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2

The cosmological distance to a faraway galaxy only depends on its cosmic redshift $z_\text{cos}$, i.e. the redshift caused by the expansion of the universe; it does not depend on the Doppler redshift $z_\text{dop}$ caused by the galaxy's motion within its local cluster. So we have $$\frac{a_0}{a(t)} = 1 + z_\text{cos}.$$ Now, what we observe is the total ...

2

Is there an equivalent formulation of classical electrodynamics in terms of action at a distance that is completely equivalent to the formulation in terms of fields (Maxwell's equations)? Yes, but only if special boundary conditions on the fields are assumed. For example, if the fields are purely retarded (wiki: Retarded and Advanced Potentials), one ...

11

The only stars you can reliably see are ones that are spewing enough photons at your eyeballs to appear stable. Any star which is so dim that photons entering your eye can literally be counted one by one, simply will not register in your vision, because your eye's retina is not sensitive enough. So your question is basically embroiled in observer bias; it ...

4

Yes. More specifically, if $d$ is the distance between the planets in their rest frame, then in the astronaut's frame the distance between the planets will be $\frac{d}{\gamma}$ so the travel time as measured from his frame will be \begin{align} t_\mathrm{astro} = \frac{d/\gamma}{v} = \frac{1}{\gamma}\frac{d}{v} \end{align} Notice that the quantity $d/v$ ...

23

Although I agree with all three of the above answers let me present a slightly different perspective on the problem. It's tempting to think of the light from the star as a flood of photons that behave like little bullets. However this is oversimplified because a photon is a localised object i.e. we observe a photon when something interacts with the light ...

45

The answer is simple: Yes, stars really do produce that many photons. This calculation is a solid (though very rough) approximation that a star the size of the sun might emit about $10^{45}$ visible photons per second (1 followed by 45 zeros, a billion billion billion billion billion photons). You can do the calculation: If you're 10 light-years away from ...

8

Allow me to channel something akin to the anthropic principle here. You can only see the stars that have a lot of photons reaching your eye. If a star were so far away that photons were reaching your eyes only occasionally then the star would be too dim for you to see in in the first place. Even if you could see the photons, the star would appear to ...

5

A star radiates in all directions. You would still see the star regardless of the number of steps you take to any side, just not the same photons. A laser radiates in only one direction (or in a very small cone). If you took a large enough step to the side (larger than the angular size of the emitted beam) so as to exit this cone, then you would no longer ...

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