I spoke many times about quantum entanglement and slit experiments here - see Entanglement and slit experiments for example. This is actually the reason which sparked my interest in physics and I wish that has happened while I was at high school as I would probably be something else today. I personally find hard to imagine being anything else than scientist working with either astronomy or physics in general. Both areas are connected of course I would assume area called astrophysics is the one I'm interesting the most. In physics, action at a distance is the nonlocal interaction of objects that are separated in space. This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant objects. More generally "action at a distance" describes the failure of early atomistic and mechanistic theories which sought to reduce all physical interaction to collision. The exploration and resolution of this problematic phenomenon led to significant developments in physics, from the concept of a field, to descriptions of quantum entanglement and the mediator particles of the standard model.
Spooky action at distance was term coined by Albert Einstein and has become synonymous with one of the most famous episodes in the history of physics - his battle with Bohr in the 1930s over the completeness of quantum mechanics. Einstein’s weapons in this battle were thought experiments that he designed to highlight what he believed were the inadequacies of the new theory. The most famous of these is the EPR paradox, announced in 1935 and named after its inventors Einstein, Boris Podolsky, and Nathan Rosen. It involves a pair of particles linked by the strange quantum property of entanglement (a word coined much later). Entanglement occurs when two particles are so deeply linked that they share the same existence. In the language of quantum mechanics, they are described by the same mathematical relation known as a wave function. Entanglement arises naturally when two particles are created at the same point and instant in space, for example. Entangled particles can become widely separated in space. But even so, the mathematics implies that a measurement on one immediately influences the other, regardless of the distance between them. Einstein pointed out that according to special relativity, this was impossible and therefore, quantum mechanics must be wrong, or at least incomplete. Einstein famously called it spooky action at a distance. The EPR paradox stumped Bohr and was not resolved until 1964, long after Einstein’s death. CERN physicist John Bell resolved it by thinking of entanglement as an an entirely new kind of phenomenon, which he termed “nonlocal". The basic idea here is to think about the transfer of information. Entanglement allows one particle to instantaneously influence another but not in a way that allows classical information to travel faster than light. This resolved the paradox with special relativity but left much of the mystery intact. These days, the curious nature of entanglement is the subject of intense focus in labs around the world. If still available, following video might be also interesting to you too.
When studying wave-particle duality, however, so-called interferometric quantum eraser experiments – in which wave-like behavior can be restored by erasing path information – allow researchers to perform differential measurements on each of two entangled quantum systems. (Double-slit experiments not involving quantum erasure utilize superposition of single particles, while in quantum eraser experiments two particles are entangled.) Specifically, the particle feature's welcher-weg (which-path) information is erased (or not) from one system, and interference-based measurements in the other system are used to observe (or not, as the case may be) its wave feature.
While previous quantum eraser experiments made the erasure choice before or (in delayed-choice experiments) after the interference - thereby allowing communications between erasure and interference in the two systems, respectively - scientists in Anton Zeilinger's group at the Austrian Academy of Sciences and the University of Vienna recently reported a quantum eraser experiment in which they prevented this communications possibility by enforcing Einstein locality. They accomplished this using hybrid path-polarization entangled photon pairs distributed over an optical fiber link of 55 meters in one experiment and over a free-space link of 144 kilometers in another. Choosing the polarization measurement for one photon decided whether its entangled partner followed a definite path as a particle, or whether this path-information information was erased and wave-like interference appeared. They concluded that since the two entangled systems are causally disconnected in terms of the erasure choice, wave-particle duality is an irreducible feature of quantum systems with no naive realistic explanation. The world view that a photon always behaves either definitely as a wave or definitely as a particle would require faster-than-light communication, and should therefore be abandoned as a description of quantum behavior. What does this mean for scientists describing a quantum state without relying purely on mathematics? One way is that the quantum state can be viewed, as Erwin Schrödinger wrote, as an expectation-catalogue or sum of knowledge - that is, a probability list for all possible measurement outcomes. Whether the outcome of each individual measurement is wave, particle or their superposition depends on the state and measurement context.
Below is (A) scheme of the Vienna experiment: In Lab 1, the source (S) emits polarization entangled photon pairs, each consisting of a system and an environment photon, via type-II spontaneous parametric down-conversion. Good spectral and spatial mode overlap is achieved by using interference filters with1-nm bandwidth and by collecting the photons into single-mode fibers. The polarization entangled state is subsequently converted into a hybrid entangled state with a polarizing beam splitter (PBS1) and two fiber polarization controllers (FPC). Interferometric measurement of the system photon is performed with a single-mode fiber beam splitter (BS) with a path length of 2 m, where the relative phase between path a and path b is adjusted by moving PBS1’s position with a piezo-nanopositioner. The polarization projection setup of the environment photon consists of an electro-optic modulator (EOM) and another PBS (PBS2). Both photons are detected by silicon avalanche photodiodes (DET 1–4). The choice is made with a QRNG. (B) Space–time diagram. The choice-related events Ce and the polarization projection of the environment photon Pe are space-like separated from all events of the interferometric measurement of the system photon Is. Additionally, the events Ce are also space-like separated from the emission of the entangled photon pair from the source Ese. Shaded areas are the past and the future light cones of events Is. This ensures that Einstein locality is fulfilled.
When two events are separated by a space-like interval, not enough time passes between their occurrences for there to exist a causal relationship crossing the spatial distance between the two events at or below the speed of light. While the two events can be observed to occur at the same time, there is no reference frame in which the two events can occur in the same spatial location or where they can occur in each other's future or past. To maintain entanglement between the path and the polarization of photon pairs, researchers first produced bright highly-entangled polarization pairs using a spontaneous parametric down-conversion process. They converted the polarization states of the system photon into its path states in an interferometer via a polarizing beam splitter and polarization controllers, while maintaining the polarization state of the environment photon. By carefully adjusting these components, they eliminated the polarization distinguishablity of the path states of the system photon and generated hybrid entangled photon pairs. In order to maintain this hybrid entanglement, they paid exceptional attention in keeping these photons away from decoherence. As per early results of experiment above itself, it seems there is no actual particle or wave - the underlying reality, apart from observation, is neither. To make an observation requires the use of concepts at our scale, in constructing apparatus and interpreting results, and this adds the form to the underlying reality, a particle or a wave. In other words the act of 'conceptualizing' reality adds something artificial, which is not existent apart from an observer. The non-intuitive nature of quantum mechanics means that it is not possible to conform reality within our conceptual framework consistently, demonstrating that some of our concepts are artifacts of thought, and so dependent upon mind, rather than something intrinsic to Reality itself.
One thing people have been asking themselves ever since is - if the spooky action does exist, what is its speed? And most recently, Juan Yin at the University of Science and Technology of China in Shanghai offered the answer in new paper. Measuring the speed of spooky action is no trivial task. The method is to create a pair of entangled particle photons and separate them by a significant distance, in this case 15 km or so. The experiment involves performing a measurement on one photon and then timing how long it takes for the other photon to be influenced. Of course, this is tricky to do with a single pair of photons because of the tiny periods of time involved and the rotation of the Earth which moves the experiment by distances that are significant over these time scales. So the trick is to create a stream of entangled photons and to measure the spooky action continuously for 12 hours or more. If the experiment is aligned in an East-West direction, the contribution from the Earth’s rotation should drop out over that time. Juan perfected this technique by sending photons through the atmosphere from a fish farm near Qinghai Lake in the Tibetan Plateau. The results are clear but do not measure the speed of spooky action directly. Instead, the results place a lower bound on how fast it must be. The answer is that it is at least four orders of magnitude faster than light, and may still turn out to be instantaneous, as quantum mechanics predicts. To some, this result may sounds familiar and this is because a European team based at the University of Geneva in Switzerland carried out a similar experiment in 2008 getting a similar result. However, this turned out to contain a loophole which allowed the results to be explained without entanglement. All previous experiments along this direction have locality loopholes and thus can be explained without having to invoke any "spooky action". Juan's team claim to have closed this loophole and say theirs is the first legitimate measurement of the speed of spooky action. It’ll be interesting to see whether they can raise this bound in future and find out how fast they can go. However, what do you do with the fact that information or switch of properties goes faster than light? Nothing, because entanglement most likely has nothing to do with classic mechanism of traveling, but rather using medium itself to communicate. This is similar to inflation where negative pressure had Universe stretching out faster than light. And, keep in mind that information is transferred by light when it comes to us, but this is not necessary so for anything else - therefore, this finding does not go against anything we knew before. Brian Greene does nice introduction here.
Although the particle-wave duality of electrons has been demonstrated in a number of different ways since Feynman popularized the idea in 1965, none of the experiments have managed to fully replicate the methodology set out in Volume 3 of Feynman's famous Lectures on Physics. The technology to do this experiment has been around for about two decades; however, to do a nice data recording of electrons takes some serious effort and has taken three years Herman Batelaan from the University of Nebraska-Lincoln to do so. Previous double-slit experiments have successfully demonstrated the mysterious properties of electrons, but none have done so using Feynman's methodology, specifically the opening and closing of both slits at will and the ability to detect electrons one at a time. Akira Tonomura's brilliant experiment used a thin, charged wire to split electrons and bring them back together again, instead of two slits in a wall which was proposed by Feynman. The experiments by Guilio Pozzi were the first to use nano-fabricated slits in a wall; however, the slits were covered up by stuffing them with material so could not be open and closed automatically. In new experiments Batelaan and his team created a modern representation of Feynman's experiment by directing an electron beam, capable of firing individual electrons, at a wall made of a gold-coated silicon membrane. The wall had two 62-nm-wide slits in it with a centre-to-centre separation of 272 nm. A 4.5 µm wide and 10 µm tall moveable mask, controlled by a piezoelectric actuator, was placed behind the wall and slid back and forth to cover the slits.
In Feynman's double-slit thought-experiment, a specific material is randomly directed at a wall which has two small slits that can be opened and closed at will - some of the material gets blocked and some passes through the slits, depending on which ones are open. Based on the pattern that is detected beyond the wall on a backstop - which is fitted with a detector - one can discern whether the material coming through behaves as either a wave or particle. When particles are fired at the wall with both slits open, they are more likely to hit the backstop in one particular area, whereas waves interfere with each other and hit the backstop at a number of different points with differing strength, creating what is known as an interference pattern. In 1965, Feynman popularized that electrons - historically thought to be particles - would actually produce the pattern of a wave in the double-split experiment.
Unlike sound waves and water waves, Feynman highlighted that when electrons are fired at the wall one at a time, an interference pattern is still produced. He went on to say that this phenomenon "has in it the heart of quantum physics [but] in reality, it contains the only mystery."
Researchers created an experiment where both slits can be mechanically opened and closed at will and, most importantly, combined this with the capability of detecting one electron at a time. Series on left shows the patterns of electrons produced when the mask is at different locations. The position of the mask (orange rectangle) relative to the two slits (bright lines) is shown on the left of each image. When both slits are exposed, the diffraction pattern is seen; whereas when only one slit is exposed, the pattern is not there.
The intensity of the electron source was set so low that only about one electron per second was detected - which ensured that only one electron at a time would ever pass through the slits. At this rate it took about two hours for a pattern to build up on the detector - a process that was recorded in real time. Measurements were repeated with the mask in a series of positions: first blocking both slits, then one slit, then none and then the opposite slit. As expected, the double-slit pattern was seen when the electrons had access to both slits, but not seen when one slit was blocked.
For inclined reader, I suggest also to read following document: [1103.1922v10] Unified Theory of Wave-Particle Duality, the Schr\"odinger Equations, and Quantum Diffraction.
You can understand the double slit mechanism without single line of math. After all, thanks to Yves Couder and Emmanuel Fort we have mechanical analogy of double slit experiment already many years, though it is not clear how much applicable it is to slit experiment and quantum world itself. This is not an abstract phenomena, but a real effect, which everyone can replicate in its kitchen. See what Couder and Fort have found:
It might be fair to say that Couder and Fort accomplishment has less to do with quantum mechanics than with an observation once considered experimentally impossible: the wave-particle double nature of a macroscopic object (an oil droplet and its associated surface wave). Although there is no specific dividing line between the quantum and macroscopic scales, an object larger than an atom generally has much too small a wavelength to be detected. Wave-particle duality means that all objects (quantum and macroscopic) sometimes behave like waves and show interference, and other times like particles - objects that have mass and obey conservation laws. Duality, though strange, could explain why objects seem to be in two places at the same time and communicate instantaneously across distances. These abilities, to scientists, would be even more difficult to reckon with than wave-particle duality, which is accepted as an "interpretation" of the world rather than a literal description.
Most recently, entanglement may splash also in discussions related to firewalls and black holes. So-called firewall paradox shocked the physics community when it was announced in 2012 since its predictions about large black holes contradicted Einstein's crowning achievement - the theory of general relativity. Those results suggested that anyone falling into a black hole would be burned up as they crossed its edge - the so-called event horizon. Sam Braunstein and Dr Stefano Pirandola in a paper published in Physical Review Letters invoked quantum information theory, a modern branch of quantum mechanics that treats light and atoms as carriers of information. The key insight from quantum mechanics is the existence of spooky quantum entanglement across a black hole's event horizon. Quantum mechanics shows that entanglement can exist across the event horizon, between particles inside and outside the black hole. But should this entanglement ever vanish, a barrier of energetic particles would be created: an energetic curtain (or firewall) would descend around the horizon of the black hole. The greater the entanglement, the later the curtain descends. But if the entanglement is maximal, the firewall never occurs. Indeed, entanglement has long been believed to exist for some types of black holes, taking on exactly this maximum value.