Andromeda paradox

[somanystylez]

Hi, I've been reading recently on the, let's call it famous, Andromeda paradox stated by Riejdtnik/Putnam. So I understand what happens, or why the motion affects plane of simultaneity, but I don't understand why is there such a big time lapse between what's happening on the Andromeda galaxy right now according to the observers. It is clearly stated that because it is distant, the lapse between events is huge (about a day if they are walking slowly). So when we compare it to the train experiment, when the difference is only a few seconds, it seem confusing. What role does the distance of event to the observer play here, and how does it affect the judgement of the temporal order of events?

[xyzt]

Hi, I've been reading recently on the, let's call it famous, Andromeda paradox stated by Riejdtnik/Putnam. So I understand what happens, or why the motion affects plane of simultaneity, but I don't understand why is there such a big time lapse between what's happening on the Andromeda galaxy right now according to the observers. It is clearly stated that because it is distant, the lapse between events is huge (about a day if they are walking slowly). So when we compare it to the train experiment, when the difference is only a few seconds, it seem confusing. What role does the distance of event to the observer play here, and how does it affect the judgement of the temporal order of events?

Here is a very good explanation as to why the effect depends on the distance to Andromeda.

Basically, it all stems from the Lorentz transform for time:

 

[math]t_a=\gamma(t_e+vx_e/c^2)[/math]

 

Above, [math]t_e[/math] represents "when" the Andromeda effect happened as measured in the Earth frame and [math]x_e[/math] represents "where" the Andromeda effect happened as measured in the Earth frame.

[math]t_a[/math] represents "when" the Andromeda effect happened as measured in the Andromeda frame.

[math]v[/math] represents the relative speed between the Earth and Andromeda.

 

In general, [math]vx_e<<c^2[/math] but, for cosmological distances, like in the case of Earth-Andromeda, [math]x_e[/math] becomes large enough such that [math]vx_e[/math] is comparable with [math]c^2[/math] such that the "advancement effect" [math]vx_e/c^2[/math] is no longer negligible.

The reason that there was (and still is) so much controversy around the effect in the physics and philosophy circles is that the effect isn't measurable.

Edited June 7, 2013 by xyzt

[Iggy]

Above, [math]t_e[/math] represents "when" the Andromeda effect happened as measured in the Earth frame and [math]x_e[/math] represents "where" the Andromeda effect happened as measured in the Earth frame.

[math]t_a[/math] represents "when" the Andromeda effect happened as measured in the Andromeda frame.

[math]v[/math] represents the relative speed between the Earth and Andromeda.

 

Earth and Andromeda are in the same frame for the purpose of this thought experiment. They have no relative velocity.

 

The two frames belong to two earthlings who have a small relative velocity. V, in that equation, represents their relative speed. Like Somanystylez says, walking speed.

 

---

 

 

Hi, I've been reading recently on the, let's call it famous, Andromeda paradox stated by Riejdtnik/Putnam. So I understand what happens, or why the motion affects plane of simultaneity, but I don't understand why is there such a big time lapse between what's happening on the Andromeda galaxy right now according to the observers. It is clearly stated that because it is distant, the lapse between events is huge (about a day if they are walking slowly). So when we compare it to the train experiment, when the difference is only a few seconds, it seem confusing. What role does the distance of event to the observer play here, and how does it affect the judgement of the temporal order of events?

 

All of the events that are simultaneous for the one fella, and all the events that are simultaneous for the second fella, make two lines of a triangle in sapcetime. It's like the image on wikipedia. The further away something is, the greater the distance between the lines.

 

It might be intuitive that two people right next to each other with a small velocity won't disagree much at all about the present time of a clock that is right next to them. The further away the clock gets, the more they disagree.

[xyzt]

Earth and Andromeda are in the same frame for the purpose of this thought experiment. They have no relative velocity.

 

The two frames belong to two earthlings who have a small relative velocity. V, in that equation, represents their relative speed. Like Somanystylez says, walking speed

...or the earthling is stationary on the Earth and Andromeda is moving away from the Earth. This is exactly what the Lorentz transform I showed reflects. I am quite sure that you know that motion is relative.

[Iggy]

...or the earthling is stationary on the Earth and Andromeda is moving away from the Earth.

 

But, that isn't the Andromeda paradox. There are two observers on earth who have a small relative velocity. The link you gave, which is pretty terse but pretty good, says the following,

 

Assume, for simplicity, that the galaxy and the Earth remain momentarily at this fixed distance, with no relative motion.

[xyzt]

But, that isn't the Andromeda paradox. There are two observers on earth who have a small relative velocity. The link you gave, which is pretty terse but pretty good, says the following,

You realize that the effect is exactly the same, don't you?

[Iggy]

You realize that the effect is exactly the same, don't you?

Not at all.

 

The equation you gave works like this...

 

[math]t = \frac{t'+vx/c^2}{\sqrt{1-v^2/c^2}}[/math]

 

where,

• t is the time between present instants at a distance of x by the stationary earth observer
• x is the distance to the Andromeda galaxy (2.3 x 10²² meters)
• v is the velocity between the stationary earth observer and the earth observer who is walking past him toward the Andromeda galaxy (1.3 m/s)
• t' is zero (the present instant as defined by the walking earth observer)

 

[math]t = \frac{0+(1.3)(2.3 \times 10^{22})/299792458^2}{\sqrt{1-1.3^2/(299792458)^2}}[/math]

 

[math]t = 332682 \ \mbox{seconds} = 3.8 \ days[/math]

 

3.8 days separate the present instant in the Andromeda galaxy between two observers on earth who have a relative walking speed. That is the Andromeda paradox.

 

The Andromeda galaxy is approaching our solar system at 130 km/s. When you say "v represents the relative speed between the Earth and Andromeda" that is simply untrue. Plugging 130 km/s into the above equation would give the wrong answer. That number doesn't enter into the above equation, or this scenario, or the Andromeda paradox.

Edited June 7, 2013 by Iggy

[D H]

xyzt, Iggy is right. You should retract your downvote on Iggy's post.

 

The Andromeda paradox has absolutely nothing to do with the relative velocity between the Earth and the Andromeda galaxy. It is about how the planes of simultaneity for two different observers can differ significant at large distances even if the relative velocity between the two observers is small.

 

 

Going back to the original post,

Hi, I've been reading recently on the, let's call it famous, Andromeda paradox stated by Riejdtnik/Putnam. So I understand what happens, or why the motion affects plane of simultaneity, but I don't understand why is there such a big time lapse between what's happening on the Andromeda galaxy right now according to the observers. It is clearly stated that because it is distant, the lapse between events is huge (about a day if they are walking slowly). So when we compare it to the train experiment, when the difference is only a few seconds, it seem confusing. What role does the distance of event to the observer play here, and how does it affect the judgement of the temporal order of events?

The two observers' planes of simultaneity are tilted with respect to one another. The angle is small for non-relativistic velocities. Given that we're talking walking speed, the angle is very very small. However, at a far enough distance, this small angle will still result in large separations.

 

What this means is that it doesn't make sense to talk about a universal now. There is no such thing. Your concept of "now", your plane of simultaneity, is not necessarily the same as mine. It has absolute no meaning with regard to free will, metaphysics, or any of that other philosophical excrement (see the ongoing thread "Is Philosophy crap?")

[Iggy]

you forgot to square the speed of light:

 

Typo. I edited the post.

[Iggy]

Perhaps it would help if you could link to an example that doesn't use Wolfram's unorthodox approach?

It isn't the best, but there is really nothing unusual about Wolfram's explanation. It doesn't make the mistake of thinking v is the velocity between earth and Andromeda. And, it does have two observers, in so far as this is two observers:

To a stationary observer on Earth, the Supreme Galactic Council on Andromeda might be engaged in a debate on whether to attack Earth, whereas to an observer strolling at a leisurely pace of 2 feet per second, the Intergalactic Battle Fleet has already been launched toward Earth.

 

-The Andromeda Paradox

Just had to give Wolfram their props

[swansont]

!

Moderator Note

 

I have split off most of the disagreement on the interpretation of the paradox

http://www.scienceforums.net/topic/75581-disagreement-on-the-interpretation-of-the-andromeda-paradox/

 

This thread is for discussion of the scenario in the OP, wherein there is no relative motion of earth and the Andromeda galaxy.

 

[Delta1212]

It isn't the best, but there is really nothing unusual about Wolfram's explanation. It doesn't make the mistake of thinking v is the velocity between earth and Andromeda. And, it does have two observers, in so far as this is two observers:

 

To a stationary observer on Earth, the Supreme Galactic Council on Andromeda might be engaged in a debate on whether to attack Earth, whereas to an observer strolling at a leisurely pace of 2 feet per second, the Intergalactic Battle Fleet has already been launched toward Earth.

 

-The Andromeda Paradox

Just had to give Wolfram their props

I figured as much but thought I'd ask to be sure.

[hypervalent_iodine]

!

Moderator Note

xyzt,

It would be much appreciated if you could please stay on topic and, for what seems like the millionth time, your attitude is growing tiresome. It stops. Now.

[D H]

So, getting back on topic,

From Wikipedia: (last line bolded mine)

Roger Penrose^[4] advanced a form of this argument that has been called the Andromeda paradox in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. If this occurs, it would have dramatic effects on our understanding of time. Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda Galaxy. As Penrose put it:
"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'?"<sup>[5]

Literally...that was the point of the Andromeda Paradox</sup>

The above post is from that silly thread that was split off from this one.

 

I quoted it here in this thread because the quoted post, rather than all of the above nonsense, is the Andromeda Paradox.

So, what does the Andromeda Paradox add to the age-old and never ending philosophical debate on determinism, free will, and all that? Nothing. At least that is my opinion. Per the physics as we know it, the only events I can see / observe / measure are those that are on or inside my past light cone. The only events I can somehow influence are those that are on or inside my future light cone. My "now" lies in that no-mans land of uninfluenceable, unobservable events that lies between my past and future light cones. There is no way I, a mere mortal who is subject to the laws of physics, can know of the existence of that Andromedan invasion fleet.

 

I could know of that fleet if instead I was an omniscient, omnipresent, supernatural being. Posit the Andromedan invasion fleet mandates supernatural knowledge, particularly omniscience and omnipresence. The Andromeda Paradox is just the age-old debate on determinism, free will, and all that writ relativistically.

Edited June 9, 2013 by D H

[md65536]

So, what does the Andromeda Paradox add to the age-old and never ending philosophical debate on determinism, free will, and all that? Nothing. At least that is my opinion. Per the physics as we know it, the only events I can see / observe / measure are those that are on or inside my past light cone. The only events I can somehow influence are those that are on or inside my future light cone. My "now" lies in that no-mans land of uninfluenceable, unobservable events that lies between my past and future light cones. There is no way I, a mere mortal who is subject to the laws of physics, can know of the existence of that Andromedan invasion fleet.

In other words, in theory the simultaneity of events that are not causally related, is inconsequential.

 

In the Wolfram link above, they say "this paradox has stimulated a great deal of controversy, even leading some to doubt the metaphysical underpinnings of the theory of relativity." I think that one would have to attach some extra meaning to the simultaneity of unconnected events, in order to have a metaphysical problem with relativity. There's no accepted theoretical possible consequence to whether for an Earthling it's "now" Tuesday or Wednesday in Andromeda depending on which way you're walking. I don't see how it could be a problem, without consequences.

 

The paradox only exists assuming that standard simultaneity is non-conventional. Related topics:

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

http://plato.stanford.edu/entries/spacetime-convensimul/

 

There would be no paradox if the clocks were set using radar time (source: something I read recently, I could try to dig it up).

 

I see no problem with the "paradox", because regardless of whether remote simultaneity is physically unique, it seems to make no theoretical measurable difference to anyone, if the two Earthlings disagree on what day it is in Andromeda. In other words, it's debatable whether the paradoxical effect is even "real" in any way, but if it is, there's no accepted theoretical effect that says it could matter.

Edited June 16, 2013 by md65536

[JVNY]

 

So, what does the Andromeda Paradox add to the age-old and never ending philosophical debate on determinism, free will, and all that? Nothing. At least that is my opinion. Per the physics as we know it, the only events I can see / observe / measure are those that are on or inside my past light cone. The only events I can somehow influence are those that are on or inside my future light cone. My "now" lies in that no-mans land of uninfluenceable, unobservable events that lies between my past and future light cones.

 

Here is a different version of the paradox that may illustrate DH's view.

 

If an earthling's acceleration to a high velocity toward Andromeda causes Andromeda's distance to length contract and its clock to advance (in both cases in the earthling frame), then a subsequent earthling deceleration should cause Andromeda's remaining distance (after reduction for the earthling's actual travel during the acceleration and deceleration) to length expand backward, and its clock to regress. But you can't turn back time by decelerating, and so you cannot always reconcile the earthling and Andromeda reference frames.

 

Consider a rocket and a probe that are at rest with respect to each other 100 apart (example uses consistent unitless dimensions, such as years, light years, and light years per year^2). The probe is programmed to self destruct at probe time Tp=99.8. The rocket and probe have clocks set at the same time 0 in their common rest frame. The rocket then accelerates at proper rate 300 for probe time Tp=0.07, then decelerates at the same rate back to rest over Tp=0.07. In the inertial probe frame, very little happened. The rocket began and ended at rest, and it traveled probe frame distance Xp of only Xp=0.133, in only Tp=0.14 (all calculations are based on the relativistic rocket formulas from http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html). The probe is nowhere near exploding.

 

In the rocket frame, the acceleration takes rocket time Tr=0.0125 (significantly less than Tp=0.07 because of time dilation). If the distance to the probe contracts and the probe clock advances per the formulas above, then the probe clock reads Tp=99.82 to the rocket at the end of the acceleration. During the rocket's acceleration (specifically, at Tr=0.0121), the probe reaches its programmed destruction time and blows up in the rocket's frame -- and then for an additional Tp=0.02 scatters some debris (but not the core) in all directions (including some toward the rocket), and sends a flash of light from the explosion in all directions (including toward the rocket).

 

Next, the rocket decelerates in its frame over Tr=0.0125, and ends at rest only 0.133 closer to the probe than at the start. What happens in the rocket's frame to the flash of light from the explosion? What happens to the debris? Does the probe reassemble and race backward during the deceleration? Debris that flew forward cannot distance expand backward to meet the core, because the expansion should be proportional (like the contraction). The light flash that went forward also cannot distance expand backward to disappear into the core for the same reason. Yet the rocket has returned to rest and rejoined the probe in a common frame, and the probe is unexploded in that frame when the rocket has returned to rest in that frame.