Would approaching a distant star at near the speed of light unfold its entire history in "fast-forward"? The light we detect today in our telescopes from distant stars is really old.
If we could travel fast (lets say, 90% the speed of light) towards a star a million lightyears away, all the time looking straight at it, would we see that star's entire history unfolds in fast-forward ▶▶ until we reach it? (if it's still there, of course). 
It seems reasonable that "newer" photons emitted from that star would hit our eyes at a faster rate while we approach it.
Thanks.
 A: We certainly would, or at least we would if we had telescopes powerful enough. However, better still, we could choose to watch its history unfold at an arbitrarily high fast-forward rate! Suppose our universe were classical/Newtonian/Galilean (or whatever you want to call it) but with a finite speed of light propagation (and let's just say that we're still unable to travel faster than light in this hypothetical world). Then, by the good old Doppler effect, we would receive the photons coming from this star faster than they were emitted. How much faster? Well, suppose we were travelling towards the star at approximately the speed of light. The photons would be travelling towards us at the speed of light, and so by Galilean relativity (which isn't correct, note!) the photons would be arriving at us twice as quickly as they were emitted. Hence we would receive a pleasant 2X FF. This is consistent: if our planet is $x$ light years away from the star in question, then we would (from Earth) be seeing the star $x$ years ago. Then, if we hurtled towards it at the speed of light, the time taken to get there would also be $x$ years, and by the time we arrived, we should both be 'in the present', so to speak. Hence we must be catching up by one year per year, which corresponds to a 2X fast-forward.
But this isn't the universe we live in! We live in a universe governed, to the best of our knowledge, by Einstein's relativity. In our case, since we're mostly concerned with a journey through deep space (where gravity is negligible) we want the theory of special relativity. This theory tells us that as we get to faster and faster speeds relative to a given object, that object becomes contracted in length (along the direction we're travelling) and time runs more slowly for it. These are very strange results indeed --- what is their implication? Well, as we approached the speed of light, the distance between this far away star and our spaceship would contract. In fact, it would contract to an arbitrarily small distance as we got arbitrarily close to the speed of light. Consequently we could get to the star in not years, but in practically no time at all!
From the star's perspective it works like this: the star sees a spaceship travelling at almost the speed of light towards it. The near light-speed relative velocity entails that to the star, time is running particularly slowly aboard the spaceship --- by the time we get very, very close to the speed of light, time has almost halted to a stop, from the perspective of the star. So by the point of our arrival, very little time has passed aboard our spaceship.
What this means is that (for one, it means that with enough energy, we can get to basically anywhere in the universe within our lifespans) it now takes us only a short length of time to reach the star, but in that time we must have caught up those $x$ years that the star was 'in the past', from Earth's perspective. If we did the journey in $x/2$ years, say, we would be watching the star at a fast-forward rate greater than 2X. Faster still and we could watch the star's history unfold in a matter of mere days, or minutes.
A: Assumptions we start with an observer and a star at rest with respect to each other and 1000 lightyears apart. Both observer can agree on these facts.
The observer then sets out toward the star in a reasonable fast starship, arriving after 10,000 years as measured in their original frame, recording the light from the star as he goes. The traveller experiences
$$t' = (10000 \,\mathrm{years}) \sqrt{1 - .1^2} = 9950 \,\mathrm{years} $$
of travel.
On his arrival in the neighborhood of the star he has recorded 11,000 years of data from the star in (depending on whose time you prefer to use here) either 10,000 or 9950 year. A 10--10.5% overcrank.
So, yes, he is seeing things in fast forward, but you have to go really fast to get much effects. And once you get to the star you can't fast forward any more (but you can go to slow mo).

If we boost the speed to 0.5 c, we get $t' = 1730\,\mathrm{years}$ to see 3000 years of the stars light for a overcrank of about 73% from the travelers prospective. In general the expression we want for the ratio is
$$\begin{align*} 
r &= \frac{d_0 + t}{t'} \\
&= \frac{d_0 + \frac{d_0}{v}}{\frac{d_0}{v}\sqrt{1 - v^2}}\\
&= \frac{v + 1}{\sqrt{1 - v^2}}
\end{align*}$$
where the velocity $v$ is expressed in terms of a fraction of c and $d_0$ is the starting distance (but note that it drops out of the answer).
A: Firstly, if we travel at 90% the speed of light, the relativistic effects will be too magnified to ignore. If you are travelling at a speed of $0.9c$ towards the star, according to your frame of reference, the star is coming towards you at $0.9c$ too. You'll observe that the speed of rotation of the star slows down by a factor of $\sqrt{1-(0.9c)^2/c^2}=0.44$. You'll also observe that the star contracts and its mass increases by the same factor. Also, the distance between you and the star will also contract, thereby reducing the length of the journey itself.
The second thing that will happen is that you will see colours from the stars changing consistently.
As far as the 'newer' photons hitting your eyes is concerned, yes, you will fast forward through a part of it's life cycle but since the distance is also contracted, it wouldn't be much. Also, you will have to keep predicting the changing position of the star. What you were travelling towards at the beginning of the journey was not the position of the star at that moment, and this will keep happening all throughout the journey.
How this effect will take place along with the relativistic and other effects would be an interesting thing to see.
A: History normally refers to the past, but none of the answers seem to take this interpretation.
You wouldn't be able to look back in time, to see any state of the star that happened earlier than what you are currently observing. So no, you won't see its entire history unfold at all. 
You would see a "fast forward" of what happened to the star from the state that you are currently observing and up to its current state (as seen from near the star itself). 
