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Galaxy paradox?

  1. Dec 6, 2005 #1
    I decided to post a new thread to distinguish from my other post

    The paradox is as this: suppose that 10 billions years ago a guy was born ( lets call him "Universeguy"), in a place near the Earth (because obviously Earth doesnt exist yet), first, he was a lucky guy , he discover how to live eternally and he is alive now.
    Second, he loves Astronomy, and one day turn up his eyes to the sky and saw a beautiful galaxy (lets call it "Pary galaxy"), that was just forming ,he was obsesed with it,and he look at the Pary Galaxy every day and every day he took a photo of it, first he could saw it easily with naked eyes but as the time pass over because of expanding Universe, he has to began to use telescopes more and more powerful, but still every day he tooks a photo of PG, during 10 billions years until our times.
    As Mr Universeguy is live now, one day he attend a conference featured by a famous astronomer of our times, and discover surprisingly that this astronomer was precisely studying the PG, the astronomer shows a photo of the Galaxy and SAY THAT THE IMAGE OF THE GALAXY IS OF HOW IT LOOKED 10 BILLIONS YEARS AGO
    Can you see the paradox? For "universeguy" an actual photo of the Galaxy is how it looks NOW, For the astronomer, an actual photo of the Galaxy is how it looked in the PAST,10 billion years ago
    So, what could be happening here?
  2. jcsd
  3. Dec 6, 2005 #2


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    I suspect that you're seeing a paradox where there isn't one. The old photo and the new one won't be the same, for one thing, because the redshift will be greater in the new one. In any event, the two will match reasonably well because the same light was used to create both of them.
  4. Dec 6, 2005 #3
    What you're describing is not possible, unless I am misunderstanding you.

    If UniverseGuy took a photo the same day as the conference he would be seeing the galaxy as it was ten billion years ago. If he had a picture that he had taken ten billion years previously, that picture would not be a picture of what the galaxy looked like then, but a picture of what it looked like ten billion years before that picture was taken. Of course, thats if the universe weren't expanding and had been around that long, but it stil makes my point.
  5. Dec 6, 2005 #4


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    Right, Franz. I misinterpreted that, I think. I assumed he meant that the galaxy was right there in Universeguy's face, not way off (ie; universe expansion hadn't cut in yet) when the first picture was taken. I shouldn't try to read things like this while I'm tired. :redface:
  6. Dec 6, 2005 #5


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    A couple of things:
    1) in order for the astronomer to say that the photo is how the galaxy looked as it was 10 billion years ago, the Pary galaxy would have had to have been 10 billion light years away at the time the light left it. Since it took the light ten billion years to reach Earth from the Galaxy, it would have had to be receding at faster than the speed of light. In which case, neither Universeguy or the Astronomer would have ever been able to take any photos of it at all.

    2) Instead we'll assume that the galaxy receded form Universeguy at the speed of light, then Universeguy would see the galaxy as "frozen" in time during the 10 billion years. (the galaxy would appear exactly the same in every photograph he took over the course of that 10 billion years).
    It also means that the galaxy was 5 billion light years away when the light that eventually forms the atronomer's photo left it.

    So when the astronomer shows his photo to Universeguy and says that this is how the galaxy looked 5 billion years ago, Universeguy will looked at his series of photos, which will be exactly the same and the same as the one taken by the Astronomer, and say, "Yep, it sure is."
  7. Dec 6, 2005 #6


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    Which, of course raises all sorts sof paradoxes.

    For every photo to look identical, it means that, at one instant in time, all 10 billion years worth of photons would have had to be emitted from the galaxy in that instant. If the photon emissions were spread over any length of time that means the galaxy changed between the first emission and the last.
  8. Dec 6, 2005 #7


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    True, So we can't get a photo if the P-galaxy is receding at c either(all the electromagnetic emisions would have been red- shifted to 0). So the galaxy would have to recede at less than c in order for us to get a photo of any kind. . If we have the galaxy recede at very close to the speed of light, universeguy could see it change imperceptively over the 10 billion years. (we'll assume that he can compensate his photos for the extreme red-shift.) But even here, universe guy has to agree with the astronomer with how the universe looked was 5 billion years ago. because he also has to account for the amount of time it takes for the light to reach him from the increasing distance of the galaxy.
  9. Dec 7, 2005 #8
  10. Dec 7, 2005 #9


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    You can see galaxies that are receding at faster than light speed (up to a point where it passes ones event horizon). Keep in mind what we mean by 'receding faster than the speed of light', its slightly misleading, light still reaches us at exactly the speed 'c', otoh what we mean by distance is changing.

    This has always caused confusion, the above link from Ned Wright explains it correctly.

    Distinguish between the event horizon and our hubble sphere at both instances in time.
  11. Dec 7, 2005 #10
    Janus- you seem to have succumbed to some common misconceptions about cosmology. Galaxies which appear to be receding at faster than the speed of light do not have their light redshifted to 0. This only happens if you take the special relativistic doppler effect case (in which case they would be redshifted to infinite wavelengths). You need to use a general relativistic approach for high redshifts ie;
    [tex] v_{rec}(t,z) = {c\over{R_0}} {d\over{dt}} R(t) {\int^{z}_{0}{dz'\over{H(z')}}}[/tex]
    So at about z~1.5 the recession velocities exceed the speed of light. However, it is true that galaxies receding at FTL are leaving our event horizon, so we will never be able to see what they look like at the present time. So we observe objects receding at FTL all the time, but we observe them as they were 'y' amount of years ago, and we will never be able to observe them at their present state. See http://arxiv.org/abs/astro-ph/?0310808.
    For the OP;
    10 billion years ago, the P-galaxy would have been closer to Earth, so when Universeguy took the photo 10 billion years ago the light from the P galaxy would have taken 'x' (less than 10 billion) years to reach him, hence his photo shows how it appeared (10 billion+x) years ago. (I can't be bothered working out what 'x' is!)
    Now when the famous astronomer observes it, he sees it as it was 10 billion years ago. The two photos will differ due to the age difference, ie. one will be 10 billion years ago, the other will be (10 billion +x) years ago. However let's assume (albeit unphysically) x =0 for now. In this case, the photos will be the same (although Universeguy's will be more detailed, since the galaxy was very near when he took the photo) so there really is no paradox. This is just because the finite speed of light only allows us to observe things as they were in the past.
    Last edited: Dec 7, 2005
  12. Dec 7, 2005 #11

    But what happens if "universeguy" decides that he just take a photo of the birth of the galaxy , and for the next years he record the passing of time by making a line in the rocks every day, for example, without observing actually the Pgalaxy, so he is confident that in 10 billions years when he meets famoustronomer the galaxy is still there?
    Sorry if im misleading this discussion , but can this example could be related with that is called "cosmological time" "arrow of time" , and the "psychological time" that we have in our minds?
    Last edited: Dec 7, 2005
  13. Dec 7, 2005 #12
    ok first, userguy could not have seen the galaxy the first day it was created. He obsverved it x seconds after the light had time to reach him.

    Second, just because he took a picture everyday doesn't mean he has daily picture of PG. as the universe expands and days pass, the image he sees of PG changes. for exaple: lets say he takes a picture everyday for 5 billion years. and in this time the uiverse moves away, due to to expanding uiverse, 1 billion light years.

    so userguy had (5 billion x 365 pictures) of PG, but in reality he sees the 5 year old PG as a 4 billion year old uiverse. (so his pictues are of PG every 19.2 hours not every 24 hours)

    the picture shown by the astronimer according to user guy is a picture of the universe as it looks now, but userguy is wrong, because he deont understand the conept of the expanding universe, so there is no paradox,
    Last edited: Dec 7, 2005
  14. Dec 7, 2005 #13


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    I'm really not sure where you think the paradox lies here. No current model of the universe (that obeys the cosmological principle) claims that a single image of a galaxy can age backwards with cosmic time. In other words, if I now see a galaxy, there is no time in the future when it will appear younger.

    There are some technical exceptions to this, but none of them are currently mainstream. There are models of the universe in which objects can appear in multiple positions in the sky (sometimes with different ages), but even in this case, there isn't really a paradox as you describe it. Another technicality relates to:

    There are indeed some ambiguities in the origin of the arrow of time in various models of the universe. This is another discussion entirely, however. In [itex]\Lambda[/itex]CDM (the most popular model of the universe), there should be no paradox like you're describing.
  15. Dec 8, 2005 #14


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    Just to restate what has pretty much already been said, let's say you had a picture of a distant galaxy taken from earth 5 billion years ago and a picture of the same galaxy taken from earth last night. The picture taken last night would not show what that galaxy looked like after aging another 5 billion years. Due to time dilation, it would appear to have aged at a much slower rate than earth appears to have aged in between the time [by earth clocks] the two pictures were taken.
  16. Dec 8, 2005 #15


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    I'm not 100% sure we've, between us, answered 100% of the OP's question(s). But then, I don't fully understand that/those questions anyway, so I will paint a different picture, ask some questions, and see if anything interesting emerges.

    Here is an HST image of Abell 2218, a rich cluster acting as a gravitational lens. Today, with the help of tools such as NED, we can easily learn such things as its initial designation (by Abell and Corwin, back in 1989), and retrieve (at least some) images of it, from several different 'cameras' attached to different 'telescopes'. With a bit of digging, we could compile quite an impressive library of images, taken at many different times, going back to what, the 1920s? (of course, many images would be exceedingly dull - not sensitive enough to show anything but the dimmest of smudges for the brightest of cD galaxies in the cluster). Never mind, suppose we had taken an HST image of the cluster, every day, since Hubble had its contacts installed. What would that sequence of some thousand or three images show?

    Now, suppose the HST had been in business since Newton, doing its daily thing with Abell 2218, and we ran a movie of the images, backwards, at the standard 24 frames a second (the movie would last something over an hour); how exciting a movie would it be?

    Let's imagine the ancient Chinese, in the Xia dynasty, had an HST, and it had been taking daily snaps ever since. To keep the movie of a manageable length, we'll need to speed it up, say 400 frames/sec. Would it be any more exciting than the 'Newton' version?

    and so on ....

    What 'time compression factor' (a.k.a. frames per second) would we need to make our ~1 hour long movie interesting, but not tooo interesting (we want to see interesting things happen within ~seconds to ~minutes, in the movie, not in <1 second)? What would (likely) be the 'first' interesting thing that we would see? The first dozen?

    Of course, just like japam's Universeguy, we will assume that somehow many, many, many generations of HST's were built and maintained, and that the cameras, filters, etc all had the same characteristics as WFPC2 (etc), despite there being (for example) no solar system around from which to obtain the Si, O, P, Au, etc to make such things (not to mention the machine shops, test instruments, and so on). We will also assume that our 'HST' could always have a nice clear vantage point from which to see Abell 2218 (some dozens of kly from SagA*, not inside a giant molecular cloud, etc).

    Running our ~13 billion year long movie backward (from today's HST piccie to one taken a long, long time ago) - hugely compressed, of course! - would Abell 2218 ever disappear? What about the lensed objects?
    Last edited: Dec 8, 2005
  17. Dec 8, 2005 #16
    Abell 2218 would certainly disappear! You have to allow for evolution and we don't expect to see a massive cluster like A2218 beyond z~2.
    Last edited: Dec 9, 2005
  18. Dec 9, 2005 #17


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    Now I am confused. Time on earth moves faster than it appears to move for distant galaxies. If you run the movie backwards, our time appears to slow down, and theirs appear to speed up. If you run our clock back to t = 0, our clocks would be in perfect agreement.
  19. Dec 10, 2005 #18

    for illustrate where's the paradox:

    suppose that the galaxy is receeding closer to c

    for universeguy , the simple fact that you can take a photo of the galaxy NOW is a proof that the galaxy still exists NOW, however, because of the recesion we are condemned to see the galaxy closer to his birth probably forever

    and theres is the paradox , that we can SEE the past and DETECT the present state of the galaxy simultaneously, IS LIKE IF THE LIGHT WOULD HAVE TRAVELLED FASTER ( IN FACT INFINITELY FASTER) THAN THE OWN LIGHT

    How the light could perform this , i have no idea
  20. Dec 10, 2005 #19
    No, this interpretation is incorrect. We can not know what the galaxy is doing NOW. We can only ever observe it in its past state. Just because we can take a photo of it in this present epoch does not mean we can infer that it still exists in this epoch.
  21. Dec 10, 2005 #20
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