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I am wondering whether or not A can cause B with A occurring after B. Something about this seems nonsensical. But is it logically contradictory?

If it is not logically contradictory, does this mean we also can’t rule out that A can cause B with A occurring after B? Something about A causing B seems to necessarily imply A preceding B in time and hence it seems to be a contradiction.

An interesting follow up is this: If A causing B necessarily implies A preceding B in time, does this also rule out or atleast make meaningless the notion of atemporal causes?

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    From a physics perspective, time is unidirectional and so A cannot cause an event B in the past. However, if we assume time is bidirectional- capable of two degrees of movement, forward and backwards. Then there is nothing inherently contradictory about event A causing some event B in the past. It's no more a logical contradiction than asking, can a car hit someone behind it, if it moves in reverse? Commented Aug 31, 2023 at 22:22
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    This called retrocausality, and some prominent physicists, like Feynman, entertained the possibility of it in describing quantum fields. Closed timelike curves in relativity allow some forms of time travel, so it would also be theoretically possible. But by and large, retrocausality is considered fanciful.
    – Conifold
    Commented Aug 31, 2023 at 23:18
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    @Stef The OP is not asking about misperceptions, but about actual causation. Commented Sep 1, 2023 at 9:29
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    @IñakiViggers Thank you for your comment
    – Stef
    Commented Sep 3, 2023 at 9:50
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    Fantastic question that shows how the space of knowledge&thinking that once belonged to philosophy(and religion), nowadays is fully covered by physics&maths.
    – EarlGrey
    Commented Sep 6, 2023 at 11:50

5 Answers 5

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From a physics perspective, it is mathematically possible, as shown by Einstein's paper on the tachyon anti-telephone. Einsteinian Relativity shows that, if FTL motion occurred, where one could either communicate information or physically travel FTL, in some frames of reference one would observe the signal's reception as happening before the signal was sent. A clever but simple arrangement of such tachyon antitelephones would allow one to receive a message before they ever sent that message. Same for superluminal warp drives and wormholes.

Now, most physicists don't take these situations to be something we'll ever observe in our world. But tachyons from Special Relativity or closed-timelike-curves in General Relativity are not contradictory: one can use the math to produce these situations.

Epistemic possibility is relevant here, since I'm relying on mathematical possibilities from physics. Given what we know, tachyon particles are not likely to occur if ever. Quantum Field Theory (QFT) predicts that a quantum field with imaginary mass never produces tachyon particles, but instead represents an unstable vacuum. Superluminal warp drives and wormholes are different. Nothing outright forbids such phenomena (yet), but they rely on negative mass-energy in astronomical quantities (which has never been observed).

Important to note here, is that even if someday we learn that tachyon particles and CTCs are forbidden by the laws of physics, their logical possibility is secured by the consistency of the math that allowed us to even hypothesize them.

So to answer your question: no, they are not logically impossible, since the math permits them in both SR and GR. We are getting a picture from QFT that at least tachyon particles will probably never be observed. Closed-timelike-curves are an open question: we'll need a theory of quantum gravity to get a definitive answer on that. Yet, even if that happens, it just means our universe won't have these phenomena (logically possible, but physically impossible).

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    One of the distinctions that might enrich this answer is "logical possibility" vs "epistemic possibility", although this answer is already on-topic as-is.
    – Galen
    Commented Sep 6, 2023 at 4:48
  • @Galen modified answer to reflect that, good call! Feel free to correct me if I made an error in my reference to epistemic possibility.
    – Hokon
    Commented Sep 6, 2023 at 5:04
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One quick argument that it can't be logically contradictory is that people can enjoy movies about time travel. If, by definition, we considered all causal-level correlations between A and B to always have the cause before the effect, then we would mis-interpret the evident direction of causation portrayed in those movies. If this were logically contradictory, while watching the beginning of Back to the Future, we would infer that Marty McFly's arrival in 1955 was the cause of his departure in 1985, rather than the other way around.

The reason why we don't mis-interpret those movies is almost certainly that most people have an innate "interventionist" viewpoint of causation, where the intervention is considered to be the cause. Consider flipping a lightswitch, connected to a lightbulb in a sealed box. Suppose you were later shown a video (taken from inside the box) proving that the state of the bulb was always perfectly correlated with the position of the switch one second in its future. How would you interpret this? Would you infer that the bulb caused the future switch position, according to the usual time-order of causation? Doubtful. You would more likely infer that you had somehow been able to control the past, to cause the state of the bulb one second into the past. After all, your intervention is at the switch, not the bulb, so the switch is naturally viewed as the cause. (Putting the bulb in the box prevents bilking paradoxes, allowing one to better imagine this scenario – but the topic here is logical coherence, not physical plausibility.)

The philosopher most closely associated with taking retrocausality seriously is Huw Price; some of the chapters in this book are focused on applying interventionist causation to such scenarios. Emily Adlam has also been recently writing on this topic. (I'm not a philosopher, but I take it seriously over on the quantum foundations side of the aisle.)

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  • I forget the phrasing and don't have my copy of Pearl 2009 handy, but for your interest in further reading I think he discusses a conjecture of there always being a statistical time consistent with physical time.
    – Galen
    Commented Sep 6, 2023 at 4:39
  • Yes, I think I remember that. Pearl posed it as an open puzzle/question, why interventionist causation always seemed to line up with temporal order, when one can define interventionist causation without any reference to temporal order. Nevertheless, his point was that it's not inconceivable that it would line up the other way, it just never seems to in real life. Commented Sep 6, 2023 at 5:16
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A bank hires guards that shoot to kill anyone trying to rob the bank. Bank robbers stay away in droves. Including one bank robber who didn’t rob a bank in the morning because the guard started his job that day - in the afternoon.

So the guard starting in the afternoon caused the robber to not rob the bank in the morning.

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As far as we know, all of the particles that form the Universe, including all of the particles responsible for the transmission of forces, are moving through spacetime in a direction of increasing time, so a chain of events is always from earlier events to later ones.

I would encourage you, my friend, to be extremely skeptical of any mention of faster than light travel or closed timeline loops in connection with changing events that occurred in the past. Such ideas are based on a fundamental assumption about reality which is entirely unsupported by mainstream physics, namely that if you, say, were to go back to last Tuesday, you would find the Universe there as it then was, a rather odd idea given that the Universe has since moved on and is here where you left it before you headed back in time. According to modern physics, particles move on trajectories through spacetime, known as world-lines, and since you are a collection of particles, you move along a world-line too, which means that at a later time you no longer occupy the position you did at an earlier time; hence if you were to find a way to go back to that earlier time, you would certainly not find your old self there.

Likewise with closed timeline curves. Were you to travel round one, you would do just that- travel around it. You would no more meet your old self on completing a lap than you would if you were to complete a lap on a running track.

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    Wouldnt CTCs in theory allow you to meet your old self on a lap though, because the "track" in such a scenario involves a temporal loop, so when you're at the start of the loop you're also at the starting time? From what I've always understood, the math just says that if such a loop existed, it would be self consistent, so if you went back in time to see yourself, that event would have necessarily already happened in the past. Time travel doesnt allow you to change anything in the past.
    – JMac
    Commented Oct 6, 2023 at 11:50
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    @JMac no! Think about it... your 'old self' is no longer at the starting time. Your old self is you, and has moved on through time. Commented Oct 6, 2023 at 12:09
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    What do you mean "your old self is no longer at the starting time"? Your "old self" cant leave its "starting time". Existing in the present doesnt mean you didnt exist in the past, so travelling from the present to the past doesnt logically suggest that the past you wouldnt still be there. The past you has to still exist in the past when you travel back, or else you wouldnt exist in the present and someone who doesnt exist cant travel in time, or do anything.
    – JMac
    Commented Oct 6, 2023 at 12:26
  • @JMac, no, you are still not getting it. The atoms that comprise your body move forward through spacetime. A particle that is at t=0 has moved forward to t=1 a second later, and is no longer at t=0. Commented Oct 6, 2023 at 13:26
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    What's all this business about traveling? It's 4-space. A point-process evolving in time in 3-space is a non-evolving curve-object in 4-space, an area-process evolving in time is a non-evolving volume-object in 4-space, and a volume-process evolving in time in 3-space is a non-evolving hyperspace-object in 4-space. It doesn't travel anywhere or do anything, it just is.
    – g s
    Commented Oct 6, 2023 at 17:27
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There's an interpretation of quantum mechanics where exactly this happens: the transactional interpretation of quantum mechanics.

So yes, what you said is 100% with infinite sigfigs logically possible. There is nothing in the definition of causality that requires that causes temporally precede their effects.

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