# Time dilation and Doppler

1. Aug 11, 2015

### Gaz

[Mentor's note - split off from https://www.physicsforums.com/threads/are-time-dilation-experiments-conclusive.826952/ as this is a different question]
This makes sense.

And fact they appear to slow down is due to red shift of light created between the two frames?

Last edited by a moderator: Aug 11, 2015
2. Aug 11, 2015

### phinds

First, it's not "between two frames" it's between two objects in the same frame. It's due to the fact that light seems (based on calculations) to travel a different amount of distance depending on how fast the "moving" object in the frame is moving. "Appears" is a misleading term here because it's a calculation not actual observation. "Appears" here is used in the sense of "seems" not "is directly seen to be".

3. Aug 11, 2015

### Mentz114

I would say that the clock rates and the freqency shift are not the same thing but both are caused by the relative velocity between the objects.

4. Aug 11, 2015

### phinds

I agree

5. Aug 11, 2015

### Staff: Mentor

No. One way of seeing thie is to consider that if the observers were moving towards one another instead of away, there would be a blue shift instead of a red shift - but the time dilation would still be there.

If two observers moving towards one another are watching each other's clocks (through a telescope?), they will both see the other clock running fast because of the Doppler effect. If two ticks of the moving clock are separated by time $T$ according to the watcher's clock, the light from the first tick will reach the watcher's eyes at time $d_1/c$ and the light from the second tick will reach the watcher's eyes at time $T+d_2/c$, where $d_1$ and $d_2$ are the distance the light had to travel. Because the two observers ae moving towards each other, $d_2$ is less than $d_1$ so the time between the two arrivals will be less that $T$ - the clock is seen to be running fast and the incoming light is blue-shifted. Eventually they'll pass each other in opposite directions and start moving apart, and then the opposite happens: $d_2$ is greater than $d_1$, the light is red-shifted instead of blue-shifted, and the clocks are observed to be running slow.

Time dilation only comes into the picture when we subtract out the light travel time by asking a different question: If at time $t$ according to my clock light from when the other clock was a distance $d$ away arrives at my eyes... what did my clock read when that light was emitted? The answer is, of course $t-d/c$ and when the result of that calculation doesn't match what the other clock says that's time dilation.

6. Aug 11, 2015

### Gaz

Yes but if you consider that a frequency shift would be like compressing of the light then the data the light holds will also be compressed and that data is what holds the clock information. So they are linked directly.

7. Aug 11, 2015

### phinds

You need to re-read the first paragraph in Nugatory's post.

8. Aug 11, 2015

### Gaz

The time dilation would be the opposite if it is blue shifted it would appear to move or tick faster.

9. Aug 11, 2015

### Mentz114

the non-relativistic Doppler is $f_{rec}/f_{emit}=c \pm v$ and the relativistic Doppler is $f_{rec}/f_{emit}=\gamma (1 \pm v)$ ( setting $c=1$ for convenience).
The time dilation is there in the form of $\gamma$.

10. Aug 11, 2015

### Gaz

I get this i did not know this was time dilation i was under the impression time dilation was created by motion. I totally understand objects at distance away from us are seen as being at a different time due to the time it takes light to travel to us.

11. Aug 11, 2015

### Gaz

Here is another one cosmological red shift.

A supernova lasts 20 days i read. So light leaving the supernova stretches 20 light days in distance.
As it travels the expansion of the universe red shifts the light making it longer. By the time it reached earth it is stretched out to 40 light days in length and because of this we see it in the night sky for 40 days as that's how long it takes to pass us.

Now do you say the supernova was slowed down in time to last twice as long? or do you say red shift stretched the light to create the appearance that the supernova lasted twice as long?

12. Aug 11, 2015

### A.T.

It is.

That is not time dilation, that's why you have to account for it, to get just the time dilation.

13. Aug 11, 2015

### Gaz

I think a decent explanation of light would be to think of it like a roll of film that is running at the speed of c.
The faster you travel through it the faster it runs.
Stationary to it it runs at normal speed.
And travelling away from it slows the film down.

Of course it is relative to you because time itself is not changing just your perspective of it.

14. Aug 11, 2015

### Janus

Staff Emeritus
He's not saying that this is time dilation, but that time dilation is what is left over after you account for this.

When you see relativistic Doppler shift, there are two factors to take into account. The fact that the distance between the source and you is changing, and time dilation. If the source is receding then both effects contribute to making the clock appear to run slow. When the source is coming towards you, the two factors are in opposition to each other. The changing distance acts to make the clock appear to run fast, but time dilation still acts to make it appear to run slow. The changing distance factor wins out and the net effect is that you see the clock run fast, but it is still running slow according to time dilation. In other words, if you factor out the changing distance effect, you end up with time dilation, which the same regardless of what direction the clock is moving with respect to you.

15. Aug 11, 2015

### PAllen

I suggest that until your understanding of Doppler versus time dilation is for special relativity is solid, do not try bring in Cosmology. Proper understanding of that requires general relativity.

16. Aug 11, 2015

### Gaz

[Mentor's note - edited to fix the formatting]
so what your saying is the Dopler effect creates the appearance of time changing and motion in any direction causes atoms to slow down. Ok I can understand that.

Last edited by a moderator: Aug 11, 2015
17. Aug 11, 2015

### phinds

Gaz, I like your attitude. We get a depressing number of people here who get all huffy and then finally just go away when they realize that we're not going to go along with whatever snake oil they are selling. It's nice to see someone who is here to learn and not pontificate (besides, pontificating on this forum is MY job )