Questions relating to time dilation

[salzrah]

[...] - and thus according to FoR1 at that distant point the event has already happened while it has not yet happened according to FoR2 at that point.[...]

When you say "at that distant point" are you talking about a point with x,y,z and t coordinates? So, to answer my question, are you saying yes it is possible that if I switch into being at rest wrt FoR2, event A has not yet occurred in my frame?

 

[harrylin]

When you say "at that distant point" are you talking about a point with x,y,z and t coordinates? So, to answer my question, are you saying yes it is possible that if I switch into being at rest wrt FoR2, event A has not yet occurred in my frame?

Almost. I explained that while it has necessarily occurred in both frames at that location where it occurred, it has not yet occurred according to the accounting at another, distant location in FoR2 when it has already occurred according to the accounting of FoR1 at that distant point; and that you will better understand that when you have made that sketch with the clocks.

As a matter of fact, it is extremely difficult to correctly say with words what is immediately clear with that sketch. It is more instructive if you do it, but if you don't know how, I or someone else can sketch it for you. Some textbooks and articles show it too.

 

[Erland]

Let's say there are two FoR moving relative to each other. If I am at rest in FoR1 and I see event A occur, then is it possible that if I switch to FoR2 event A has not yet occurred in that frame?

I think it is easiest to take a specific example.

Assume that a very fast (near light speed) spaceship passes next to the Earth in this very moment, in a directtion towards or away from the Sun. Also, at this very moment, we on the Earth see a protuberance erupt on the Sun. Finally, at this same moment, you jump from the Earth into the space ship.
Has then the protuberance erupted yet in your new spaceship frame?

Yes, it has, because it has already been seen. It has been seen from the spaceship (at least it could have) as well as from the Earth, since they are just next to each other.

But people on the Earth and on the spaceship will have different opinions about when the protuberance erupted on the Sun. We on the Earth say it happened eight minutes ago, since the light from the Sun takes eight minutes to reach the Earth. In your new spaceship frame, you will say that it happened at some other passed point of time (depending upon the relative velocity between the spaceship and the Earth), not eight minutes ago.

Assume instead that the protuberance erupted two minutes ago in the Earth frame, so that it will be seen on the Earth in six minutes from now. The spaceship and your jump are the same as before.

Then it is possible that it has not yet erupted for you in your new spaceship frame (it depends upon the relative velocity whether or not it has happened in this system).

But the protuberance has not yet been seen, neither from the Earth nor from the space ship, so neither people on Earth nor people on the spaceship have any information that it has happened.

 

[salzrah]

Assume instead that the protuberance erupted two minutes ago in the Earth frame, so that it will be seen on the Earth in six minutes from now. The spaceship and your jump are the same as before.

Then it is possible that it has not yet erupted for you in your new spaceship frame (it depends upon the relative velocity whether or not it has happened in this system).

But the protuberance has not yet been seen, neither from the Earth nor from the space ship, so neither people on Earth nor people on the spaceship have any information that it has happened.

Okay, great example. However, what if the protuberance erupted eight minutes ago in the Earth frame so at the same instant that I see it happen in the Earth frame I jump into the space ship.

Then it is possible that it has not yet erupted for you in your new spaceship frame (it depends upon the relative velocity whether or not it has happened in this system).

If that sentence you say is true, then isn't it possible for me to tell the crew of the spaceship that an event will occur in their reference frame before it does?

As a matter of fact, it is extremely difficult to correctly say with words what is immediately clear with that sketch. It is more instructive if you do it, but if you don't know how, I or someone else can sketch it for you. Some textbooks and articles show it too.

I'm having a hard time visualizing this sketch. If you have any quick links for an example that would be great.

 

[Erland]

Okay, great example. However, what if the protuberance erupted eight minutes ago in the Earth frame so at the same instant that I see it happen in the Earth frame I jump into the space ship.

This situation was described in the first half of my post. We on the Earth, the crew on the ship and you see the protuberance erupt at this very instant.

If that sentence you say is true, then isn't it possible for me to tell the crew of the spaceship that an event will occur in their reference frame before it does?

No, since you have no knowledge of the event yet (unless you have some scientific method to predict protuberances in advance, like e.g. weather forecasts, but that's not the kind of knowledge which is relevant here).
You, and the crew on the ship will see the protuberance erupt at some point of time in the future, which depends upon the velocity of the ship (relative to the Earth frame).

 

[salzrah]

Assume that a very fast (near light speed) spaceship passes next to the Earth in this very moment, in a directtion towards or away from the Sun. Also, at this very moment, we on the Earth see a protuberance erupt on the Sun. Finally, at this same moment, you jump from the Earth into the space ship.
Has then the protuberance erupted yet in your new spaceship frame?

Yes, it has, because it has already been seen.It has been seen from the spaceship (at least it could have) as well as from the Earth, since they are just next to each other.

No, as we have already agreed on before, the spaceship is moving away from the sun so it will see the eruption at a later time then when the Earth-frame sees it. The second postulate is not violated because we account for length contraction in the spaceship's rest frame. The Earth-frame and spaceship frame do not see the eruption at the same time just because they're next to each other...the spaceship has a relative velocity wrt the sun, which affects the time.

No, since you have no knowledge of the event yet (unless you have some scientific method to predict protuberances in advance, like e.g. weather forecasts, but that's not the kind of knowledge which is relevant here).

The knowledge of the event occurring comes from me originally seeing the eruption happen in the Earth frame. Then, I instantly jump on the space ship.

Assume instead that the protuberance erupted two minutes ago in the Earth frame, so that it will be seen on the Earth in six minutes from now. The spaceship and your jump are the same as before.

Then it is possible that it has not yet erupted for you in your new spaceship frame (it depends upon the relative velocity whether or not it has happened in this system).

Why does it matter if the Earth sees the eruption in six minutes or eight minutes or if it has just seen it? In all cases, the above underlined quote from you should be true. The eruption happens, then there is some X amount of time before the Earth-frame sees it. This time should not affect the possibility that the eruption has or hasn't occurred in the spaceship frame (the underlined sentence you said above).

 

[Erland]

No, as we have already agreed on before, the spaceship is moving away from the sun so it will see the eruption at a later time then when the Earth-frame sees it.

In the case we are talking about here, the ship passes next to the Earth, with a negligible distance, at the same instant as the eruption is seen on the Earth (and you also jump at this same instant). Since it is seen at the Earth, it must certainly be seen on the ship too, since the Earth and the ship have effectively the same location at this instant.

The knowledge of the event occurring comes from me originally seeing the eruption happen in the Earth frame. Then, I instantly jump on the space ship.

Right, and since you haven't seen it yet, you have no knowledge about it.

Why does it matter if the Earth sees the eruption in six minutes or eight minutes or if it has just seen it? In all cases, the above underlined quote from you should be true. The eruption happens, then there is some X amount of time before the Earth-frame sees it. This time should not affect the possibility that the eruption has or hasn't occurred in the spaceship frame (the underlined sentence you said above).

I don't understand what you mean. An event at the Sun is always seen eight minutes later on the Earth, in the Earth-Sun-frame, as long as the distance between the Earth and the Sun is unchanged.

 

[harrylin]

[..] I'm having a hard time visualizing this sketch. If you have any quick links for an example that would be great.

It's roughly like this, for a certain velocity, system S' moving to the right according to system S at t=0:

_____________________________ S'
+0.3 +0.2 +0.1 +0.0 -0.1 -0.2 -0.3 t'

The line corresponds to the x' axis of S'; typically one puts also x'=0 (as well as x=0) in the middle. Below the line are the clock times of S' at t=0 according to S. The point is that the two systems map distant time differently.

Say that a rocket takes off from Earth at position x=0 and time t=0 according to S, after a ten second count-down. Then an observer on the moon who is completely to the right on the sketch and who uses S will look at his clock and say when it reads 0 that it must be happening "right now" (t=0). However, if he would have switched to using system S', then he would say that it is going to happen in 0.3 seconds from now (reckoned in seconds of S').

 

[Adrian07]

Dont know if this is relevant to the argument but if the frequency of the light from both sources is the same then the the light received by the stationary observer will have the same frequency from both sources whereas the moving observer will still say the events happened at different times and also the frequency is different, doppler effect, by comparing the change in frequency the moving observer will know that the difference in the timing of the 2 events is caused by their motion and surely could even work out their speed relative to the 2 events and so could agree with the stationary observer about the timing of the 2 events. Or have I got this wrong.

 

[Erland]

Why does it matter if the Earth sees the eruption in six minutes or eight minutes or if it has just seen it? In all cases, the above underlined quote from you should be true. The eruption happens, then there is some X amount of time before the Earth-frame sees it. This time should not affect the possibility that the eruption has or hasn't occurred in the spaceship frame (the underlined sentence you said above).

What we can say for certain is that, at the instant when the ship passes the Earth, the eruption has already been seen on the Earth if and only if it has already been seen on the ship.

For if it has been seen on the Earth but not on the ship, then, at the instant of the passage, people on the Earth can tell people on the ship about it (using you as a jumping messenger, for example), and then the people on the ship receives the information about the eruption before they see it (which they will not do until at a later point of time), which means that the infomation they receive about the eruption has been traveling faster than light, and that is impossible.
Likewise if it has been seen on the ship but not on the Earth.

If it has not been seen at the instant of passage (by either observer), then observers on the Earth and on the ship may have different opinions about when the eruption occurred (but they can of course not form these opnions until after they see the eruption, and of course, any observer says it erupted before (s)he saw it). It may be so that one says it happened before the passage and the other says after, or it may not be so, it depends partially upon the velocity of the ship relative to the Earth.