages; they do not reconstruct the historical apparatus.

[Continuous-wave NMR Spectrometer](https://sandboxphysics.com/labs/cw-nmr-spectrometer/)

[NMR Power Saturation Analyzer](https://sandboxphysics.com/labs/nmr-power-saturation/)

## Laws and the formation of quantum mechanics

Compare a measured distribution and a spectral rule with what a theory actually predicts.

1. ### [Blackbody radiation: a whole curve, not one quantum](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/)

   How did the long-wavelength evidence force a change in the law of thermal radiation?

2. ### [Atomic spectra: evidence for states, not photographs of orbits](https://sandboxphysics.com/stories/quantum-evidence/atomic-spectra-stationary-states/)

   How did a set of wavelengths become a test of atomic structure?

3. ### [de Broglie: a wavelength for matter, a speed for the packet](https://sandboxphysics.com/stories/quantum-evidence/de-broglie-matter-waves-phase-packets/)

   What did assigning a wavelength to an electron predict, and which wave speed describes its motion?

4. ### [Matrices and waves: two routes to the same predictions](https://sandboxphysics.com/stories/quantum-evidence/matrix-wave-mechanics-observables/)

   What changed when atomic theory stopped assigning a path to every electron?

5. ### [Dirac’s electron: a successful equation with an unfinished story](https://sandboxphysics.com/stories/quantum-evidence/dirac-electron-spin-relativity/)

   What did the relativistic equation explain, and what still required new physics?

## Charge, excitation and photon recoil

Look at the current, trajectory or spectrum itself before inferring a quantum.

1. ### [Photoelectric evidence: the voltage is not yet the energy](https://sandboxphysics.com/stories/quantum-evidence/photoelectric-stopping-potential-contact/)

   How did a family of current–voltage curves become a test of Einstein’s law?

2. ### [Oil drops: finding a charge unit in falling times](https://sandboxphysics.com/stories/quantum-evidence/millikan-oil-drop-charge-inference/)

   Why is one suspended drop not enough to establish an elementary charge?

3. ### [Franck–Hertz: what a drop in current can show](https://sandboxphysics.com/stories/quantum-evidence/franck-hertz-discrete-excitation/)

   Why does a loss of collected electrons reveal an atomic excitation energy?

4. ### [Compton scattering: light must balance momentum too](https://sandboxphysics.com/stories/quantum-evidence/compton-scattering-energy-momentum/)

   What does a shifted X-ray wavelength add to the evidence from photoemission?

## Probability and exclusion

Tell the historical argument apart from what a modern state model already assumes.

1. ### [Born: how a scattering direction became a probability](https://sandboxphysics.com/stories/quantum-evidence/born-scattering-probability/)

   What connects a wave spread over many directions to one recorded collision?

2. ### [Pauli: count the states before filling the shells](https://sandboxphysics.com/stories/quantum-evidence/pauli-spectra-exclusion-principle/)

   How did sorting spectral lines lead to a rule about which electron states are allowed?

## Fields, spins and precision spectra

Ask what shifted, what the instrument recorded and which baseline was being tested.

1. ### [Why a magnetic field splits a spectral line](https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/)

   How did the lines Zeeman observed and the polarization Lorentz predicted support the same explanation?

2. ### [How an electric field splits hydrogen’s spectral lines](https://sandboxphysics.com/stories/quantum-evidence/stark-effect-electric-field-spectra/)

   How did Stark use colour and polarization to see that an electric field changed atomic energies?

3. ### [Reading atomic motion in the colours of canal rays](https://sandboxphysics.com/stories/quantum-evidence/stark-canal-rays-doppler-emitters/)

   Why do approaching and receding hydrogen atoms give different observed colours?

4. ### [What two silver traces revealed about atoms](https://sandboxphysics.com/stories/quantum-evidence/stern-gerlach-silver-beam-spin/)

   What did Stern and Gerlach observe in 1922, and when did electron spin enter the explanation?

5. ### [Measuring the proton’s magnetism with a hydrogen beam](https://sandboxphysics.com/stories/quantum-evidence/stern-proton-moment-molecular-hydrogen/)

   How could the deflection of neutral hydrogen molecules reveal a property of the proton?

6. ### [How to tell when a nucleus is in resonance](https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/)

   Why can missing molecules, absorbed radio waves and a voltage in a coil all reveal nuclear magnetism?

7. ### [How light moves atoms into states that stop absorbing](https://sandboxphysics.com/stories/quantum-evidence/optical-pumping-populations-double-resonance/)

   How can shining polarized light prepare atoms and make a radiofrequency resonance visible?

8. ### [How missing hydrogen atoms revealed the Lamb shift](https://sandboxphysics.com/stories/quantum-evidence/lamb-shift-microwave-evidence/)

   How did a dip in a downstream signal reveal energy missing from a theory of hydrogen?

9. ### [How Kusch and Foley found the electron’s extra magnetism](https://sandboxphysics.com/stories/quantum-evidence/kusch-foley-electron-magnetic-moment/)

   How can comparing atoms reveal a small correction to the magnetic response of an electron?

10. ### [How a crystal takes the recoil of an emitting nucleus](https://sandboxphysics.com/stories/quantum-evidence/mossbauer-recoil-free-resonance/)

    Why can putting nuclei in a solid restore an extremely narrow gamma-ray resonance?

## Clocks, traps and single-quantum control

Follow each experiment from state preparation through the stored detector data to an estimate and its sources of error.

1. ### [How Ramsey and ion traps gave atoms more time](https://sandboxphysics.com/stories/quantum-evidence/ramsey-ion-traps-measurement/)

   Why does a longer conversation with an atom make finer measurements possible?

2. ### [Reading a cavity phase error in an atomic fountain](https://sandboxphysics.com/stories/quantum-evidence/ramsey-cavity-phase-frequency-bias/)

   How can a microwave field move a clock frequency even when the Ramsey fringes look clean?

3. ### [Counting the quantum noise left by a perfect detector](https://sandboxphysics.com/stories/quantum-evidence/quantum-projection-noise-population-counts/)

   How do you separate random atomic outcomes from noisy state detection?

4. ### [Following a fountain clock’s extrapolation to zero density](https://sandboxphysics.com/stories/quantum-evidence/fountain-clock-collision-density-extrapolation/)

   What must stay the same when changing the atom number to correct a clock frequency?

5. ### [How a changing electric field holds an ion](https://sandboxphysics.com/stories/quantum-evidence/paul-trap-dynamic-stability-micromotion/)

   How can a particle stay in a trap whose electric field keeps changing direction?

6. ### [How Dehmelt listened to the spin of one electron](https://sandboxphysics.com/stories/quantum-evidence/dehmelt-single-electron-penning-spin-readout/)

   How can an electron reveal a spin flip while staying inside its trap?

7. ### [When sodium atoms came out colder than expected](https://sandboxphysics.com/stories/quantum-evidence/laser-cooling-below-doppler-limit/)

   How did several thermometers turn an unexpectedly low temperature into a clue about atomic structure?

8. ### [Keeping a slowing atomic beam in tune with one laser](https://sandboxphysics.com/stories/quantum-evidence/zeeman-slowing-neutral-atom-beam/)

   How can a changing magnetic field keep one fixed laser frequency pushing against a slowing atom?

9. ### [How six laser beams slowed Chu’s atoms](https://sandboxphysics.com/stories/quantum-evidence/chu-optical-molasses-diffusion-escape/)

   Why did atoms linger in optical molasses even though they could still drift out?

10. ### [Reading a cold-atom thermometer from the flight of the cloud](https://sandboxphysics.com/stories/quantum-evidence/cold-atom-ballistic-thermometry/)

    How do measurements after release separate random velocity, initial cloud size and drift?

11. ### [How an atom loses energy climbing hills made of light](https://sandboxphysics.com/stories/quantum-evidence/sisyphus-cooling-polarization-energy/)

    How can light cool an atom when its total intensity stays the same from place to place?

12. ### [How helium atoms escaped the light and formed two narrow peaks](https://sandboxphysics.com/stories/quantum-evidence/subrecoil-cooling-dark-state-momentum/)

    What became cold in the 1988 experiment that selected atoms with a dark quantum state?

13. ### [How one trapped ion switches its fluorescence off and on](https://sandboxphysics.com/stories/quantum-evidence/electron-shelving-single-ion-jumps/)

    When does a missing fluorescence signal become evidence for an internal-state transition?

14. ### [Reading the sidebands in the first ion ground-state cooling experiment](https://sandboxphysics.com/stories/quantum-evidence/sideband-asymmetry-ground-state-cooling/)

    How do you read the 1989 mercury-ion spectra without confusing a weak red sideband with a complete temperature measurement?

15. ### [Let a second ion read out a narrow transition](https://sandboxphysics.com/stories/quantum-evidence/quantum-logic-spectroscopy-shared-motion/)

    How can an ion with inconvenient cooling and detection transitions become a useful spectroscopic reference?

16. ### [How to measure one quantum system and keep it available](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)

    How can a detector learn about one quantum system without simply consuming it?

17. ### [A cavity cat loses coherence before it loses its energy](https://sandboxphysics.com/stories/quantum-evidence/cavity-cat-coherence-energy-decay/)

    Which observation distinguishes a fading superposition from an ordinary mixture or a leaking cavity?

18. ### [Counting stored photons one atom at a time](https://sandboxphysics.com/stories/quantum-evidence/qnd-photon-counting-atomic-records/)

    How does a string of binary atomic outcomes become a photon-number estimate without absorbing the field?

19. ### [Keeping a chosen number of photons in a cavity](https://sandboxphysics.com/stories/quantum-evidence/quantum-feedback-photon-number-verification/)

    What distinguishes preparing a chosen number state from merely reporting that the controller has found it?

## Bell tests and photon information

Each conclusion depends on how trials were defined, which events were kept, the timing and what communication was possible.

1. ### [How Bell tests distinguish quantum correlations](https://sandboxphysics.com/stories/quantum-evidence/bell-tests-correlations-loopholes/)

   Which assumptions turn a surprising correlation into evidence against a local hidden-variable model?

2. ### [Freedman and Clauser test Bell’s inequality with calcium light](https://sandboxphysics.com/stories/quantum-evidence/freedman-clauser-coincidence-normalization/)

   How did the calcium photon experiment test a numerical limit on local explanations?

3. ### [Aspect changes the analyzers while photons are in flight](https://sandboxphysics.com/stories/quantum-evidence/aspect-switching-spacetime-records/)

   What did rapidly changing the optical path add to the 1982 Bell experiment, and what remained assumed?

4. ### [A readiness signal makes the Bell trial countable](https://sandboxphysics.com/stories/quantum-evidence/event-ready-bell-trials-finite-statistics/)

   Why does a herald before the setting choice differ from keeping only favourable detections afterwards?

5. ### [Photon Bell tests keep the trials where detectors stay silent](https://sandboxphysics.com/stories/quantum-evidence/photon-bell-losses-optical-trials/)

   How did efficient detectors, a new way of counting events and local clocks bring separate loophole advances into one experiment?

6. ### [Three-photon GHZ correlations defeat a shared answer sheet](https://sandboxphysics.com/stories/quantum-evidence/ghz-parity-three-photon-records/)

   Why does an argument built on perfect certainty still need careful counting of imperfect detections?

7. ### [How the 1997 photon experiment transferred a quantum state](https://sandboxphysics.com/stories/quantum-evidence/quantum-teleportation-conditional-records/)

   What was transferred in the photon experiment, and which events were included in its evidence?

8. ### [A photon announces when to look for its partner](https://sandboxphysics.com/stories/quantum-evidence/heralded-photon-anticorrelation-gates/)

   How can counting clicks after a trigger tell a single-photon source from an attenuated beam?

9. ### [Two photons leave the beam splitter together](https://sandboxphysics.com/stories/quantum-evidence/hong-ou-mandel-dip-mode-overlap/)

   Where do the two photons go when the coincidence count falls?

10. ### [A joint measurement entangles two photons that never met](https://sandboxphysics.com/stories/quantum-evidence/entanglement-swapping-fourfold-records/)

    How do you tell a conditionally entangled pair from a correlation created just by sorting?

11. ### [The later measurement sorts earlier photon detections](https://sandboxphysics.com/stories/quantum-evidence/delayed-choice-swapping-sorted-records/)

    What changes when the joint analyzer is chosen after the outer photons have been detected?

12. ### [Dense coding sends three distinguishable messages with one photon](https://sandboxphysics.com/stories/quantum-evidence/dense-coding-three-messages-resources/)

    What did the 1996 three-message experiment demonstrate beyond an ideal four-state protocol?

13. ### [Reconstructing a photon state from calibrated counts](https://sandboxphysics.com/stories/quantum-evidence/photon-tomography-counts-physical-states/)

    What does reconstruction add to raw detector counts, and what assumptions does it bring in?

## Try a model, then read the evidence

Five Labs on control, reconstruction and relativistic analogues each link to an evidence article. Each entry says which comparison the Lab can support.

- [Cavity excitation exchange](https://sandboxphysics.com/labs/cavity-quantum-exchange/)

  Can an empty mode exchange an excitation? [Read the evidence](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)

- [Homodyne quantum tomography](https://sandboxphysics.com/labs/homodyne-quantum-tomography/)

  Can the reconstruction predict a new projection? [Read the evidence](https://sandboxphysics.com/stories/quantum-evidence/photon-tomography-counts-physical-states/)

- [STIRAP dark-state transfer](https://sandboxphysics.com/labs/stirap-dark-state-transfer/)

  What does changing pulse order change? [Read the evidence](https://sandboxphysics.com/stories/quantum-evidence/subrecoil-cooling-dark-state-momentum/)

- [Dirac trembling motion](https://sandboxphysics.com/labs/dirac-trembling-motion/)

  Does the oscillation survive one energy branch? [Read the evidence](https://sandboxphysics.com/stories/quantum-evidence/dirac-electron-spin-relativity/)

- [Klein wave-packet tunnelling](https://sandboxphysics.com/labs/klein-wavepacket-tunneling/)

  Can raising the barrier reopen a channel? [Read the evidence](https://sandboxphysics.com/stories/quantum-evidence/dirac-electron-spin-relativity/)

## A coil records two kinds of recovery

Turn the recorded quadrature voltages into a free-induction spectrum, then compare an inversion-recovery scan that keeps the sign of the signal. These pulse methods came later; the Labs do not recreate the 1946 experiments, which used continuous driving.

[NMR Free Induction Spectrometer](https://sandboxphysics.com/labs/nmr-free-induction-spectrometer/)

[NMR Inversion Recovery Relaxometer](https://sandboxphysics.com/labs/nmr-inversion-recovery/)

## Light reads atomic lifetimes

Compare how the ground-state population relaxes after optical pumping with the width of the excited-state Hanle polarization signal. The two methods use different clocks, geometries and photon signals, so keep them apart.

[Optical Pumping and Relaxation](https://sandboxphysics.com/labs/optical-pumping-relaxation/)

[Hanle Lifetime Spectrometer](https://sandboxphysics.com/labs/hanle-lifetime-spectrometer/)

## Charge and magnetic response

Estimate an oil drop’s charge from its motion as a continuous value, then compare two atomic resonances to separate a spin factor from the field they share. Read the historical evidence alongside the simulated measurement.

[Oil-Drop Charge Measurement](https://sandboxphysics.com/labs/oil-drop-charge/)

[Atomic Magnetic-Moment Comparator](https://sandboxphysics.com/labs/atomic-magnetic-moment-comparator/)

## A split line, or a moving source?

Compare polarized magnetic splitting with the motion of emitting atoms. Collect counts, change the viewing direction, and read the fitted result separately from the source’s reference values.

[Zeeman Polarization Spectrometer](https://sandboxphysics.com/labs/zeeman-polarization-spectrometer/)

[Canal-Ray Doppler Spectrometer](https://sandboxphysics.com/labs/canal-ray-doppler-spectrometer/)

## Three ways to resolve a small energy

Record polarized Stark spectra, count the metastable atoms that survive a Lamb resonance, and scan Mössbauer transmission by changing the source velocity. Each instrument has its own model limits and raw data; the historical evidence is discussed separately.

[Stark Splitting Spectrometer](https://sandboxphysics.com/labs/stark-splitting-spectrometer/)

[Lamb Shift Microwave Bench](https://sandboxphysics.com/labs/lamb-shift-microwave/)

[Mössbauer Doppler Observatory](https://sandboxphysics.com/labs/mossbauer-doppler-resonance/)

## Measure a thermal spectrum

Use the blackbody teaching instrument to take simulated open and dark readings, compare three radiation laws and export the data. The readings are simulated; the historical evidence is discussed separately.

[Open the Blackbody Radiation Observatory](https://sandboxphysics.com/labs/blackbody-radiation/)

## Evidence dates and prize years

The dates below show when the evidence in each article was obtained. Prize years are listed separately, and the articles point out later tests and technical improvements. The linked papers name the full author teams.

Show all 26 prize contributions

1. **1890s–1901** · Wien laws and their spectral limits

   Prize: [1911 · Thermal radiation](https://www.nobelprize.org/prizes/physics/1911/summary/)

   Laureates: Wilhelm Wien

   - [Blackbody radiation: a whole curve, not one quantum](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/)

2. **1896–1897** · Zeeman and Lorentz: split lines and polarization

   Prize: [1902 · Magnetic radiation effects](https://www.nobelprize.org/prizes/physics/1902/summary/)

   Laureates: Hendrik A. Lorentz / Pieter Zeeman

   - [Why a magnetic field splits a spectral line](https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/)

3. **1900–1901** · Planck: distribution and energy elements

   Prize: [1918 · Energy quanta](https://www.nobelprize.org/prizes/physics/1918/summary/)

   Laureates: Max Planck

   - [Blackbody radiation: a whole curve, not one quantum](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/)

4. **1905–1913** · Stark: moving emitters and field splitting

   Prize: [1919 · Electric splitting and canal-ray Doppler effect](https://www.nobelprize.org/prizes/physics/1919/summary/)

   Laureates: Johannes Stark

   - [Reading atomic motion in the colours of canal rays](https://sandboxphysics.com/stories/quantum-evidence/stark-canal-rays-doppler-emitters/)
   - [How an electric field splits hydrogen’s spectral lines](https://sandboxphysics.com/stories/quantum-evidence/stark-effect-electric-field-spectra/)

5. **1905–1916** · Light-quantum hypothesis and stopping-potential tests

   Prize: [1921 · Photoelectric law](https://www.nobelprize.org/prizes/physics/1921/summary/)

   Laureates: Albert Einstein

   - [Photoelectric evidence: the voltage is not yet the energy](https://sandboxphysics.com/stories/quantum-evidence/photoelectric-stopping-potential-contact/)

6. **1913** · Bohr: stationary states and spectral differences

   Prize: [1922 · Atomic structure and radiation](https://www.nobelprize.org/prizes/physics/1922/summary/)

   Laureates: Niels Bohr

   - [Atomic spectra: evidence for states, not photographs of orbits](https://sandboxphysics.com/stories/quantum-evidence/atomic-spectra-stationary-states/)

7. **1913–1916** · Millikan: drop motion and photoelectric slopes

   Prize: [1923 · Charge and photoelectric measurements](https://www.nobelprize.org/prizes/physics/1923/summary/)

   Laureates: Robert A. Millikan

   - [Oil drops: finding a charge unit in falling times](https://sandboxphysics.com/stories/quantum-evidence/millikan-oil-drop-charge-inference/)
   - [Photoelectric evidence: the voltage is not yet the energy](https://sandboxphysics.com/stories/quantum-evidence/photoelectric-stopping-potential-contact/)

8. **1914** · Franck and Hertz: current minima and energy loss

   Prize: [1925 · Electron-impact excitation](https://www.nobelprize.org/prizes/physics/1925/summary/)

   Laureates: James Franck / Gustav Hertz

   - [Franck–Hertz: what a drop in current can show](https://sandboxphysics.com/stories/quantum-evidence/franck-hertz-discrete-excitation/)

9. **1922–1933** · Stern and collaborators: silver atoms and hydrogen molecules

   Prize: [1943 · Molecular beams and the proton moment](https://www.nobelprize.org/prizes/physics/1943/summary/)

   Laureates: Otto Stern

   - [What two silver traces revealed about atoms](https://sandboxphysics.com/stories/quantum-evidence/stern-gerlach-silver-beam-spin/)
   - [Measuring the proton’s magnetism with a hydrogen beam](https://sandboxphysics.com/stories/quantum-evidence/stern-proton-moment-molecular-hydrogen/)

10. **1923** · Scattered wavelengths versus angle

    Prize: [1927 · Compton scattering](https://www.nobelprize.org/prizes/physics/1927/summary/)

    Laureates: Arthur H. Compton

    - [Compton scattering: light must balance momentum too](https://sandboxphysics.com/stories/quantum-evidence/compton-scattering-energy-momentum/)

11. **1924** · De Broglie: phase, wave packets and how to test them

    Prize: [1929 · Matter waves](https://www.nobelprize.org/prizes/physics/1929/summary/)

    Laureates: Louis de Broglie

    - [de Broglie: a wavelength for matter, a speed for the packet](https://sandboxphysics.com/stories/quantum-evidence/de-broglie-matter-waves-phase-packets/)

12. **1925** · Heisenberg: observable transition arrays

    Prize: [1932 · Quantum mechanics](https://www.nobelprize.org/prizes/physics/1932/summary/)

    Laureates: Werner Heisenberg

    - [Matrices and waves: two routes to the same predictions](https://sandboxphysics.com/stories/quantum-evidence/matrix-wave-mechanics-observables/)

13. **1925** · Pauli: spectral classification and occupancy

    Prize: [1945 · Exclusion principle](https://www.nobelprize.org/prizes/physics/1945/summary/)

    Laureates: Wolfgang Pauli

    - [Pauli: count the states before filling the shells](https://sandboxphysics.com/stories/quantum-evidence/pauli-spectra-exclusion-principle/)

14. **1926–1928** · Schrödinger eigenstates and Dirac spinors

    Prize: [1933 · New atomic theories](https://www.nobelprize.org/prizes/physics/1933/summary/)

    Laureates: Erwin Schrödinger / Paul A.M. Dirac

    - [Matrices and waves: two routes to the same predictions](https://sandboxphysics.com/stories/quantum-evidence/matrix-wave-mechanics-observables/)
    - [Dirac’s electron: a successful equation with an unfinished story](https://sandboxphysics.com/stories/quantum-evidence/dirac-electron-spin-relativity/)

15. **1926** · Born: scattering amplitudes and outcomes

    Prize: [1954 · Probability interpretation](https://www.nobelprize.org/prizes/physics/1954/summary/)

    Laureates: Max Born

    - [Born: how a scattering direction became a probability](https://sandboxphysics.com/stories/quantum-evidence/born-scattering-probability/)

16. **1938** · Rabi and collaborators: atoms lost from a refocused beam

    Prize: [1944 · Resonance of nuclear moments](https://www.nobelprize.org/prizes/physics/1944/summary/)

    Laureates: Isidor Isaac Rabi

    - [How to tell when a nucleus is in resonance](https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/)

17. **1946** · Purcell–Torrey–Pound absorption; Bloch–Hansen–Packard induction

    Prize: [1952 · Nuclear magnetic measurements](https://www.nobelprize.org/prizes/physics/1952/summary/)

    Laureates: Felix Bloch / E. M. Purcell

    - [How to tell when a nucleus is in resonance](https://sandboxphysics.com/stories/quantum-evidence/magnetic-resonance-beams-absorption-induction/)

18. **1947** · Lamb and Retherford: metastable-beam loss

    Prize: [1955 · Hydrogen fine structure](https://www.nobelprize.org/prizes/physics/1955/summary/)

    Laureates: Willis E. Lamb

    - [How missing hydrogen atoms revealed the Lamb shift](https://sandboxphysics.com/stories/quantum-evidence/lamb-shift-microwave-evidence/)

19. **1947–1948** · Kusch and Foley: atomic resonance comparisons

    Prize: [1955 · Electron magnetic moment](https://www.nobelprize.org/prizes/physics/1955/summary/)

    Laureates: Polykarp Kusch

    - [How Kusch and Foley found the electron’s extra magnetism](https://sandboxphysics.com/stories/quantum-evidence/kusch-foley-electron-magnetic-moment/)

20. **1949 onward** · Ramsey interrogation and later clock corrections

    Prize: [1989 · Separated oscillatory fields](https://www.nobelprize.org/prizes/physics/1989/summary/)

    Laureates: Norman F. Ramsey

    - [How Ramsey and ion traps gave atoms more time](https://sandboxphysics.com/stories/quantum-evidence/ramsey-ion-traps-measurement/)
    - [Reading a cavity phase error in an atomic fountain](https://sandboxphysics.com/stories/quantum-evidence/ramsey-cavity-phase-frequency-bias/)
    - [Counting the quantum noise left by a perfect detector](https://sandboxphysics.com/stories/quantum-evidence/quantum-projection-noise-population-counts/)
    - [Following a fountain clock’s extrapolation to zero density](https://sandboxphysics.com/stories/quantum-evidence/fountain-clock-collision-density-extrapolation/)

21. **1950s** · Kastler, Brossel and collaborators: pumping and double resonance

    Prize: [1966 · Optical methods for atomic resonance](https://www.nobelprize.org/prizes/physics/1966/summary/)

    Laureates: Alfred Kastler

    - [How light moves atoms into states that stop absorbing](https://sandboxphysics.com/stories/quantum-evidence/optical-pumping-populations-double-resonance/)

22. **1950s–1980s** · Paul dynamic confinement; Dehmelt single-particle detection

    Prize: [1989 · Ion trapping](https://www.nobelprize.org/prizes/physics/1989/summary/)

    Laureates: Hans G. Dehmelt / Wolfgang Paul

    - [How a changing electric field holds an ion](https://sandboxphysics.com/stories/quantum-evidence/paul-trap-dynamic-stability-micromotion/)
    - [How Dehmelt listened to the spin of one electron](https://sandboxphysics.com/stories/quantum-evidence/dehmelt-single-electron-penning-spin-readout/)

23. **1958** · Mössbauer: resonance in a bound lattice

    Prize: [1961 · Recoil-free resonance absorption](https://www.nobelprize.org/prizes/physics/1961/summary/)

    Laureates: Rudolf Mössbauer

    - [How a crystal takes the recoil of an emitting nucleus](https://sandboxphysics.com/stories/quantum-evidence/mossbauer-recoil-free-resonance/)

24. **1972–2015** · Clauser, Aspect, Zeilinger and collaborating teams: separate experiments

    Prize: [2022 · Entangled photons, Bell tests and information](https://www.nobelprize.org/prizes/physics/2022/summary/)

    Laureates: Alain Aspect / John Clauser / Anton Zeilinger

    - [How Bell tests distinguish quantum correlations](https://sandboxphysics.com/stories/quantum-evidence/bell-tests-correlations-loopholes/)
    - [Freedman and Clauser test Bell’s inequality with calcium light](https://sandboxphysics.com/stories/quantum-evidence/freedman-clauser-coincidence-normalization/)
    - [Aspect changes the analyzers while photons are in flight](https://sandboxphysics.com/stories/quantum-evidence/aspect-switching-spacetime-records/)
    - [Photon Bell tests keep the trials where detectors stay silent](https://sandboxphysics.com/stories/quantum-evidence/photon-bell-losses-optical-trials/)
    - [Three-photon GHZ correlations defeat a shared answer sheet](https://sandboxphysics.com/stories/quantum-evidence/ghz-parity-three-photon-records/)
    - [How the 1997 photon experiment transferred a quantum state](https://sandboxphysics.com/stories/quantum-evidence/quantum-teleportation-conditional-records/)
    - [A joint measurement entangles two photons that never met](https://sandboxphysics.com/stories/quantum-evidence/entanglement-swapping-fourfold-records/)
    - [Dense coding sends three distinguishable messages with one photon](https://sandboxphysics.com/stories/quantum-evidence/dense-coding-three-messages-resources/)
    - [Reconstructing a photon state from calibrated counts](https://sandboxphysics.com/stories/quantum-evidence/photon-tomography-counts-physical-states/)

25. **1982–1989** · Chu, Cohen-Tannoudji, Phillips and teams: cooling mechanisms and thermometry

    Prize: [1997 · Laser cooling and trapping](https://www.nobelprize.org/prizes/physics/1997/summary/)

    Laureates: Steven Chu / Claude Cohen-Tannoudji / William D. Phillips

    - [When sodium atoms came out colder than expected](https://sandboxphysics.com/stories/quantum-evidence/laser-cooling-below-doppler-limit/)
    - [Keeping a slowing atomic beam in tune with one laser](https://sandboxphysics.com/stories/quantum-evidence/zeeman-slowing-neutral-atom-beam/)
    - [How six laser beams slowed Chu’s atoms](https://sandboxphysics.com/stories/quantum-evidence/chu-optical-molasses-diffusion-escape/)
    - [Reading a cold-atom thermometer from the flight of the cloud](https://sandboxphysics.com/stories/quantum-evidence/cold-atom-ballistic-thermometry/)
    - [How an atom loses energy climbing hills made of light](https://sandboxphysics.com/stories/quantum-evidence/sisyphus-cooling-polarization-energy/)
    - [How helium atoms escaped the light and formed two narrow peaks](https://sandboxphysics.com/stories/quantum-evidence/subrecoil-cooling-dark-state-momentum/)

26. **1986–2011** · Wineland and Haroche teams: ions, cavity photons and control

    Prize: [2012 · Single-quantum measurement and control](https://www.nobelprize.org/prizes/physics/2012/summary/)

    Laureates: Serge Haroche / David J. Wineland

    - [How to measure one quantum system and keep it available](https://sandboxphysics.com/stories/quantum-evidence/single-quantum-measurement-backaction/)
    - [How one trapped ion switches its fluorescence off and on](https://sandboxphysics.com/stories/quantum-evidence/electron-shelving-single-ion-jumps/)
    - [Reading the sidebands in the first ion ground-state cooling experiment](https://sandboxphysics.com/stories/quantum-evidence/sideband-asymmetry-ground-state-cooling/)
    - [Let a second ion read out a narrow transition](https://sandboxphysics.com/stories/quantum-evidence/quantum-logic-spectroscopy-shared-motion/)
    - [A cavity cat loses coherence before it loses its energy](https://sandboxphysics.com/stories/quantum-evidence/cavity-cat-coherence-energy-decay/)
    - [Counting stored photons one atom at a time](https://sandboxphysics.com/stories/quantum-evidence/qnd-photon-counting-atomic-records/)
    - [Keeping a chosen number of photons in a cavity](https://sandboxphysics.com/stories/quantum-evidence/quantum-feedback-photon-number-verification/)

## Terms that change what you can conclude

- **[Spectral density](https://sandboxphysics.com/stories/quantum-evidence/blackbody-spectrum-planck-wien/)**: Radiation per unit interval of frequency, or per unit interval of wavelength. Switching from one interval to the other changes the density and its peak.
- **[Excitation and ionization](https://sandboxphysics.com/stories/quantum-evidence/franck-hertz-discrete-excitation/)**: Excitation changes an atom’s internal state; ionization removes a bound electron. How to read a current minimum depends on the apparatus.
- **[Amplitude and probability](https://sandboxphysics.com/stories/quantum-evidence/born-scattering-probability/)**: Coherent alternatives add as amplitudes first; the outcome probabilities are calculated afterwards. The probability interpretation and the first Born approximation are separate ideas.
- **[Spin-orbital](https://sandboxphysics.com/stories/quantum-evidence/pauli-spectra-exclusion-principle/)**: A one-particle state labeled by both its spatial orbital and its spin. Sharing a spatial orbital does not by itself put two fermions in the same forbidden state.
- **[Precision and systematic shift](https://sandboxphysics.com/stories/quantum-evidence/ramsey-cavity-phase-frequency-bias/)**: A statistically narrow estimate can still carry a bias shared by every measurement. Fringe width, counting uncertainty and apparatus corrections each need their own check.
- **[Cooling and confinement](https://sandboxphysics.com/stories/quantum-evidence/laser-cooling-below-doppler-limit/)**: Narrowing a velocity distribution and holding particles in one region are different jobs. A trapped cloud is not necessarily colder.
- **[Coherence and populations](https://sandboxphysics.com/stories/quantum-evidence/cavity-cat-coherence-energy-decay/)**: Populations that match in one basis do not prove phase coherence. That takes a suitable complementary measurement.
- **[Quantum non-demolition](https://sandboxphysics.com/stories/quantum-evidence/qnd-photon-counting-atomic-records/)**: A measurement that leaves one chosen observable unchanged under its specified interaction. Other properties and later evolution may still be disturbed.
- **[Heralding and postselection](https://sandboxphysics.com/stories/quantum-evidence/quantum-teleportation-conditional-records/)**: What matters is when the signal that accepts a trial becomes available, compared with the inputs and outputs. The quality of accepted trials and the success probability are divided by different totals.
- **[Fair sampling](https://sandboxphysics.com/stories/quantum-evidence/bell-tests-correlations-loopholes/)**: The assumption that the detections kept for analysis represent all the intended trials. Strong correlation among the selected coincidences does not prove it.
- **[A p-value](https://sandboxphysics.com/stories/quantum-evidence/event-ready-bell-trials-finite-statistics/)**: A bound on the probability of a result at least this extreme, under a specified null model and analysis rule. It is not the posterior probability that the model is true.
- **[Tomography](https://sandboxphysics.com/stories/quantum-evidence/photon-tomography-counts-physical-states/)**: Inferring a state from many repeated preparations measured with calibrated settings. A fitted matrix that comes out positive does not prove the detectors are calibrated or the result device-independent.

## Continue across topics

- [Nuclei, particles and detectors through their experiments](https://sandboxphysics.com/stories/nuclear-particle/)
- [Condensed matter: devices, superconductors and quantum circuits](https://sandboxphysics.com/stories/condensed-matter/)
- [Probes, light and measurement: six evidence reading paths](https://sandboxphysics.com/stories/probe-evidence/)
- [Electron probes: diffraction, Ruska’s microscope and Kai Siegbahn’s spectroscopy](https://sandboxphysics.com/stories/electron-evidence/)
- Matter-wave phase leads on to a question about apparatus: [electron diffraction](https://sandboxphysics.com/labs/electron-diffraction/) · [waves and imaging roadmap](https://github.com/yangzichao/sandboxphysics/issues/15).
- Lamb shifts and magnetic anomalies lead to radiative corrections: [how QED predicts small electromagnetic corrections](https://sandboxphysics.com/stories/nuclear-particle/qed-renormalization/).
- Cooling, BEC and circuit qubits produce different kinds of data: [condensate matter waves](https://sandboxphysics.com/labs/condensate-matter-wave-collision/) · [Transmon spectroscopy](https://sandboxphysics.com/labs/transmon-artificial-atom/) · [condensed-matter roadmap](https://github.com/yangzichao/sandboxphysics/issues/17). Each teaching model has its own approximations and a limited range in which it has been checked.

## The scope of this collection

53 articles, each in English and Chinese, cover the six reading branches and 26 prize contributions in the Nobel A roadmap. Each article says which evidence it uses and how far that evidence goes. The historical argument, the simulated data and the testing of the linked Labs are handled separately.