I'd disagree with the statement "we know what it is". What we know are the symptoms of QE when we see them. What we DON'T know is WHY it happens, since it doesn't fit into our models of how the world works. It's like the two-slit experiment, where light is both a particle and a wave... we can demonstrate it, but we don't know why it happens. So we can currently point at something that makes no sense and say "that's quantum entanglement", but we cannot say how it works or why ... and then on to your next question; is it something we can use in some way? I hope I live long enough to learn the mechanics of how QE works... "But... we know what quantum entanglement is. Quantum entanglement is quantum entanglement. We have the mathematics that allow us to describe the relatively complex system of two entangled atoms, and we have obviously designed an experimental setup and procedure that allows us to do it."
To build on what Devac said, e.g. the "spooky action at a distance" (spukhafte Fernwirkung) of entanglement is actually a successful prediction and self-consistency of our existing quantum mechanical model of the universe. It's a very successful model. We do know how (or why? unclear in this context) the magic happens. The photon's wave function collapse occurs if a measurement of the photon is made as it passes through one of the two slits; then it passes through one of the two slits localized in space, as a particle, and is thus unable to interfere/interact at the slits like a wave. If the photon isn't measured at the slits, there is instead a pattern of many peaks and troughs observed after the slits, because the photon is behaving as a wave, as indicated by the wave refraction physics and resulting interference pattern produced by the slits. The wave interference pattern is only significant/noticeable because the separation between the two slits is close to the photon's wavelength. At large, people-size scales, the same, small wavelength (say, visible) photon behaves more simply, and we are able to treat the physics more simply than with quantum mechanics, like with e.g. geometric optics. And that's really the crux of all physics models, actually; It's always about scale-size. And sometimes a characteristic scale-time. Where I physics, it's the average radius of gyration and the average time an electron takes to gyrate around the local magnetic field (~1 km and ~1 ms, in my very specialized neck of the woods, about 11 Earth radii sunwards of Earth), but it's much smaller and quicker for quantum mechanical dynamics, typically, like modeling the way an electron recombines with an ion in a plasma to form a neutral atom, which usually occurs on scales of nanometers and nanoseconds (or faster!), approximately. Bottom line is we know wave function collapse happens, and how to cause it, and how it's happening all the time, every moment, even just because your personal matter is interacting with the environment around you, on top of with itself. But who knows how to interpret it. Have you seen Everything Everywhere All at Once? I haven't. But the existence of the multiverse is one fairly common interpretation of wave function collapse. There are some other juicy and recent propositions Devac linked in response to my original comment, too. Whether or not another, better model of the universe might unlock a very clever method of transmitting information via entanglement... is a question that I just thought of, but for now, we believe that it is impossible to transmit information using entanglement. Information transfer would require interacting with a subset of the entangled system, which of course causes wave function collapse of the entire entangled system, which then prevents instantaneously sending information between the spatially-separated subsets. edit2: Hahah, gaming this out even more simply, I call my buddy, to whom I gave one of my two entangled matter boxes, and I'm like "ok so #1 is up!", and then wait to hear back "#1 is down, over here..". Ultimately, I am not able to exchange information more quickly (past lightspeed) than I would have been if the matter we're describing wasn't entangled. I didn't know mine would be up, nor did my buddy know he'd measure down, and I can't encode a message if I don't know (in the simplest case) if I've got the zero particle or the one particle. So, we think faster-than-light information exchange simply doesn't take place. But black holes get weird. And maybe other sectors of the universe, dunno. It makes some sense, at least. Not the most. How entanglement works or why? I have trouble like ascribing meaning to a coat hanger a panhandler bent into the shape of guitar that I display on the desk I play my guitar next to, so I guess I'm mostly sitting this one out. I am gonna get back to Devac's other reply, but first I wanna go through my own (bullshit) cosmological model of the universe for a couple more days. And some other ideas. Oh do we ever already. There are so many applications of entanglement, including quantum computing. Some applications are intentional (lol bose-einstein condensates could never arise "in the wild" on the surface of Earth except for in our top laboratories), and some may arise as a side effect of requiring something like guaranteeing a secure method of quantum cryptography; If 1/2 of the entangled system's wave function was already collapsed before you measured it, someone accessed the information, causing the whole entangled system to collapse. It almost sounds like gibberish, sorry, I know, but these are an attempt at concise, yet sweeping statements built on having suffered through some maths. Navigating the delineation between where the model ends and interpretation begins is a very healthy exercise, especially for experimentalists like me. edit: Some of my QFT, standard model, and information theory isn't quite right, I think, and I'm looking forward to any corrections, no worries :).two-slit experiment
So we can currently point at something that makes no sense and say "that's quantum entanglement", but we cannot say how it works or why
is it something we can use in some way?
Allow me to dumb-splain some of this stuff, as a person who sat through six quarters of intro physics (once without calculus, once with): Two weeks from being done with "physics that isn't mechanics", our professor spent ten minutes as an aside to the whole "particle/wave duality of light." He cautioned us that the maxim "light is both a particle and a wave" is a platitude invented for intro physics students, and that quantum mechanics, as presented to the amateur or neophyte, is an assortment of disparate models presented as a unified one. He further cautioned us that the methods of discovery and exploration of quantum mechanics, as presented at the intro-to-electricity-and-magnetism-with-calculus level, could not be made unified without a great deal more math and many concepts that simply were not germane to anyone but students, professors and researchers of quantum physics. He lamented this because bright classes invariably drew conclusions from their learning that simply should not be drawn, and he felt it necessary from time to time to give this speech and implore anyone curious about all the stuff they weren't being taught to continue on their physics path, but also that those of us who were wrapping up their journey with Physics 131 could be happy that their knowledge was good enough for parties, casual conversation and a basic grasp of the physical world far beyond the average layman. Speaking as someone who sold books with titles like "Radiation Hydrodynamics" to employees of the Los Alamos National Labs Theoretical Physics division, I can say with confidence that the physics the normie world is familiar with and the physics practiced by actual investigators of quantum phenomena do not touch in many points. I was heartened to discover that my best friend's dad's pet project was actually pretty simple: it's just a precision 3-axis Michelson interferometer. Of course, that's only "simple" if you're comfy with ideas like Michelson interferometers and even I had to look it up to get rid of the "t" I wanna throw in that name. Which is not to say "you'll never understand it?" It's more to say "you'll never understand it if you take journalists for granted." "Gell-Mann amnesia" was literally coined by a theoretical physicist to describe what a cockup the press makes of theoretical physics, thereby it's safe to say they make a cockup of everything, but we forget that or else we start wearing WWG1WGA shirts. If the navel-staring of quantum mechanics is what you're interested in, goobster, I wholeheartedly recommend Max Tegmark.
EDIT: What follows is a horrid simplification, but I believed it needed for discussion to proceed. Ask questions or ignore, your choice, but mine and am_U's answers don't come from ignorance or some low-brow contentment. The topic is incredibly complex, and what you said in comment doesn't do it justice. Before any other discussion, I'd like to dispel a possible notion where you might think that 'wave' and 'particle' are mutual opposites or choices. You could take photons or electrons from a double-slit experiment and use 'same objects' in Compton scattering a couple meters away, but that's because they measure different aspects of stuff. If you permit a stretched analogy, it's kinda like when an apple can be checked for color or sugar content -- doesn't mean they're suddenly only either color or sugar, but you're measuring different aspects at the time. Different properties, measured by different principles and methods. What a photon is, is dependent on (and restricted to) the model. It can be modeled like a ball with energy that'll bounce. It can be modeled like a wave that'll reflect. It can be a cloud of probability with properties of a boson. It can be a 4d submanifold that interacts by an exchange of different 4d submanifolds with other 4d submanifolds (or itself). And that's the thing: it will always be a model. Don't think I'm trying to brush you off, but I want it to be both informed and informative.It's like the two-slit experiment, where light is both a particle and a wave... we can demonstrate it, but we don't know why it happens.