What does Bohr's complementarity principle say about wave and particle descriptions?

Wave and particle descriptions can both be observed in the same experiment with good enough equipment Wave and particle properties are both valid but mutually exclusive — any experimental setup reveals one or the other, never both simultaneously Quantum objects are actually only waves — the particle description is a mathematical approximation Quantum objects are actually only particles — the wave description is just a statistical average over many particles

How does quantum field theory resolve the wave-particle duality puzzle?

QFT shows that duality was a mistake — light is only a particle; interference is caused by gravity QFT splits quantum physics into a wave department and a particle department It describes particles as quantised excitations of underlying quantum fields — fields are wave-like, their discrete excitations are particle-like; both are aspects of one unified reality QFT proves that only electrons show duality — photons are purely particles

Why is the statement 'an electron is really a particle that just looks like a wave' incorrect?

It is actually correct — quantum mechanics just uses wave language for mathematical convenience Bell's theorem and experiments rule out 'hidden variable' local realism — the electron has no definite trajectory until measured; its wave nature is not a statistical illusion The statement is technically correct for electrons but not for photons It is incorrect only for slow electrons — fast electrons do have definite trajectories

What is the Born rule?

The particle is always found at the position where |Ψ|² is largest — the peak of the wave The probability of finding a particle at position x is |Ψ(x)|² — the square of the absolute value of the wave function at that point The wave function Ψ directly gives the particle's position — no squaring needed Particles are found randomly regardless of Ψ — the Born rule does not constrain outcomes

A photon passes through a beam splitter (50/50 chance of transmission or reflection). Where is the photon before it is detected?

The photon must have taken one definite path — we just don't know which The photon is in a quantum superposition of both paths — it has no definite location until a detector collapses the wave function The photon splits in half and travels both paths simultaneously as two half-photons The beam splitter creates a copy of the photon — both copies travel separately

Why do classical objects in everyday life not appear to be in superpositions?

Classical objects are too large to be quantum — different laws apply above atomic scale Decoherence: macroscopic objects interact with enormous numbers of environmental particles, which entangle with the object and destroy quantum superpositions almost instantaneously Classical objects are always in superposition — we just can't perceive it with human senses Gravity collapses quantum superpositions for objects larger than about 1 atom

Which interpretation of quantum mechanics says the wave function represents our knowledge, not reality itself?

The Many-Worlds interpretation — it says the wave function is entirely physical The Copenhagen (epistemic) interpretation — Ψ encodes our information about the system; 'collapse' is an update of our knowledge, not a physical event The pilot wave interpretation — it says particles have definite positions at all times The thermal interpretation — it says quantum effects are just thermal fluctuations

What is the significance of the 'which-path' information in double-slit experiments?

Only conscious human observation destroys interference — automatic detectors have no effect If which-path information exists anywhere in the universe (even if not observed by humans), quantum interference disappears — observation is about information, not human consciousness Which-path information has no effect on interference — the double-slit result is always the same Interference is destroyed only when the detector physically touches the particle

A student says: 'Wave-particle duality just means we haven't found the right classical model yet.' What is the decisive experimental argument against this?

No such argument exists — the student's view is a reasonable scientific position Bell test experiments prove no local hidden variable theory — no classical model with pre-set particle properties — can reproduce quantum predictions The right classical model was found in 1980 — but it is too mathematically complex to teach Classical models work fine for electrons but fail for photons — so duality is real only for light

Which real technology most directly exploits wave-particle duality of electrons?

The mobile phone camera — it uses light's particle nature to detect photons The transmission electron microscope (TEM) — electrons are accelerated to achieve short de Broglie wavelengths enabling sub-nanometre resolution impossible with light The MRI scanner — it uses hydrogen nuclei's wave properties to image tissue The laser — it forces photons to choose wave behaviour by keeping them coherent