Two 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.

I'm not sure how "according to one of the people" is supposed to be interpreted. Are these two people supposed to have magical physics defying clairvoyance?

As it says they don’t know that it’s the case, but the reasoning suggests that it is the case for one of them. It’s better to understand it as saying that according to their their reference frame rather than according to their beliefs.

But in that case I'm having trouble making sense of "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."

Isn't that saying that they can hark back to something that didn't happen?

I know I'm nitpicking on details somewhat irrelevant to answering the question, but I'll give others time to think about it before suggesting an answer.

Isn't that saying that they can hark back to something that didn't happen? — wonderer1

No? It's just saying that they conclude that at some point in the past, it was true for one of them that the ships had set off and false for the other.

I don't think it's a paradox at all. It's only a paradox if one assumes the absolute Newtonian serial time must exist. It's consistent with local becoming.

A false dichotomy is often set up by advocates of eternalism in the physics literature between some sort of absolute, serial ordering of time and all moments existing at all times in an eternal "block universe." These arguments rely more (arguably entirely) on philosophy than scientific support, since the conjecture is arguably unfalsifiable.

The "Andromeda Paradox" has been a popular vehicle for this, as has the "Twin Paradox." Neither of these are actually paradoxical given an assumption of local becoming, and no reference to rods or clocks is needed to ground our sense of time, although the mathematics involved being abstruse might be why rejections of the paradoxes, which have been around for a century, are less well known than the paradoxes.

We'd probably see a resurgence of interest in these explanations if the evidence for quantum scale time irreversibility hadn't come out at the same time as the Higgs boson discovery, thus overshadowing it. It's not the end of the debate, but we certainly have a universe that appears to run differently forwards in time as opposed to backwards, at both large scales and quantum ones. This isn't at all surprising IMO, since all empirical evidence suggests time only goes in one direction and decoherence/collapse only occur in one direction.

We have seen that SR rules out the idea of a unique, absolute present: if the set of events that is simultaneous with a given event O depends upon the inertial reference frame chosen, and in fact is a completely different set of events (save for the given event O) for each choice of reference frame in inertial motion relative to the original, then there clearly is no such thing as the set of events happening at the same time as O. As Paul Davies writes (in a variant of the example given by Penrose above), if I stand up and walk across my room, the events happening “now” on some planet in the Andromeda Galaxy would differ by a whole day from those that would be happening “now” if I had stayed seated (Davies 1995, 70).


From these considerations Gödel concludes that time lapse loses all objective meaning.But from the same considerations Davies concludes, along with other modern philosophers of science, that it is not time lapse that should be abandoned, but the idea that events have to “become” in order to be real. "Unless you are a solipsist."

As I argued in Chap. 3 above, events “exist all at once” in a spacetime manifold only in the sense that we represent them all at once as belonging to the same manifold.But we represent them precisely as occurring at different times, or different spacetime locations, and if we did not, we would have denied temporal succession...


...in each case we are presented with an argument that begins with a premise that all events existing simultaneously with a given event exist (are real or are deter- mined), and concludes that consequently all events in the manifold exist (are real or determined). But the conclusion only has the appearance of sustainability because of the equivocation analysed above in Chap. 3.If a point-event exists in the sense of occurring at the spacetime location at which it occurs, it cannot also have occurred earlier. But if the event only exists in the sense of existing in the manifold, then the conclusion that it already exists earlier—that such a future event is “every bit as real as events in the present” (Davies), or “already real” (Putnam)—cannot be sustained.Thus, far from undermining the notion of becoming, their argument should be taken rather to undermine their starting premise, that events simultaneous with another event are already real or already exist for it in a temporal sense. For to suppose that this is so, on the above analysis of their argument, inexorably leads to a conclusion that denies temporal succession.

This, in fact, was Gödel’s point.As mentioned in the introduction to this chapter, he had already anticipated the objection that the relativity of time lapse “does not exclude that it is something objective”. To this he countered that the lapse of time connotes “a change in the existing”, and “the concept of existence cannot be relativized without destroying its meaning completely” (Gödel 1949, 558, n. 5).To this he countered that the lapse of time connotes “a change in the existing”, and “the concept of existence cannot be relativized without destroying its meaning completely” (Gödel 1949, 558, n. 5).As we saw in Chap. 3, however, the sense in which events and temporal relations “exist” in spacetime is not a temporal sense.This would amount to a denial of the reality of temporal succession.20

So the root of the trouble with the “layer of now’” conception of time lapse is a failure to take into account the bifurcation of the classical time concept into two distinct time concepts in relativity theory. The time elapsed for each twin—the time during which they will have aged differently—is measured by the proper time along each path. The difference in the proper times for their journeys is not the same as the difference in the time co-ordinates of the two points in some inertial reference frame, since they each set off at some time t1 and meet up at a time t2 in any one ...

We may call this the Principle of Chronological Precedence, or CP. As can be seen, it presupposes the Principle of Retarded Action discussed in Chap. 4, according to which every physical process takes a finite quantity of time to be completed.Note that so long as CP holds for the propagation of any physical influence, it will not matter whether light or anything else actually travels with the limiting velocity.41


As Robb showed in 1914, this means that—restricting temporal relations to these absolute relations only—a given event can be related in order of succession to any event in its future or past light cones, but cannot be so related to any event outside these cones (in what came to be called the event’s “Elsewhere”).There are therefore pairs of events that are not ordered with respect to (absolute) before and after, such as the events happening at the instants A and B on Robb’s “Fig. 6.1" The event B, being too far away from A for any influence to travel between them, is neither before nor after A.



For example, B could be the event on some planet in the Andromeda Galaxy that Paul Davies asked us to imagine, in the Elsewhere of me at the instant A when I am considering it. It is true that by walking this way and that I could describe that event as being in the past or in the future according to the time coordinate associated with the frame of reference in which I am at rest. But that event is not present to me in the sense of being a possible part of my experience. It bears no absolute temporal relation to my considering it...

All the events I experience, on the other hand, will be either before or after one another, and therefore distinct. In fact, they will occur in a linear order.They will lie on what Minkowski called my worldline.


There is nothing unique about my worldline, however. On pain of solipsism, what goes for me goes for any other possible observer (this is the counterpart in his theory to Putnam’s “No Privileged Observers”).42 Thus if we regard time as constituted by these absolute relations, time as a whole does not have a linear order: not all events can be ordered on a line proceeding from past to future, even though two events that are in each other’s elsewhere (i.e. lying outside each other’s cones) will be in the past of some event that is suitably far in the future of both of them. In this way, all events can be temporally ordered, even if not every pair of events is such that one is in the past or future of the other. This is Robb's "conical order." In the language of the theory of relations, it is a strict partial order, rather than a serial order.

In a paper of 1967 the Russianmathematician Alexandrov showed how the topology of Minkowski spacetime is uniquely determined “by the propagation of light or, in the language of geometry, by the system of the light cones”, noting the equivalence of this derivation to Robb’s derivation on the assumption of chronological precedence.

The Reality of Time Flow: Local Becoming in Modern Physics

Simultaneity is frame of reference dependent. Since they do not share the same frame of reference, they don't need to refer to the same event happening at the same time. The "paradox" resolves itself as the light of event travels to earth.

Formula (I don't know mathjax sorry):

Time differential: (distance * velocity)/c-squared

Where velocity is the speed at which the observer moves to or away from the observed event while the other stands still or moves in opposite direction.

Let's take a velocity of 5 m/s, gives about 15 days at 2.5 million light years. As the distance is reduced, the time differential nears zero. Since nothing travels faster than light the "pretend" observation of knowing what happens simultaneously lightyears away in a theoretical frame of reference is simply nonsense.

Since nothing travels faster than light the "pretend" observation of knowing what happens simultaneously lightyears away in a theoretical frame of reference is simply nonsense. — Benkei

But if it wasn't, at least we would have 2.5 million years to get the Milky Way defense fleet ready.

If true, what does this suggest about free will, — Michael

It doesn't seem to me that either of them has anything to do with the decision of whether or not the fleet launches.

what does this suggest about free will, the future, and truth? — Michael

I don't think it suggests anything. The text from the Wikipedia article you includes more that you didn't include:

If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity, and hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. — Wikipedia - Rietdijk–Putnam argument

The bolded text is certainly not true in any meaningful sense. The two observers are in the same frame of reference. Any inconsistencies between their so-called "differing" three-dimensional universes are trivial - light can travel from any point on Earth to any other in much less than a second.

Hi Benk.

If true, what does this suggest about free will, the future, and truth? — Michael

To suggest anything about these is to confuse coordinate simultaneity (which is what the Andromeda scenario utilizes) with actual simultaneity (certain events having a metaphysical state of 'has happened' or not). Special relativity really only concerns itself with coordinate simultaneity (merely a convention) and not with any statement of presentism or the lack thereof.

I don't think it's a paradox at all. It's only a paradox if one assumes the absolute Newtonian serial time must exist. — Count Timothy von Icarus

Indeed, not a paradox, even if absolute time exists. 1) It cannot be Newtonian time. That has been falsified. If there is absolute time, then there is no 'according to person X or frame F', there is just reality and any coordinate system that doesn't correspond to that reality is simply wrong. No paradox whatsoever either way.

These arguments rely more (arguably entirely) on philosophy than scientific support, since the conjecture is arguably unfalsifiable. — Count Timothy von Icarus

Yes

Since nothing travels faster than light the "pretend" observation of knowing what happens simultaneously lightyears away in a theoretical frame of reference is simply nonsense. — Benkei

Nothing in the Andromeda scenario suggests anybody 'knows' what's going on. OK, I take that back because the implication is that Andromedans want to attack humans, and there's no way they could yet have detected them since we didn't exist 2.5 MY ago. Similarly, Penrose says that 'the launch is inevitable' which bolsters the suggestion of lack of free will about it. But that's Penrose doing that, not Einstein.

The bolded text is certainly not true in any meaningful sense. The two observers are in the same frame of reference. Any inconsistencies between their so-called "differing" three-dimensional universes are trivial - light can travel from any point on Earth to any other in much less than a second. — T Clark

This is wrong. The whole point is that trivial differences in frame change have large swings of simultaneity at large distances. Sure, nothing suggests that a frame change (a mere abstract choice) has any kind of causal effect, but the difference in simultaneity is very much on the order of months in this case. Your statement seems to be in denial of this.

BTW, Relational Quantum Mechanics handles this sort of "paradox" quite well, even if we consider that any full theory must deal with gravity and attendant issues from relativity at extremely small scales.

If discrete objects do not exist, and things only exist in how they interact (i.e., relations exist, persistent objects with properties at all times do not), then the idea that all becoming is local doesn't seem strange at all. The conception seems to work well with Wheeler's "many fingered time," and arguably also with his more provocative "it from bit."

The idea that things only exist in their relations works
quite well with the holographic principle as well.

Having not spent too much time diving into RQM, it does seem, at first glance, like it would be quite compatible with Floridi's maximally portable ontology of bare, essential ontic difference or various quantum variants that have been proposed. Certainly, it seems to fit well with ontic structural realism, but does so in a way that avoids having to have a multiverse, which in turn avoids having an theory where it still seems like the vast majority of human observers should be Boltzmann Brains.

Interactions are ontologically primitive, not "stuff." These (mostly) occur locally, although one also needs a way to explain (apparent?) non-locality. Best of all, RQM seems to not only deal with this "paradox" quite well, but also experimental results that suggest it is fundementally possible for two observers to observe different facts about a system, leaving no room for a bedrock "objective" world outside of one that is posited based on philosophical inclinations, but which we have to accept as completely inaccessible to all observers.

I consider this "paradox" untenable since simultaneity cannot apply to distant events.

I consider this "paradox" untenable since simultaneity cannot apply to distant events. — jgill

So do distant events occur in the past relative to my reference frame? Or the future? Or not at all?

So do distant events occur in the past relative to my reference frame? Or the future? Or not at all? — Michael

When the Mars rover sends a message back to Earth it takes, what, about five to twenty minutes to reach us. When we receive it about five to twenty minutes has elapsed, in our time, since the message was sent. That's how I see it, but I've been wrong before.

This is wrong. — noAxioms

Nunh unh.

The whole point is that trivial differences in frame change have large swings of simultaneity at large distances. Sure, nothing suggests that a frame change (a mere abstract choice) has any kind of causal effect, but the difference in simultaneity is very much on the order of months in this case. — noAxioms

Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months?

Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months? — T Clark

I'll second that. Curious. Does chaos theory intersect relativity?

Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months? — T Clark

There’s some math here that might explain it: https://medium.com/mathadam/the-andromeda-paradox-b4bb30a0e372

Given the distance to the Andromeda galaxy one person moving towards another nearby person at just 5 m/s changes the frame of reference enough that there’s a 15 day difference between which events in Andromeda are simultaneous.

And the further the distance the lower the velocity needed to establish such a significant difference. So given a far enough away location even small head movements can bring about a sufficiently different reference frame.

I do not understand the paradox. Why would people walking in different directions have radically different perspectives of events in the Andromeda galaxy? I get that it has to do with relativity of simultaneity. I don't get how walking in different directions has such radical consequences (it seems that the relative velocities are not that different).

See the formula in my previous post as to how.

They don't. You can't perceive something 2.5 million light years away that is simultaneous with what you see looking at this text. Not until 2.5 million light years have passed, and as that light nears the "paradox" resolves itself.

BTW, Relational Quantum Mechanics handles this sort of "paradox" quite well — Count Timothy von Icarus

The Andromeda thing is an illustration of spacetime geometry, not relevant to interpretations of quantum mechanics. Sure, the state of affairs at distant location X would constitute a counterfactual statement, meaningless under any interpretation that does not presume counterfactuals, RQM being one of those. But the event over there simultaneous with a given event here is still very much frame dependent regardless of the state (an invasion fleet existing at all say) at that distant location, hence no interpretation of QM really having any relevance at all to this problem.

I consider this "paradox" untenable since simultaneity cannot apply to distant events. — jgill

Andromeda is not sufficiently distant to invalidate Einstein's simultaneity convention, but admittedly something much further away (say 17 BLY) is indeed too distant for the convention since signals cannot be exchanged between the locations. There is no limit under special relativity, but special relativity does not describe spacetime at large scales.

Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months? — T Clark

I didn't claim the universe was three dimensional, nor did I claim multiple universes. Even the slightest angle results in an arbitrarily large separation at large distances since X sin(a) for a very small angle a can still be a large value if X is large enough. Likewise even a tiny change in reference frames results in a large (months) change in the 3D plane of simultaneity at a sufficiently large distances.
But a plane of simultaneity being 'a universe' seems to be something you're assuming. You seem to suggests a multiverse of different planes rather than some kind of single preferred plane of simultaneity, so perhaps not a stance of presentism. I would admit that simultaneity has nothing to do with frames and motion under presentism, hence the Andromeda thing being mostly irrelevant under it, but I suspect you're not asserting that.

Why would people walking in different directions have radically different perspectives of events in the Andromeda galaxy? — NotAristotle

They don't. They both see the same thing. But it's not about what they see, it's about which moment they consider to be simultaneous with moments here, no more radical than somebody facing north to consider London to be exact to his right, but somebody facing a tiny bit clockwise of north to consider London to be many km north of a line directly to his right.

Right, I didn't mean RQM has direct relevance to this particular issue; IMO that is explained quite well by the arguments laid out in the quotes in my first post. I meant that the ontological picture painted by RQM flows very nicely with the conception of local becoming existing without any universal serial ordering.

The Andromeda Paradox and the results of modified Wigner's Friend experiments are similar, despite being different areas of physics, in that they paint a picture of a world where observers do not seem to be able to point to an absolute, observer free context for grounding claims about states of affairs. However, it is able to do this without making claims about the necessity of consciousness for existence or a truly absolute relativism, because it can be consistent with a sort of ontic structural realism where knowledge about the relations that generate observations is possible, at least in theory.

absolute relativism, because it can be consistent with a sort of ontic structural realism where knowledge about the relations that generate observations is possible, at least in theory — Count Timothy von Icarus

Can the laws of physics about unknowable worlds be real, here meaning absolute, or must they be tentative as well?

Please explain how "even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content." And how can this purported difference in content cause a difference in simultaneity of months?
— T Clark

I didn't claim the universe was three dimensional, nor did I claim multiple universes. Even the slightest angle results in an arbitrarily large separation at large distances since X sin(a) for a very small angle a can still be a large value if X is large enough. Likewise even a tiny change in reference frames results in a large (months) change in the 3D plane of simultaneity at a sufficiently large distances. — noAxioms

Things like slight angles of the head and difference in position aren't particularly relevant to the special relativity scenario under consideration. The key thing to consider is the difference in the velocity of the two 'observers', and particularly the component of velocity in the direction of Andromeda. (If the two observers were moving past each other in a direction perpendicular to the direction to Andromeda, they would be viewing the same point in Andromeda's history.)

Given the distance to the Andromeda galaxy one person moving towards another nearby person at just 5 m/s changes the frame of reference enough that there’s a 15 day difference between which events in Andromeda are simultaneous.

And the further the distance the lower the velocity needed to establish such a significant difference. So given a far enough away location even small head movements can bring about a sufficiently different reference frame. — Michael

As the article asks "Can we meaningfully discuss what is happening right now in a galaxy far, far away?" Answer - of course not.

Since nothing travels faster than light the "pretend" observation of knowing what happens simultaneously lightyears away in a theoretical frame of reference is simply nonsense. — Benkei

Isn't this the same thing I wrote? If not, I don't understand what you're saying.

I didn't claim the universe was three dimensional, nor did I claim multiple universes. — noAxioms

The text about the three-dimensional universe and differing content I took from the Wikipedia article linked in the OP.

As the article asks "Can we meaningfully discuss what is happening right now in a galaxy far, far away?" Answer - of course not. — T Clark

Is that just because we don't know what is happening, or is it because there's nothing happening? A realist would presumably say that something is happening right now in a galaxy far, far way, but if special relativity is true then what's happening right now depends on our individual, relative velocities, such that what's happening right now in a galaxy far, far way in your reference frame isn't what's happening right now in a galaxy far, far away in my reference frame.

Things like slight angles of the head and difference in position aren't particularly relevant to the special relativity scenario under consideration. The key thing to consider is the difference in the velocity of the two 'observers', and particularly the component of velocity in the direction of Andromeda. — wonderer1

Totally agree, and the 'angle of head thing' was relevant to the London example. 'Movement of head' came from wiki, as if it's our head velocity that matters for some reason.
The movement of one frame as compared to another (either having a stationary head being irrelevant) causes a different angle in the time axis and at least one spatial axis in spacetime which produces large time discrepancy for worldlines of distant objects. That's the geometry of the situtation.

The text about the three-dimensional universe and differing content I took from the Wikipedia article linked in the OP. — T Clark

I think it was confusing for Wiki to introduce the notion of 'movement of the head' which at least suggests a velocity difference, but also 'offset in distance between observers' which seems to be totally irrelevant if they're stationary with respect to each other. Hopefully the actual Rietdijk–Putnam argument
was worded more carefully than that.

Imagine the plane of simultaneity for a pigeon walking with his head bobbing back and forth. I don't think anybody considers 'the universe' for the pigeon to be tipping wildly as it walks.

Each observer considers their set of present events to be a three-dimensional universe — Wikipedia - Rietdijk–Putnam argument

This line is also questionable, equivocating a plane of simultaneity with a universe, which makes it sound causal. I cannot think of a single interpretation of time that suggests such a thing. It's flat our wrong to consider any such thing,.

They apparently do quote some actual text from Penrose:

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. — Penrose

The latter bit seems unreasonable. If one is a presentist (there being an ontological division between past and future events), then movement of anything has nothing to do with where this division lies, but the statement suggests otherwise. If one does not posit such a division of events, then there is no 'uncertain future' and 'uncertain past'. The statement is thus wrong from any valid point of view. It seems to be there only to attempt to frame the scenario as paradoxical when in fact there is none.

As the article asks "Can we meaningfully discuss what is happening right now in a galaxy far, far away?" Answer - of course not. — T Clark

But despite the discussion of such events (the supposed invasion), it actually isn't what is happening that's important in the illustration, it is the time over there, which is the same for a given event despite the lack of measurement. So assuming two relatively moving observers (by a bicycle pace) on Andromeda looking at Earth, they see a clock over here, and very much know where Earth is at any given time, even if humans don't meaningfully exist to them. Yes, 2.5 million years is a long time to extrapolate the orbit of our planets, but it's a pretty predictable clock nonetheless.

Is that just because we don't know what is happening, or is it because there's nothing happening? — Michael

Answer to that is interpretation dependent of course.

but if special relativity is true then what's happening right now depends on our individual, relative velocities.

But SR just says that simultaneity is a convention, not any kind of ontological fact. So yes, the convention is dependent on definition of a frame, and it gets really tricky with Andromeda since the planet way over there is hardly stationary relative to Earth, so there isn't an obvious frame where both are stationary. Pretty hard to find an object stationary relative to Earth, even momentarily. Statistics say that something has to get close by chance now and then, but less likely for anything not nearby.

I don't think it's a paradox at all. It's only a paradox if one assumes the absolute Newtonian serial time must exist. It's consistent with local becoming. — Count Timothy von Icarus

In the case where people assume there is an absolute time or some absolute reference frame, then one doesn't really encounter a paradox either. One of the two observers or some other third party has it right while the others are just plain wrong.

The paradox seems to come about from accepting the relativity of simultaneity, and not taking it seriously enough. It assumes that we can simply stitch together different presents in order to get the conclusion that everything is present which is where this idea of the future being "fixed" comes from.