Quantum physics: reading the evidence

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

   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

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

3. de Broglie: a wavelength for matter, a speed for the packet

   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

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

5. Dirac’s electron: a successful equation with an unfinished story

   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

   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

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

3. Franck–Hertz: what a drop in current can show

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

4. Compton scattering: light must balance momentum too

   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

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

2. Pauli: count the states before filling the shells

   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

   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

   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

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

4. What two silver traces revealed about atoms

   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

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

6. How to tell when a nucleus is in resonance

   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

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

8. How missing hydrogen atoms revealed the Lamb shift

   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

   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

    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

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

2. Reading a cavity phase error in an atomic fountain

   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

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

4. Following a fountain clock’s extrapolation to zero density

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

5. How a changing electric field holds an ion

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

6. How Dehmelt listened to the spin of one electron

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

7. When sodium atoms came out colder than expected

   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

   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

   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

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

11. How an atom loses energy climbing hills made of light

    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

    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

    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

    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

    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

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

17. A cavity cat loses coherence before it loses its energy

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

18. Counting stored photons one atom at a time

    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

    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

   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

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

3. Aspect changes the analyzers while photons are in flight

   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

   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

   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

   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

   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

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

9. Two photons leave the beam splitter together

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

10. A joint measurement entangles two photons that never met

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

11. The later measurement sorts earlier photon detections

    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

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

13. Reconstructing a photon state from calibrated counts

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

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.

Terms that change what you can conclude

Spectral density

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

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

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

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

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

Narrowing a velocity distribution and holding particles in one region are different jobs. A trapped cloud is not necessarily colder.

Coherence and populations

Populations that match in one basis do not prove phase coherence. That takes a suitable complementary measurement.

Quantum non-demolition

A measurement that leaves one chosen observable unchanged under its specified interaction. Other properties and later evolution may still be disturbed.

Heralding and postselection

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

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

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

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
• Condensed matter: devices, superconductors and quantum circuits
• Probes, light and measurement: six evidence reading paths
• Electron probes: diffraction, Ruska’s microscope and Kai Siegbahn’s spectroscopy
• Matter-wave phase leads on to a question about apparatus: electron diffraction · waves and imaging roadmap.
• Lamb shifts and magnetic anomalies lead to radiative corrections: how QED predicts small electromagnetic corrections.
• Cooling, BEC and circuit qubits produce different kinds of data: condensate matter waves · Transmon spectroscopy · condensed-matter roadmap. Each teaching model has its own approximations and a limited range in which it has been checked.