# Travelling to a Distant Object

1. Dec 4, 2014

### Filip

For this distant object let's say that we'll be travelling to the sun.
As we are approximately 8 light minutes away from the sun, I was wondering if we were travelling towards the sun at a constant speed, such as 1/2 the speed of light, would we see things that happen on the sun go 1.5x as fast?

2. Dec 5, 2014

### Simon Bridge

1.5x as fast as what?
We would see things on the Sun happen at the rate that we see them happen.

3. Dec 5, 2014

### Filip

Why would we see the events happen at the same rate?

4. Dec 5, 2014

### jaydnul

Yes, you are accelerating relative to the sun, so your clock will tick more slowly. Relative to you, the sun's time will tick faster.

edit: Note that the speed of light is still constant, it is just the rate of photon detection that has increased.

5. Dec 5, 2014

### Filip

The twin paradox is a different effect than what I was thinking of, you're thinking of special relativity.

6. Dec 5, 2014

### jaydnul

What are you thinking of? :)

7. Dec 5, 2014

### Filip

You receiving the photons more often because you're shortening the distance between you and them. Of course I'm not sure if it would work this way, hence my question :P

8. Dec 5, 2014

### Simon Bridge

... "same rate" as what?? You are making comparative statements without saying what you are comparing the rate to.
It is always possible to find some reference frame where the rate that stuff happens is faster or slower or the same.
You need to be more specific.

Special relativity applies for inertial observers. There is also a time dilation when clocks are accelerated with respect to each other ... look up: gravitational time dilation.

... This is the doppler effect. Yes - in the absence of other factors - it would make normal actions look like a slightly sped-up movie as you and the scene move towards each other. The effect is more easily understood in terms of light waves and pulses than in terms of individual photons.

This is not specific to the Sun - your choice of example means that general relativity could play a part, which is why you were having trouble getting the kind of reply you wanted.

9. Dec 5, 2014

### Filip

""same rate" as what??", I thought you could infer from what I wrote that I meant the rate that you would have if you did not have this new velocity.

Last edited: Dec 5, 2014
10. Dec 5, 2014

### Staff: Mentor

That still doesn't quite address the issue I think Simon Bridge was raising. Let me re-state what I think you mean in a way that I think addresses it.

For simplicity, let's suppose that the object is not the Sun but a pulsar, so that we have a definite timing signal--the pulsar's pulses of radio waves--that defines the "rate" we are observing. Suppose that you start out at rest relative to the pulsar, and you observe one pulse arriving per second, by your clock.

Now suppose you start moving towards the pulsar at 0.6c. (You'll see in a moment why I picked that velocity.) You will now observe two pulses arriving per second, by your clock. Why? Because of the relativistic Doppler effect. The general formula for the Doppler factor (the ratio of the "rate" you observe while moving relative to the source, to the "rate" you observe when at rest relative to the source) for velocity $v$ (note that this only holds if you are moving directly toward or directly away from the source) is

$$\frac{\omega}{\omega_0} = \sqrt{\frac{1 + v}{1 - v}}$$

(in units where $c = 1$). As you can see, if you plug in $v = 0.6$, you get a Doppler factor of $2$.

Note that I made the key qualification, that we are comparing the rate you observe while you are moving relative to the source, with the rate you observe while you are at rest relative to the source. In other words, it's not just "velocity" per se, but specifically velocity relative to the source, that counts.

11. Dec 6, 2014

### Ken G

Also note that in the formula given by PeterDonis, both of the effects that have come up in the thread are present, and they are fighting each other-- and since v>1 means moving toward the Sun, we can see that the effect of shortening the time of flight always wins, and we see blueshift. However, the two effects are of similar magnitude when the speed is as fast as c/2, so it is best to unify them, as that formula does-- it would be awkward to separate them. In particular, separating them loses the symmetry you get that switching the sign of v simply inverts the frequency ratio, a symmetry that is important in deriving that result.

12. Dec 6, 2014

### Staff: Mentor

I think you mean v > 0, correct? v > 1 would mean moving faster than light, which is impossible. A positive v (v > 0) means moving toward the light source (the Sun in this case), and a negative v means moving away from it.

This is a misleading way of putting it, because it invites the incorrect inference that there is some speed where the two effects balance so we don't see any frequency shift at all. (Someone started a thread fairly recently based on this misconception.) In fact, as is evident from the formula, we get blueshift for any v > 0, and redshift for any v < 0, and the frequency shift is monotonic in v.

13. Dec 6, 2014

### Ken G

Oops, absolutely yes.
I can't agree there, saying that two effects compete at a similar magnitude, and that competition results in something simpler than analyzing either one independently, does not in any way imply they could necessarily be made to cancel. The point of noticing that the two effects are of similar magnitude is not to say they could possible cancel (I agree they cannot), it is simply to recognize that at high speeds, there is little value in distinguishing two similar-magnitude effects that can be more elegantly written as a single effect. Indeed, if you write down the simple expression when you combine the two, it exhibits symmetries that the two separate effects do not. So unless you want to maintain that the two effects somehow combine to respect a symmetry that neither one does independently, it is clear that the more elegant understanding combines them from the outset, thereby maintaining that key symmetry throughout.
Yes, I agree that conclusion is obvious, which is why there is no reason to think the two effects should ever be able to cancel. But even more importantly, replacing v by -v inverts the ratio, which reflects a symmetry not present in either time dilation, or the Doppler shift, independently of each other.

14. Dec 6, 2014

### Staff: Mentor

I think this is a bit misleading too, because the "Doppler shift" you refer to here is the non-relativistic Doppler shift. But the world is not non-relativistic, so the non-relativistic Doppler shift formula does not refer to any "real" physical effect; it's just an approximation to the correct relativistic Doppler shift formula, for the case where the speed is much less than the speed of light.

So I don't think there are "two effects" here. I would say that the relativistic Doppler shift is the "real" effect, since it's what is directly observed. Time dilation is a calculation we make if we want to assign coordinates to events in a particular inertial frame; but coordinates don't have any direct physical meaning.

15. Dec 6, 2014

### Ken G

But that is my entire point-- there is just one effect here. I am saying the best language unites the time-of-flight effects (which are often called the Doppler shift, a term invented long before there was relativity, as referred to above by Simon Bridge when he said "this is the doppler effect") and the time-dilation effects into a single thing. Conceptually, we can imagine there are two separate things going on there (as the OPer is clearly doing, as he said he was asking about the Doppler effect but not the time dilation effect), but my point was that it is better to think of them as part and parcel of the same thing when the speeds are high. I was telling the OPer that he should not focus his question on only one of those, he is really asking about both in his scenario.
That's why I said above that " so it is best to unify them, as that formula does-- it would be awkward to separate them. In particular, separating them loses the symmetry." All the same, it is certainly possible to separate them into two separate effects, which is an especially valid thing to do at low speeds-- it's just not such a good idea at high speeds, which was my point.

16. Dec 6, 2014

### Staff: Mentor

This is really an issue of language and pedagogy, not physics; but to me, if there is just one effect, one should not say that "both effects are present", or "both effects are combined"; one should say "there is only one effect", full stop. But it really depends on how the OP responds.

17. Dec 6, 2014

### Simon Bridge

P is making observations about what sort of thing often ends up being misleading to students even though they, arguably, should not.
When we attempt to address a possible misunderstanding it is best practice to try to be more careful with statements that is perhaps usual; ie we cannot expect people starting out to draw connections from maths, after all.
It may or may not be so much of an issue in this case: learning styles are personal. It's just something to watch.

18. Dec 6, 2014

### Ken G

Let me summarize: the OP said they were asking a question about the effect of changing the time of flight. They specifically said they were not talking about relativistic time dilation. I said that at c/2, it is unwise to separate those two effects-- they make sense to separate at low speeds because one is order v/c and the other order (v/c)2. However, when v~c, the two have similar magnitude, so they no longer make sense to separate, especially since you lose certain important symmetries when you separate them, symmetries that are only restored by combining them. So I don't find it terribly relevant to claim I am "misleading" anyone by talking about these separate effects-- it was the OPer who asked to separate them. In contrast, my point is all about when it makes more sense to think of them in a combined way-- which is when the speed is high. Even so, the effects are routinely separated-- hence the common language "relativistic time dilation," which always represents separating that from time-of-flight effects. So not misleading students certainly doesn't involve ignoring language they will no doubt encounter.

19. Dec 6, 2014

### Staff: Mentor

I'm not sure the OP really understood the implications of asking the question that way. But in any case, as I said before, this is a question of pedagogy, not physics.

Your method of pedagogy is to say: yes, there are conceptually two effects--the time of flight effect (light takes a shorter time to get to you from the source as you move towards it) and the time dilation effect (in your rest frame, the source's clock runs slow relative to yours). But as v -> c, it's better to look at these two effects as one effect.

My method of pedagogy is to say: physically, there is only one effect, the relativistic Doppler effect. Splitting it up into "time dilation" and "time of flight" effects is not a matter of physics; it's a matter of helping some people to understand the physics, by thinking of it as two different things going on, even though there aren't. For example, splitting out the time dilation effect might help some people to understand why the relativistic Doppler formula is different from the non-relativistic Doppler formula. But nature doesn't do any splitting.

Since this is a question of pedagogy, not physics--we agree on all the predictions of experimental results--I would like to see the OP's response to our respective ways of presenting this.

20. Dec 7, 2014

### Ken G

Actually, my pedagogy is to neither claim there is one effect, nor that there is two, for either approach is a way of looking at the issue. I am saying that there is good reason to look at the issue as two separate effects when the speed is slow, and good reason to unify them when the speed is large. Indeed, every time you have ever heard the phrase "time dilation", it was an example of separating the two effects. Since this is quite a common term, we can tell that separating the effects is also quite common, so my main point was that it is not always good to separate them-- despite that commonly heard term. Instead, it behooves us to understand the advantages of separating them, and the advantages of unifying them, and there are both
I'd say that's more or less just what I said above. So we are not disagreeing on anything substantive. But if we are to split those hairs, I would say that it is just as wrong to say there is only one thing going on, as it is wrong to say there are two things going on-- how many things are going on is always a matter of perspective, we don't get to know how many things are "really" going on there. There are advantages to mentally separating those two effects, and there are advantages of mentally unifying them. The OPer seemed well aware of the advantages of separating them, that's why he asked about only one part, so all he was missing was the advantages of unifying them, so I was talking about how to unify them and how to see the advantages of the symmetry there.

Last edited: Dec 7, 2014