Disagreement on the interpretation of the Andromeda paradox

[xyzt]

 

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.

This is the problem with your insistence of "plugging in numbers" instead of using symbolic calculations. I defined the variables in my post quite clearly, [math]v[/math] is the speed between the Earth and Andromeda (or any other galaxy). assuming that the galaxy moves away from the Earth, you get the same exact effect with the earthling fixed wrt. the Earth. Both scenarios are a direct consequence of the same Lorentz transform , [math]t'=\gamma(t+vx/c^2)[/math]. Like I said, you realize that motion is relative, right? The fact that Andromeda is moving towards the Earth (with a higher speed than "pacing") is also inconsequential, just replace it with a galaxy that is moving away from the Earth, you will get a much stronger effect than the one with the two earthlings as in the original paradox. Both scenarios have the same exact (simple) explanation. As long as I defined the variables correctly (and I did), the example stands. The OP question was "why does the distance play a role?". I explained that.

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}{\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.

This is clearly incorrect due to a basic mistake in your arithmetic, you forgot to square the speed of light:

 

 

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

 

The result is very far off from 3.8 days, it is more like 1ms. Ain't arithmetic a bitch?

Edited June 7, 2013 by xyzt

[D H]

I defined the variables in my post quite clearly, [math]v[/math] is the speed between the Earth and Andromeda (or any other galaxy).

 

This is not the Andromeda paradox.

 

 

assuming that the galaxy moves away from the Earth, you get the same exact effect with the earthling fixed wrt. the Earth.

 

No, you don't. The Andromeda paradox is about two observers who are co-located but are moving with respect to one another. It is a question about the relativity of simultaneity.

 

 

This is clearly incorrect due to a basic mistake in your arithmetic, you forgot to square the speed of light:

 

 

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

 

The result is very far off from 3.8 days, it is more like 1ms. Ain't arithmetic a bitch?

 

 

Iggy posted the equation wrong but has the results correct. It's clearly a typo. Here's the calculation:

 

http://www.wolframalpha.com/input/?i=%28%282.3e22+m%29*%281.3+m%2Fs%29%2F%28speed+of+light%29%5E2%29%2Fsqrt%281-%28%281.3+m%2Fs%29%2F%28speed+of+light%29%29%5E2%29

[xyzt]

 

This is not the Andromeda paradox.

 

 

 

No, you don't. The Andromeda paradox is about two observers who are co-located but are moving with respect to one another. It is a question about the relativity of simultaneity.

So is the scenario I pointed out from the Wolfram page in post 2:

 

"Suppose an Earthling is slowly strolling in the direction of Andromeda.

Then events on Andromeda that occur, in concept, simultaneously in the

Earthling's frame of reference, depend rather sensitively on his or her

walking speed. Roughly, an increase in walking speed

of one foot per second corresponds to a simultaneous event occurring on

Andromeda about an Earth day later! This can be deduced from the

Lorentz-transformation equation , where is the time advance on Andromeda, which can be considered simultaneous with an event on Earth occurring at ,

most conveniently set equal to 0. Note that the observer on Earth can

only "infer" what is happening simultaneously on Andromeda. He would not

actually "see" what is occurring until 2.5 million years later."

 

Once again, I do hope that you realize that motion is relative: earthling fixed on Earth moving wrt Andromeda is the same thing as earthling moving wrt. Earth fixed wrt Andromeda.

The amusing thing is that you insist on the latter, when, in fact, Andromeda is moving wrt the Earth.

Edited June 7, 2013 by xyzt

[Delta1212]

So is the scenario I pointed out from the Wolfram page in post 2:

 

"Suppose an Earthling is slowly strolling in the direction of Andromeda.

Then events on Andromeda that occur, in concept, simultaneously in the

Earthling's frame of reference, depend rather sensitively on his or her

walking speed. Roughly, an increase in walking speed

of one foot per second corresponds to a simultaneous event occurring on

Andromeda about an Earth day later! This can be deduced from the

Lorentz-transformation equation , where is the time advance on Andromeda, which can be considered simultaneous with an event on Earth occurring at ,

most conveniently set equal to 0. Note that the observer on Earth can

only "infer" what is happening simultaneously on Andromeda. He would not

actually "see" what is occurring until 2.5 million years later."

 

Once again, I do hope that you realize that motion is relative: earthling fixed on Earth moving wrt Andromeda is the same thing as earthling moving wrt. Earth fixed wrt Andromeda.

The amusing thing is that you insist on the latter, when, in fact, Andromeda is moving wrt the Earth.

The point that is being made is that the Andromeda paradox is about the comparatively small difference in velocity of co-located observers creating a great difference in what time can be considered simultaneous when comparing events at a very large distance. You could replace Andromeda with a galaxy that is at rest with regard to Earth at the same distance and you would still observe the Andromeda paradox in full effect. It's not about the relative motion of Andromeda with the observers; it's about the relative motion between the observers themselves.

[xyzt]

The point that is being made is that the Andromeda paradox is about the comparatively small difference in velocity of co-located observers creating a great difference in what time can be considered simultaneous when comparing events at a very large distance. You could replace Andromeda with a galaxy that is at rest with regard to Earth at the same distance and you would still observe the Andromeda paradox in full effect. It's not about the relative motion of Andromeda with the observers; it's about the relative motion between the observers themselves.

You can have one description or you can also go by the Wolfram description, they are both valid. I cited the Wolfram page and I explained the Wolfram page <shrug>

[Delta1212]

You can have one description or you can also go by the Wolfram description, they are both valid. I cited the Wolfram page and I explained the Wolfram page <shrug>

Yes, but in that explanation, it says to assume that the Earth and Andromeda remain at a fixed distance with no relative motion. You said that the v in the equation is the relative velocity between Earth and Andromeda. It is actually the relative velocity between observers co-located on Earth.

 

Per the explanation on the page you were citing.

Edited June 7, 2013 by Delta1212

[xyzt]

Yes, but in that explanation, it says to assume that the Earth and Andromeda remain at a fixed distance with no relative motion. You said that the v in the equation is the relative velocity between Earth and Andromeda. It is actually the relative velocity between observers co-located on Earth.

 

Per the explanation on the page you were citing.

You do understand that motion is relative, right? You do realize that earthling fixed on Earth moving wrt Andromeda is the same thing as earthling moving wrt. Earth fixed wrt Andromeda.

The amusing thing is that you insist on the latter, when, in fact, Andromeda is moving wrt the Earth.

Edited June 7, 2013 by xyzt

[Delta1212]

You do understand that motion is relative, right? You do realize that earthling fixed on Earth moving wrt Andromeda is the same thing as earthling moving wrt. Earth fixed wrt Andromeda.

The amusing thing is that you insist on the latter, when, in fact, Andromeda is moving wrt the Earth.

Except, again, taken straight from the page you cited, it's being assumed that Earth and Andromeda are fixed with regard to each other. Nobody is fixing an observer with regard to Andromeda and having them move with Earth. The relative motion between Earth and Andromeda is just being ignored because it isn't the cause of the Andromeda paradox. It's the, comparatively minor, relative motion between the two observers, who are both on Earth, not moving with respect to Earth, and who will see a major difference between what events on Earth are simultaneous to what events on Andromeda.

 

It says this in the Wolfram description that you linked to. The v in the equation is the relative velocity between the two observers, not the relative velocity between Earth and Andromeda, as you stated in your initial explanation.

Edited June 7, 2013 by Delta1212

[xyzt]

Except, again, taken straight from the page you cited, it's being assumed that Earth and Andromeda are fixed with regard to each other.

If you continue to take things straight, without making the effort of understanding, you will never learn. Your choice.

 

It says this in the Wolfram description that you linked to. The v in the equation is the relative velocity between the two observers, not the relative velocity between Earth and Andromeda, as you stated in your initial explanation.

In relativity , motion is ... relative.

[J.C.MacSwell]

If you continue to take things straight, without making the effort of understanding, you will never learn. Your choice.

 

In relativity , motion is ... relative.

Sorry, xyzt. You may be very clear on your understanding, and in that you may be correct, but the paradox is not about the relative speeds of Earth and Andromeda. It is about the distance between them, and how the subtle difference in walking speed of the Earthly observer, in the direction of Andromeda, having a very significant effect on what day it is on Andromeda when he/she considers his/her now.

 

Try not to focus on the simplification "assume Earth and Andromeda are at rest/in the same frame". It is unfortunate that it was used in one example, as it is irrelevant and unnecessary to explain the paradox.

Edited June 8, 2013 by J.C.MacSwell

[xyzt]

Sorry, xyzt. You may be very clear on your understanding, and in that you may be correct, but the paradox is not about the relative speeds of Earth and Andromeda.

You do understand that motion is relative, right? You do realize that earthling fixed on Earth moving wrt Andromeda is the same thing as earthling moving wrt. Earth fixed wrt Andromeda.

The amusing thing is that you insist on the latter, when, in fact, Andromeda is moving wrt the Earth.

[Delta1212]

If you continue to take things straight, without making the effort of understanding, you will never learn. Your choice.

 

 

In relativity , motion is ... relative.

You can keep repeating that, but it doesn't make you less mistaken in your assumption of what the paradox is about. Yes, all motion is relative, but the relative motion between Earth and Andromeda is irrelevant to the different between the "nows" of two observers moving with respect to one another on Earth. Neither is at rest with respect to Andromeda (unless Andromeda is treated as being at rest with respect to Earth, as was the case in the example that you linked to).

 

If you want to go the route of "motion is relative" then yes, we all understand that you can say that Andromeda is moving toward the Earth, or Earth is moving toward Andromeda, but if two observers are just sitting on Earth, the Andromeda galaxy is not moving faster towards one than the other. If one of those two starts moving toward Andromeda, then, yes, you could say that Andromeda is moving slightly faster toward one than the other, just as easily as saying that one is moving slightly faster toward Andromeda than the other.

 

But it is the relative difference between these velocities that causes the Andromeda paradox, not Andromeda's net velocity. The relative velocities being compared are between two observers that are very close and have a very small difference in speed, and the difference in what they consider to be simultaneous with "now" over very large distances, such as that of the distance between Earth and Andromeda.

 

Andromeda's relative velocity is irrelevant. Only the very small difference between the velocities of the observers is what is being considered for this particular effect. It even says that in the explanation that you linked to, a fact which you have not addressed.

[xyzt]

 

 

Andromeda's relative velocity is irrelevant. Only the very small difference between the velocities of the observers is what is being considered for this particular effect. It even says that in the explanation that you linked to, a fact which you have not addressed.

....because you get the same exact effect if you consider the earthling observer co-moving with the Earth , while the Earth is moving wrt. Andromeda. Sure , Andromeda's speed wrt the Earth is bigger than the pacing speed of the earthling, I already mentioned that but that is irrelevant. This is basic relativity....

Edited June 8, 2013 by xyzt

[Delta1212]

 

....because you get the same exact effect if you consider the earthling observer co-moving with the Earth , while the Earth is moving wrt. Andromeda. Sure , Andromeda's speed wrt the Earth is bigger than the pacing speed of the earthling, I already mentioned that but that is irrelevant. This is basic relativity....

But both observers are on Earth. Or are you just using 'earthling observer' to mean the one that is standing still (with respect to Earth) rather than the one walking past him?

[xyzt]

But both observers are on Earth. Or are you just using 'earthling observer' to mean the one that is standing still (with respect to Earth) rather than the one walking past him?

There is no two observers in the example in post 2, there is only one observer. You can stop negging my posts, if you do not understand the basics, just ask.

[ACG52]

The amusing thing is that you insist on the latter, when, in fact, Andromeda is moving wrt the Earth

 

Everyone here knows that's the fact. For the purposes of the op, there's a simplified assumption, that applies not to the real world, but only for purposes of the discussion.

[Delta1212]

 

There is no two observers in the example in post 2, there is only one observer. You can stop negging my posts, if you do not understand the basics, just ask.

The Andromeda paradox is about the difference in what is considered to be "now" at a distant location between two co-located observers with small relative motion. There is no example of the Andromeda paradox that only has one observer.

[xyzt]

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.

Quite a few posters have missed the fact that the above is a variant of the "Andromeda paradox", one with only one observer, NOT two. Nevertheless, the "paradox" works just the same and the above explanation is perfectly correct.

 

Now, if one insists on having two observers, the math gets just a tad more complicated but the outcome is just the same.

Say that two earthlings observe the event [math](x_a,t_a)[/math] on Andromeda. The earthlings are in relative motion with speed [math]v[/math] along what they call the [math]x-axis[/math]

 

The observers have speeds [math]v_1=0[/math] respectively [math]v_2=v[/math] wrt Andromeda, so:

 

[math]t_{e2}-t_{e1}=\gamma(t_a+v_2 x_a/c^2)-\gamma(t_a+v_1 x_a/c^2)=\gamma vx_a/c^2[/math]

Everyone here knows that's the fact. For the purposes of the op, there's a simplified assumption, that applies not to the real world, but only for purposes of the discussion.

So, I solved a slightly different scenario, people familiar with relativity should have had no difficulty in realizing that the scenarios are equivalent. Instead, they posted repeatedly stuff that reflects their lack of understanding .

The Andromeda paradox is about the difference in what is considered to be "now" at a distant location between two co-located observers with small relative motion. There is no example of the Andromeda paradox that only has one observer.

Actually, this is false, the Wolfram page has only one observer. You can stop negging my posts now, I am simply explaining away your misconceptions.

Edited June 8, 2013 by xyzt

[Delta1212]

xyzt, what is it, exactly, that you think the Andromeda paradox states?

[xyzt]

xyzt, what is it, exactly, that you think the Andromeda paradox states?

Why don't you make the effort to read the post just above yours? Then, you'll find out.

[Delta1212]

Why don't you make the effort to read the post just above yours? Then, you'll find out.

Ok, so what you seem to have demonstrated is that a moment in Andromeda that is observed to be simultaneous with "now" on Earth will not be observed to be simultaneous with the same time on Earth when observed from Andromeda's frame?

[xyzt]

Ok, so what you seem to have demonstrated is that a moment in Andromeda that is observed to be simultaneous with "now" on Earth will not be observed to be simultaneous with the same time on Earth when observed from Andromeda's frame?

Aren't these the exact words on the Wolfram website?

[D H]

Aren't these the exact words on the Wolfram website?

 

No.

 

You have hijacked this thread with your complete misunderstanding of the Andromeda paradox. It has nothing, absolutely nothing, to do with the relative velocity between the Andromeda galaxy and the Earth.

[xyzt]

No.

 

You have hijacked this thread with your complete misunderstanding of the Andromeda paradox. It has nothing, absolutely nothing, to do with the relative velocity between the Andromeda galaxy and the Earth.

I understand that dogma is difficult to overcome, I deal with this sort of attitude all the time. The people at Wolfram, would disagree with your statement. For people who are not that fixated in their thinking, I made post 27, perhaps you could take some time and read it.

Edited June 8, 2013 by xyzt

[Delta1212]

Aren't these the exact words on the Wolfram website?

No. What you're describing is true, and is down to the same effect as the Andromeda paradox, but the paradox is a very specific case of this effect. I do think I may have found the bit on the Wolfram site that is responsible for the confusion, however.

 

"[math]t_a[/math] is the time advance on Andromeda, which can be considered simultaneous with an event on Earth occurring at , most conveniently set equal to 0."

 

This looks like it might be saying that [math]t_a[/math] is the difference between the time of the as measured by the Earth and that observed on Andromeda. It's not, however, the advanced time on Andromeda as observed by Andromeda but rather the advance of time on Andromeda as observed by the other, walking, observer on Earth.

 

That is, if [math]t_e[/math] is set to 0, then a velocity of 0 (the observer on Earth at rest) will give you a [math]t_a[/math] of 0. That is Andromeda time "0" representing the moment that the stationary Earth observer beloved is simultaneous to Earth's "now."

 

If you plug in the velocity of a person walking right past this stationary Earth observer, the velocity will be that of the person working, and [math]t_a[/math] will give you the time on Andromeda that this walking observer measures to be simultaneous to Earth's "now," a time that will be in advance of the time that the stationary observer measures.

 

The Andromeda paradox is a demonstration of the fact that observers that are very close together moving at only slightly different speeds can have a significant difference in the time they measure to be simultaneous with "now" at very large distances. So that someone walking past you in the street may believe that the events going on "now" in Andromeda are days off from the events that you believe are going on in Andromeda "now" (retrospectively since we have to wait for the light to reach us, obviously) solely because of the slight difference in your relative velocities and the very great distance from here to Andromeda.