Traditionally causes come before effects, but according to modern physics things aren't that simple. Special relativity shows that `before' and `after' are relative, and quantum measurement is even more subtle. Since the nonlocality of Bell's theorem, it has been known that quantum measurement has an uneasy relation with special relativity, described by Shimony as `peaceful coexistence'. Hardy's theorem says that quantum measurement requires a preferred Lorentz frame. The original proofs of the theorem depended on there being no backward causality, even at the quantum level. In quant-ph/9803044 this condition was removed. It was only required that systems with classical inputs and outputs had no causal loops. Here the conditions are weakened further: there should be no forbidden causal loops as defined in the text. The theory depends on a transfer function analysis, which is introduced in detail before application to specific systems.
Traditionally causes come before effects, but according to modern physics things aren't that simple. Special relativity shows that before' and after' are relative, and quantum measurement is even more subtle. Since the nonlocality of Bell's theorem, it has been known that quantum measurement has an uneasy relation with special relativity, described by Shimony as `peaceful coexistence'. Hardy's theorem says that quantum measurement requires a preferred Lorentz frame. The original proofs of the theorem depended on there being no backward causality, even at the quantum level. In quant-ph/9803044 this condition was removed. It was only required that systems with classical inputs and outputs had no causal loops. Here the conditions are weakened further: there should be no forbidden causal loops as defined in the text. The theory depends on a transfer function analysis, which is introduced in detail before application to specific systems.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
It has been debated whether quantum mechanics and special relativity are incompatible and whether there is a preferred Lorentz frame if they are incompatible. Bell's theorem is an important cornerstone, but it does not give us a definite positive answer due to the existence of supplementary assumptions or theoretical loopholes; there are unitary quantum theories which evade Bell's theorem and claim that they are compatible with special relativity. In this paper, I address the important issue of whether unitary quantum theories are compatible with special relativity. I propose a new Gedankenexperiment, a variant of the EPR-Bohm experiment with a superobserver who can undo a measurement. In this experiment, there is a stronger correlation (between the results of two spacelike separated measurements) than the correlation investigated in Bell's theorem. Based on an analysis of the correlations in different Lorentz frames, I prove that unitary single-world theories are incompatible with special relativity, and in order to avoid the incompatibility, there must exist a preferred Lorentz frame in these theories. Moreover, I argue that the incompatibility proof also applies to a proper version of the many-worlds interpretation of quantum mechanics. This closes the major theoretical loopholes of Bell's theorem, including relationalism, retrocausality, and superdeterminism. Finally, I argue that the stronger correlation found in the Gedankenexperiment cannot be explained by retrocausal processes or even the common causes in the past, but only be explained by nonlocal processes or actions at a distance. This provides a test of unitary quantum theories, as well as a further support for the new incompatibility proof beyond Bell's theorem.
Hardy's theorem states that the hidden variables of any realistic theory of quantum measurement, whose predictions agree with ordinary quantum theory, must have a preferred Lorentz frame. This presents the conflict between special relativity and any realistic dynamics of quantum measurement in a severe form. The conflict is resolved using a ‘measurement field’, which provides a time–like function of space–time points and a definition of simultaneity in the context of a curved space–time. Locally this theory is consistent with special relativity, but globally, special relativity is not enough; the time dilation of general relativity and the standard cosmic time of the Robertson–Walker cosmologies are both essential. A simple but crude example is a relativistic quantum measurement dynamics based on the non–relativistic measurement dynamics of Luders.
Abstract Although Bell’s theorem tells us that any interpretation of quantum mechanics must fail to satisfy Bell’s locality condition, the question of Lorentzinvariance is apparently left open by Bell’s theorem. In deed, it has been argued by many that nonlocality is compatible with Lorentzinvariance, given certain interpretations of the latter, or of the former. Some give a ‘weak’ interpretation of Lorentz invariance, compatible with a ‘strong’ violation of locality. For example, Bohm’s (1952) theory violates locality in a way that requires a preferred frame; but empirical Lorentzinvariance is preserved in the Bohm theory there is no experiment that could determine the preferred frame. (See, for example, Valentini (199la,b), Bohm and Hiley (1993), and Cushing (1994).) On the other hand, ‘orthodox’ interpretations of special relativity maintain a notion of ‘fundamental
Thus far I have been primarily concerned with how an interpretation of quantum mechanics might, or might not, be local. This question is traditionally not sharply distinguished from the question of whether quantum mechanics is consistent with the theory of relativity. However, the two questions are indeed quite distinct, and should be recognized as such explicitly. The theory of relativity What does relativity require? As a first approximation, we may make the distinction by noting that the requirements of the theory of relativity are themselves unclear. Minimally, relativity seems to require that there be no way to distinguish one reference frame from another – i.e., that there be no experimental procedure that can determine which of two inertial observers is ‘really’ moving, or more generally that there be no way to discover an observer's absolute velocity. Most authors are willing to find in (special) relativity a stronger requirement: namely, Lorentz-invariance. They say that relativity requires that in fact there is no such thing as absolute velocity. This requirement goes beyond the minimum – it might be that there is an absolute rest frame (so that absolute velocities are given by motion relative to this frame) while there is no way to find it. (As I will discuss in chapter 9, exactly this situation occurs in Bohm's theory.)