question: Why do particles behave differently when being observed? How can a particle be both a wave and a particle?
comment: This is really hotly debated subject with no good answer. We simply don't know why it's true, only that it is. Even Richard Feynman, one of the greatest physicists of all time, said, (and I'm paraphrasing here) that anyone who claims to understand *why* quantum physics works is a liar. All we can do is acknowledge that it does work.
passages: When first discovered, particle diffraction was a source of great puzzlement. Are "particles" really "waves?" In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989). Evidently, quantum particles are indeed particles, but whose behaviour is very different from classical physics would have us to expect. 
   Variations of the double-slit experiment have been performed using electrons, atoms, and even large molecules, and the same type of interference pattern is seen. Thus it has been demonstrated that all matter possesses both particle and wave characteristics.
   Through the work of Albert Einstein, Satyendra Nath Bose, Louis de Broglie, and many others, current scientific theory holds that "all" particles also have a wave nature. This has been verified not only for elementary particles but also for compound particles like atoms and even molecules. In fact, according to traditional formulations of non-relativistic quantum mechanics, wave–particle duality applies to all objects, even macroscopic ones; although the wave properties of macroscopic objects cannot be detected due to their small wavelengths.
   Bohr has brought to my attention [that] the uncertainty in our observation does not arise exclusively from the occurrence of discontinuities, but is tied directly to the demand that we ascribe equal validity to the quite different experiments which show up in the [particulate] theory on one hand, and in the wave theory on the other hand.
   where is the position of the th particle in three-dimensional space, and is time. Altogether, this is a complex-valued function of real variables.
  
  In quantum mechanics there is a fundamental distinction between "identical particles" and "distinguishable" particles. For example, any two electrons are identical and fundamentally indistinguishable from each other; the laws of physics make it impossible to "stamp an identification number" on a certain electron to keep track of it. This translates to a requirement on the wave function for a system of identical particles:
   Because of their extremely small size, the study of microscopic and subatomic particles fall in the realm of quantum mechanics. They will exhibit phenomena demonstrated in the particle in a box model, including wave–particle duality, and whether particles can be considered distinct or identical is an important question in many situations.
  
  Section::::Conceptual properties.:Composition.
   It was found that subatomic particles and electromagnetic waves are neither simply particle nor wave but have certain properties of each. This originated the concept of wave–particle duality.
   Through the work of Max Planck, Albert Einstein, Louis de Broglie, Arthur Compton, Niels Bohr, and many others, current scientific theory holds that all particles exhibit a wave nature and vice versa. This phenomenon has been verified not only for elementary particles, but also for compound particles like atoms and even molecules. For macroscopic particles, because of their extremely short wavelengths, wave properties usually cannot be detected.
  
  Although the use of the wave-particle duality has worked well in physics, the meaning or interpretation has not been satisfactorily resolved; see Interpretations of quantum mechanics.
   Even if the source intensity is turned down, so that only one particle (e.g. photon or electron) is passing through the apparatus at a time, the same interference pattern develops over time. The quantum particle acts as a wave when passing through the double slits, but as a particle when it is detected. This is a typical feature of quantum complementarity: a quantum particle acts as a wave in an experiment to measure its wave-like properties, and like a particle in an experiment to measure its particle-like properties. The point on the detector screen where any individual particle shows up is the result of a random process. However, the distribution pattern of many individual particles mimics the diffraction pattern produced by waves.
   BULLET::::- the theory has realism (meaning that its concepts exist independently of the observer);
  
  BULLET::::- the theory has determinism.
  
  The positions of the particles are considered to be the hidden variables. The observer not only doesn't know the precise value of these variables of the quantum system considered, and cannot know them precisely because any measurement disturbs them. On the other hand, one (the observer) is defined not by the wave function of one's atoms, but by the atoms' positions. So what one sees around oneself are also the positions of nearby things, not their wave functions. 
   According to pilot wave theory, the point particle and the matter wave are both real and distinct physical entities (unlike standard quantum mechanics, where particles and waves are considered to be the same entities, connected by wave–particle duality). 
  
  The pilot wave guides the motion of the point particles as described by the guidance equation.
   An important version of this experiment involves single particles (or waves—for consistency, they are called particles here). Sending particles through a double-slit apparatus one at a time results in single particles appearing on the screen, as expected. Remarkably, however, an interference pattern emerges when these particles are allowed to build up one by one (see the adjacent image). This demonstrates the wave–particle duality, which states that all matter exhibits both wave and particle properties: the particle is measured as a single pulse at a single position, while the wave describes the probability of absorbing the particle at a specific place on the screen. This phenomenon has been shown to occur with photons, electrons, atoms and even some molecules, including buckyballs. So experiments with electrons add confirmatory evidence to the view that electrons, protons, neutrons, and even larger entities that are ordinarily called particles nevertheless have their own wave nature and even a wavelength (related to their momentum).
   According to the complementarity principle, a photon can manifest properties of a particle or of a wave, "but not both at the same time". What characteristic is manifested depends on whether experimenters use a device intended to observe particles or to observe waves. When this statement is applied very strictly, one could argue that by determining the detector type one could force the photon to become manifest only as a particle or only as a wave. Detection of a photon is a destructive process because a photon can never be seen in flight. When a photon is detected it "appears" in the consequences of its demise, e.g., by being absorbed by an electron in a photomultiplier that accepts its energy which is then used to trigger the cascade of events that produces a "click" from that device. A photon always appears at some highly localized point in space and time. In the apparatuses that detect photons, the locations on its detection screen that indicate reception of the photon give an indication of whether or not it was manifesting its wave nature during its flight from photon source to the detection device. Therefore, it is commonly said that in a double-slit experiment a photon exhibits its wave nature when it passes through both of the slits and appears as a dim wash of illumination across the detection screen, and manifests its particle nature when it passes through only one slit and appears on the screen as a highly localized scintillation.
   Although it is difficult to draw a line separating wave–particle duality from the rest of quantum mechanics, it is nevertheless possible to list some applications of this basic idea.
  
  BULLET::::- Wave–particle duality is exploited in electron microscopy, where the small wavelengths associated with the electron can be used to view objects much smaller than what is visible using visible light.
  
  BULLET::::- Similarly, neutron diffraction uses neutrons with a wavelength of about 0.1 nm, the typical spacing of atoms in a solid, to determine the structure of solids.
   BULLET::::- Photos are now able to show this dual nature, which may lead to new ways of examining and recording this behaviour.
  
  Section::::See also.
  
  BULLET::::- Arago spot
  
  BULLET::::- Afshar experiment
  
  BULLET::::- Basic concepts of quantum mechanics
  
  BULLET::::- Complementarity (physics)
  
  BULLET::::- Einstein's thought experiments
  
  BULLET::::- Electron wave-packet interference
  
  BULLET::::- Englert–Greenberger–Yasin duality relation
  
  BULLET::::- EPR paradox
  
  BULLET::::- Faraday wave
  
  BULLET::::- Hanbury Brown and Twiss effect
  
  BULLET::::- Kapitsa–Dirac effect
  
  BULLET::::- Photon polarization
  
  BULLET::::- Scattering theory
  
  BULLET::::- Wavelet
  
  BULLET::::- Wheeler's delayed choice experiment
  
  Section::::External links.
  
  BULLET::::- Animation, applications and research linked to the wave-particle duality and other basic quantum phenomena (Université Paris Sud)
   At least one physicist considers the "wave-duality" as not being an incomprehensible mystery. L.E. Ballentine, "Quantum Mechanics, A Modern Development", p. 4, explains:
   It has been argued that there are never exact particles or waves, but only some compromise or intermediate between them. For this reason, in 1928 Arthur Eddington coined the name ""wavicle"" to describe the objects although it is not regularly used today. One consideration
  
  is that zero-dimensional mathematical points cannot be observed. Another is that the formal representation of such points, the Dirac delta function is unphysical, because it cannot be normalized. Parallel arguments apply to pure wave states. Roger Penrose states:
   There also exists a wave frame of detection, where, for example, light is divided into two paths so as to interfere with each other. To measure and analyze such an effect, one also needs to place an array of detectors on the interfering plane, from which one can infer an additional set of quantities such as the frequency, wavelength, and also the phase velocity from the interference fringes; thus one constructs a "wave picture". However, as far as Newtonian mechanics is concerned, such a wave frame of detection seems to be not necessary, and with the localizability discussed above, it makes sense to ascribe only the concept of particle to the cases investigated in the Newtonian domain. 
   Thus, a wave is a foliated set of moving two-dimensional surfaces. In classical physics, it is not part of the definition of a wave that it be distinctly vibratory.
  
  One difference between wave and particle conceptions is thus in the spatial dimensionality of their moving objects.
  
  On one hand, a ray can be regarded as the orbit of a particle of light. It successively punctures the wave surfaces. The successive punctures can be regarded as defining the trajectory of the particle.
   Section::::History.
  
  Section::::History.:Classical particle and wave theories of light.
   Section::::In quantum mechanics.
  
  In quantum mechanics, there is a distinction between an elementary particle (also called "point particle") and a composite particle. An elementary particle, such as an electron, quark, or photon, is a particle with no internal structure. Whereas a composite particle, such as a proton or neutron, has an internal structure (see figure).
  
  However, neither elementary nor composite particles are spatially localized, because of the Heisenberg uncertainty principle. The particle wavepacket always occupies a nonzero volume. For example, see atomic orbital: The electron is an elementary particle, but its quantum states form three-dimensional patterns.
   Section::::History.:de Broglie–Bohm theory.
  
  De Broglie himself had proposed a pilot wave construct to explain the observed wave-particle duality. In this view, each particle has a well-defined position and momentum, but is guided by a wave function derived from Schrödinger's equation. The pilot wave theory was initially rejected because it generated non-local effects when applied to systems involving more than one particle. Non-locality, however, soon became established as an integral feature of quantum theory and David Bohm extended de Broglie's model to explicitly include it.
   BULLET::::- Quantum mechanics: In quantum mechanics, which deals with the behavior of very small objects, it is not possible to observe a system without changing the system, and the "observer" must be considered part of the system being observed. In isolation, quantum objects are represented by a wave function which often exists in a superposition or mixture of different states. However, when an observation is made to determine the actual location or state of the object, it always finds the object in a single state, not a "mixture". The interaction of the observation process appears to "collapse" the wave function into a single state. So any interaction between an isolated wave function and the external world that results in this wave function collapse is called an "observation" or "measurement", whether or not it is part of a deliberate observation process.
   In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle. Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions; likewise, just as it is nonsensical to discuss the wavelength of a "pulse" wave traveling down a string, particles do not have perfectly precise momenta that corresponds to the inverse of wavelength. Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength, and thus momentum. And conversely, when momentum, and thus wavelength, is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.
   The fundamental feature of quantum mechanics that distinguishes it from classical mechanics is that particles of a particular type are indistinguishable from one another. This means that in an assembly consisting of similar particles, interchanging any two particles does not lead to a new configuration of the system (in the language of quantum mechanics: the wave function of the system is invariant up to a phase with respect to the interchange of the constituent particles). In the case of a system consisting of particles of different kinds (for example, electrons and protons), the wave function of the system is invariant up to a phase separately for both assemblies of particles.
  