Early on, Albert Einstein and Niels Bohr heatedly debated wave-particle duality. To explain duality Bohr postulated his principle of complementarity, which is now widely accepted, but has mystifying metaphysical implications. Albert Einstein disagreed. Richard Feynman called it the “only mystery�? in quantum mechanics. Ingenious experiments including those using entanglement have confirmed Bohr’s complementarity. In this paper a new Duality Theorem is presented with proof which explains duality with particle always remaining particle and wave always remaining wave throughout, without using wave-particle complementarity or “which way�? (welcher-weg) observation. We explain results of reported experiments by showing the equivalence: Coherence and alignment ≡ Interference ≡ No “which way�? observation; No coherence or alignment ≡ No interference ≡ “which way�? observation That is, complementarity is redundant; conventional criteria of alignment and coherence alone suffice for interference. Our explanation does not require that photon somehow “know�? about the test setup or “which way�? observation and change its behavior from particle to wave and vice versa. No new assumptions are made, only new reasoning. In the context of entanglement we also help explain non-local action at a distance, and rephrase Albert Einstein’s unanswered question “Is quantum mechanics complete?�? at a more fundamental level.
Early on, Albert Einstein and Niels Bohr heatedly debated wave-particle duality. To explain duality Bohr postulated his principle of complementarity, which is now widely accepted, but has mystifying metaphysical implications. Albert Einstein disagreed. Richard Feynman called it the “only mystery�? in quantum mechanics. Ingenious experiments including those using entanglement have confirmed Bohr’s complementarity. In this paper a new Duality Theorem is presented with proof which explains duality with particle always remaining particle and wave always remaining wave throughout, without using wave-particle complementarity or “which way�? (welcher-weg) observation. We explain results of reported experiments by showing the equivalence: Coherence and alignment ≡ Interference ≡ No “which way�? observation; No coherence or alignment ≡ No interference ≡ “which way�? observation That is, complementarity is redundant; conventional criteria of alignment and coherence alone suffice for interference. Our explanation does not require that photon somehow “know�? about the test setup or “which way�? observation and change its behavior from particle to wave and vice versa. No new assumptions are made, only new reasoning. In the context of entanglement we also help explain non-local action at a distance, and rephrase Albert Einstein’s unanswered question “Is quantum mechanics complete?�? at a more fundamental level.
An Axiom is presented and justified which (a) Explains duality in interference without complementarity or “which way” (welcher-weg) observation (b) Shows the equivalence: Coherence and alignment ≡ Interference ≡ No “which way” observation; No coherence or alignment ≡ No interference ≡ “which way” observation (c) Explains Wheeler’s delayed choice thought experiment (d) Explains results of experimental implementations of Wheeler’s experiment which show retro-causality with and without entanglement (e) Explains non-local action at a distance, and (f) Rephrases Albert Einstein’s unanswered question “Is quantum mechanics complete?” at a more fundamental level than just duality and non-locality. The explanation given does not require that the particle (photon) somehow “know” about the test setup or “which way” observation or change its behavior from particle to wave and vice versa as required by currently accepted explanation based on Niels Bohr’s complementarity principle. No new assumptions are made, only a new complete interpretation of probability which is already a fundamental assumption of quantum mechanics.
To explain Young’s Double Slit Experiment Niels Bohr postulated his Complementarity Principle according to which if the observation is for interference pattern the particle will change to wave. Albert Einstein had objected: how can inanimate particle know what the observation is about? Experiments have confirmed Bohr’s Complementarity Principle. Upon investigation, the author was able to explain all experiments without invoking Complementarity Principle, using only coherence and alignment considerations. This research recently culminated in revolutionary finding by the author, that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave or vice-versa and published a paper in the Journal of High Energy Physics and Cosmology (JHEPGC), 9, 596 – 601, widely acclaimed by readership and reviewers. It restores objectivity to science and opens new vistas of research developing new concepts, advancing science.
On the question of wave-particle duality, from the historic Bohr-Einstein debates a century ago, to this day, the view expressed in Niels Bohr’s Complementarity Principle has become well established, confirmed by numerous experiments: If the observation is for wave nature, then the particle changes to wave, and if the observation is for particle nature, then the particle remains particle. However, recently this view has been challenged. With proof based on the definition of wave function, it has been shown that particle always remains particle and its wave function always remains wave, no mysterious change from particle to wave and vice versa.
In an interesting series of articles published few years ago Afshar and coworkers [1,2] reported an optical experiment in which they claimed to refute the well known N. Bohr principle of complementarity [3, 4]. Obviously this result, if justified, would constitute a serious attack against the orthodox interpretation of quantum mechanics (known as the Copenhagen interpretation). This work stirred much debate in different journals (see for examples references [5–12]). We think however that there are still some important misunderstandings concerning the interpretation of this experiment. In a preprint written originally in 2004 [5] (and following some early discussions with Afshar) we claimed already that the interpretation by Afshar et al. can be easily stated if we stay as close as possible from the texts written by Bohr. The aim of the present article (which was initially written in 2005 to precise a bit the thought developed in [5]) is to comment the interpretation discussed in [1]. We will in the following analyze the meaning of Bohr principle and show that far from disproving its content the experiment [1] is actually a complete confirmation of its general validity. The difficulties associated with the understanding of this principle are not new and actually complementarity created troubles even in Einstein mind [3] so that we are here in good company. To summarize a bit emphatically Bohr’s complementarity we here remind that this principle states that if one of a pair of non commuting observables of a quantum object is known for sure, then information about the second (complementary) is lost [3, 4, 15, 16]. This can be equivalently expressed as a kind of duality between different descriptions of the quantum system associated with different experimental arrangements which mutually exclude each other (read in particular [3,4]). Later in the discussion we will try to precise this definition but for the moment it is enough to illustrate the concepts by examples Consider for instance the well known Young double-pinholes interference experiment made with photons. The discrete nature of light precludes the simultaneous observation of a same photon in the aperture plane and in the interference pattern: the photon cannot be absorbed twice. This is already a trivial manifestation of the principle of Bohr. Here it implies that the two statistical patterns associated with the wave in the aperture plane and its Fourier (i. e., momentum) transform require necessarily different photons for their recording. It is in that sense that each experiment excludes and completes reciprocally the other. In the case considered before the photon is absorbed during the first detection (this clearly precludes any other detection). However even a non-destructive solution for detection implying entanglement with other quantum systems has a radical effect of the same nature: the complementarity principle is still valid. For example, during their debate Bohr and Einstein [3] discussed an ideal which-way experiment in which the recoil of the slits is correlated to the motion of the photon. Momentum conservation added to arguments based on the uncertainty relations are sufficient to explain how such entanglement photon-slits can erase fringes [15–19]. It is also important for the present discussion to remind that the principle of complementarity has a perfidious consequence on the experimental meaning of trajectory and path followed by a particle. Indeed the unavoidable interactions existing between photons and detectors imply that a trajectory existing independently of any measurement process cannot be unambiguously defined. This sounds even like a tragedy when we consider once again the two-holes experiment. Indeed for Bohr this kind of experiments shows definitely the essential element of ambiguity which is involved in ascribing conventional physical attributes to quantum systems. Intuitively (i. e., from the point of view of classical particle dynamic) one would expect that a photon detected in the focal plane of the lens must have crossed only one of the hole 1 or 2 before to reach its final destination. However, if this is true, one can not intuitively understand how the presence of the second hole (through which the photon evidently did not go) forces the photon to participate to an interference pattern (which obviously needs an influence coming from both holes). Explanations to solve this paradox have been proposed by de Broglie, Bohm, and others using concepts such as empty waves or quantum potentials [20, 21]. However all these explanations are in agreement with Bohr principle (since they fully reproduce quantum predictions) and can not be experimentally distinguished. Bohr and Heisenberg proposed for all needed purposes a much more pragmatic and simpler answer: don’t bother, the complementarity principle precludes the simultaneous observation of a photon trajectory and of an interference pattern. For Bohr [3]: This point is of great logical consequence, since it is only the circumstance that we are presented with a choice of either tracing the path
Ninety years ago in 1927, at an international congress in Como, Italy, Niels Bohr gave an address which is recognized as the first instance in which the term "complementarity", as a physical concept, was spoken publicly [1], revealing Bohr's own thinking about Louis de Broglie's "duality". Bohr had very slowly accepted duality as a principle of physics: close observation of any quantum object will reveal either wave-like or particle-like behavior, one or the other of two fundamental and complementary features. Little disagreement exists today about complementarity's importance and broad applicability in quantum science. Book-length scholarly examinations even provide speculations about the relevance of complementarity in fields as different from physics as biology, psychology and social anthropology, connections which were apparently of interest to Bohr himself (see Jammer [2], Murdoch [3] and Whitaker [4]). Confusion evident in Como following his talk was not eliminated by Bohr's article [1], and complementarity has been subjected to nine decades of repeated examination ever since with no agreed resolution. Semi-popular treatments [5] as well as expert examinations [6-9] show that the topic cannot be avoided, and complementarity retains its central place in the interpretation of quantum mechanics. However, recent approaches by our group [10-13] and others [14-20] to the underlying notion of coherence now allow us to present a universal formulation of complementarity that may signal the end to the confusion. We demonstrate a new relationship that constrains the behavior of an electromagnetic field (quantum or classical) in the fundamental context of two-slit experiments. We show that entanglement is the ingredient needed to complete Bohr's formulation of complementarity, debated for decades because of its incompleteness.