Travelling towards distant stars

[User11037]

It is often quoted that, when we see stars from Earth through, for example, a telescope, we are not seeing them as they are now, but how they were millions of years ago (because the travel of light is not instantaneous).

However, say if I take a picture of a star from Earth, then jump into a spaceship and travel at 0.999999... of the speed of light towards the star (assume my acceleration is virtually instantaneous). If the star is say, 4,000,000 light years away, when I see the star, will it appear just after as in my photo, or approximately 4,000,000 years older than it does in my photo, or something else?

 

[roughycannon]

If the star is 4 million light years away and you traveled at the speed of light towards it, it would take you 4 million years to get there, so you would see the star as it would look 4 million years in the future.

An easier way to do it would be to stay put on planet Earth and wait 4 million years for the light from the star to come here and you'll see the same thing...

 

[PeterDonis]

if I take a picture of a star from Earth, then jump into a spaceship and travel at 0.999999... of the speed of light towards the star (assume my acceleration is virtually instantaneous). If the star is say, 4,000,000 light years away, when I see the star, will it appear just after as in my photo, or approximately 4,000,000 years older than it does in my photo, or something else?

When you reach the star, you will see it to be 8,000,000 years older than it looked in the picture taken from Earth at the instant you left. That's because it took 4,000,000 years for the light that made the picture to get to Earth, and then, as roughycannon points out, it takes you 4,000,000 years to get to the star. So a total of 8,000,000 years has elapsed at the star between the light that made the picture being emitted, and you arriving.

 

[User11037]

Time Dilation

Surely time dilation would have an effect?

 

[roughycannon]

I was just going to post the same as Peter the picture you have would be of the star 8 million years ago.

 

[phinds]

Surely time dilation would have an effect?

You misunderstand time dilation. I suggest you Google it and read up a bit.

 

[User11037]

But, that would imply that, while I am traveling, I would see the star ageing at twice its normal rate?

 

[PeterDonis]

Surely time dilation would have an effect?

Effect on what? It will certainly affect how much time elapses on your clock during the trip (which will be almost no time at all since you're traveling so close to the speed of light), but it doesn't affect anything I said, since what I said had nothing to do with the time elapsed on your clock during the trip.

 

[roughycannon]

But, that would imply that, while I am traveling, I would see the star ageing at twice its normal rate?

The picture you took in the first place is already the star 4 million years ago, add the 4 million years of you traveling there and now the pic is of the star 8 million years ago.

 

[Dale]

But, that would imply that, while I am traveling, I would see the star ageing at twice its normal rate?

Yes, if you are traveling at 0.6 c then you will visually see it aging at twice its normal rate, according to the relativistic Doppler effect. If you go faster the rate will be even higher.

 

[User11037]

Yes, if you are traveling at 0.6 c then you will visually see it aging at twice its normal rate, according to the relativistic Doppler effect. If you go faster the rate will be even higher.

But surely that's a contradiction, because the star is emitting light at a constant rate and this light will always travel at the speed of light, regardless of my speed, I must continue to see the star age at its normal aging rate?

Also, I just thought, if you model it as the star moving towards me nearly at the speed of light, which special relativity states has the same validity, then surely the star will experience very little aging in this time due to time dilation?

 

[PeterDonis]

But, that would imply that, while I am traveling, I would see the star ageing at twice its normal rate?

You'll see it aging a lot faster than that, because you're traveling so close to the speed of light. You will see the star age by 8 million years (from its age in the picture, taken at the instant you leave, to its age at the instant you arrive, which is 8 million years older than in the picture, as I posted before) in a very short time by your clock, because almost no time elapses on your clock during the trip (as I posted before).

 

[PeterDonis]

the star is emitting light at a constant rate

Rate in whose frame? "Rate" is frame-dependent.

this light will always travel at the speed of light, regardless of my speed

Yes, this is true.

I must continue to see the star age at its normal aging rate?

How does that follow? The rate at which you see the star age doesn't just depend on the speed of the light; it depends on your speed relative to the star as well.

if you model it as the star moving towards me nearly at the speed of light, which special relativity states has the same validity, then surely the star will experience very little aging in this time due to time dilation?

Sure, but very little aging between which two events? In this frame (your rest frame during the trip), the event at the star which is simultaneous with your departure from Earth will be only a very, very short time, in the star's rest frame, before the event of your arrival; virtually all of the 8 million years elapsed at the star between the light being emitted that made the picture, and your arrival, happens to the past of your departure from Earth, according to your rest frame during the trip.

It's extremely easy to get yourself confused by trying to think about time dilation without also considering relativity of simultaneity. The best cure I know of for this is to draw a spacetime diagram of the scenario; that makes the relationships between the events much clearer.

 

[User11037]

You'll see it aging a lot faster than that, because you're traveling so close to the speed of light. You will see the star age by 8 million years (from its age in the picture, taken at the instant you leave, to its age at the instant you arrive, which is 8 million years older than in the picture, as I posted before) in a very short time by your clock, because almost no time elapses on your clock during the trip (as I posted before).

But, why is it valid to say that during my trip the star is aging and I am not, but not to say that I am aging and the star is not. Surely the two situations are symmetric?

 

[PeterDonis]

But, why is it valid to say that during my trip the star is aging and I am not, but not to say that I am aging and the star is not. Surely the two situations are symmetric?

See my next post after the one you quoted. As I said there, the cure for your confusion is to draw a spacetime diagram of the scenario.

 

[Dale]

But surely that's a contradiction, because the star is emitting light at a constant rate and this light will always travel at the speed of light, regardless of my speed, I must continue to see the star age at its normal aging rate?

Why would you think that is a contradiction? The speed of a wave and the visually detected rate of aging are not the same thing, why would you think that the invariance of one would imply the invariance of the other?

Also, I just thought, if you model it as the star moving towards me nearly at the speed of light, which special relativity states has the same validity, then surely the star will experience very little aging in this time due to time dilation?

You seem to be confusing three things here:
1) speed of light is invariant (i.e. it is the same in all frames)
2) time dilation (i.e. moving clocks go slow and moving stars age slowly)
3) relativistic Doppler (i.e. what you actually see is blueshifted as you approach)

I don't know how to help you understand the difference because I don't know why you are confusing them. Are you aware of these three different (but related) phenomena? If not, which one is new for you? If so, can you explain what you think the similarities and differences are?

 

[Dale]

For concreteness, let's suppose that we have an astronaut and a star moving towards each other at v = 0.6 (in units where c=1). Let's further suppose that in the star's frame the astronaut is 3 Mly away and let's suppose that every 1 y the star briefly goes dark and it has done so for the past 3 My, meaning that right now (in the star's frame) the astronaut receives the first dark pulse.

Now, the astronaut is traveling a distance of 3 Mly at a speed of 0.6 ly/y which will require a travel time of 5 My. During this time the astronaut will receive a total of 8 M pulses. Because of time dilation (γ=1.25) the astronaut's clock will advance only 4 My, which means that the astronaut will receive the pulses at a rate of 2 pulses/y according to his clock, even though they are sent at a rate of 1 pulse/y according to the star.

In the astronaut's frame, at the time that he receives the first pulse the star is only 2.4 Mly distant (length contraction). In the astronaut's frame, the star has been sending pulses for 6 My (relativity of simultaneity), since it was 6 Mly away and it has traveled 3.6 Mly in that time. It will take the star a further 4 My to finish the last 2.4 Mly, for a total of 10 My of emitting pulses, however in the astronaut's frame the star is time dilated (γ=1.25) so it will only emit a total of 8 M pulses, which means that the astronaut will receive the pulses at a rate of 2 pulses/y according to his clock even though they are sent at a rate of 1 pulse/y according to the star.