# I Two twins moving towards each other in a circular orbit

1. Jan 8, 2017

### Bartolomeo

Yes, that's right.

2. Jan 8, 2017

### Ibix

Let's do some analysis and see what happens. Let Joe be at some point on the y axis shining his laser along it. The aliens pass through the beam at $x=0$ moving in the $+x$ direction. Let's assume their ship is sufficiently long to receive two successive wave crests. The first one arrives at $t=0$ and the second at $t=1/f$. What time do the aliens measure between wavecrests? The first one is obviously $t'=0$ and the second arrives at $t'=\gamma/f$. That gives a frequency of $f'=f/\gamma$, as expected.

You are correct that the question is sloppily worded because the aliens are only looking straight down in Joe's frame. In the context of a page about the transverse Doppler effect, though, I think it is clear what is meant.

Of interest: the emission events for the two wavecrests occur at $(t,x,y)=(-T,0,Y)$ and $(-T+1/f,0,Y)$, where $cT=Y$. Transforming those into the aliens' frame gives us $(t',x',y')=(-\gamma T,\gamma vT,Y)$ and $(-\gamma(T-1/f),\gamma v(T-1/f),Y)$. So the aliens will certainly attribute their frequency measurement to a mixture of the movement and consequent time dilation of the source, whereas Joe attributes it entirely to time dilation on the part of the receiver. But the fact remains that the received frequency will be about 2.3 times the frequency printed on Joe's laser pointer.

No. It means pretty much what I said in my last paragraph. Depending on the frame in which you do the analysis, your analysis process will be different because the state of motion you assign to source and receiver will be different. However, physical invariants such as "was the alien looking in the right direction?" and "what did the alien's spectrometer read?" will necessarily come out the same. In the symmetric case mentioned in the Wikipedia article, it means that the difference in emitted and received frequencies is attributed entirely to the classical Doppler effect, whereas in any other frame you need to factor in a time dilation calculation.

Last edited: Jan 8, 2017
3. Jan 8, 2017

### Ibix

The aliens will see a blue shift, but won't agree that the light was red when emitted (correcting only for classical Doppler). In the end, they'll agree that they receive light at a lower frequency than that printed on the laser pointer.

4. Jan 8, 2017

### jartsa

Well, I think they receive gamma times higher frequency than what is printed on the laser pointer. I used four-vectors to find that out! IOW I looked at the energy-momentum boosting formula here:
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html#c2
... and it seems to me that if x-momentum is zero, then E' = γ E

So the energy of a photon or the energy of a light pulse is multiplied by gamma. And frequency is proportional to energy.

EDIT: And of course aliens say that the pointer emits at lower frequency than what is printed on the pointer, because the pointer is moving.

Last edited: Jan 8, 2017
5. Jan 9, 2017

### Bartolomeo

The Aliens don’t do any analysis. They find the angle experimentally. They turn their tube at different angles until they see Joe’s light. If the Aliens are “at rest and look straight down” and Joe is “in motion and tilts his pointer backward”, green photon turns red. If the Aliens are “in motion and look into front” and Joe is “at rest and hold the pointer straight up”, green photon turns blue.
Champeney and Moon time dilation test (1965). Absorber and source were placed on the opposite sides of rotating disc. No frequency shift was detected.
Kholmetskii at all time dilation test. Absorber rotates - blueshift. Absorber is in the center - redshift.

Last edited: Jan 9, 2017
6. Jan 9, 2017

### Bartolomeo

The Aliens conduct spectrum analysis of Joe’s radiation. For example, they see Balmer series and realize, that received frequency is higher than proper one. They even know how much it is higher.

There is a mark on the laser pointer: „this laser pointer releases frequency f(s)“. In special relativity we call it „proper frequency“ which is equivalent to „proper time“. The aliens see that received frequency is not f(s), not f(s)/gamma but f(s)*gamma. Do you want to say, that the aliens think that the „proper frequency“ was not proper? Ok, the Aliens move relative to Joe and hold a mirror. Joe is „at rest“ and holds pointer (which is an observation tube too) straight up. Joe releases green photon. Photon reflects from the mirror and comes back to Joe. Color is green again. What color of photon was at the mirror?

You maybe think how to fit all this mess into the SR. That‘s easy! Both Aliens and Joe have tube – pointers. Aliens look straigt down, Joe tilts pointer backward. Aliens measure dilaton.

Then Joe forgets, that he was „in motion“ and changes direction of his tube - pointer into „straight up“. So as Joe would see the beam the Aliens also change direction of their tube – pointer „backward“. Now Joe measures dilation.

Thanks God, everything is allright, and the both measure dilation.

Please look at this diagram. https://en.wikipedia.org/wiki/Time_dilation#/media/File:Time_dilation02.gif

Synchronized clocks – it is inertial Einsteinian reference frame. Single clock moves in this reference frame. How many oscillations moving clock makes during time of travel? How many every synchronized in the same time? Does moving red clock „sees“ dilation or acceleration of time in the reference frame? What has to be done, so as red clock would meaure dilation of any of green clock?

Well, it has to leave „green“ reference frame and introduce it‘s own „red“, in which it is „at rest“. Now the red clock considers itself not in motion, but at rest. Now every moving single green clock dilates. This is the special relativity. Joe is at rest, Aliens are at rest too, everyone is at rest and nobody is in motion, since motion is „undetectable“ and is „the same as rest“. Everyone „sees“ only dilation and contraction.

Page 4, chapter Time Dilation

http://isites.harvard.edu/fs/docs/icb.topic455971.files/l09.pdf

7. Jan 9, 2017

### Bartolomeo

By the way. Imagine that red moving clock is the Aliens. Row of green synchronized clock are identical brothers Joes. Clockfaces of green clocks are higlighted in green monochromatic light. Aliens compare their own single clock rate with the time in the „Joes green“ reference frame. They see that the set of clocks runs faster at gamma. What color of clockfaces they will see? If they look straight down, it will be red. But since they move, they have to look into front. Clockfaces will be blue. Frequency increases at gamma too. Now set of clock (time in reference frame) runs faster and every single clock too.

8. Jan 9, 2017

### jartsa

The photon is a green photon in Joe's frame all the time, and the photon is a blue photon in the mirror frame all the time.

In the mirror frame the blue photon is produced by a device that emits wave crests at slow pace, the wave crests move away from the device at slow pace, because the device is moving, chasing the crests. The crests are placed close to each other, in the mirror frame. And that's why it's a blue photon in the mirror frame: Wave crest distance is a blue photon wave crest distance, in the mirror frame.

(for a less incorrect version of that replace "photon" by "light pulse")

If a light bulb is moving very fast, then it is chasing almost all the photons it emits, so almost all photons it emits are blue shifted. I mean the bulb moves so fast that there's a lot of relativistic beaming occurring.

Last edited: Jan 9, 2017
9. Jan 9, 2017

### Ibix

Agreed. I made a mistake in my analysis above and didn't account for the motion of the receiver. Serves me right for trying to cure insomnia with physics...

10. Jan 9, 2017

### Ibix

I think this is true, but it's worth pointing out that these are two separate experiments. They are done at different times, one when the aliens see Joe moving purely transversely and one when Joe sees the aliens moving purely transversely. If you are aware of that it hasn't come across to me in your writing. As @jartsa says in his last post, the photons don't change frequency depending on the thinking; rather the frequency of the light received by Joe from the aliens and vice versa is time dependent and two observations made at different times do, indeed, have different frequencies.

Again, say that in Joe's frame the aliens travel along the x axis and pass through the origin at t=0, and Joe lies on the y axis at y=Y. Let Joe continually illuminate the alien ship with his laser. The light Joe emitted at t=-Y/c is the light Joe considers to have been emitted parallel to the y axis (he has to lead a moving target) while the light he emitted at t=t'=0 is what the aliens consider to have been emitted parallel to the y axis (he's a moving source aiming at the spatial origin). It's this difference in times that drives the difference in received frequency in your two cases.

And, dragging this back on topic before Dale yells at me again, this is all irrelevant to the original case of circular motion compared to an inertial observer on the axis, because there's a time symmetry there that isn't present in the linear motion being discussed since #15.

11. Jan 10, 2017

### Bartolomeo

At least we agree, that if we say that „the aliens move“ or „the mirror move“ a photon of „green“ proper frequency appears to be „blue“ at reception. It can be only blue, not red. Blue means time acceleration.
We also agree, that if we say, that „the source move“,
SR claims, however, that photon of proper frequency „green“ can only be observed as „red“ at reception, i.e. clock dilates.

Your jump into another frame. In that frame Joe moves but not Aliens. It is a different story. This effect is not transverse, but longtitudal in this frame since photon does not move at normal between patches of motion of source and receiver. It takes long path. This interpretation says nothing about clock rate. But yes, there maybe this interpretation of observations. Either Transverse, or longtitudal, this is a matter of taste.

12. Jan 10, 2017

### Bartolomeo

It is exactly what Special Relativity does – conducts two separate experiments and they lead to the same outcome. I have already noted that in previous post. Reciprocity of observations takes place when we change frame and conduct another experiment. The task about Aliens means, that it is not that easy and each observer has to take into account „opinion“ of other one. They have decide who at which relative velocity moves relatively to each other. They cannot admit state of proper rest simultaneously.
Light received when they are at the closest approach. That means the Aliens are in motion and Joe is at rest (Aliens see blueshift, since their own clock dilates).

Light emitted when they are at the closest approach. That means the Aliens are at rest and Joe is in motion (Aliens see redshift, since their own clock tick as usual and moving clock dilates)

„ simple way of expressing this is to point out that the null frequency shift occurs for the pulse that travels the shortest distance from emitter to receiver, and this pulse is obviously neither emitted nor received at the point when the emitter and receiver are at their point of closest approach” http://mathpages.com/home/kmath587/kmath587.htm
That means, Joe and Aliens admit motion at „equal“ velocities (simplified 0,45 c and 0,45 c) and their clocks dilate at the same magnitude, i.e. they see the same clock rate. They tilt their tubes at equal angles backward and into front respectively.

What if the Aliens admit that they move with velocity 0,1 c and Joe with 0,8 c?

But which observation is the "correct" one? First? Second? Third? Fourth? Only the second one?

Do you still think that it doesn‘t matter what the Aliens think about their own state of motion?

This animation is on the first page of google: Please look at the last episode.
For rotating observer accumulated amount of time dilation solely depends on linear velocity. If two observers rotate with the same LINEAR velocity, accumulated time dilation amount will always be the same and their clock will always show the same time. Direction of rotation does not affect it.

Last edited: Jan 10, 2017