Does determinism exclude retrocausality?

[Stephen Tashi]

You are right. For me, I think it means that if the universe is deterministic, there are still several ways in how it could be that. I mean, different histories are conceivable.

The free-will deamon picks a history by choosing a state of the present (A or B).

To reach conclusions about causality, you'll have to be specific about the model of the universe that you're using. A free-will demon contradicts the definition of "state" and the definition of "deterministic" by making exceptions. With the free-will demon present, we can no longer call your model of the universe deterministic by the usual definition of deterministic.

It's one intellectual exercise to consider how causality and retro-causality are defined in the conventional model of a deterministic physical process. It's a different exercise to consider how to define a not completely deterministic model and then define causality in that context.

 

[Jarvis323]

By coincidence, there was a relevant paper published this week. I haven't read it thoroughly yet, but at first glance, it seems like it might give a sort of an answer to your question.

Reversible dynamics with closed time-likecurves and freedom of choice
https://iopscience.iop.org/article/10.1088/1361-6382/aba4bc

1. Introduction

The dominant paradigm in physics relies on the idea that systems evolve through time according to dynamical laws, with the state at a given time determining the entire history of the system.
General relativity challenges this view. The Einstein equations, describing the relationship between spacetime geometry and mass-energy [1], have counterintuitive solutions containing closed time-like curves (CTCs) [2–17]. An event on such a curve would be both in the future and in the past of itself, preventing an ordinary formulation of dynamics according to an 'initial condition' problem. The question then arises whether some more general type of dynamics is possible.

Although it is an open question whether CTCs are possible in our Universe [18–22], considering dynamics beyond the ordinary temporal view is relevant to other research areas as well. In a theory that combines quantum physics with general relativity, it is expected that spacetime loses its classical properties [23, 24], possibly leading to indefinite causal structures [25–27]. In a quite different direction, it has been suggested that quantum physics could be reduced to some kind of 'retrocausal' classical dynamics [28–39].

The main problem arising when abandoning ordinary causality is the so called 'grand father paradox' [40]: a time traveller could kill her own grandfather and thus prevent her own birth, leading to a logical inconsistency. A popular approach holds that the grandfather paradox makes CTCs incompatible with classical physics, while appropriate modifications to quantum physics could restore consistency [41–56]. A common feature of the proposals within this approach is that they postulate a radical departure from ordinary physics even in regions of space-time devoid of CTCs, or in scenarios where the time traveling system does not actually interact with anything in the past [57, 58].

A different approach is the so called 'process matrix formalism', which takes as a starting point the local validity of the ordinary laws of physics and asks what type of global processes are compatible with this assumption [59–74]. This framework enforces that all operations that would normally be possible in ordinary spacetime should still be available in local regions. First considered in the quantum context, this approach has been applied to classical physics too, with the remarkable discovery of classical processes that are incompatible with any causal order between events [75–77].

In reference [78], a classical, deterministic version of the formalism was proposed as a possible model for CTCs. In this model, one considers a set of regions that do not contain any, but might be traversed by, CTCs. Agents in the regions receive a classical state from the past boundary, perform an arbitrary deterministic operation on it, and then send the system through the future boundary. Dynamics outside the regions determines the state each agent will observe in the past of the respective region, as a function of the states prepared by other agents. A simple characterisation was found for all processes involving up to three regions; furthermore, it was found that, for three regions, all non causally ordered processes are essentially equivalent.

In this work, we extend the characterisation of deterministic processes to an arbitrary number of regions. We provide some simple interpretation of the characterisation: when fixing the state on the future of all but two regions, the remaining two must be causally ordered, with only one directional signalling possible. We show, by explicit examples, that there are inequivalent, non causally ordered quadripartite processes, which cannot be reduced to tripartite ones. Our results show that CTCs are not only compatible with determinism and with the local 'free choice' of operations, but also with a rich and diverse range of scenarios and dynamical processes.

Some more relevant links:

https://en.wikipedia.org/wiki/Closed_timelike_curve
https://plato.stanford.edu/entries/qm-retrocausality/

 

[maline]

Does anyone here know of any model containing retrocausality, in any well-defined sense?

 

[Jarvis323]

Does anyone here know of any model containing retrocausality, in any well-defined sense?

Several models discussed in the stanford link I gave, and the one (and several cited) in the research paper I linked, do.

 

[entropy1]

Again, how do you define retrocausality? Until you define exactly what you mean by that word your question literally has no meaning.

Perhaps this is what is mean:

1. If the probability P(A) of event A occurring can be experimentally increased or decreased, and that is experimentally non-zero correlated with an increase or decrease of probability P(B) of event B subsequentially occurring, I define that, then, A is a cause for B.
2. If the reverse, that the probability P(B) of event B occurring can be experimentally increased or decreased, and that is experimentally non-zero correlated with an increase or decrease of probability P(A) of event A precedingly occurring, is true, then I define that, then, B is a retrocause for A.
3. If there is a third event that is cause for both A and B, thereby correlating the probabilities of A and B occurring, then manipulating the probability of A correlates to the probability of B, following first (2) and then (1), and vice-versa.

 

[Dale]

In a deterministic setting then every effect is a retrocause by 2)

 

[entropy1]

I have an opinion about this, but I am not allowed to share it here. Thanks for letting me share a definition of retrocausality.

 

[entropy1]

Perhaps this is very simplified, but: If the setting is deterministic, we could say that for example $P \rightarrow Q$, or P implies Q, right? P in the past, Q in the future (relatively).

$P \rightarrow Q$ is equivalent with $NOT(Q) \rightarrow NOT(P)$.

So if Q can be manipulated, this could influence P in this deterministic setting, right? I consider the possibility of gradations of P and Q.

Or otherwise put: the value (gradation) of P is related to the value (gradation) of Q.

If the deterministic premisse is posed, every effect has a cause (one or more), which can be expressed as every effect is implied by a cause, right?

 

[Dale]

Yes. As discussed above, in a deterministic scenario every cause is both a necessary and a sufficient cause.

 

[entropy1]

Yes. As discussed above, in a deterministic scenario every cause is both a necessary and a sufficient cause.

Are you saying that in a deterministic scenario, both causality and retrocausality are possible (simultaneously), or are you saying that only causality is possible?

 

[Dale]

Are you saying that in a deterministic scenario, both causality and retrocausality are possible (simultaneously), or are you saying that only causality is possible?

Again, that depends on your definition. According to the definition you gave above, in a deterministic setting every effect is a retrocause.

I doubt all definitions of retrocausality would do that, but I don’t know the literature on retrocausality very well.

 

[Stephen Tashi]

Perhaps this is very simplified, but: If the setting is deterministic, we could say that for example $P \rightarrow Q$, or P implies Q, right? P in the past, Q in the future (relatively).

Time is not explicitly represented in propositional logic. If you want to study a logic where time is explicitly represented, there are "temporal logics" https://plato.stanford.edu/entries/logic-temporal/

 

[Dale]

At this point we will go ahead and close this thread. I strongly recommend studying the existing literature in this topic, perhaps including the time symmetric formulation of quantum mechanics. It is best to use definitions from the literature as they are more likely to have addressed some of the basic issues mentioned so far.

For any future threads on this topic please start with a professional scientific reference that can serve as the basis of discussion.