Abstract According to the Special Theory of Relativity, there is no such thing as absolute simultaneity, contrary to the view defended in the book. However, this chapter demonstrates that the Special Theory of Relativity can be modified so as to allow absolute simultaneity. This modification involves reference to absolute space and the causal relations between space‐time points, and drops the assumption that the one‐way speed of light is constant through all frames of reference. Contrary to the orthodox theory, the modified version has the additional advantage of avoiding a clash with quantum mechanics, such as brought out by the Einstein‐Podolsky‐Rosen thought experiment and Bell's Theorem.
Abstract According to the Special Theory of Relativity, there is no such thing as absolute simultaneity, contrary to the view defended in the book. However, this chapter demonstrates that the Special Theory of Relativity can be modified so as to allow absolute simultaneity. This modification involves reference to absolute space and the causal relations between space‐time points, and drops the assumption that the one‐way speed of light is constant through all frames of reference. Contrary to the orthodox theory, the modified version has the additional advantage of avoiding a clash with quantum mechanics, such as brought out by the Einstein‐Podolsky‐Rosen thought experiment and Bell's Theorem.
This paper constitutes a background to the paper 'Quantum mechanics as space-time statistical mechanics?', arXiv:quant-ph/0501133, presented previously by the author. But it is also a free-standing and self-contained paper. The purpose of this paper is to give the reader an increased and a deeper understanding of the special theory of relativity, and the ideas lying behind the above mentioned paper. We will here consider, discuss, define, analyse, and explain things such as, e.g., the constancy of the speed of light, synchronization, simultaneity, absolute simultaneity, absolute space and time, the ether, and spacetime. Albert Einstein's original version of the special theory of relativity is fundamentally an operational theory, free from interpretation. But the old Lorentzian interpretation and the standard spacetime interpretation of the special theory of relativity will also be considered. This paper also discusses and analyses aspects of the philosophy of science that in my opinion are relevant for an understanding of the special theory of relativity.
In Mundy [a] I offered an axiomatic analysis of the physical content of the kinematics of special relativity which suggests that, contrary to common belief, there is no incompatibility between special relativity and spacelike (faster-than-light) causation. An anonymous referee pointed out that this conclusion might have some bearing on problems in the interpretation of quantum mechanics such as the Einstein-Podolsky-Rosen problem, since one line of solution to these problems involves the postulation of spacelike causal processes. The present note will develop this idea.
The relation between quantum theory and special relativity is peculiar. On the one hand it is close and essential. Steven Weinberg [1], for example, takes the position that the standard model is an inevitable consequence of the marriage of the two theories. On the other, the action at a distance implied by the famous paper by Einstein, Podolsky, and Rosen [2] is certainly contrary to the implications of special relativity in spite of the fact that it does not allow transmission of information. The setting of quantum theory is a Hilbert spaceH and a path inH whose development in time is governed by a one parameter group of unitary transformations while the setting for special relativity can be thought of as Minkowski space with the time development not absolute, but dependent on the inertial system of the observer. The problem is to show how these two very different viewpoints can be reconciled in a way that includes an explanation of the "action at a distance" conundrum.
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.)
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.
This paper builds on no-go theorems to the effect that quantum theory is inconsistent with observations being absolute; that is, unique and non-relative. Unlike the existing no-go results, the one introduced here is based on a theory-independent absoluteness assumption, and there is no need to assume the validity of standard probability theory or of modal logic. The contradiction is derived by assuming that quantum theory applies in any inertial reference frame; accordingly, the result also illuminates a tension between special relativity and absoluteness.