# Criteria of simultaneity

1. Jul 1, 2013

### analyst5

Hi guys,

I've recently started studying relativity and I thought I was on a good path but I got a little confused with some concepts. I've red a lot about the Andromeda paradox, the train and tunnel experiment and so on so I'll present my question in a way related to those topics.

In my first 'understanding' of the criteria why simultaneity varies I've thought that if an object is moving towards one event and away from the second that he will have the first one before the second in its plane of simultaneity. This seems true, but I've also found out that if he is moving towards the both with the same velocity as the previously mentioned example he will also have the first before second (along the same axis, parallel that is to say). So combining this with the Andromeda paradox made it fuzzy, because it was clearly stated that while moving towards something you will have its future (relative to the stationary observer) in you present, and moving away causes you to have the past in your frame.
But clearly, the observer that moves towards both of them sees one before or another, so I'm interested in the correlation between that situation and the view of the stationary observer. How will the events relate to both of those frames? And what is the criteria to know when an event you have as present while moving is in the future or the past viewed by a stationary observer?

I hope somebody will clear these misconceptions. Thanks in advance.

2. Jul 1, 2013

### ghwellsjr

Simultaneity is a coordinate issue. It's not an observer issue. The confusion comes from the common practice of claiming that every observer has a coordinate system automatically assigned or attached to them and that whatever applies to "their" coordinate system equally applies to the observer.

If instead of getting caught up in that kind of understanding, you think in terms of any single arbitrary inertial coordinate system, you can have any number of observers and objects with complete freedom to do anything you want them to do. They can be stationary at any locations. They can be traveling at any speed (short of c) in any direction. They can accelerate with any desired profile. Whatever you want. Simultaneity becomes a simple matter: if two events have the same time coordinate, they are simultaneous. Please note that an event has both spatial and time coordinates.

Then after you set up your scenario in this Inertial Reference Frame (IRF)with all of its coordinates, you can transform the coordinates of all the events into another IRF moving at any speed short of c with respect to the original IRF using the Lorentz Transformation equations and now all the events will have a different set of simultaneity factors. It's real simple if you do it this way. No confusion at all.

3. Jul 1, 2013

### analyst5

Hey there,

thanks for the reply. I didn't really mean the observer in the sense of what he sees, but rather an intertial reference frame and then consider an observer to be a synonym for it. I partially understand your proposed process of calculating, but I don't understand the issues behind my example.

4. Jul 1, 2013

### ghwellsjr

I also don't understand the issues behind your example because I don't understand your example. What does moving towards or away from an event mean?

Please specify your example according to an IRf. Then it will be clear.

5. Jul 1, 2013

### analyst5

How does the direction of motion affect measurements of simultaneity from relative to the stationary observer who measures the same events? In the Andromeda paradox, it is stated that movement towards Andromeda causes the observer to have the future events in his plane of simultaneity relative to the stationary observer with respect to the Andromeda? How can this be explained in terms of motion?

6. Jul 1, 2013

### ghwellsjr

I'm sorry, but I cannot make sense out of your sentences (except the last one). Please go back and edit your post so that it makes sense. Please also, in the future, preview your posts and proofread them before you submit them.

7. Jul 1, 2013

### analyst5

I apologize.

Suppose we have an intertial frame that is moving towards Andromeda.
How does the direction of motion affect measurements of simultaneity in that frame relative to the frame that is stationary with respect to Andromeda? In the Andromeda paradox, it is stated that when an object moves towards Andromeda its plane of simultaneity is different than the plane of simultaneity of the object that is stationary with respect to Andromeda. So the object will have the future events on Andromeda in his present (future relative to the events that a stationary observer has). What's behind this? How can we know what events are future and past to the stationary observer, just by analyzing a moving inertial reference frame? Could you give me an example that is correlated to Andromeda or something similar? I know that Lorentz transformations play a big role but can it be shown on some real-life example (like the rain and tunnel thought experiment) how this works?

8. Jul 1, 2013

9. Jul 1, 2013

### ghwellsjr

You shouldn't think of an IRF moving except when you are using the Lorentz Transformation to determine the coordinates of another IRF.

You shouldn't think of multiple IRF's when setting up a scenario. Do it all in one IRF and then let the Lorentz Transformation process determine the simultaneity issues for you in any other IRF you desire.

You shouldn't associate simultaneity with objects, just with IRF's. You can always transform to more IRF's in which each object is at rest.

Here's what I suggest you do:

Put three observers at the origin of an IRF and put Andromeda at 2.5 million light-years away and stationary. Have one of the observers move toward Andromeda at some speed v and one move away at the same speed while the third one remains stationary. Draw a spacetime diagram. Mark off some events on Andomeda's worldline and on the observer's worldlines.

Then transform everything into a second IRF moving at v and into a third IRF moving at -v and draw two more diagrams for them. Can you do that?

Last edited: Jul 1, 2013
10. Jul 2, 2013

### analyst5

Thanks for the suggestion, but I'm afraid I can't. I'm really a newbie at all of this...
Could you instead give me an example how the plane of simultaneity moves regarding those 3 observers (if you choose random events on the Andromeda worltube). Is moving towards something a neccessary criteria for having the future of a stationary observery in your present, and otherwise, regarding moving away and therefore having the past in your frame? Could you give me more details how motion affects this relative to the observer who is at rest. Thank you in advance.

11. Jul 2, 2013

### ghwellsjr

OK, here's what I asked you to draw. First, we have the rest frame for Earth (blue) and Andromeda (red) located 2.5 million light-years away from Earth. We count the blue Earth as one of the 3 observers. In addition, we have a black observer moving at 0.6c and a green observer moving at -0.6c:

Now you can see that the top end of the green and black worldlines occurs at a Coordinate Time of 2.5 million years which is also the same as the Proper Time indicated by the dots on the worldlines for Earth and Andromeda. You have to count the dots up from the bottom to see that their clocks are at 2.5 million years. Note also that that the green observer's clock is always simultaneous with the black observer's clock.

Now if we transform all the coordinates of this IRF into an IRF moving at 0.6c, then the black observer will be at rest:

Now all the simultaneity has changed. The end of the black line at the Coordinate Time of 2 million years is simultaneous with about 1.6 million years of Proper Time on Earth, 3.1 million years on Andromeda and 0.9 million years for the green observer.

Transforming again to -0.6c brings the green observer to rest:

Now if we look at the end of the green observer's worldline we can see that it is at the Coordinate time of 2 million years and is simultaneous with 1.6 million years of Proper Time on Earth, 0.9 million years for the black observer and 0.1 million years for Andromeda.

Does this allow you to see the issues you are concerned about?

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12. Jul 2, 2013

### analyst5

Thank you ghwellsjr, I'll take my time studying these diagrams (because it really takes time if you're a starter).

But the main issue still remains, what determines how events from the plane of simultaneity of the moving observer fit into the past and the future of the stationary observer? How to determine the barrier in a plane of simultaneity of a moving observer by which can we say 'these events occur in the future of the stationary observer, and these occur in it past'? Any suggestions?

13. Jul 2, 2013

### pervect

Staff Emeritus
If you are asking about cause and effect, that is determined by light cones.

I'm sure there are a number of threds on the concept, basically all cause and effect relationships are limited to light speed.

Thus if light can reach you from an event it's definitly in your past, and causes from that event can affect you.

No cause and effect relationships are possible until a light signal can travel from one event to the other.

14. Jul 2, 2013

### ghwellsjr

I've drawn three different diagrams in which each observer is moving differently and in which each observer is stationary in one of them. When you ask about a moving and a stationary observer, do you mean the same observer who is moving in one IRF but stationary in another IRF? Or are you picking a single IRF and asking about one stationary observer and a different moving observer?

Let me do another IRF moving at 0.1c with respect to the original IRF:

Note that in this IRF there is no stationary observer. So how does your question apply? Remember, one of the main tenets of Special Relativity is that there is no preferred IRF--any IRF is just as good as any other IRF. I really don't understand what you think the main issue is.

Barrier??? I'm not aware of any barrier that fits with your question. Where did you get the idea that there was a barrier?

Are you aware that you can take any two events that are simultaneous in one IRF and pick another IRF in which they are not simultaneous? That means that one of them is in the future of the other one. And by the same token, one of them is in the past of the other one. And you can pick a third IRF so that the two events switch in terms of which one is in the future or past with respect to the other one.

Here is another IRF moving at -0.1c with respect to the original one:

Now if you go to the first IRF in my first post and pick any pair of events that are simultaneous and look at those same two events in the two IRF's in this post, you will see that they are no longer simultaneous and one of them is in the future (or past) of the other one in the first IRF of this post but that same one is in the past (or future) of the other one in the second IRF of this post.

This is most easily seen by looking at the dots for Earth and Andromeda in all three of these IRF's or by looking at the dots for the green and black observers in all three IRF's. Do you see what I'm talking about?

Yes, pay attention to what I said in my first post: simultaneity is an issue for the coordinates of IRF's not for observers.

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15. Jul 2, 2013

### analyst5

Hey ghwellsjr

Thank you very much for your patience and diagrams. I think I'm starting to get into this.

So what would happen is somebody is moving towards me, with a random relative speed? Would he see my future (the future of my body), even though I haven't experienced it yet?

16. Jul 2, 2013

### ghwellsjr

You're welcome and I'm glad you're comprehending.

I hope you realize that you have changed the subject because back in post #3 you said:

As a result, I did not include any considerations of what any observers would actually see. But rest assured, no observer will be able to see your future before you have experienced it.

Nevertheless, we do want to see how observations fit in with the different IRF's and what you need to learn is that it doesn't matter which IRF we use, changing IRF's does not change what any observer sees. In other words, simultaneity issues are disconnected from observations.

Now rather than start in on a whole bunch more scenarios and diagrams, I'm going to point you to the thread that Naty1 referenced in post #8. There you will find a lot of discussion about what observers see. I pick up the discussion in post #32 on page 2 where I show how different IRF's depict the same observations for an observer who is stationary with respect to the thing being observed.

It's important for you to realize that the Proper Time for an observer (or object) moving in an IRF is dilated, meaning it takes longer for his clock (or time) to progress through an equal interval of Coordinate Time.

Then you must also understand that the light signals (which carry the visual observations) always travel at c along 45 degree diagonals in these IRF diagrams.

Now after you digest post #32, go to the next page where I show what you are asking about where an observer is approaching an event to see how the different IRF's (and their different simultaneities) have no bearing on what he actually sees.

After you digest posts #42 and #43, see if your questions have been answered, otherwise, ask again.