# Lapsing Quickly into Fatalism: Bell on Backward Causation

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## Abstract

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## 1. Introduction

## 2. Price (I)

In the ontological models framework, it is assumed that the probability measure representing a quantum state is independent of the choice of future measurement setting. (Leifer [3] (140))

I have not myself been able to make any sense of the notion of backward causation. When I try to think of it I lapse quickly into fatalism.

It has been assumed that the settings of instruments are in some sense free variables—say at the whim of the experimenters—or in any case not determined in the overlap of the backward lightcones. Indeed without such freedom I would not know how to formulate any idea of local causality, even the modest human one [8].

In any scientific experiment in which two or more variables are supposed to be randomly selected, one can always conjecture that some factor in the overlap of the backwards light cones has controlled the presumably random choices. But, we maintain, skepticism of this sort will essentially dismiss all results of scientific experimentation. Unless we proceed under the assumption that hidden conspiracies of this sort do not occur, we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation.

- No, my fair cousin:
- If we are mark’d to die, we are enow
- To do our country loss; and if to live,
- The fewer men the greater share of honour. (Henry V, Act IV, Sc. III)

The freedom-of-choice loophole refers to the requirement, formulated by Bell, that the setting choices are “free or random” [16] (232). For instance, this would prohibit a possible interdependence between the choice of measurement settings and the properties of the system being measured.

A ... major loophole, known variously as the freedom-of-choice, measurement-independence, or setting-independence loophole ..., concerns the choice of measurement settings. In particular, the derivation of Bell’s inequality explicitly assumes that there is no statistical correlation between the choices of measurement settings and anything else that causally affects both measurement outcomes. Bell himself observed 40 years ago that, “It has been assumed that the settings of instruments are in some sense free variables—say at the whim of experimenters—or in any case not determined in the overlap of the backward light cones”.

As far as I know, this was first argued by Einstein, in the context of special relativity theory. In 1907, he pointed out that if an effect followed its cause sooner than light could propagate from the one place to the other, then in some other inertial frames of reference the ‘effect’ would come before the ‘cause’! He wrote:… in my opinion, regarded as pure logic … it contains no contradictions; however it absolutely clashes with the character of our total experience, and in this way is proved the impossibility of the hypothesis … of a causal chain going faster than light.

## 3. Norsen (I)

## 4. Price (II)

The following idea characterises the relative independence of objects far apart in space (A and B): External influence on A has no direct influence on B. [26] (109)

Bell’s … mathematical formulation … is intended to capture the qualitative idea, motivated by relativity, that the causal influences on a given event are to be found exclusively in that event’s past light cone, and the causal influences of a given event … are to be found exclusively in the future light cone. The idea, in short, is that causal influences propagate (from the past toward the future) always at the speed of light or slower.

[V]ery few physicists paid attention to Russell’s enigma. They continued to write equations in the office and talk cause-effect in the cafeteria; with astonishing success they smashed the atom, invented the transistor and the laser. [28]

- A matter of definition. Following Hume, we can treat CAT as a matter of definition. This view holds that the basic relations of dependence are among the symmetric relations identified by physics, and the terms ‘cause’ and ‘effect’ are just labels for the earlier and later of a pair of events related in this way;
- Thermodynamics. We can try to explain CAT in terms of the thermodynamic arrow of time (and in particular the so-called Past Hypothesis, or low entropy initial boundary condition). This view has been defended in recent years by writers such as Kutach, Albert, and Loewer;
- Interventionism. The third possibility seems to originate with Frank Ramsey [30]. Ramsey, one of the fathers of the subjectivist approach to probability, takes a similar line on causation. As he puts it, “from the situation when we are deliberating seems to … arise the difference of cause and effect”. In effect, Ramsey proposes an explanation of the time-asymmetry of causation (indeed, causality itself) in terms of the epistemic perspective of agents like us. This approach has been influential in recent decades, thanks to the work of writers such as Jim Woodward, and Judea Pearl himself [28,31]. It is now called Interventionism, alluding to the central role of the idea of intervening on a system of interest—reaching in ‘from the outside’, to fix the value of an exogenous variable.

If you wish to include the entire universe in the model, causality disappears because interventions disappear—the manipulator and the manipulated lose their distinction. However, scientists rarely consider the entirety of the universe as an object of investigation. In most cases the scientist carves a piece from the universe and proclaims that piece in—namely, the focus of investigation. The rest of the universe is then considered out or background and is summarised by what we call boundary conditions. This choice of ins and outs creates asymmetry in the way we look at things, and it is this asymmetry that permits us to talk about “outside intervention” and hence about causality and cause-effect directionality. [28]

For me, [the] Costa de Beauregard zig zag in space time, which you seem to consider equivalent to retrocausation, is nothing else than nonlocality. The addition of one time-like vector to the past and one time-like vector to the future, connecting the detections, results in a space-like vector, and a causal relation between both ends, spacelike separated, amounts to a non local relation.

## 5. Norsen (II)

Note, by the way, that our definition of locally causal theories, although motivated by talk of ‘cause’ and ‘effect’, does not in the end explicitly involve these rather vague notions. [16] (240)

In this matter of causality it is a great inconvenience that the real world is given to us once only. We cannot know what would have happened if something had been different. We cannot repeat an experiment changing just one variable; the hands of the clock will have moved, and the moons of Jupiter. Physical theories are more amenable in this respect. We can calculate the consequences of changing free element in a theory, be they only initial conditions, and so can explore the causal structure of the theory. [16] (101)

A theory may appear in which such conspiracies inevitably occur, and these conspiracies may then seem more digestible than the nonlocalities of other theories. When that theory is announced I will not refuse to listen, either on methodological or other grounds. But I will not myself try to make such a theory. [16] (103)

## 6. Price (III)

Indeed, in the context of such [fundamental] theories, my concern about the retrocausalist proposal is not so much that backward causation is impossible or unconscionable, but rather that the distinction between forward and backward causation seems to melt away. In Maxwellian electrodynamics, for example, the state of the particles and fields at one time determines the state of the particles and fields at a later time. So did the former cause the latter, or vice versa? The laws of the theory certainly don’t answer that question; they just tell us that the states at the two times are necessarily connected. (This, I take it, was Russell’s point.) So is Maxwellian electrodynamics a retrocausal theory? Maybe? I am honestly not even sure what the question means.

## 7. Norsen (III)

...will essentially dismiss all results of scientific experimentation. Unless we proceed under the assumption that hidden conspiracies of this sort do not occur, we have abandoned in advance the whole enterprise of discovering the laws of nature by experimentation. [8]

## 8. Price (IV)

[Y]ou will want to say I am begging the question here by inserting the word “conspiratorially”. Your whole point is that, if the settings retro-causally influence the pair states, the needed correlations between (on the one hand) a and b and (on the other hand) $\lambda $ would not need to be conspiratorial at all.

## 9. Norsen (IV)

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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Norsen, T.; Price, H. Lapsing Quickly into Fatalism: Bell on Backward Causation. *Entropy* **2021**, *23*, 251.
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Norsen T, Price H. Lapsing Quickly into Fatalism: Bell on Backward Causation. *Entropy*. 2021; 23(2):251.
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Norsen, Travis, and Huw Price. 2021. "Lapsing Quickly into Fatalism: Bell on Backward Causation" *Entropy* 23, no. 2: 251.
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