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This is a question that has been gnawing on me for many years now. Back a long time ago, as I recall in reference to a scene in a popular science show on TV, I was asked the following.

The claim is that when you look out into the universe, you see the universe as it appeared at some past time. (This follows from the speed of light being finite, and looking at objects by observing their emitted light or other EM radiation.) The amount of time that one looks backwards is equal to the distance to the observed object in light-distance (so looking at something ten lightyears away means you are observing it as it was ten years ago).

Matter moves at a rate of speed less than the speed of light (it has to, since matter has mass, even if miniscule at the atomic level). So $v_{mass} \lt v_{EM}$ (probably significantly less, since $v_{EM} = c$).

So let's say you're looking at an object $10^{10}$ lightyears away by observing something for which $v=c$. To the observer, that object appears as it was $10^{10}$ years ago. But the Earth is much younger than $10^{10}$ years and we established that matter moves at a slower speed than EM radiation, so wouldn't the radiation that was emitted $10^{10}$ years ago long since have passed Earth's current position?

If, say, $v_{mass} = 0.5 \times c$ (a big assumption, but bear with me for a second), it would seem that the radiation emitted $10^{10}$ years ago would have passed Earth's current position $10^{10} - (0.5 \times 10^{10}) = 5 \times 10^{9}$ years ago, around the time when the solar system was still forming. Setting $v_{mass} = 0.25 \times c$ (which seems more realistic) means the radiation would have passed "us" around $7.5 \times 10^{9}$ years ago. So how could we be observing it now?

I'm not sure I'm posing this question in the best possible way (I'll admit I do find the concept somewhat confusing), and I'm sure that there's a simple explanation for it all. Just what am I missing?

I did find Is it possible to look into the beginning of the Universe? which seems peripherally related but not quite the same thing. Qmechanic brought up Seeing cosmic activity now, really means it happens millions/billions of years ago? but that question seems to be about whether it is so, not why it is so.

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@Qmechanic That question asks if it is so; I am asking more specifically why it is so. (And thanks for proper tagging.) –  Michael Kjörling Mar 27 '13 at 21:51

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I think you're missing out on one of the basic results that motivated special relativity.

Light moves at the speed of light with respect to everything, regardless of the speed of that object relative to the source of the light. It doesn't matter how fast the source of the light is moving, the light emitted from the source is always going to move at the same speed light always moves at with respect to everything else in the universe: $c$.

If this sounds contradictory, it's because the equations we use for figuring out the relative speeds of things on earth don't work for speeds close to the speed of light.

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It wasn't easy to pick an answer, but I do think this is the key to understanding what's going on. I'll just have to do a bit more reading, and/but now I have a much better idea where to start. –  Michael Kjörling Mar 28 '13 at 12:47

As nothing can travel faster than the speed of light then if we're seeing the light from an object as it was $10^{10}$ years ago then the radiation will take at least $10^{10}$ years to reach us too.

This means that it's perfectly possible for an observer on Earth to see something that existed before the Earth did.

Image a circular lake into the centre of which is dropped a large stone. The ripples from the stone's entry into the water will travel across the lake whether or not there's a boat in the lake to be affected by them and equally the boat will be affected even if you put it into the water after the stone was dropped. If we extend the analogy a bit further - the ripples move away from the stone's entry point in all directions, therefore it doesn't matter where on the edge of the lake we put the boat it will experience the waves at the same time.

So taking a star, the light is emitted in all directions so it doesn't matter where the Earth is/was/or will be but as long as it's position intersects the expanding sphere of light from the star when it's radius is $10^{10}$ light-years we will see the star.

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But wouldn't the matter which makes up Earth have travelled significantly less than $10^{10}$ lightyears in $10^{10}$ years? I can understand how this would work in a fixed size (even infinite size) universe, but not in an expanding universe especially when observing objects far enough away to be near the point of the creation of the universe. –  Michael Kjörling Mar 28 '13 at 8:47
@MichaelKjörling - yes the matter will have travelled less than $10^{10}$ light years, but that doesn't matter ;). As Dan points out light always travels at the same speed regardless of the speed of the source or observer. I'm not sure I understand your question then - the fact we can see something means that it's light hasn't "passed by" by definition. –  ChrisF Mar 28 '13 at 8:52
That's pretty much the part I don't understand. I edited the question to hopefully clarify what I find confusing - please have a look. It's perfectly possible that I am overlooking something (relatively) trivial (I'm not a physicist or cosmologist, and don't even play one on TV). –  Michael Kjörling Mar 28 '13 at 9:00

To expand on Chris' answer with a hopefully more familiar analogy;

Consider lightning and thunder. For any distance you're likely to be seeing it from, the flash you see from lightning basically coincides with the actual event (that is the light gets to you so quickly on Earth that the time between the lightning strike and you seeing it is negligible). But the thunder doesn't reach you until sometime after, depending on how far away it was.

Let's say you were inside, and so didn't see the flash of lightning, but happened to walk outside as the thunder hit. Even though you weren't outside when the event actually occurred, because the thunder takes finite time to reach you, you can hear into the past.

The exact same thing happens with the Earth - it doesn't matter that the Earth hasn't been around as long as the body emitting the light, because the Earth had time to develop while that light was on its way (in our analogy, we had time to walk outside while the sound was on its way to us).

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