# How observation of a distant galaxy changes when travelling towards it

1. Nov 16, 2012

### doudou1910

Dear All,

If the image we see from a distant galaxy shows how it looked 1 billion year ago, what would that galaxy appear if we are travelling towards it at the speed of light?

Do we see the galaxy developing twice as fast? It would be great if someone could explain it with both a simple description as well as in the form of mathematics.

Thanks!

2. Nov 16, 2012

### phinds

First of all, you can't travel at the speed of light and if you don't understand that, you would do well to study some cosmology.

Taking your question to be "near the speed of light", which is theoretically possible, then yes, you would see the galaxy develop more quickly than if you were watching it from Earth.

3. Nov 16, 2012

### PAllen

If you are seeing it as a billion years old, and you travel so close to the speed of light relative to it that you reach it in, say, 1000 years your time (possible due to time dilation and distance contraction), then you would see the galaxy extremely blue shifted and evolving at 1 million times normal rate.

Note: what you would see as visible light would be what the galaxy emitted as radio waves, due to the degree of blue shift. Visible light from the galaxy would be detected as hard gamma radiations.

Last edited: Nov 16, 2012
4. Nov 20, 2012

### stu dent

i've often wondered about this, and i love thinking of things like this with relativity. the thing is for me, is that the speed of light is supposed to be constant regardless of whether you are moving towards it or away from it.

now, in this example, i could imagine that that the spectrum would change, and the increase in speed of events on said galaxy could be attributed to time dilatations due to your velocity.

so then, you'd have to expect the same result, even if you move away from the galaxy.

now, say i move away from earth at let's say x->c so, essentially C i'll just say c to make typing easier, so, you travel for one lightyear. now, you will have aged, basically 0, and earth will have aged at a much greater rate, and you will see from your new position as they were a lightyear ago. but, as you were travelling at only a large fraction of the speed of light, light would still have been surpassing you at the speed of light.

so you'd be seeing earth a lightyear ago, but also the earth would be way farther in the future than when you left.

and the same thing would happen on your way back.

that question is confusing because one tends to think of light as one does of other things.

i mean, if i see the past of a galaxy from here, then i will need to see the present by the time i get there, so on my way over there everything will need to be in fast forward so that when i get there it could at least be the present again, and if i could travel at the speed of light, i would get there at exactly the present, because i am x lightyears away, and it would take me x years to get there at the speed of light. or, whatever, if you assume it is the present there now, you'd get there at x years in the future of now.

but this is not the case.

the light would need to arrive at me at the same rate. that is necessary. the spectrum would change though, at those rates into the invisible spectrum i guess, but we could ignore that.

however time dilates. i'm not sure exactly what's the rate at which time dilates, i guess i could maybe work it out, but if i see a galaxy at x years in the past, travelling at nearly c, i would get there at some time in the future, and i do believe much much much farther in the future.

i mean, time would have to compensate for you travelling so close to the speed of light, so that the speed of light is still moving at the speed of light as compared to you. your rate of aging would be near 0 if you are nearly at the speed of light, whereas everyone else would be motoring along like crazy everywhere. not just at your destination. i guess you'd be aging at tending to zero, which i suppose might mean that others would be speeding along at basically speed tending to infinity. i mean, if you're infinitely close to the speed of light, then i guess as compared to you, everything else is infinitely slower.

iow, i guess, if, for the sake of argument, you travelled to that galaxy at the speed of light, from your perspective you'd arrive at the instant you left, but by the time you'd arrive, the universe would be over.

at least, that is my understanding. somebody please correct me if i misinterpreted something.

5. Nov 21, 2012

### ghwellsjr

Actually, you would see the galaxy evolving at 2 million times normal rate. At high speeds, the Relativistic Doppler Factor is almost double the gamma factor.

A good way to think about this is if you are traveling toward something at a very high speed, not only do you watch its past history unfold before your eyes, you also watch its future unfold by the same amount.

Or another way to put it is in the rest frame of the distant object before you start out, you are seeing it in the past by the number of years equal to its distance in light years. If you could travel to it instantly, you would see it age by that number of years but since it will take at least that same number of years for you to get to that object (in your original rest frame), you will see it age by another of that same number of years for a total of twice the number of light years away.

6. Nov 21, 2012

### ghwellsjr

The assignment of the speed of light being constant in all reference frames has nothing to do with what you are seeing as you move toward or away from a distant object. This is called Relativistic Doppler and we'll see how it works later on.
Don't confuse time dilation with Relativistic Doppler. You cannot observe time dilation which is based only on the speed of an object as defined in a given Frame of Reference and is the same no matter what the direction of motion.

Relativistic Doppler is what you do observe and it makes a difference what direction you are traveling compared to the source of light.
Again, you don't want to be concerned about the speed of light when considering what you actually see.

You are correct that if you travel away from the earth at almost c, you will have aged basically 0 but you will not see the earth aging at all either, even though in its rest frame it will have aged a year, so you will see it in your new position as it was a year ago (not a lightyear ago), just as it was when you left it a year ago.
You'd be seeing earth a year ago but it would actually be just one year in the future (from your age).
No, on the way back, you will see it age by two years, the year that you "lost" on your outbound trip, and the year that it takes you to get back (although for you it's basically 0).
But it is the case, at least if I understand you correctly. It sounds like you are saying that if it is x lightyears away, you will see it x years in the past before you leave, then if you could get there instantly, it would age x years but since it will take you x years to get there, it will be x years into the future of when you left. In other words, you will see it age by 2x years.
Here again, you're mixing time dilation with Relativistic Doppler. If you want to talk about time dilation, you have to specify a Reference Frame. If you specify the Reference Frame as the one in which you were at rest before you started, then you are the one [STRIKE]experiencing[/STRIKE] time dilation is applied to during the trip and everything else is aging normally. If you specify the Reference Frame in which you are at rest during the trip, then you are aging normally and everyone else [STRIKE]is time dilated[/STRIKE] has time dilation applied to them. But either way, what you see and experience is the same, no matter what Frame of Reference you use.
Well, I think the universe has a lot more time to go, but you're right, when you arrive at the distant galaxy, it will be as much in the future as it was in the past before you left.

Last edited: Nov 21, 2012
7. Nov 21, 2012

### phinds

Uh ... my understanding is that no one ever "experiences" time dilation, it is an observational artifact of other reference frames. In YOUR reference frame, everything is always normal. Is that not correct?

8. Nov 21, 2012

### Staff: Mentor

Please don't do that - even though you've survived this post unscathed, relativity discussion threads are easily driven into unspeakable confusion through sloppy language. It's no harder to type "v" than "c", and you can say just once at the beginning what you mean by v ("v close to c" or some such works).

9. Nov 21, 2012

### ghwellsjr

I wish there were a better way to express this in the English language.

As I said, you cannot observe time dilation, so I would not say that it is an observational artifact.

And when you say "YOUR reference" frame, you mean a reference frame in which you are at rest. I said, "If you specify the Reference Frame in which you are at rest during the trip, then you are aging normally and everyone else is time dilated. But either way, what you see and experience is the same, no matter what Frame of Reference you use."

And this is why I would not say, "In YOUR reference frame, everything is always normal" because it does not depend on any reference frame.

What we need is a word that unambiguously means that something is applied to you based on the coordinates of a Reference Frame but in such a way that you cannot tell. Since I know of no single word that works, I try to explain using many words, but obviously it wasn't good enough.

10. Nov 21, 2012

### ghwellsjr

Hey, maybe "applied" is the word I'm looking for. I'll go back and edit my post and see if that works.

11. Nov 21, 2012

### phinds

OK, I do agree there's some confusion in terminology.

12. Nov 21, 2012

### PAllen

13. Nov 21, 2012

### stu dent

I don't get it. if my moving towards a light source at near c, has the effect that time at the destination appears to be in fast forward, and this is not time dilatation, and this is completely dependent on your travelling in that direction, then how can it be possible that this is the result, and yet the speed of light is constant?

either light is coming at me faster, and therefore, things appear to be moving faster, or light continues to come at me at the same speed, in which case one would expect that either things at the destination ARE moving faster relative to you, or they will be moving at a normal rate, which would cause problems should you ever reach there.

why are time dilatation effects not observable?

14. Nov 22, 2012

### ghwellsjr

First off, time dilation refers to clocks ticking slower so that the ticks are farther apart. Shouldn't this tell you right off the bat that you are not observing time dilation when you see a clock ticking more rapidly? Secondly, it might be helpful for you to study and consider normal Doppler shifts in a medium such as air or water.

But let me just ask, if you have a distant source of sound emitting a tone of some frequency, and you are at rest with respect to that source of sound, wouldn't you expect to hear the same pitch even if there were a head wind or tail wind blowing toward or away from the sound source? What matters is the rate at which the sound cycles are emitted compared to the rate at which you hear them, not how slowly or quickly the sound reaches your ear, don't you think?

So I'm just wondering why in the case of light, you would "jump" to the conclusion that its speed would have any bearing on the color of the light you see.
Time dilation is the ratio of the clock rate to the coordinate time rate of a particular reference frame. If it were observable, then how would it know what rate to tick at since we can pick any particular reference frame we want? They're all equally valid.

Last edited: Nov 22, 2012
15. Nov 22, 2012

### stu dent

well, i would consider that semantics, that's like saying that if i'm looking out the window of a train, and i say, look the train is slowing down. and you say, well you can't see the train slowing down, that's the trees slowing down. i mean, it's nearly the same thing, except in the dilatation case, i would look outside and see the world speed up and exclaim how i am seeing the train slow down.

you're talking about speeds i've never tested with, and neither result seems to me more probable than the other. this is something i would need to try, to be certain of. since sound is carried through air, i do believe the state of the air will affect the sound. i mean that would make sense to me. in what way exactly, idk. but sound is not light. i do expect sound to be coming towards me at a greater rate as i travel towards it. if you imagine the waves of sound through the air, a song would be a certain length, and i would hear it for a given period of time as it passes me by. if i travel through those waves of sound at a much greater speed, then the time it would take me to pass them would be shorter, and therefore the song would be shorter, and therefore would have sounded sped up.

light is always at the same speed. the wavelengths are to do with color. as you move towards or away from light the color changes. it's that way. i didn't jump to any conclusions. you can observe this fact with a telescope when watching stars wobble from having large massive objects in orbit with them as they move towards and away from us.

light is totally different from anything you are accustomed to observing in regular newtonian life. i would never jump to conclusions based on my observations when thinking about relativity. i would make hypotheses and question, and postulate, and think to a degree, but i would not jump to conclusions.

problems of arriving before the present.

time ticks depending on your speed relative to the constant c. what you are or are not able to observe for objects moving at other speeds relative to that, doesn't matter.

that was my understanding. i'm not sure waht you mean, coordinate time rate.

16. Nov 22, 2012

### ghwellsjr

Well, stu dent, if you don't know what coordinate time is, then you have a lot to learn about Special Relativity. I'm not going to be able to teach you everything from the very beginning right now but later on I'll try to respond more fully.

Let me just say right now that your concept of Doppler is wrong. You are looking just at what happens at the receiver. You are not considering what happens at the transmitter. If you are listening to music coming from speakers remote to you and there is a wind blowing so that the air is bringing the sound to you in less time than it would in still air, then, yes, this will affect the pitch of the sound that you hear when considered just from the wavelengths of the sound in air at your location but what you are overlooking is that the wavelengths are also distorted at the speakers in the opposite way so the two effects cancel out and you hear the sound exactly the same as if there was no wind.

Now in the case of air, we have other ways to determine that there is in fact a wind blowing and so we can determine how long it takes for the sound to get from the speakers to your ear but in the case of light, we cannot know how long it takes. We cannot measure how long it takes for light to get from its source to our eyes. We have to make assumptions and depending on what assumptions we adopt, we will get a different interpretation of how long it takes. And those assumptions lead directly into our interpretation of which clock is time dilated and by how much. But those assumptions have to be consistent with what we actually observe and they cannot modify what we observe.

I'm trying to point out simple things to you and you reject them. How can we progress?

17. Nov 23, 2012

### stu dent

I will continue to reject any idea you put forth until it is proven to me, and explained to me in a way that it makes sense to me, and in a way that it seems to me that it must be.

i am not rejecting any of your ideas because i think they are wrong, i mean, i think they are wrong, otherwise i would just agree with you, but that doesn't mean that they are wrong, or that i think that i am certain that i am right. it may mean, that what i think is wrong, and i am cognisant of that. that i disagree with you now, does not mean that i will disagree with you later, but in order to get to a stage where i agree with you, i will have to challenge every idea you put forward that is inconsistent with my view. i will never take your word for it. i will never just trust what you, or anyone else says. i will try to show you as precisely as i can, in which way it doesn't make sense to me. i will do this, because in doing so, i might be able to find exactly what is the error with my current view.

this is how i build knowledge. so please, don't be offended, and don't think that i think you're full of bs, but i will challenge you on every point that i disagree with, because in doing so, you will be able to set me right, and i may be able to understand more clearly.

don't forget also, in a forum, it is easy to misunderstand what someone says, to misinterpret it also. i mean, it is easy enough to do that in person, where you can use visual, and auditory queues to help in deciphering the message someone is conveying. this is especially true for me as well, since i tend to use simple words, and simple ways of thinking of things, without knowing the technical terms people in the field use to identify things. so that is a hurdle for sure as well. I may have much to learn about relativity, it is certain that i do, and in fact, i think this is even true for every human on earth as well, if you think about it. but i may also know more than you think, even though i don't know some terminology, because i didn't learn it from a textbook.

i learn quickly. questions i ask are precisely devised for this purpose. i noticed you skipped some questions i had asked. this will make it difficult for me to arrive at a point where i agree with you. you do not know what i know and what i don't know. or what i have hunches about, and whatnot. i do. and my questions are carefully crafted based on that.

as for your speaker analogy, i'm not sure what you mean by what is happening at the speaker. you mean the wind blowing against the speaker itself?

if so, i purposefully ignored that, the same way i would ignore air resistance when calculating the trajectory of a projectile. it was not pertinent to the discussion. it was necessary to isolate that variable. you were talking about how slowly or how quickly the sound reaches my ear affecting the pitch. not a specific scenario in the real world with actual wind blowing. ok, so, let's say then, a speaker sends sound through an ultra high powered dyson typed fan, that is pumping out a perfectly steady stream of air towards me, now would that not affect the pitch of the sound? from what i read of your post, you believe that it would. therefore, is that not the equivalent of the speed at which sound reaches you, that affects the pitch?

imagine a wave, a sine wave, made out of a solid piece of plastic, the period is pitch, the amplitude is volume, as obviously you know, now, imagine a laser beam, imagine that this laser beam is attached to an audio recording machine. this audio recording machine, records at a given beat rate, a sound wave. it does this, when something interrupts it. the location along the laser beam where it gets interrupted records that amplitude of volume.

now, you can take this plastic sine wave and pass it through the laser beam at some speed, this will record a tone, if you pass it through at another speed, it will record another tone. the faster you pass it through, the higher the pitch.

now, correct me if i'm wrong, but that's a perfect analogy as to humans perceive sound, and is representative of the fact, that yes, indeed, the speed at which sound passes by you, affects what pitch it is.

now, i re-read your post, and maybe you're saying what matters is the difference of speed of the sound passing by you, versus the speed of the sound produced by the source, them being equal produces the correct pitch, and them being different producing each a different pitch, if you know what i mean.

now, a light source moving very quickly away from me, will appear a different color than if it were moving toward me very quickly, given the same source of light.

right?

i do not see, why, it would be any different, from a physics standpoint, whether the source is moving towards me quickly, or away from me quickly, versus, it being still, and me moving quickly towards it, or me moving quickly away from it. for sound or light.

these two scenarios, aside from the absolute speed of i or the light in relation to the constant c, should be exactly the same, and i do not see how either of our speeds relative to the constant c, would have any bearing on the doppler effect.

i'm not sure what you mean that we cannot measure how long it takes for light to reach us. if a light source is a light year away, then can't we just say that the light takes a year to reach us?

i asked this question, and it seemed clear to this guy, and he even had a formula to explain it to me.

Last edited: Nov 23, 2012
18. Nov 23, 2012

### stu dent

if you are wondering which questions i was referring to in earlier post, it was these.

you did explain time dilatation part, but i think that was a semantics thing, and you didn't respond to my train analogy explaining what i had meant, by observing time dilatation.

i don't want to come off bossy or whatever, hopefully i don't. i mean you don't have to answer these questions for me obviously, i would appreciate it if you would, but i just want to point out to you, what i am unclear about, if you could help me out with that.

Last edited: Nov 23, 2012
19. Nov 23, 2012

### ghwellsjr

I did not have time to respond to your train analogy but I also don't understand what you are trying to say:
I can't tell when you say "speed up" and "slow down" whether you mean the velocity of the train/world or time for the train/world. If you could use terminology that makes this clear, and you still care, then I will respond accordingly.

20. Nov 23, 2012

### ghwellsjr

Yes, I was imagining that you were outdoors at a concert and very far away from the speakers and there is a steady wind blowing in the direction from the speakers toward you so that the sound gets from the speakers to you in less time than if there was no wind.
In the situation that I just described, you will not hear any difference in the music even though the sound gets to your ears in less time than if there was no wind.
That's a good analogy and the speed of the air (the wind) that is bringing you the sound does affect the pitch. However, as I pointed out before, you have to also consider what happens at the speakers. If a wind is blowing there, it will change the wavelength of the sound compared to still air. And the two effects cancel each other out so that you will hear the same thing whether there is a wind or not. (We're assuming a steady wind because if it is changing, then you will hear differences in the pitch in some complicated way that we don't want to consider.)
Yes, that is what I was trying to say.
Right.
There won't be any difference in the case of light but there will be for sound.
Here is the formula from the wikipedia article for the Doppler Effect:
Now let's use a speed of 80% the speed of sound and plug it into the formula for your two comparison scenarios. In your first scenario, you are comparing the source moving towards you quickly versus you moving quickly towards it. In the first case, the Doppler factor evaluates like this:

c/(c-0.8c) = c/0.2c = 5

In the second case we get:

(c+0.8c)/c = 1.8c/c = 1.8

There is a big difference.

In your second scenario, you are comparing the source moving away from you quickly versus you moving quickly away from it. In the first case, the Doppler factor evaluates like this:

c/(c+0.8c) = c/1.8c = 0.556

In the second case we get:

(c-0.8c)/c = 0.2c/c = 0.2

Again, there is a big difference.

Now let's do the same evaluation for light. We will use the formula that Ben gave you in your referenced post at the end of your post #17. Note that the formula does not have two different terms for velocity like the one for normal Doppler had. There is just one speed to consider and that is the relative speed between the source and the receiver. In this case, we'll use 80%c.

So for your first scenario, where you and the source are rapidly approaching, we have to use the reciprocal form of the formula and we get:

√((1+0.8)/(1-0.8)) = √((1.8)/(0.2)) = √9 = 3

Note that this number is "half way" between the two different numbers we got for sound. In fact, it is the geometric mean of those two numbers:

√(5*1.8) = √(9) = 3

And for your second scenario, where you and the source are rapidly diverging, the formula gives us:

√((1-0.8)/(1+0.8)) = √((0.2)/(1.8)) = √0.111 = 0.333

And this is the geometric mean of the two numbers we got for sound:

√(0.556*0.2) = √(0.111) = 0.333

So the bottom line is that Doppler for light is different than Doppler for sound. For light it is called Relativistic Doppler and for sound it is just the normal Doppler Effect. You can look these up on wikipedia or anywhere else if you want more explanation.
Only if we have previously defined light to take that long to traverse that distance which is what we do in Special Relativity but it's important to realize that it's a definition and not a measurement. I challenge you to come up with a way to measure how long it takes for light to propagate any given distance without previously defining how long it takes. This is what Einstein's second postulate does and is the basis for the concept of a Frame of Reference. When you specify a frame, then you are defining how long it takes for light to propagate any distance according to the coordinates of that frame. Notice how I did this in post #5:
And notice how the OP's question was worded that avoided the need to specify a frame:
Do you see the difference? He did not mention any distance and so no frame was required to unambiguously interpret the question or to answer it. His question was about what he would see and is independent of any frame or defining the time it takes for light to propagate a given distance. His question, whether he realized it or not, was purely about Relativistic Doppler which has nothing to do with time dilation which requires the coordinates of a specified frame. That's what I'm trying to get you to understand.

Last edited: Nov 23, 2012