Can we use the Andromeda Paradox?

[alphawolf50]

Can we "use" the Andromeda Paradox?

Perhaps the term I should be using is "relativity of simultaneity"... anyway :)

Usually I see the Andromeda Paradox stated in terms of a stationary observer and another who is moving toward the galaxy. I did find one source that said the reverse effect is observed if you are moving away from the galaxy (you see the "past"). I was wondering:

A) Is the reverse (observing the "past") actually true?

B) It it is true, then could we use it to observe astronomic events that we see, but "missed". For example, if we see evidence that a star that had gone supernova (or maybe collapsed into a black hole), but we missed the actual event -- could we move one of our telescopes away from this star, and get a second chance at observing the actual event?

 

[Hurkyl]

At large distances, there's a big difference between "what events are happening now?", and "what events am I seeing happen?", because of the time it takes for light to travel from there to here.

If I'm walking by you, and we both use orthonormal coordinate charts as usual, then we would disagree on what events are happening right now in Andromeda. However, we would both agree on which events we can actually see through our telescopes.

 

[alphawolf50]

Thanks, Hurkyl. So basically this paradox requires you to have some manner of instantaneous "remote viewing" of Andromeda, rather than relying on light to travel across the universe and let you know what has happened?

 

[Drakkith]

You could not move further away from the star to see into the past, because you cannot move your telescope backwards faster than the speed of light.

 

[alphawolf50]

Hi Drakkith,

Technically, everything we see with a telescope is "the past", specifically because the speed of light is finite :) But, yes, I believe you are correct if you're saying we can't see *further* into the past by moving our telescope away. However, in the context of the Andromeda paradox, I believe moving away from Andromeda would shift your plane of simultaneity toward the "past" relative to a stationary observer, even if we can't actually observe the effect without the imaginary instantaneous "remote viewing" ability.

As sort of an extension of the paradox, I'm imagining two people standing on a large turntable (no telescopes this time, just the "remote viewing"). Alice stands on a pedestal in the middle which does not rotate, and Bob stands on a pedestal on the outer edge which rotates the opposite direction of the turntable, allowing him to always face the same direction as Alice. As the turntable turns clockwise, I imagine that when Bob passes behind Alice, his plane of simultaneity starts shifting toward the Andromeda "future", reaching a maximum at the leftmost point of the ring. Then it shifts back toward Alice's "present" as moves to the position directly in front of her. Has he begins moving from the front to the right, his plane of simultaneity should shift toward Alice's "past", reaching a maximum at the spot directly to the right of Alice. I imagine you could plot this as a sine wave, showing Bob's plane of simultaneity relative to Alice's. Anytime Bob's plane of simultaneity is shifting toward the "past", it seems he would "observe" time to move backward in Andromeda. In effect, he would see some events at least twice -- once forward and once in reverse. Any thoughts on that?

 

[JesseM]

As sort of an extension of the paradox, I'm imagining two people standing on a large turntable (no telescopes this time, just the "remote viewing"). Alice stands on a pedestal in the middle which does not rotate, and Bob stands on a pedestal on the outer edge which rotates the opposite direction of the turntable, allowing him to always face the same direction as Alice. As the turntable turns clockwise, I imagine that when Bob passes behind Alice, his plane of simultaneity starts shifting toward the Andromeda "future", reaching a maximum at the leftmost point of the ring. Then it shifts back toward Alice's "present" as moves to the position directly in front of her. Has he begins moving from the front to the right, his plane of simultaneity should shift toward Alice's "past", reaching a maximum at the spot directly to the right of Alice. I imagine you could plot this as a sine wave, showing Bob's plane of simultaneity relative to Alice's. Anytime Bob's plane of simultaneity is shifting toward the "past", it seems he would "observe" time to move backward in Andromeda. In effect, he would see some events at least twice -- once forward and once in reverse. Any thoughts on that?

It's not like planes of simultaneity are physical entities that are intrinsically associated with a given observer--a plane of simultaneity is a human convention about which set of events we choose to label with the same time-coordinate in our chosen coordinate system. Of course in SR there is a special collection of coordinate systems which we call "inertial" which have the property that each one is moving at constant coordinate speed relative to every other one, and the laws of physics obey the same equations in each of them, whereas in non-inertial coordinate systems the equations of the laws of physics would have a different form. For an accelerating observer like Bob, one could design a variety of equally valid non-inertial coordinate systems where Bob is at rest, with different simultaneity conventions. It's only if you choose to design the non-inertial coordinate system in such a way that its definition of simultaneity at each point on Bob's worldline matches the definition used in the inertial frame where Bob is instantaneously at rest at that point that what you say would be true, but there's no compelling physical reason why we must prefer that non-inertial coordinate system over other possible non-inertial coordinate systems.

 

[alphawolf50]

Hi JesseM,

That makes sense. I had forgotten about the inertial/non-inertial reference frames. I just want to paraphrase what you said to make sure I actually understood :)

Since Bob is accelerating, his frame of reference is non-inertial. But if we were to take snapshots of the universe at say every 90 degrees of rotation, we could declare in each snapshot that Bob's reference frame is inertial by saying something like "Bob is at rest, and the instantaneous velocities of Andromeda and Alice are parallel to the tangent of the circle at Bob's present location". If we then compared the planes of simultaneity of each snapshot as experienced by Bob and Alice, distant events would appear at different locations of the time coordinate system for each snapshot. At 0 and 180 degrees (front and behind), Bob and Alice would agree on the simultaneity of events in Andromeda, but at 90 and 270 degrees, they would argue over what is happening "right now".

Did I get that right?

 

[pervect]

As Jesse mentioned, the notion of "simultaneity" is observer dependent. The notion of cause and effect, however, isn't observer dependent. So, while one may be used to using "time coordinates" as a way to determine cause and effect, this approach does not generalize so well to relativity. From my POV, the andromeda paradox is not a paradox, it's just suggesting that we approach the issue of causality differently. The basic idea is simple - effects must lie within the light cone of the cause, i.e. a light-signal must be able to travel from the "cause" event to the "effect" event.

 

[JesseM]

Since Bob is accelerating, his frame of reference is non-inertial. But if we were to take snapshots of the universe at say every 90 degrees of rotation,

But I'd think "snapshot of the universe" would mean "snapshot of everything happening in the universe at a single moment", but of course if simultaneity is relative there is no frame-independent way to define "single moment".

we could declare in each snapshot that Bob's reference frame is inertial by saying something like "Bob is at rest, and the instantaneous velocities of Andromeda and Alice are parallel to the tangent of the circle at Bob's present location".

Don't understand this sentence. What does it mean to "declare in each snapshot that Bob's reference frame is inertial"? And what "circle" are you talking about?

If we then compared the planes of simultaneity of each snapshot as experienced by Bob and Alice,

How can planes of simultaneity exist in a snapshot of a single moment? Are you talking about a "snapshot" of spacetime rather than everything in space at a single moment, or some third alternative?

 

[alphawolf50]

But I'd think "snapshot of the universe" would mean "snapshot of everything happening in the universe at a single moment", but of course if simultaneity is relative there is no frame-independent way to define "single moment".

Would it work better if I said "Bob and Alice each take a snapshot of spacetime from their unique frames of reference" ?

Don't understand this sentence. What does it mean to "declare in each snapshot that Bob's reference frame is inertial"? And what "circle" are you talking about?

I was attempting to rephrase what you said about designing coordinate systems where Bob is at rest, but apparently it was a poor rephrase :) The circle I'm talking about is Bob's path around the turntable as viewed by Alice. She would normally describe Bob's instantaneous velocity as a vector in the direction of the tangent of Bob's location on this circle. But, if Bob views himself as "at rest", then he must describe Alice and Andromeda's motion as being in the opposite direction of that tangent (I think).

How can planes of simultaneity exist in a snapshot of a single moment? Are you talking about a "snapshot" of spacetime rather than everything in space at a single moment, or some third alternative?

I think I mean snapshots of spacetime -- but I'll admit my question is seeming more "over my head" than I originally anticipated.

 

[JesseM]

Would it work better if I said "Bob and Alice each take a snapshot of spacetime from their unique frames of reference" ?

So you mean something like a spacetime diagram drawn from the perspective of two different frames? But If Bob is moving non-inertially, what do you mean when you talk about Bob's "unique frame of reference"? Do you mean his unique inertial rest frame at a single point on his worldline, even though he doesn't remain at rest in that frame?

I was attempting to rephrase what you said about designing coordinate systems where Bob is at rest, but apparently it was a poor rephrase :) The circle I'm talking about is Bob's path around the turntable as viewed by Alice. She would normally describe Bob's instantaneous velocity as a vector in the direction of the tangent of Bob's location on this circle. But, if Bob views himself as "at rest", then he must describe Alice and Andromeda's motion as being in the opposite direction of that tangent (I think).

In the inertial frame where he's at rest at that instant, yes.