This is the way we thought about our universe in the 19th century and earlier; and it is still the way we understand it as we go about our day-to-day lives. In fact, the main difference in the way we think of the universe today, compared to the way an educated European thought of it in the wake of Galileo and Newton, is probably in terms of its sheer immensity: we now know that our Sun and planets occupy a miniscule portion of an immense, lenticular galaxy (the Milky Way), which itself is just one of hundreds of billions of galaxies we can see in the part of the universe that is visible to us.<\/p>\n\n\n\n
You probably know that Einstein\u2019s special and general relativity theories (1905 and 1915, respectively) overthrew our common-sense, classical understanding of space and time. In classical physics \u2013 and in our common-sense way of thinking about it, even today \u2013 space and time are quite different things. Space <\/em>is understood, metaphorically at least, as a container in which every physical thing occupies a place. Time <\/em>is something that inexorably passes, for everybody everywhere in exactly the same way: minute by minute, day by day, we move further and further into what is, for us now<\/em>, the future.<\/p>\n\n\n\n Einstein\u2019s relativity theories brought some radical changes to our conceptions of space and time. Time ceased to be an absolute<\/em>, passing in the same way for everybody in the universe, becoming instead something that depends upon one\u2019s state of motion<\/p>\n\n\n\n Einstein\u2019s relativity theories brought some radical changes to our conceptions of space and time. Some physicists and philosophers have even argued that relativity theories force us to give up on the idea that time passes<\/p>\n<\/blockquote>\n<\/div>\n\n\n\n Some physicists and philosophers have even argued that relativity theories force us to give up on the idea that time passes at all. The well-known slogan is that, after Einstein, time became no more than a fourth dimension of reality alongside the three spatial dimensions, albeit a dimension that differs from the spatial dimensions in important ways. Finally, according to general relativity theory, even space was radically changed: instead of a homogeneous container in which the laws of Euclidean geometry hold everywhere, space became \u201ccurved\u201d, variably bent and stretched by the gravitational effects of massive bodies. And not only space is warped in general relativity: time itself may become so curved by intense gravity fields that time loops back on itself. Time travel into the past becomes a physical possibility, as depicted in the 2014 movie Interstellar<\/em>.<\/p>\n<\/div>\n<\/div>\n\n\n\n All these revisions to our everyday conceptions of space and time are fascinating and radical, and it is a shame we cannot explore them here. But I mention them because, as radical as they were, Einstein\u2019s innovations did not change our ability to think of the world as consisting of three-dimensional objects, spread around in an immense container (space), and existing through time. Nor did relativity theories undermine our belief that spatially distant objects barely affect what happens in the here and now. On the contrary, they reinforced that belief. According to Einstein\u2019s theories, spatially separated objects can only influence each other via the propagation of some material body or field between them, and that influence can never propagate faster than the speed of light (contrasting sharply with Newton\u2019s theory of gravity as an instantaneous force that diminished with distance in proportion to the inverse of the square of the distance between the objects). This Einsteinian prohibition of influences that are instantaneous, or that propagate faster than the speed of light (c), came to be considered a fundamental bedrock of physics in the 20th century, and is often known as the principle of locality<\/em> or Einstein locality<\/em> (hereinafter referred to as \u201clocality\u201d). Einstein himself thought that locality was so fundamental to the physical sciences that we could barely make progress in physics were we to give it up. [1]<\/a>1 \u2014 Einstein thought that, if arbitrarily distant events could influence events in the here and now, with a strength of impact not diminished by distance, then it would never be possible to rule out any hypothesis dreamed up to explain what happens here and now partly in terms of things happening on the other side of the globe, or even in distant galaxies. He therefore believed that the principle of locality was needed in order for experimenters to be able to isolate and control the factors that determine the outcomes of their experiments.\n<\/span><\/span><\/p>\n\n\n\n Given that Einstein was one of the early founders of quantum mechanics, it is ironic that one of the most significant but least well-known ways in which quantum physics revolutionises our understanding of the physical world is precisely that it overthrows locality! Einstein saw this very early on, and it was the main reason for his opposition to the quantum theory developed in the 1920s. Einstein could not accept the \u201cspooky action at a distance\u201d that quantum theory seemed to postulate, and for many years he searched for an alternative theory, consistent with known quantum phenomena, that would preserve locality.<\/p>\n\n\n\n What Einstein did not realise \u2013 what nobody realised, until the seminal works of John Bell in the 1960s \u2013 is that it would turn out to be possible to definitively establish, in the laboratory, whether nature displays failures of locality. The 2022 Nobel Prize in Physics was awarded to experimental physicists who established, through a series of experiments carried out between the 1970s and early 2000s, that nature does violate locality, just as quantum theory predicts. Bell might well have been a co-recipient of the Nobel had his demise in 1990 not rendered him ineligible.<\/p>\n\n\n\n In order to understand all this better, we need to back up a bit and discuss how quantum mechanics predicts non-local phenomena.<\/p>\n\n\n\n According to quantum mechanics, particles that have interacted in the past, or which share a common origin (for example, pairs of photons generated in a collision of heavier particles), have states that are entangled<\/em>, i.e., the properties of one particle are related to \u2013 coordinated with \u2013 the properties of the other particle. Importantly, this connection remains a feature of both particles, no matter how far apart they may travel, until (perhaps) some interaction with a third system occurs to break their entanglement. The connection does not diminish with distance. [2]<\/a>2 \u2014 Entanglement has become an important tool and resource for the burgeoning fields of quantum computing and quantum cryptography, as described in other articles in this issue.\n<\/span><\/span><\/p>\n\n\n\n For example, two photons may be emitted by an atom in a high-energy state, in such a way that one will be detected on one side of a laboratory, and the other on the opposite side. The spins of the photons (spin is a kind of intrinsic angular momentum possessed by particles) are represented in the quantum state as indeterminate<\/em>: they possess no definite value prior to measurement, only probabilities for manifesting various values. But the values are inexorably linked: once one photon is detected and measured on one side of the laboratory, it becomes certain that, if the partner photon is measured in the same way, on the other side of the laboratory, a specific definite result will be obtained. In the language sometimes used to speak of quantum measurements, the measurement of one photon\u2019s spin \u201ccollapses\u201d the state of both photons into having definite values. In a sense, to measure one of the pair is to measure both of them \u2013 even if they are separated by miles, or millions of miles. Spin measurements are always made using devices that are oriented along a certain spatial axis, as shown in the figure. Entangled particles in a quantum \u201csinglet\u201d state will always give opposite results, if measured by apparatuses oriented in the same direction, regardless of the direction chosen. Later on we will see what happens when the apparatuses are not oriented in exactly the same direction.<\/p>\n\n\n So we have two ways of thinking of entangled particles. According to quantum mechanics, they do not possess definite properties of, say, spin along a given axis, prior to measurement; but measurement of the spin of one particle instantly makes it the case that measurement of the partner particle will yield the opposite result, if the measurements are made by apparatuses pointing in the same direction. For measurements where, say, one particle\u2019s spin is measured in the x-direction, while the partner particle\u2019s is measured along an axis \ud835\udef3 degrees away from x, quantum mechanics predicts how anti-correlated the results will be, as a function of \ud835\udef3. According to Einstein\u2019s way of thinking, from the moment of separation, each particle possesses definite properties that will determine the result of the measurement, whether measured along the same axis or along different axes.<\/p>\n\n\n\n Bell\u2019s brilliant insight in the early 1960s was that, if Einstein\u2019s perspective were correct, then there were upper limits to how much correlation could be observed between measurements made at various angles \ud835\udef3. In fact, with a simple but ingenious argument, Bell proved that, for a large number of spin measurements on opposite sides of a laboratory, made at one of three axis angles (we shall call them 1, 2, and 3, the angles to measure on a given run to be determined by a randomising procedure such as flipping a coin), there is a mathematical limit to the sum of the correlations for measurements at angles (1, 2), (1, 3) and (2, 3). [3]<\/a>3 \u2014 For example, (1,2) means that the particle arriving on the left side of the lab is measured along axis 1, and the particle on the right side of the lab is measured along axis 2.\n<\/span><\/span> This limit is imposed strictly by logic, assuming that the particles cannot directly influence each other\u2019s measurement outcomes; rather, that the measurement results are determined purely by whatever properties the particle already has when it enters the measurement apparatus. This assumption, of course, is precisely the principle of locality.<\/p>\n\n\n\n According to quantum mechanics, particles that have interacted in the past, or which share a common origin have states that are entangled. The connection does not diminish with distance<\/p>\n<\/blockquote>\n<\/div>\n\n\n\n\n
Locality<\/h5>\n\n\n\n
Quantum non-locality<\/h5>\n\n\n\n
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Thinking about these connections between measurement results, it is natural to suspect that all the measurements are actually doing is revealing properties that the quantum particles already possessed. These pre-existing properties are sometimes called \u201chidden variables\u201d, because they are not found in the quantum mechanical description of the pair of particles. This idea, then, involves an assumption that the quantum mechanical description of the particles (which, you will recall, described them as indeterminate with respect to such properties as position, momentum or spin) is incomplete. Hence quantum mechanics would be merely a useful theory for making statistical predictions, but not a theory that directly and completely describes microscopic reality. This is precisely what Einstein maintained. A famous paper co-authored by Einstein, Nathan Rosen and Boris Podolsky in 1935, now usually known as the EPR paper, was titled \u201cCan quantum-mechanical description of physical reality be considered complete?\u201d.<\/p>\n\n\n\nBell\u2019s insight<\/h5>\n\n\n\n
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