The Rietdijk–Putnam argument and Penrose’s Andromeda paradox

Perhaps surprisingly, this is a continuation of the previous topic of time. It concerns how events are ordered in time.

Special relativity (SR) is based on  the relativity of simultaneity, that the order in time of two spatially separate events cannot be determined  absolutely, but instead depends on the motion of the observer. Thus it is impossible to order two events in time if they occur in different places (hence difference frames of reference). There is no preferred inertial frame in SR. Taken to its limits this suggests that people live in different states of the universe depending on their relative velocity, hence the Rietdijk–Putnam argument and Penrose’s Andromeda paradox.

The Andromeda paradox. Image from Wikipedia

Here is how the paadox is expressed:

“people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already ‘fixed’?”

The Cordus theory of time, offers a way to interpret the situation. In doing so it dissolves the paradox, as will be shown. Here is how the explanation works.

First, whether this is even a paradox is doubtful, because the two people, A and B, in Penrose’s Andromeda thought experiment cannot know, at the time of their meeting, what events are transpiring far away in their difference versions of the universe. So what happens in  Andromeda is unknowable to the people at the time, and any difference in perception of remote events (whether or not the aliens have decided to invade Earth) is likewise unknowable.

Therefore there is no contradiction in world-lines at the time of the meeting, and hence no paradox. It only appears to be a paradox to us because in a thought experiment we can ‘know’ what our subjects themselves do not, which is what the aliens are up to.

Penrose ponders whether, at the time his subjects were meeting, there was any real uncertainty about that future, i.e. a predetermination type of question.  But that assumes that A was already in a version of the universe that was more temporally advanced than B, which is not the case. He was only in version of the universe that would differ in simultaneity from B, if he had continued with his motion relative to B. But at the ppoint in time and space where A and B meet, they are in the same frame. Any subsequent velocity would distance A from B, and any communication from A to B would then be limited by light-speed. But that limitation did not apply at the moment of their meeting. Thus we suggest that the act of meeting is key to the paradox, and much of the paradox arises simply from an ambiguity in Penrose’s defintion of meeting.

Or to look at it the other way, person A had not at the time of meeting B been able to realise the potential advantage of foreknowledge that his temporal advancement might seem to promise. He only experiencees accelerated passage of time after he leaves the meeting, by which time it is too late to tell B. Also, he does not actual have information about the aliens at the time of meeting, but only potentially in the future. Nor would he ever be able to have that information early, since the information on which that knowledge was based (i.e. what decision the aliens had made) could only reach him at light-speed, by which time both he and his acquaintance B would both have moved forward in time (moved on the Minkowski diagram).

Nor does B have any ability to change the unfolding decisions of the aliens, because to do so would require sending a signal back to Andromeda which would also take too long (it would only be received by the aliens after they had already made their decision).

So while A might appear to have the benefit of advanced information about the alien’s plans, that advantage cannot be realised, and therefore that information cannot be transferred to B either, and B has no real ability to communicate that information into her retarded version of the universe, and therefore has no ability to cause her retarded universe to diverse from that inhabited by A. Therefore she cannot tamper with her retarded version of the universe to change the future. There is only one world-line for the universe as a whole.

Therefore what is decided by the aliens stays decided, and to answer Penrose, there is no uncertainty about the future. The future of both people is not already ‘fixed’. That’s quite the wrong way to think about it. instead it is simply indeterminate. The situation only looks like a paradox to an omniscient external observer (i.e. ourselves) who knows what A and B might know in the future.

Thus another way to dismiss the paradox is to point out it employs circular logic: it requires its observer to be in a highly preferred reference frame, free of the relativity of simultaneity, which of course is not-permitted by special relativity.

The bottom line is that the Cordus time theory suggests that there is only one reality for the universe, and that what happens stays happened, though observers in different situations (frames of reference) might get to know of it at different times. But since they are in different situations they cannot communicate that knowledge to the other. So there is no advantage (and no paradox) in the relativity of simultaneity.

For more on the Cordus theory of time, and the proposed fabric mechanisms whereby what happens to person A is reconciled with the experience of person B, see our time paper here. Or read one of the other thought-provoking links provided below.

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