I often hear about the wave-particle duality, and how particles exhibit properties of both particles and waves. However, I wonder, is this actually a duality? At the most fundamental level, we 'know' that everything is made up out of particles, whether those are photons, electrons, or maybe even strings. That light for example, also shows wave-like properties, why does that even matter? Don't we know that everything is made up of particles? In other words, wasn't Young wrong and Newton right, instead of them both being right?
[Physics] Is the wave-particle duality a real duality
dualityquantum mechanicsquantum-field-theorywave-particle-duality
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The uncertainty principle is much more general than anything you might say about the wave-particle duality. In particular, wave-particle duality is a vague and imprecise statement about how certain types of quantum systems qualitatively behave, while the uncertainty principle is a very general and quantitative statement about the standard deviations of operators.
While, in settings like the double-slit, it is true that you may think about the quantum objects as being represented by a probability wave, this breaks down whenever one considers finite-dimensional Hilbert spaces, as they occur e.g. in the setting of quantum information and its qubits. There's no continuous set of generalized position operators - not ever a position operator at all - and hence no "wavefunction". Nevertheless, the relation $$ \sigma_A(\psi)\sigma_B(\psi) \geq \frac{1}{2}\lvert\langle \psi \vert [A,B] \vert \psi \rangle\rvert$$ holds for all operators $A,B$ and all states $\psi$.
And even in the infinite-dimensional setting where you might claim that we have a "wave nature" and a "particle nature", this relation holds for all operators, not just position and momentum, and the proof just relies on basic properties of Hilbert spaces like the Cauchy-Schwarz inequality.
To stress this crucial fact: The uncertainty relation is a general consequence of the axioms that states are rays in a Hilbert space and the rule how these states give expectation values. No conception of "particle" or "wave" ever enters into the derivation, and the fact that waves also exhibit a type of uncertainty relation in their widths is a simple consequence of the properties of the Fourier transform. Since the Fourier transform is also intimately related to the position and momentum operators by the Stone-von Neumann theorem about their essentially unique representation as multiplication and differentiation, this explains the similarity without any reference to "wave-particle duality".
No, this is not at all how quantum field theory works.
A "quantum field" does not have a definite value at any time, it is an operator in the quantum theory, not something that has a fixed numerical value, therefore representing it as a lattice as you have done does not reflect the quantum nature of the field. This is the classical picture of the field, just like a point particle is the classical picture of the electron, not its quantum picture.
The quantum field and the particle states are different things - the field is an operator and the particle is a state in the quantum theory. You can use (parts of) the quantum field operator to create particles, but the notion of particle is much more elusive than it being a simple ripple in a classical field. For more on this see this answer of mine on real particles and this question and its answers on virtual particles.
The "wave-particle duality" is, in any case, a somewhat vague notion that has no real formal counterpart in modern quantum mechanics. Quantum objects are just that, quantum objects. They have aspects of waves (e.g. they can "interfere", they can obey wave-like equations, they "spread") and they have aspects of particles (e.g. they can (but not must be) localized at "points", they have mass) but they are neither. And I'm sure you can find quantum behaviour that you'll not be able to attribute to either a wavy or a particle nature, such as Bell experiments about entanglement (which cannot be explained classically, and hence any attempt to explain them with a particle or wave picture must necessarily fail).
Best Answer
Duality is the relationship between two entities that are claimed to be fundamentally equally important or legitimate as features of the underlying object.
The precise definition of a "duality" depends on the context. For example, in string theory, a duality relates two seemingly inequivalent descriptions of a physical system whose physical consequences, when studied absolutely exactly, are absolutely identical.
The wave-particle duality (or dualism) isn't far from this "extreme" form of duality. It indeed says that the objects such as photons (and electromagnetic waves composed of them) and electrons exhibit both wave and particle properties and they are equally natural, possible, and important.
In fact, we may say that there are two equivalent descriptions of particles – in the position basis and the momentum basis. The former corresponds to the particle paradigm, the latter corresponds to the wave paradigm because waves with well-defined wavelengths are represented by simple objects.
It's certainly not true that Young was wrong and Newton was right. Up to the 20th century, it seemed obvious that Young was more right than Newton because light indisputably exhibits wave properties, as seen in Young's experiments and interference and diffraction phenomena in general. The same wave phenomena apply to electrons that are also behaving as waves in many contexts.
In fact, the state-of-the-art "theory of almost everything" is called quantum field theory and it's based on fields as fundamental objects while particles are just their quantized excitations. A field may have waves on it and quantum mechanics just says that for a fixed frequency $f$, the energy carried in the wave must be a multiple of $E=hf$. The integer counting the multiple is interpreted as the number of particles but the objects are more fundamentally waves.
One may also adopt a perspective or description in which particles look more elementary and the wave phenomena are just a secondary property of them.
None of these two approaches is wrong; none of them is "qualitatively more accurate" than the other. They're really equally valid and equally legitimate – and mathematically equivalent, when described correctly – which is why the word "duality" or "complementarity" is so appropriate.