EPR Paradox as Evidence for the Emergent Nature of Spacetime Armin Nikkhah Shirazi∗ University of Michigan Ann Arbor, MI 48109 March 16th, 2011 Abstract After a providing a review of the EPR paradox which draws a distinction between what is here called the locality and the influence paradoxes, this paper presents a qualitative overview of a framework recently introduced by this author in which spacetime is assumed to emerge from areatime. Two key assumptions from this framework allow one to make the notion of quantum effects originating from `outside' spacetime intelligible. In particular, this framework assumes that until a quantum object is measured, it does not actually exist in spacetime and that there are connections between quantum particles in areatime which are independent of metric relations in spacetime. These assumptions are then shown to permit one to conceptually understand both the locality and the influence paradoxes, and lead to the overall conclusion that spacetime is emergent in the sense that a very large number of discrete events which correspond to `measurements' in quantum mechanics aggregate to give rise on a large scale to the apparently smooth reality we experience in our daily lives. Keywords: Non-locality, EPR locality Paradox, EPR influence paradox, Bell's Theorem, Dimensional The- ory, Emergence of Spacetime 1 Introduction It is well known that one of the most mystifying features of quantum theory, which is also one of its most pervasive [4], is what is commonly called non-locality [1, pp. 131-144][3, pp. 437-455]. In general terms, non-locality in non-relativistic quantum mechanics refers to the phenomenon in which the measurement of some property of one part of a quantum system seems to somehow influence the outcome of a similar measurement at some distance of another part in cases in which the two parts of the system are described by a non-separable wavefunction, or, in more colorful language, when they are `entangled'. The type of experiment which demonstrates that entanglement really is a feature of nature was first described in a paper by Einstein, Rosen and Podolsky, and hence the mystery it describes is often called the `EPR paradox'. There are actually two separately mysterious aspects which pertain to the EPR paradox. The first one is that which already appears in non-relativistic quantum mechanics and involves the non-local influence which enforces the correlations. The other aspect is an extra twist which appears when this phenomenon is considered in a more fully special relativistic context. Here the mystery is that for any spacelike separated measurements of entangled particles two distinct frames can be found in which the order of the influence is reversed. In order to keep these two issues separate, we will refer to the first as the EPR locality paradox and to the second as the EPR influence paradox. This paper is organized as follows: Section 2 will provide a brief overview of the EPR paradox which emphasizes the distinction between the EPR locality and influence paradoxes. Section 3 will introduce as a `story' i.e. in purely qualitative terms, a framework recently proposed by this author which is meant to elucidate the fundamental physical processes behind the formalism of quantum mechanics. The two key ∗[email protected] 1 points of this framework specifically applicable to the EPR paradox are (1) the idea that quantum objects do not actually exist in spacetime until they are `measured' (in a manner to be described more clearly below) and (2) the metric relations which they obey prior to measurement are independent from the spacetime metric, so that at least in the sense of this independence, (both versions of) the EPR paradox can be said to involve transmission of an influence `outside' spacetime. Section 4 uses these two key ideas to reduce the EPR influence paradox to a spacetime version of the EPR locality paradox. Finally, section 5 presents a `story' of how one might intuitively `make sense' of the spacetime version of the EPR locality paradox, given these two assumptions. The overall conclusion drawn is that if the explanations provided are correct, then the EPR paradox is evidence that spacetime is emergent. 2 Background: Quantum Non-locality vs. Special Relativity As Maudlin has pointed out, the non-local influence associated with entangled particles is different from other kinds of influences which occur in physical theories and are commonly labeled as action-at-a-distance in at least three notable ways [5, pp. 22-24]: • It is unattenuated: The `strength' of the influence seems to be unaffected by distance. • It is discriminating: The influence only seems to act exclusively on those specific parts of the system which are described by the same non-separable wave-function. • It is faster than light or instantaneous: In fact, a recent experiment to measure the speed of this influence found a lower bound of at least 104c [6]. Of these, the last property introduces a tension with special relativity (SR). That is because according to SR the speed of light c is invariant in all inertial frames and this invariance is commonly interpreted to establish c as a limit on the speed of transmission of a range of possible phenomena. The first well-known instance in which the tension between non-locality and Special Relativity came to be appreciated occurred when Einstein, Rosen and Podolsky (EPR) presented an argument in 1935 meant to demonstrate that quantum mechanics was an incomplete theory of nature: According to the argument, either \(1) the quantum mechanical description of reality given by the wave function is not complete or (2) when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality"(italics in original)[7]. This argument, applied to two entangled parts of a quantum system some distance apart, implicitly assumed that such influences could not propagate at infinite or at least superluminal speeds, and thus if according to the theory a measurement on one part instantaneously or superluminally changed the state of the other, thereby indicating that the latter did not describe a reality simultaneous with the first, then this could only confirm their conclusion, and hence there would have to be some additional specifications, commonly called `hidden variables' which would be required to give a complete account of nature beyond that provided by standard quantum mechanics. The subsequent debate it engendered seemed merely philosophical until in 1964 Bell presented a way by which two possibilities, that quantum mechanics is complete but non-local or that it is incomplete but must be supplemented by local hidden variables, could be distinguished from each other in the most general way [8]. The distinction was based on a difference in predictions between the two theories of statistical correlations between repeated measurements of the type proposed by EPR (actually a modified version proposed by Bohm and Aharanov [9]). More specifically, he showed that the difference in predictions could be phrased in terms of an inequality obeyed by any local hidden variable theory but violated by canonical quantum mechanics. In 1982, Aspect et al. performed the relevant experiments and found that Bell's inequalities were indeed violated[10]. Similar experiments were (and had been) performed by others and the results were found to also agree with the violation[11][12]. It is important to note that these experiments not only confirmed quantum mechanics but also foreclosed the possibility that any serious candidate for a successor theory would be local. Thus, at least in this respect, then, nature seems to be indeed non-local. This, however, raises the question of how such influences can apparently travel at superluminal speeds in light of the constraints imposed by SR. As mentioned in the introduction, this apparent contradiction will be referred to as the EPR locality paradox. 2 What is in this paper called the EPR influence paradox presents an added mystery arising from the relativity of time ordering for those spacelike separated events which correspond to the emission and arrival of the influence that enforces the correlations between two entangled systems: Suppose we have an EPR type set-up in which observers A and B are spacelike separated and perform the experiment in which two entangled particles are sent out in order for a certain property to be measured. If two events are spacelike separated, then there exists a frame in which the two measurements are simultaneous. For simplicity, and without loss of generality, let us suppose that for the above experiment this was the rest frame of the emitter. Figure 1 is a spacetime diagram that illustrates this situation as observed in that frame. Figure 1: A Frame in which the two measurement events (0;A) and (0;B) are simultaneous. For each particle, the two separate world lines represent a single world line to illustrate the superposition of two possible measurement outcomes of some property such as spin. It is understood that there are infinitely many other such worldlines, each corresponding to a path that is part of the path integral. Here, (0,0) marks the spacetime event which is the emission of the entangled particles, (0;A) marks the event which is A's measurement of some property of particle a which has two possible outcomes (e.g. spin if these are spin 1=2 particles) and (0;B) marks that which is B's measurement of the same property of particle b. As mentioned, in this frame (0;A) and (0;B) are simultaneous. From the path integral formulation we know that associated with each particle there are an infinite number of paths. Since the standard path integral formulation makes no distinction between paths that contribute to the path integral and classical paths, it is natural to assume that to each path there corresponds a separate worldline.