Why can't some light ever reach earth? [duplicate]

Note: I'm a layman in physics. Excuse me if this question is a duplicate, I lack the knowledge in technical terms to find the answer to this by research (I've tried).

Let's suppose there's a star moving faster than the speed of light (relative to earth) due to the expansion of the universe. My understanding is that we'll never be able to detect its existence because the emitted photons will never reach earth.

But the star still emits photons traveling at the speed of light, so shouldn't we be able to eventually detect it?

Then suddenly it hits me: If I fire a bullet through the back of a train moving at the same speed as the bullet, it will have a speed of 0 relative to the ground. (I bet this has a name... relativity?)

But then... a bullet definitely isn't anything like a photon. Light behaves like a wave...

So, is this the same principle that prevents us from detecting the star, or is something else going on? What direction do the photons travel, relative to the earth?

• I would recommend reading physics.stackexchange.com/a/67541/8143, it's really good :) Jun 16, 2013 at 3:12
• possible duplicate of What is the theoretical limit for farthest we can see back in time and distance?
– user4552
Jun 16, 2013 at 3:20
• Also possible duplicate of physics.stackexchange.com/q/41058
– user10851
Jun 16, 2013 at 5:35
• @BenCrowell, Eugene Seidel, thanks for the reference, it helped a lot! But there's still one question: what direction do the photons travel relative to the earth? If I shoot a bullet through the back of a train going as fast as the bullet, the bullet will not move (horizontally), relative to the ground. Why doesn't a photon "shot" out of a star moving at the speed of light just stand still relative to the earth? Jun 17, 2013 at 3:05
• Found the answer to my second question in this youtube playlsit: youtube.com/playlist?list=PLDB15F7E29A5F0426 Jun 18, 2013 at 11:12

The speed of light is a cosmic speed limit of sorts, so if the universe is expanding such that neither celestial object is moving faster than the speed of light, but the DISTANCE between the two is growing faster than the speed of light, then we have a situation where basically the star will be invisible because the photons simply can't cover the distance while abiding by the cosmic speed limit (speed of light).

So the short answer is no, there are cases where we would never be able to detect stars. Their photons will simply be lost traveling in space, never reaching a destination (This is why faster than light travel is necessary if we ever hope to even reach the outskirts of our own galaxy, let alone others).

To go one step further, we know for a fact that as galaxies continue to expand away from one another, we will eventually reach a point where the galaxies we can now easily see, will slowly start dimming and eventually disappearing from the night sky, until the only stars we can see are ones specifically within our galaxy. We also can't know if there are galaxies that this has already occurred with, which is why people generally talk about the universe in terms of our observable universe, since there could be plenty of things out there that we simply cannot see.

Extras:

The Alcubierre Drive is a speculative faster-than-light engine that relies on expanding and contracting space-time to achieve a faster-than-light traveling speed between objects, even though the space craft would never actually travel faster than light. Similar to how the earth and star could move (relatively speaking) faster than the speed of light away from each other, except this work to close the distance faster than the speed of light.

Another quick example is if a train is moving at nearly the speed of light, and someone starts running forward in the train, the train's on-board time will slow down to ensure the cosmic speed limit is enforced and that the person cannot move faster than the speed of light.

Physics blows my mind. And if I made any mistakes, please correct me! Thanks!

• You're repeating a common misconception. See Davis and Lineweaver, arxiv.org/abs/astro-ph/0310808
– user4552
Jun 16, 2013 at 3:18
• When you say I'm "repeating a common misconception" could you be less vague? I've just started to read the paper, but when you are correcting me, can you at the very least state what's wrong and why, and then post the paper so myself and others can also verify it? I just don't know what I said that is a common misconception. Jun 16, 2013 at 4:20
• @bjwalls That paper is technical, but we cite it around here a lot because it lists out many such misconceptions. In your case, you are equating the Hubble sphere (recession velocity = speed of light) with the event horizon (surface beyond which we cannot get information, ever). There is indeed an event horizon, but it is outside the Hubble sphere - any galaxy receding at less than $c$ can be seen, and even some receding faster (up to about $3c$ in our universe as it turns out) can also be seen. Search site:physics.stackexchange.com davis lineweaver for more posts that explain this.
– user10851
Jun 16, 2013 at 5:29
• @bjwalls In particular, these subtleties are summarized here. (Yes, that is a plug for my own answer. ;) But I think it's worth a read.)
– user10851
Jun 16, 2013 at 5:39

Don't think of it as the other star moving away faster than light. Think of the space between them expanding faster than light, so they get further away faster than the photon can travel