# Spec-rel, two ships accelerate away from each other

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1. Sep 15, 2014

### Albertgauss

Hi all, this is a follow-up variant to an earlier post

https://www.physicsforums.com/showthread.php?p=3804580#post3804580

In that post, I wanted to know what an Earth observer would see for a ship some distance off accelerating towards Earth and then reaching constant velocity. For the below, I have two ships that start on Earth and accelerate away from each other in opposite directions, one ship travelling to the right, the other ship travelling to the left. The rightward ship emits images itself. Both ships will ultimately achieve the same speed, close to the speed of light, but will remain travelling in opposite directions. I tried a spacetime diagram but did not include it here.

Ignore Doppler, Distortion, etc. I just want to make sure the following is correct.

Part 1: In the right-ship’s frame, images are continuously released one after the other by the same, microscopically small time interval. The first images from the right-ship to the left-ship arrive at the left-ship fairly quickly. But, as the accelerations continue, and the ships separate more, the right-ship’s images take longer and longer to get to the left-ship according to the left-ship’s frame. The left-ship will perceive everything happening on the right-ship to proceed in slow motion. Instant by instant, as things happen on the right-ship, the light pulses corresponding to each moment of whatever happens on the right-ship spread out more and more, so that two events that happen quickly on the right-ship will seem to take a lot longer when the left-ships receives images from right-ship events. And, because the ships accelerate, the time intervals between flashes on right-ship get longer and longer as perceived by left-ship. The slow motion gets worse and more drawn out as the ships continue to accelerate, almost like if a person on right-ship talks, left-ship will hear the voice really drawn out.

Part 2: The right and left-ships reach their target, constant velocities (which happens at the same time for the frame of the planet they launched at some time ago). Now the left-ship perceives everything to happen on the right-ship at regular time intervals; these intervals--via time dilation--are perceived to be longer time intervals for left-ship compared to right-ship, but they are constant time intervals nonetheless. Of course, since the right-ship and left-ships are well separated in distance at this point, left-ship knows everything going in the right-ship—time_dilated/length_contracted/etc---to have happened a long time ago. Left-ship knows that, as the ships continue to separate, what left-ship sees is happening on right-ship happened longer and longer ago, but the interval between snapshots remains the same.

Is this all correct?

2. Sep 15, 2014

### Staff: Mentor

The intervals between snapshots stay the same, but for the receiving left ship they are longer than they are for the right ship.

Yes, it is correct. Note that you cannot ignore the Doppler effect, it does contribute to those time differences as well.

3. Sep 16, 2014

### Albertgauss

I realize what I'm trying to get to: What does the left-ship "see" is happening on the right-ship as the light pulses from the right-ship arrive? Obviously, this is very broad. Can someone recommend a good website that discusses this? I'll start with that, and if I have specific questions I'll ask them here later.

4. Sep 16, 2014

### Staff: Mentor

They "see" that the ship is red-shifted, and that time seems to pass slower there.

Good relativity websites... hmm, a book is probably better, but I'm sure there are good websites around as well.

5. Sep 16, 2014

### Albertgauss

“Note that you cannot ignore the Doppler effect, it does contribute to those time differences as well.”

The above statement makes me think I overlooked/didn’t-know something about Doppler Effect that I should have. Did I miss something?

Does the above statement refer to:

A) Color changes: blue-shift for moving towards you and red-shift for moving away (this concept I know about, in the example of this post they are all red-shifts)

OR

B) Does the above statement refer to the timing of the sequence of flashes coming in from sending ship to receiving ship? (this concept I did a lot of reading on today).

From part B, what I understand is that, not only do the colors red-shift to redder colors--red, infrared, radio, etc.—but that also contained in the meaning of red-shift is that snapshots are being received slower, one after the other, and these sequences of snapshots have a frequency attached to them. The actual “video stream” of what’s going on in right-ship is in slow-motion as received by left-ship.

Or is there something else I missed along these lines? Just being thorough and complete here.

Also, I didn’t mean a general book about relativity; I have some of those and they all talk about the usual time dilation, length contraction, simultan, etc., but they are hard pressed as to what people actually perceive going on in the other frame. Probably cause that’s harder that it sounds. But, Nevertheless, I did find two websites that talk about, at least for identical twins, what is actually perceived; what actually might “see”. They are okay, not great, but good enough. I thought I would share them with the rest of the community.

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_doppler.html

http://en.wikipedia.org/wiki/Twin_paradox
What it looks like: the relativistic Doppler shift

6. Sep 16, 2014

### Staff: Mentor

Both. They are actually the same thing, it does not matter if you count flashes or oscillations of an electromagnetic wave.

No, that's exactly what those books discuss. Once you can draw and read a spacetime diagram, everything will get easy.

7. Sep 17, 2014

### ghwellsjr

Here's a spacetime diagram to illustrate your scenario. The Earth observer is the thick blue line and the two ships are the other thick lines accelerating away from Earth in opposite directions until they reach the speed of 0.5c relative to the Earth's IRF. The red ship emits signals every second and their path to the black ship is shown as the thin red lines. Eventually, the black ship sees the red signals coming in at one-third the rate of his own clock. At that time, the relative speed between the two ships is 0.8c. The dots mark off one-second intervals of time called Proper Time for all observers.

Mfb has helped you to see that you don't want to ignore Doppler. That's precisely what you are looking for.

Actually, you probably should think in terms of three parts because the left-ship (black) does not immediately see the right-ship's signals at regular intervals. So during this intermediate time interval, both ships have reached their final speed but the left-ship has to wait some time before he sees this effect in the right-ship.

It's very close. It's important to understand that the left-ship cannot see or even be aware of the Time Dilation or Length Contraction that is going on with the right-ship. Indeed, in the Earth's rest frame, both ships are always Time Dilated and Length Contracted to the same extent throughout the scenario.

Also, when you refer to the frame of the left-ship or the right-ship, it's not clear what you have in mind since they are both non-inertial. However, we can consider the frame in which the black observer is inertial after he is done accelerating and look at that frame:

What you should notice in this diagram is that nothing changes as far as what the black ship observes of the red ship. The Time Dilations are all different in this frame. That should provide evidence for you that the Doppler is not caused by Time Dilation. Doppler does not depend on the frame while Time Dilation is and they differ by a factor of 2 to 1 as you approach the speed of light. They are two different kinds of things.

Last edited by a moderator: Sep 23, 2014
8. Sep 18, 2014

### Albertgauss

Wow, that is really great stuff. I'm very impressed by those spacetime diagrams. Much easier to see that way than to try and draw them yourself. Boy, they really help a lot. It is true that spacetime diagrams are the way to go to see what's going on in relativity. I’m really impressed and thankful.

I still wanted to clear up a couple points

1) "Also, when you refer to the frame of the left-ship or the right-ship, it's not clear what you have in mind since they are both non-inertial. "

What I meant by "frame" was the point of the view of the pilots. I agree I was not being rigorously correct enough. It seemed just easiest to say frame when I should've said "observer." I agree that "frame" refers to inertial reference frames, which change as the ship's accelerate. The word “observer” I will take to mean as being a passenger in either ship or on Earth.

2) Also I had a question on this: "It's important to understand that the left-ship cannot see or even be aware of the Time Dilation or Length Contraction that is going on with the right-ship."

It seems that there is still something temporal slowing down, due to Doppler, even if not time dilation. The best I can come up with is that left-ship perceives right-ship’s reality to run in—best word I can think of—“slow motion.” I understand that Doppler takes into account all time dilation effects and light-distance travel effects that the source travels across space from emitter to reciver but Doppler seems to weave all of these temporal effects into a “slow-motion” reality left-ship perceives to be happening to right-ship.

For example, from the first spacetime diagram of ghwellsjr, Let’s say both ships and the Earth watch exactly the same movie and they begin the title screen of that movie at launch. Reading from the graph, look at right and left-ship time coord 13 seconds, Earth-time-coord ~ 13.5 seconds. Right-ship gets so excited about the last scene of the movie that he must tell left-ship about it, and sends the message immediately. Left-ship receives the message at left-ship-time-coord 23 seconds. Then, at right-ship-time-coord 14.0 seconds, right-ship emits another message. That message is received by left-ship at left-ship-time-coord 26 seconds. 1.0 seconds passed for right-ship, and the incoming interval received by left-ship is 3.0 seconds. Left-ship, it seems to me, could say that, in left-ship’s observing, 3 seconds passed in its reality while it perceives the 1.0 second to pass for right-ship. It seems left-ship could say that right-ship’s reality is in slow motion by a factor of a one-third. Left-ship knows the signals travelling across space but knows Doppler takes care of all that. For this part of the spacetime diagram, I worked out the math from the Doppler formula and found that the predicted frequency left-ship receives of signals emitted by right-ship drops by a third, in agreement with what is said here.

Thinking through the above helped me to understand what ghwells jr meant by “Mfb has helped you to see that you don't want to ignore Doppler. That's precisely what you are looking for.”

I would then say that as the ship’s separate, they perceive each other’s reality to slow down as handled by Doppler. As they accelerate away, they perceive each other to slow down more and more. When they hit constant speed, left-ship still perceives right-ship’s reality to go more and more into slow motion. Eventually, the first signals from right-ship’s achieving constant velocity will reach left-ship, but sometime after right-shop stopped accelerating. When this happens, left-ship perceives right-ship’s “slow motion” as constant, for every 1.0 sec of right-ship that comes in, 3.0 secs of left-ship time pass.

That’s a lot to say, but is this what is meant by 2) above, as originally mentioned by ghwellsjr?

9. Sep 19, 2014

### ghwellsjr

You're sure welcome and I appreciate the kind words.

When I said "they are both non-inertial", I was referring to the ships, not the frames. It's permissible to have a non-inertial frame in Special Relativity but there is no standard definition for them like there is for an Inertial Reference Frame. There are lots of different ways to do it so if you had meant a non-inertial frame, then you would have had to state which kind it is. That's why I said it's not clear (what kind of non-inertial frame) you have in mind.

But since you meant "the point of the view of the pilots", that also needs clarification. It makes sense to me that "point of view" means what the pilots would actually see and that's what we've been talking about with regard to Doppler, it doesn't matter what frame you use when you make a spacetime diagram, they all show exactly the same images propagating from remote events to the observers so in that sense, the point of view of the pilots doesn't depend on the frame.

However, some people mean by "point of view" a non-inertial frame where a non-inertial observer remains at the spacial origin of the spacetime diagram and the other objects/observers move in relation to him. And, as I said, there are many ways to do this. My favorite is one based on radar measurements because it is something that an observer can actually establish himself and it works the same for inertial and non-inertial observers. Maybe later when I get enough time I'll make a spacetime diagram for the inertial earth observer just to illustrate the process and then I'll make one for the black observer to show how the same technique provides a useful diagram for a non-inertial observer and how these observers can actually establish the Time Dilation of the other observers and their clocks. The concepts are simple but the implementation is rather complex.

The problem with associating the "slow motion" Doppler images with Time Dilation is that if the ships were moving towards each other, the Doppler images would be "fast motion" even though the Time Dilation would be "slow motion".

Here you are getting mixed up with the terminology. Look back at the end of the first paragraph of post #7 where I said, "The dots mark off one-second intervals of time called Proper Time for all observers." You should be labeling those time values as "Proper Time" not "time-coord". The Coordinate Time is marked off by the grid lines. Time Dilation refers to the "stretching out" of the Proper Time on the Coordinate Time chart. So if you look at the first diagram at black's Proper Time dot of 23 seconds which is on the Coordinate Time grid line of 25 seconds and the dot representing one second later, you see that it is more the one second later on the Coordinate Time. But if you look at the same area on the second diagram, you see that the dots have the same spacing as the gridlines which means no Time Dilation or more precisely, a Time Dilation factor of one.

What I was trying to point out is that the Doppler that each observer sees is the same in all IRF's but the Time Dilation is different.

Last edited: Sep 19, 2014
10. Sep 19, 2014

### Albertgauss

Just when I think I am about finished, I get a few more questions. This is worth it for me, though. The answers and understanding I am getting now at the end of all these posts is nothing what I expected, to my benefit, but shows how much I oversimplified my original thinking and how much I’ve learned at the end of all all this.

First, Yes, in the future, I will be more precise about proper time, coord time, etc.

To clear up some of the terminology:

1) Could I say the following all together:

The two ships, if I assume constant acceleration for both according to Earth’s inertial frame, are each in a non-inertial reference frame, then when they hit constant velocity of 0.5c, they are now in those inertial reference frames with respect to Earth?

2) It makes sense to me that "point of view" means what the pilots would actually see and that's what we've been talking about with regard to Doppler,

Yes, this is exactly what I meant the whole time when I got “frames” confused.

3)
it doesn't matter what frame you use when you make a spacetime diagram, they all show exactly the same images propagating from remote events to the observers so in that sense, the point of view of the pilots doesn't depend on the frame.

I agree. I understand this part.

4)
The problem with associating the "slow motion" Doppler images with Time Dilation is that if the ships were moving towards each other, the Doppler images would be "fast motion" even though the Time Dilation would be "slow motion".

Suppose we were to say, trying to simplify, that Doppler is the perception to go to, and Doppler has taken everything into account. Do we agree that, as the final, perceived effects of what the receiving ship receives from the sender when the images come in is that the receiver sees the sender’s reality progress in “slow motion” when the ships recede and “fast forward” when they approach? (I did not include an “approach” case as an example for this post.)

For the non-inertial-frame-of-constant-acceleration part of each ship’s journey, the “slow motion” perception of how reality progresses for the other ship gets longer for receding ships and the “fast-forward” speeds-up for approaching ships. It’s the same images coming in, but the rate at which they are received by the receiving ship is different from how the same images of reality were perceived by the sender and subsequently emitted. Sender sees his reality as it is now, and sends that reality, image-by-image to the recieving ship. When both ships enter their inertial frames of 0.5c with respect to Earth---and after the time needed for each other ship to learn that the other is now in inertial frames--the “slow motion” perception of the other ship’s reality is constant for receeding ships and the “fast forward” would similarly be constant for approaching ships.

How is this working? Notice I am relying on Doppler and assuming Doppler takes time dilation, light-travel delay into account.

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