The conflict between the two halves of physics has been brewing for more than a century — sparked by a pair of papers by Einstein , one outlining relativity and the other introducing the quantum — but recently it has entered an intriguing, unpredictable new phase. Two notable physicists have staked out extreme positions in their camps, conducting experiments that could finally settle which approach is paramount.

In general relativity, events are continuous and deterministic, meaning that every cause matches up to a specific, local effect. In quantum mechanics, events produced by the interaction of subatomic particles happen in jumps yes, quantum leaps , with probabilistic rather than definite outcomes. Quantum rules allow connections forbidden by classical physics. This was demonstrated in a much-discussed recent experiment in which Dutch researchers defied the local effect.

They showed that two particles — in this case, electrons — could influence each other instantly, even though they were a mile apart. When you try to interpret smooth relativistic laws in a chunky quantum style, or vice versa, things go dreadfully wrong.

## Operational Quantum Theory II: Relativistic Structures - PDF Free Download

Relativity gives nonsensical answers when you try to scale it down to quantum size, eventually descending to infinite values in its description of gravity. Likewise, quantum mechanics runs into serious trouble when you blow it up to cosmic dimensions. Quantum fields carry a certain amount of energy, even in seemingly empty space, and the amount of energy gets bigger as the fields get bigger.

Go big enough, and the amount of energy in the quantum fields becomes so great that it creates a black hole that causes the universe to fold in on itself. Craig Hogan, a theoretical astrophysicist at the University of Chicago and the director of the Center for Particle Astrophysics at Fermilab, is reinterpreting the quantum side with a novel theory in which the quantum units of space itself might be large enough to be studied directly.

To understand what is at stake, look back at the precedents. It provided the conceptual tools for the Large Hadron Collider , solar cells, all of modern microelectronics. What emerges from the dust-up could be nothing less than a third revolution in modern physics, with staggering implications. It could tell us where the laws of nature came from, and whether the cosmos is built on uncertainty or whether it is fundamentally deterministic, with every event linked definitively to a cause. The clash between relativity and quantum mechanics happens when you try to analyse what gravity is doing over extremely short distances, he notes, so he has decided to get a really good look at what is happening right there.

But Hogan questions whether that is really true. Just as a pixel is the smallest unit of an image on your screen and a photon is the smallest unit of light, he argues, so there might be an unbreakable smallest unit of distance: a quantum of space. There would be no way for gravity to function at the smallest scales because no such scale would exist.

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Or put another way, general relativity would be forced to make peace with quantum physics, because the space in which physicists measure the effects of relativity would itself be divided into unbreakable quantum units. The theatre of reality in which gravity acts would take place on a quantum stage.

Hogan acknowledges that his concept sounds a bit odd, even to a lot of his colleagues on the quantum side of things. Since the late s, a group of physicists and mathematicians have been developing a framework called string theory to help reconcile general relativity with quantum mechanics; over the years, it has evolved into the default mainstream theory, even as it has failed to deliver on much of its early promise.

Like the chunky-space solution, string theory assumes a fundamental structure to space, but from there the two diverge. String theory posits that every object in the universe consists of vibrating strings of energy. Like chunky space, string theory averts gravitational catastrophe by introducing a finite, smallest scale to the universe, although the unit strings are drastically smaller even than the spatial structures Hogan is trying to find. Chunky space does not neatly align with the ideas in string theory — or in any other proposed physics model, for that matter.

If he is right about the chunkiness of space, that would knock out a lot of the current formulations of string theory and inspire a fresh approach to reformulating general relativity in quantum terms. It would suggest new ways to understand the inherent nature of space and time.

And weirdest of all, perhaps, it would bolster the notion that our seemingly three-dimensional reality is composed of more basic, two-dimensional units. What makes them drastically different is that he plans to put them to a hard experimental test. As in, right now. Starting in , Hogan began thinking about how to build a device that could measure the exceedingly fine graininess of space.

As it turns out, his colleagues had plenty of ideas about how to do that, drawing on technology developed to search for gravitational waves. The name is an esoteric pun, referencing both a 17th-century surveying instrument and the theory that 2D space could appear three-dimensional, analogous to a hologram.

Beneath its layers of conceptual complexity, the holometer is technologically little more than a laser beam, a half-reflective mirror to split the laser into two perpendicular beams, and two other mirrors to bounce those beams back along a pair of 40m-long tunnels. The beams are calibrated to register the precise locations of the mirrors. If space is chunky, the locations of the mirrors would constantly wander about strictly speaking, space itself is doing the wandering , creating a constant, random variation in their separation.

For the scale of chunkiness that Hogan hopes to find, he needs to measure distances to an accuracy of 10 m, about m times smaller than a hydrogen atom, and collect data at a rate of about m readings per second. Amazingly, such an experiment is not only possible, but practical. To obtain the best experience, we recommend you use a more up to date browser or turn off compatibility mode in Internet Explorer. In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Help us improve our products. Sign up to take part. A Nature Research Journal. These constraints are considered to form ultimate limits for physical correlations and led to the fields of post-quantum cryptography, randomness generation besides identifying information-theoretic principles underlying quantum theory. Here we show that while these constraints are sufficient, they are not necessary to enforce relativistic causality in multi-party correlations, i. Depending on the space-time coordinates of the measurement events, causality only imposes a subset of no-signaling conditions.

Secondly, we examine the implications for device-independent cryptography against an eavesdropper constrained only by relativity, detailing among other effects explicit attacks on well-known randomness amplification and key distribution protocols.

## Book Operational quantum theory II Relativistic structures pdf

The recent experimental confirmation of the violation of Bell inequalities 1 , 2 in systems of electron spins, entangled photons 3 , 4 , 5 , etc. Quantum phenomena exhibit correlations between space-like separated measurements that appear to be inconsistent with any local hidden variable explanation. Moreover, this nonlocality has also been used to show that even a tiny amount of free randomness can be amplified 10 , 11 and that extensions of quantum theory, which incorporate a particular notion of free choice, cannot have a better predictive power than quantum theory itself The quantum nonlocal correlations are known to be fully compatible with the no-signaling principle, i.

Since the proposal of Popescu and Rohrlich 13 , 14 , it has been realized that nonlocal correlations might take on a more fundamental aspect. Not only quantum theory but any future theory that might contain the quantum theory as an approximation is now expected to incorporate nonlocality as an essential intrinsic feature. This program has led to the formulation of device-independent information-theoretic principles 15 , 16 that attempt to derive the set of quantum correlations from among all correlations obeying the no-signaling principle.

In parallel, cryptographic protocols have been devised based on the input—output statistics in Bell tests, such that their proof of security only relies on the no-signaling principle. When one considers such post-quantum cryptography 6 , 7 , randomness amplification 10 , 11 , 17 , 18 , etc. The general properties of no-signaling theories have been investigated 19 in a related program to formulate an information-theoretic axiomatic framework for quantum theory. On the other hand, quantum theory does not provide a mechanism for the nonlocal correlations.

Several theoretical proposals have been put forward to explain the phenomenon of nonlocal correlations between quantum particles via superluminal communication between them. These models go beyond quantum mechanics but reproduce the experimental statistical predictions of quantum mechanics, the most famous of these models being the de Broglie—Bohm pilot wave theory In all relativistic theories, causality is imposed, i.

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Before going further, two remarks are in order here. First, by an effect, we mean any possible event, even if it has been affected by other events causes indirectly. Second, we shall use as general a correlation point of view as possible, regardless of the physical theory from which the correlations arise.

In this context, let us also note that given an arbitrary space—time structure, the question of causal order for any two measures has been formalized using intuitions from optimal transport theory From the perspective of communication, the requirement of relativistic causality strictly demands that no faster-than-light FTL transmission of information takes place between a sender and a receiver.

The no-signaling principle being in ubiquitous use in device-independent cryptography, axiomatic formulations, etc.

emadereb.tk In this paper, we investigate this question and find several surprising results outlined here. We initially establish the setup of the Bell experiment and recall the assumptions in the Bell theorem. We then define the notion of relativistic causality that we use in this paper and that is commonly accepted, i. We then show that, in the multiparty scenario, in certain space—time measurement configurations, only a restricted subset of the no-signaling constraints is required to ensure that no causal loops appear. We explicitly identify a region of space—time for the measurement events in a Bell scenario where the usual no-signaling constraints fail.

In particular, while they considered an infinite speed jamming mechanism for nonlocal correlations, we identify the entire region of space—time for all superluminal velocities of the point-to-region influences. We then examine the implications of the restricted subset of no-signaling constraints for device-independent cryptographic tasks against an eavesdropper constrained only by the laws of relativity. We detail explicit attacks on known protocols for randomness amplification based on the GHZ—Mermin inequalities using boxes that obey the new relativistic causality conditions.

We show that from this perspective, the security theory needs revision. We also explore the implications on some of the known features of no-signaling theories 19 ; in particular, we find that the phenomenon of monogamy of correlations is significantly weakened in the relativistically causal theories and that the monogamy of CHSH inequality violation 24 disappears in certain space—time configurations.

The notions of freedom of choice and no signaling are known to be intimately related We re-examine how the notion of free choice as proposed by Bell and formalized by Colbeck and Renner 25 , 26 can be stated mathematically within the structure of a space—time configuration of measurement events. A breakthrough result in ref. We re-examine this question in light of the modified relativistic causality and free-will conditions. Both nonrelativistic quantum theory and relativistic quantum field theory are well-known to obey a no superluminal signaling condition 28 , and proposals to modify quantum theory by introducing non-linearities have been shown to lead to signaling 29 , We end with discussion and open questions concerning the feasible mechanisms for the point-to-region superluminal influences.

Let us first establish the notation for the typical Bell setup. In the Bell scenario denoted B n , m , k , we have n space-like separated parties, each of whom chooses from among m possible measurement settings and obtains one of k possible outcomes. The inputs of the i th party will be denoted by a random variable r.

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Accordingly, the conditional probability distribution of the outputs given the inputs will be denoted by. Following refs. As in typical studies of Bell experiments, here we consider the measurement process as instantaneous, i. We will have an occasion to distinguish the specific space—time location at which correlations between random variables manifest themselves, i.

The general multiparty no-signaling constraints are usually stated as follows see for example, ref. In words, the above constraints state that the outcome distribution of any subset of parties is independent of the inputs of the complementary set of parties while Eq.