Andromeda paradox and determinism?

[durant]

Can somebody explain the implications of the well known Andromeda paradox in a metaphysical sense? First, does it state that all events are determined? If one observer already knows what happens on the Andromeda galaxy, could it be possible that that event still happened in an indeterministic way (by chance)?

And also, what does the paradox say about the proper time of events? Does the Andromeda paradox imply that the future already exists, or that there only exists a 'latest state' of the object (or event) which will eventually occur sooner or later to every observer?

 

[mfb]

First, does it state that all events are determined?

No. It just tells you that it is pointless to talk about what happens today (literally, not yesterday and not tomorrow) in other galaxies.

If one observer already knows what happens on the Andromeda galaxy

You cannot, as information cannot spread quicker than light in special relativity - and special relativity was used to create the setup you are considering.

And also, what does the paradox say about the proper time of events?

There is no unique, global time-order, but locally everything happens ordered.

 

[durant]

No. It just tells you that it is pointless to talk about what happens today (literally, not yesterday and not tomorrow) in other galaxies.

So if one observer theoretically founds out 'before' another what's happening in the Andromeda galaxy, it doesn't imply that the event was causally determined by the previous event?

So the proper time of some object/event remains invariant, and there exists a latest state of the object (in this case the Andromeda galaxy). If not it seems that somebody traveling by a great speed can see the future of an entity.

 

[Naty1]

So if one observer theoretically founds out 'before' another what's happening in the Andromeda galaxy,\...

Then the 'one observer' is closer to the event than 'another'...so light signal information arrives sooner...

 

[Nugatory]

Can somebody explain the implications of the well known Andromeda paradox in a metaphysical sense? First, does it state that all events are determined? If one observer already knows what happens on the Andromeda galaxy, could it be possible that that event still happened in an indeterministic way (by chance)?

And also, what does the paradox say about the proper time of events? Does the Andromeda paradox imply that the future already exists, or that there only exists a 'latest state' of the object (or event) which will eventually occur sooner or later to every observer?

The paradox says nothing about the "proper time of events" because there's no such thing. Proper time is defined as the distance along a path between two events, not something that you can attach to a single event (nor a pair of events, unless you're also going to specify a path between them).

Nor does the paradox require that the future "already" exists, or force future determinism on us. That is one possible interpretation of the four-dimensional formalism of SR (google for "block universe" if you want to learn more about this particular dead end), but by no means the only one.

I find that the most effective way of analyzing the Andromeda paradox is to be as rigorous as possible about exactly what it means to say that the fleet has or has not "already" taken off... Avoid using any term that cannot in principle be backed up by observation by an observer on the spot... And I think you'll find that the paradox is not in the physics, but rather in the careless way that we use natural language to informally describe the paradox.

 

[Nugatory]

So the proper time of some object/event remains invariant, and there exists a latest state of the object (in this case the Andromeda galaxy). If not it seems that somebody traveling by a great speed can see the future of an entity.

There is no such thing as "the proper time of some object/event". The invariant thing that we call "proper time" is the amount of time that elapses between two events as measured by a single clock that is present at both events. If you try to read any more than that into proper time, you WILL confuse yourself.

 

[durant]

The paradox says nothing about the "proper time of events" because there's no such thing. Proper time is defined as the distance along a path between two events, not something that you can attach to a single event (nor a pair of events, unless you're also going to specify a path between them).

Nor does the paradox require that the future "already" exists, or force future determinism on us. That is one possible interpretation of the four-dimensional formalism of SR (google for "block universe" if you want to learn more about this particular dead end), but by no means the only one.

I find that the most effective way of analyzing the Andromeda paradox is to be as rigorous as possible about exactly what it means to say that the fleet has or has not "already" taken off... Avoid using any term that cannot in principle be backed up by observation by an observer on the spot... And I think you'll find that the paradox is not in the physics, but rather in the careless way that we use natural language to informally describe the paradox.

Thanks for the explanation, Nugatory.

 

[pervect]

Can somebody explain the implications of the well known Andromeda paradox in a metaphysical sense?

We try to avoid metaphysics here and stick to physics. It's part of the PF policy.

First, does it state that all events are determined?

No.

And also, what does the paradox say about the proper time of events? Does the Andromeda paradox imply that the future already exists, or that there only exists a 'latest state' of the object (or event) which will eventually occur sooner or later to every observer?

I think you might be misusing the term "proper time" here. As far as the metaphysics goes, the ONLY thing the Andromeda "paradox" says is that simultaneity is relative, that the notion of "now" is observer dependent and not universal.

 

[durant]

But why does this effect occur? In order to see what's the 'latest state' of the object, we must be co-located with it. Depeding on the motion, in our reference frame 'the present' of the object may be 'the past' of it in some other reference frame. This doesn't make any sense to me. Would this imply that if we would travel really fast in the direction of the object we would see its future completely or something like that?

 

[mfb]

Would this imply that if we would travel really fast in the direction of the object we would see its future completely or something like that?

No!
You cannot see what happens now in the Andromeda galaxy. You can only see what happened far in the past, and all observers on Earth will see the same thing at the same time, and all agree that this happened in the past. They will give it different timestamps ("happened 4 million years ago", "happened 4 million years and 1 day ago", ...), but that does not matter.

 

[durant]

No!
You cannot see what happens now in the Andromeda galaxy. You can only see what happened far in the past, and all observers on Earth will see the same thing at the same time, and all agree that this happened in the past. They will give it different timestamps ("happened 4 million years ago", "happened 4 million years and 1 day ago", ...), but that does not matter.

So in all frames of reference the Andromeda galaxy has the same state? It's just a matter of the distance between the observers and the Galaxy in judging the temporal parts of the galaxy?

By the first sentence I mean the following, for instance if the Andromeda galaxy explodes (I know this is very hard but just for an example :P), the event will be a part of the present of each frame of reference? Or not?

 

[mfb]

So in all frames of reference the Andromeda galaxy has the same state?

What do you mean with "the same state"? We all observe the same things here on earth.

By the first sentence I mean the following, for instance if the Andromeda galaxy explodes (I know this is very hard but just for an example :P), the event will be a part of the present of each frame of reference? Or not?

I don't understand that question.
If the Andromeda galaxy explodes "tomorrow" for me and exploded "yesterday" for you, it does not matter - assuming we both stay on Earth long enough, we will see it at the same time. We will just disagree about the time that has passed since then.

As you can see, arbitrary faster-than-light journeys automatically allow time traveling - if I can travel to Andromeda in a few minutes (as seem in my current frame), I can arrive before the explosion happens. I can travel a few minutes (as seen in your current frame) back, and arrive 2 days efore I started.

 

[durant]

What do you mean with "the same state"? We all observe the same things here on earth.

I don't understand that question.
If the Andromeda galaxy explodes "tomorrow" for me and exploded "yesterday" for you, it does not matter - assuming we both stay on Earth long enough, we will see it at the same time. We will just disagree about the time that has passed since then.

As you can see, arbitrary faster-than-light journeys automatically allow time traveling - if I can travel to Andromeda in a few minutes (as seem in my current frame), I can arrive before the explosion happens. I can travel a few minutes (as seen in your current frame) back, and arrive 2 days efore I started.

What if any of us was co-located (hypotethically) with the explosion, what would be the present in that situation? I understand that the distance from the object has an impact on the fact that we alway see its 'past', but I don't get why the motion changes what is present in the reference frame of any observer. And I don't mean the appearance of those entities, but I refer to the plane of simultaneity of each reference frame. Shouldn't it be the case that in every reference frame we should have the same present state of the object, just different order between the object and other events.

 

[Naty1]

durant:

In order to see what's the 'latest state' of the object, we must be co-located with it.

yes.

Depeding on the motion, in our reference frame 'the present' of the object may be 'the past' of it in some other reference frame. This doesn't make any sense to me.

good, because that statement is incorrect. See my earlier post.

I don't get why the motion changes what is present in the reference frame of any observer.

It doesn't. It seems that idea is what is causing your confusion. Everyone measures the same local speed of light regardless of their relative velocity. Two observers on earth, one 'stationary' one moving at the same location observe an events from Andromeda at the same time.

An analogy: If you and a another moving observer are adjacent at some moment, you will observe the flash of distant lightning at the same moment...and hear the resulting thunder together a few seconds later.

 

[durant]

It doesn't. It seems that idea is what is causing your confusion. Everyone measures the same local speed of light regardless of their relative velocity. Two observers on earth, one 'stationary' one moving at the same location observe an events from Andromeda at the same time.

An analogy: If you and a another moving observer are adjacent at some moment, you will observe the flash of distant lightning at the same moment...and hear the resulting thunder together a few seconds later.

Thanks for the reply Naty. So in the particular case of the Andromeda paradox, the sequence of events on the Andromeda galaxy will be present in every distant reference frame, regardless of its motion. It's just the case that some observers will some events from the past of the Galaxy before another observer does (because of their relative distance). So it's something like the case that if we were really close to the sun we would see its specific past state before another observer on the Earth will, right?

 

[Dale]

But why does this effect occur? In order to see what's the 'latest state' of the object, we must be co-located with it.

This effect occurs because the speed of light is finite.

Depeding on the motion, in our reference frame 'the present' of the object may be 'the past' of it in some other reference frame

Yes. Note that you have no information about the present condition of a distant object in any frame. You only have information about its past. Furthermore, what you label as "the present" is a mere labeling convention with no more significance beyond the convention itself.

This doesn't make any sense to me. Would this imply that if we would travel really fast in the direction of the object we would see its future completely or something like that?

No. No velocity will ever let you see any part of the future of any object, regardless of distance.

 

[pervect]

What if any of us was co-located (hypotethically) with the explosion, what would be the present in that situation? I understand that the distance from the object has an impact on the fact that we alway see its 'past', but I don't get why the motion changes what is present in the reference frame of any observer. And I don't mean the appearance of those entities, but I refer to the plane of simultaneity of each reference frame. Shouldn't it be the case that in every reference frame we should have the same present state of the object, just different order between the object and other events.

Have you read about Einstein's train?

http://www.bartleby.com/173/9.html

That has the detailed argument for why simultaneity must be relative.

 

[durant]

Have you read about Einstein's train?

http://www.bartleby.com/173/9.html

That has the detailed argument for why simultaneity must be relative.

I've understood relative simultaneity, I think, at least the part where the temporal order of the events in the universe isn't fixed. But the Andromeda paradox confused me because it is derived from the relativity of simultaneity, and I can't find the link between those two concepts.

 

[durant]

This effect occurs because the speed of light is finite.

Yes. Note that you have no information about the present condition of a distant object in any frame. You only have information about its past. Furthermore, what you label as "the present" is a mere labeling convention with no more significance beyond the convention itself.

No. No velocity will ever let you see any part of the future of any object, regardless of distance.

So when moving away from the object (in this case the Andromeda galaxy) the different past segments of it will become present in our plane of simultaneity, but when moving towards to it all observers will have one 'future' state of it, regardless of their speed and distance towards the galaxy. So observers with different motions and distances away from the Andromeda galaxy will have different slices of the past of the Andromeda, but all observers who move towards the galaxy will have its latest state as the present in their frame of reference.

Please correct me if I'm wrong, this is what I've concluded regarding your last sentence. Thank you in advance.

 

[mfb]

I've understood relative simultaneity, I think, at least the part where the temporal order of the events in the universe isn't fixed. But the Andromeda paradox confused me because it is derived from the relativity of simultaneity, and I can't find the link between those two concepts.

The Andromeda paradox is just a visualization of relative simultaneity, I cannot understand how you can understand one and be confused by the other.

 

[Naty1]

durant posts:

I've understood relative simultaneity, I think, at least the part where the temporal order of the events in the universe isn't fixed. But the Andromeda paradox confused me because it is derived from the relativity of simultaneity, and I can't find the link between those two concepts.

mfb

The Andromeda paradox is just a visualization of relative simultaneity, I cannot understand how you can understand one and be confused by the other.

I am unable to understand durant's issue as well...let's go back to basics for a moment:

I interpret your statement
"the temporal order of events in the universe isn't fixed"

as wrong...the temporal order of events IS fixed for causally related events as we have been discussing.

IS this is what you mean by 'temporal order of events': Note the LAST SENTENCE in the
quote carefully.

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.
According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. However, if the two events are causally connected ("event A causes event B"), the causal order is preserved (i.e., "event A precedes event B") in all frames of reference.....

Hope this helps.

 

[durant]

durant posts:
mfbI am unable to understand durant's issue as well...let's go back to basics for a moment:

I interpret your statement
"the temporal order of events in the universe isn't fixed"

as wrong...the temporal order of events IS fixed for causally related events as we have been discussing.

IS this is what you mean by 'temporal order of events': Note the LAST SENTENCE in the
quote carefully.

http://en.wikipedia.org/wiki/Relativity_of_simultaneity
Hope this helps.

Naty, I understand that time-like events are always fixed, their identity and temporal order is invariant. I hope I'm not being too confusing with my question.

My main issue is that a scenario occurred in my head which is connected with the Andromeda paradox that I've already mentioned. This is the part about simultaneity I don't get. If moving away from the object causes the plane of simultaneity to move to the past of the object (or to move the past of the object, relative to its current state, to the present in somebody's reference frame), then it would seem that moving towards the object, or event that we speak of would bring us the future of the object/event (not us in the literal sense, but it would move the future of the object to the present in our plane of simultaneity). But this sounds and seems horribly wrong, since the object must have a definite current state which must occur sooner or later in all reference frames. Hence, nobody should have its future in its reference frame as its present. That's why this has been the issue. And that's why I asked if the observers in motion away from the object will have different temporal parts (past temporal parts) in their present, while all observers moving towards the object will have the same/latest state of the object as present in their frame, since, as stated in a previous post 'no velocity can make the future occur in any reference frame'.

I hope I made some things clear, I look forward to you answers and opinions. :)

 

[pervect]

I've understood relative simultaneity, I think, at least the part where the temporal order of the events in the universe isn't fixed. But the Andromeda paradox confused me because it is derived from the relativity of simultaneity, and I can't find the link between those two concepts.

There really isn't a lot to the Andromeda paradox. If you are familiar with light cones, you know that they define the limits of cause and effect - events outside the future light cone can't be effects, and events outside the past light cone can't be causes.

So the causal structure of the universe (as interpreted by special relativity) isn't defined by the idea of "now", it's defined by the idea of light cones.

The only consequence of the Andromeda paradox is that the time ordering of events that have no causal relatioship (because they are space-like separated) may be different for different observers.

 

[PeterDonis]

the object must have a definite current state which must occur sooner or later in all reference frames.

This seems to me to be your key wrong assumption. The object does not have a "definite current state". It only has a sequence of states along its worldline; none of them can be uniquely labeled as its "current state".

IMO the key lesson of the Andromeda "paradox" is that simultaneity is not a good concept in relativistic physics and should be avoided. You don't need it to get correct answers; the only reason people insist on focusing on it is our intuitions, which are based on non-relativistic assumptions. The correct response is to retrain your intuitions, not to get hung up on simultaneity as a concept.

 

[durant]

This seems to me to be your key wrong assumption. The object does not have a "definite current state". It only has a sequence of states along its worldline; none of them can be uniquely labeled as its "current state".

IMO the key lesson of the Andromeda "paradox" is that simultaneity is not a good concept in relativistic physics and should be avoided. You don't need it to get correct answers; the only reason people insist on focusing on it is our intuitions, which are based on non-relativistic assumptions. The correct response is to retrain your intuitions, not to get hung up on simultaneity as a concept.

This would imply that we would see its future completely while traveling really fast towards it. Which is a nonsense.

And it would also imply the block universe view in which all of the events are already determined and 'already exist'. Putting metaphysics aside, other members here stated that the Andromeda paradox doesn't really have to do much with the block universe view, or determinism.

 

[Nugatory]

So when moving away from the object (in this case the Andromeda galaxy) the different past segments of it will become present in our plane of simultaneity, but when moving towards to it all observers will have one 'future' state of it, regardless of their speed and distance towards the galaxy. So observers with different motions and distances away from the Andromeda galaxy will have different slices of the past of the Andromeda, but all observers who move towards the galaxy will have its latest state as the present in their frame of reference.

Please correct me if I'm wrong...

(I have to point out that you haven't yet done the thing that I asked you to do back in post #5 - be as rigorous as possible about defining what you mean by "before" and "after", "past" and "future".)

Whether the motion is towards the Andromeda galaxy or away from it is irrelevant, and this really is a basic relativity of simultaneity situation. It's only startling because we've taken the very small RoS effect between two observers moving at walking speed (about 10^-9 the speed of light) relative to one another and then multiplied that effect by the enormous distance to the Andromeda galaxy to get a startling large effect.

An easy way of seeing this is to take the coordinates of the event (t=0, x=2.5 million light years; invasion fleet takes off) according to one of the two earthbound observers and use the Lorentz transforms to calculate the coordinates of this event for the other observer. Assume that the two observers are walking in opposite directions down the street, and choose the coordinates of their meeting to be (0,0) for both. You'll discover that they have a very different notion of which events in the Andromeda galaxy are simultaneous with their meeting in the middle of the street.

And what does that mean?

Mfb already answered that question back in post #2: "It just tells you that it is pointless to talk about what happens today (literally, not yesterday and not tomorrow) in other galaxies".

The only thing I'd add to his answer is that you've been tossing around the words "past" and "future" without thinking enough about what they mean. When I say "the fleet took off in the Andromeda galaxy at noon" I'm really saying "the fleet took off in the Andromeda galaxy at the same time (there's that RoS thing again!) that my wristwatch on Earth read noon". How much metaphysical significance can I attach to the fact that someone else says "when the fleet took off from the Andromeda galaxy my wristwatch didn't read noon"?

The physical meaning of the statement "X happened before Y" is that a cause at X could in principle create an effect at Y. That's a real statement about real physical effects, and viewed that way there's no paradox in the Andromeda Paradox. It's only when you start making assumptions about how comparing wristwatches on a street on Earth might correlate to events in the Andromeda galaxy that cannot even be observed for 2.5 milion years that you can find a paradox - and the resolution is to challenge those assumptions.

 

[PeterDonis]

This would imply that we would see its future completely while traveling really fast towards it.

How so? I don't follow your argument. You will see the object "aging" faster due to relativistic Doppler if you are moving really fast towards it, but when you reach it you will reach it at some particular event on its worldline; at that point you will not have observed any events to the future (on the worldline, where "future" has a well-defined meaning) of that event.

And it would also imply the block universe view in which all of the events are already determined and 'already exist'.

Again, I don't follow the logic here. How does "simultaneity is not a good concept" imply the block universe view? Same question for "the object does not have a unique current state"?

other members here stated that the Andromeda paradox doesn't really have to do much with the block universe view, or determinism.

And I agree with them; it has to do with showing that simultaneity is not a good concept in relativistic physics.

 

[mfb]

This would imply that we would see its future completely while traveling really fast towards it.

It would not. Draw a Minkowski diagram, and all paradoxes vanish.

 

[Ookke]

Relativity does not allow immediately fast information transmit and usually there is not much point in speculating about it, but regarding Andromeda paradox and its metaphysical grounds I find this somewhat benefical.

Suppose we had some way to transmit information immediately fast, perhaps by some quantum or other currently unknown effect. Observer A walks the street towards Andromeda and, in a sense, lives at the same time with Andromeda future (say, Andromeda time +1). Observer B walks the street away from Andromeda lives at the same time with Andromeda past (Andromeda time -1).

Now, as infinitely fast information tranmit is allowed, A could get information from Andromeda future, pass it to B (remember they are at the same place and time at the street) and B could transmit this information to Andromeda past, which is simultaneous with his own time. So the Andromedans could receive information from their future and, if they wish, act accordingly to prevent this predestined future.

Moreover, in observer A's frame the event "A and B meet" is simultaneous with Andromeda future. In observer B's frame, the event when A and B meet is simultaneous with Andromeda past. But from Andromedans own frame, neither one is correct, but the event when A and B meet happens at other time (Andromeda time 0). So from Andromedans point of view, no information from future to past cannot be transmitted by routing it through A and B back to Andromeda.

So my point is this. There is no logical obstacle for infinitely fast information transfer, maybe we just don't know of any such method (I don't believe such method exists, but we cannot rule it out for sure). If the relative simultaneity was real in the most concrete "really is" sense, this combined with infinitely fast information transfer would easily create impossible situations. Therefore, I personally believe that relative simultaneity is just a calculation and not physically real in the concrete sense.

Sorry about all the metaphysics.

 

[Dale]

when moving towards to it all observers will have one 'future' state of it, regardless of their speed and distance towards the galaxy. ... all observers who move towards the galaxy will have its latest state as the present in their frame of reference.

Please correct me if I'm wrong, this is what I've concluded regarding your last sentence. Thank you in advance.

No this is completely wrong. My last comment was about what you visually see. Regardless of speed you never receive light from events in your future. The word "see" means for your eyes to receive light. I hope that clarifies.