How observation of a distant galaxy changes when travelling towards it

PeterDonis

It's not so much a matter of what words you use, as keeping distinct the several different things that are going on: Doppler effect, light travel time delay, and time dilation. "Warping of the passage of time one frame relative to another" is an OK description of time dilation, but only *after* you've corrected for the Doppler effect and light travel time delay; you can't directly observe time dilation in this sense.

Here I was using "appear" to mean "the way the incoming light actually appears to you directly", which is primarily driven by a combination of the Doppler effect and light travel time delay. You are moving towards things in front of you, so the light signals from them will appear speeded up, because of the Doppler blueshift plus the fact that as you get closer, the light travel time delay decreases. You are moving away from things behind you, so the light signals from them will appear slowed down, because of the Doppler redshift plus the fact that as you get farther away, the light travel time delay increases.

You can *calculate* that, after you've corrected for those effects, both the things in front of you and the things behind you are time dilated compared to you--they are aging more *slowly* than you are, as seen in your rest frame. See below for further comments on this.

In an actual situation, yes, this would likely happen. In discussions like this, though, we can assume that we can ignore this effect; basically we are assuming that there is always enough radiation coming from the object that will get redshifted or blueshifted into a range we can detect, so we can get enough information to construct what you call a "real representation of what is occurring".

This brings up another good point, which I briefly referred to above. "Time dilation" by itself is not enough to tell you what some other object's clock will read when you reach it. For example, suppose I fly at a speed very close to the speed of light from Earth to some galaxy a billion light years away. Suppose I know, somehow, that clocks on my destination planet in that galaxy are exactly synchronized with Earth clocks (and suppose also that the planet is exactly at rest relative to Earth). Then I expect that, if I leave Earth at time t = 0 by Earth clocks, I will arrive at t = 1 billion years (plus a little bit because I'm not quite traveling at the speed of light) by the destination planet's clocks, whereas a much shorter time (say a year) will have elapsed on my clock (and I will only have aged a year, etc.).

*But*, if I look at things from my rest frame while I am traveling, it will seem to me that clocks on Earth *and* clocks on the destination planet are running much *slower* than my clocks are. That is, once I correct for the Doppler effect and light travel time delay, I can calculate from the light signals I receive from Earth and the destination planet that they will only age by a fraction of a second during my entire trip, while I age by a year. So it seems at first glance that I should predict that clocks on the destination planet will read only t = 0 + a fraction of a second when I arrive. Why, then, do I find that they actually read a t = a billion years plus a bit?

The missing piece here is called "relativity of simultaneity". In the rest frame of Earth and the destination planet, the event of my launch from Earth happens a billion years (plus a bit) before the event of my arrival at the destination planet. That means that my launch from Earth is simultaneous (in the Earth-planet rest frame) with an event on the destination planet that happens a billion years (plus a bit) before I arrive. Call this event (when clocks on the destination planet, synchronized with Earth clocks, read t = 0) event P.

However, in my rest frame while I am traveling, those two events (my launch and my arrival) are only a year apart (because that's how much time I experience during the trip). That means that, in my rest frame while I am traveling, the event of my launch from Earth is simultaneous with some *other* event on the destination planet, call it event P'. When I calculate that only a fraction of a second elapses on clocks on Earth and the destination planet during my trip, what I am really calculating is the time, on the destination planet's clocks, between event P' and the event of my arrival. But event P' doesn't happen at time t = 0 by the destination planet's clocks; it happens at t = 1 billion years, plus a bit, minus a fraction of a second.

In other words, to predict what the destination planet's clocks will read when I arrive, it's not enough just to know about time dilation; I also have to know how the destination planet's clocks are synchronized, i.e., when their "zero" of time is. If their "zero" of time occurs when I am spatially separated from them (as it does for the destination planet--when their clocks read t = 0, I am on Earth, just launching), I have to take that into account as well as time dilation in order to know what their clocks will read.

As I hope I've shown above, it's more complicated than that.

This is a good question; let's look at what things look like from both Earth and the destination planet.

If we're on Earth watching the trip, we see the ship leave at time t = 0. Since its destination is a billion light years away, we will see the ship's arrival at time t = 2 billion years plus a bit (1 billion years plus a bit for the ship to get there, plus 1 billion years for the light to get back to us). So the whole trip will appear "slowed down"; it will take about twice as long for us to see the trip happen, as it takes for the trip to actually happen. That doesn't double the actual travel time: the ship still arrives in 1 billion years plus a bit. It just takes twice as long for us to receive all the light signals emitted from the ship during the trip.

If we're on the destination planet watching the trip, it's more interesting. Since the launch point (Earth) is a billion light years away, it will take a billion years for the light from the launch to reach us. So we will see the launch at t = 1 billion years, and the ship will actually arrive very soon after, at t = 1 billion years plus a bit. In between those two events, we will see *all* the light signals emitted by the ship during the trip, drastically speeded up.

Note that in both cases, we can correct for the Doppler effect and light travel time delay to calculate that the ship and its crew only age by 1 year during the trip. So what we actually see can be quite different from what we calculate that the ship and its crew will experience. That's why it's so important to keep the different things that are happening distinct.

ghwellsjr

Yes.
You would see at least twice as much time go by but you will see it progressing at much faster than just twice your own rate, it could be hundreds of times faster, depending on your speed relative to the earth and the galaxy
You're welcome.

ghwellsjr

Nothing that can measure time can move at v=c so there is never a case that time comes to a standstill.
Your watch slows down a lot according to the frame in which you are traveling at almost c. In other frames, it may slow down but a lot less. And in the frame in which you are at rest, it doesn't slow down at all. But whatever frame you use to attribute time dilation to your watch will also attribute the exact same time dilation to your body so you won't notice anything different.
As I said before, nothing that can measure time can move at c so the concept of time has lost all meaning at the speed of a photon.

ghwellsjr

OK, now I understand what you are thinking. You are thinking that when you look out of the train and see trees approaching you, that means from your point of view the opposite is happening: you are going toward the trees.

And by the same token, you are thinking that when you approach a clock, you will see its time going faster and therefore the opposite will be happening to you: your clock will be going slower because its time is dilated.

But this is wrong. Look at these statements of yours:
In your frame of reference, you and your clock are stationary and are not time dilated. The other clock that you are approaching is the one that is moving in your frame of reference and it is the one that is time dilated.

Note also that it is not frames of reference for which time is slowing--it is clocks moving in a frame of reference that are time dilated. All clocks are in all frames of reference. It is incorrect to say or to think of you and your clock being exclusively in your frame of reference and the other clock being exclusively in its frame of reference. You're both in each others frame of reference.

In your frame of reference, the other clock is time dilated. In the other clocks frame of reference, you and your clock are time dilated. This is why I keep saying, you can't see or measure or have any awareness of time dilation, it changes with each different frame of reference but what you can see measure and be aware of do not change with different frames of reference.
You're right, I didn't take time dilation into effect because the op's question was not about that and even if he wasn't thinking about Doppler, that provided the answer to his question.
Everything sits nicely with relativity. If it doesn't appear that way to you, it's because you don't understand relativity. In the above quote, you are mixed up with regard to time dilation and Relativistic Doppler. There is no upper limit on the Doppler factor as you are approaching other objects or clocks. But this has nothing to do with how much the other object ages. The amount that it ages is opposite to the speed at which you approach it. As I said in post #5, if you approach it at almost c, it will age by double the number of light years away when you started. If you approach it more slowly, it will age more. You've got it backwards.
Why don't you learn the math? It's very simple. I went through the math for Doppler in post #20. Didn't you think that was simple?
No, you don't have to use the formula for time dilation, the formula for Relativistic Doppler is all you need to answer the OP's question.
I have already pointed out problems with your understanding and application of time dilation.

UglyNakedGuy

I want to say thank you first, before i got any further questions...I need some time to digest these :)