Wave–particle duality

Wave–particle duality

two words, one thing

The Fifth Solvay Conference, Brussels, October 1927, whose subject was the new quantum theory. Seventeen of the twenty-nine present either held a Nobel Prize or would. Planck, Einstein, Bohr, Schrödinger, de Broglie and Compton are all in this photograph, and the argument set out below was largely conducted in that room by these people.

The question	Is light a wave or a particle?
The answer	Neither, and the question is the fault[1]
Argued from	1665, and probably earlier
Settled for particles	1704, on Newton's authority
Settled for waves	1803, on Young's evidence
Reopened	1900, and again in 1905
Extended to matter	1924
Number of things behaving oddly	One
Number of words available for it	Two, neither suitable

Wave–particle duality is the finding that light, and then matter, behaves in ways that the words wave and particle were framed to keep apart. Light spreads and interferes, which particles cannot do; it also arrives in indivisible lumps and knocks electrons about, which waves cannot do. Both are observed, reliably, in the same substance.

The usual statement is that light "is both a wave and a particle", and the usual reading of that statement is that physics has contradicted itself and is asking to be excused. It has not. The two words are classical: one describes something spread out in a medium, the other something small and hard with a location. Neither was coined with anything quantum in view, and the finding is that the thing being described answers to parts of each and the whole of neither.^[1]

Two hundred and forty years of it

The argument is old and was conducted by serious people throughout.

Newton held light to be corpuscular and said so in the Opticks of 1704, on grounds that were good: light casts sharp shadows and travels in straight lines, and waves in his experience did neither. Huygens had already published a wave account in 1690, and on the Continent it never quite went away.

Young settled it, as everyone then thought finally, in 1803: light added to light can give darkness, which is interference, and which particles have no means of doing. Fresnel put the mathematics behind it, Maxwell identified the waves as electromagnetic in 1864, and by 1880 the matter was closed in every textbook.^[2]

The reopening

It was reopened by heat, and then by a metal plate.

Planck found in 1900 that he could only account for the light emitted by a hot body if he supposed the energy came in fixed amounts, and he regarded this as an accounting trick rather than a fact about light. Einstein, in 1905, declined to regard it as a trick: he took the lumps seriously, applied them to the photoelectric effect, and explained why light below a certain frequency knocks no electrons loose however bright it is made. A wave should not care about frequency in that way. A lump must.^[3]

Compton finished the argument in 1923 by bouncing an X-ray off an electron and finding the recoil exactly as though two billiard balls had collided, momentum and all. Whatever light is, it has momentum in discrete parcels.

Matter joins in

The step that made it general was made by a graduate student.

Louis de Broglie reasoned, in his thesis of 1924, that the relation between momentum and wavelength ought not to be a peculiarity of light. If a photon of momentum $p$ has wavelength $\lambda = h/p$, then so should an electron, and so should anything else. The proposal was so bare that his examiners forwarded it to Einstein to ask whether it was serious.^[4]

It was. Davisson and Germer diffracted electrons off a nickel crystal in 1927, and George Paget Thomson did the same independently, and matter turned out to interfere exactly as light does. The wavelength is small, which is why nobody had noticed: at ordinary speeds and ordinary masses it is far below anything that could be measured. A walking adult has one. It is around $10^{-35}$ of a metre, which is why nobody has yet diffracted through a doorway.

What the duality is a fact about

Here is the part that gets lost.

An electron is not a particle that occasionally behaves like a wave, nor a wave that occasionally condenses. It is a single kind of thing, described by a single mathematical object, behaving in one consistent way in all circumstances. What varies is not the electron but which of our two inherited words fits the experiment we happen to have built.

Arrange an experiment that asks a spread-out question and the answer is wave-shaped. Arrange one that asks a which-one-and-where question and the answer is particle-shaped. The two questions cannot be asked at once, and that restriction is real and is called complementarity. It is a fact about what can be measured together, not a coyness on the electron's part.^[5]

The word duality is therefore slightly misleading, and physicists mostly stopped using it among themselves some decades ago. It survives in teaching, where it is useful, and in popular writing, where it is not.

The use made of it

The duality is quoted, in the quarters this encyclopedia documents, for two purposes.

The first is as a licence: physics admits contradictions, therefore an objection to one's own theory carries no weight. This confuses a contradiction with a vocabulary that has run out. Nothing in quantum mechanics is inconsistent; the equations have never once returned two answers, which is more than can be said for the accounts the argument is usually defending.^[6]

The second is as an appeal to mystery: if light can be two things, anything can be anything. Light is not two things. It is one thing, and the two words are ours.

See also

• The double-slit experiment – where both behaviours are displayed at once
• Thomas Young – who established the wave half and was disbelieved for it
• Luminiferous aether – the medium the waves were thought to require
• James Clerk Maxwell – who identified the waves, and took that for the end of it
• Albert Einstein – whose Nobel Prize was for the lumps, not for relativity
• Max Planck – whose packets reopened the argument, against his own wishes
• Schrödinger's cat – a third vocabulary problem, with an animal in it
• Grimble's razor – on premises kept by setting their consequences aside

References

1. ^ The phrasing matters. "Light is both a wave and a particle" invites the reply that this is impossible, and the reply is correct about the words. "Light is a thing our two words each half-fit" is longer and does not invite it.
2. ^ See Thomas Young for the twenty years the English took to accept it, and why.
3. ^ Einstein's 1905 light-quantum paper is the work the Nobel Prize was given for in 1921. It is not the relativity paper, a fact his own article records with some patience.
4. ^ $\lambda = h/p$. The thesis is a few dozen pages and contains no experiment. Einstein's verdict, relayed to Paris, was that de Broglie had lifted a corner of the great veil.
5. ^ Complementarity is Bohr's, from 1927. It is a statement about which measurements are jointly possible, and it is often quoted as though it were a statement about how things are when nobody measures, which is the opposite of what it says.
6. ^ See Grimble's razor. An account that has never produced a contradiction is being cited as permission by accounts that produce them routinely.

External links

• The Fifth Solvay Conference, 1927 – Wikimedia Commons
• Wave–particle duality – general reference