Questions relating to time dilation

[salzrah]

Hi salzrah, this can be a...

levytate, I have never tried to account for length contraction when solving these problems of relativity of simultaneity. But after reading your post, which may explain a lot to me, can you tell me why we should apply the principle of length contraction to Garrett's reference frame? That will help me justify what you are saying is correct.

 

[pervect]

Sorry to spam posts but can whoever answer this question.
Let's say I am standing between two light bulbs and they both turn on at the same time.

As someone has probably already mentioned, "at the same time" doesn't have any meaning unless you specify a reference frame.

So we can rephrase your question and add a friend to it, so we can avoid any confusion in switching reference frames. So we'll have you stay still, in your own inertial reference frame, and your friend, moving at a constant velocity, in his own inertial reference frame, and your friend will pass you so that you are both together when the light bulbs turn on. We can then phrase the question as follows:

"Let's say I am standing between two light bulbs and they both turn on at the same time in the reference frame I'm standing still in

At the same instant, my friend runs by me at .5c. Does my friend see the right light bulb light before me in his reference frame?"

The answer is yes.

And we can add another question:

Did my friend see both light bulbs turn on at the same time in his reference frame?

And the answer is no.

And we can also ask

"Suppose instead of a friend passing by me at .5c, I start to accelerate - what happens then?"

There is a certain amount of convention in specifying "now" in an accelerating reference frames / coordinates. The usual convention is to use the notion of "now" of an observer who is comoving and colocated with you at the instant that "now" is to be defined to define the notion of simultaneity in an accelerating frame. The coordinates and frames does NOT cover all of space-time - but if your acceleration is moderate, it will include you and both lights.

A detailed discussion of the conventional accelerating reference frame and the limitations of the concept are interesting, but probably too far outside the scope of the original quesiton.

Anyway, using this simultaneity convention (that of a comoving, colocated inertial observer) the answer is that you see the right light light up first.

The one thing I'll hope you'll understand and remember out of this:

"At the same time" doesn't have any meaning by itself, because time is not absolute.

 

[salzrah]

And the answer is no.

And we can also ask

Pervect, can you explain to me why the answer to that question is no. (btw I agree with you, I just want to see how you justify your answer).

 

[salzrah]

Yes. (But the only reason you can get away with saying that both light bulbs turned on "at the same time" and "at that instant" is that you started at rest relative to the two bulbs)
You used the same line of thinking in post #53... And it's not right, but I can fix it with just three little words:That is, you have just described the way in which events that are not simultaneous in one frame can be simultaneous in another. And that's what relativity of simultaneity is all about.

Where you've been going wrong is in thinking that the simultaneity in Meagan's frame is "right" while the non-simultaneity in Garett's frame is an illusion of his motion. But as far as Garett is concerned, Meagan is the one moving, not him... So as far as Garett is concerned, the non-simultaneity in his frame is real while Meagan is the one experiencing an illusion of motion.

To address the arguments in this post, look at the one right above it I posted. Look, I am not saying either frame of reference is right and another is an illusion of motion. I am saying that both lightning flashes occur at the same time in both reference frames, but in one (the reference frame moving relative to the origins of light) he only SEEEEEEEES the lightning flashes occur at different times, which does not mean that they actually happened at different times in the moving persons frame of reference.

 

[Nugatory]

That answer is incorrect. Let me explain. After the lightning flash, the lady moves relative to the point where that lightning flash occurs. The scorch mark does not. You are confusing these two to mean the same thing. Yes, the scorch mark stays the same distance away from the lady, but the origin of the light source does not remain the same distance away because the train-lady moves away from it. It'll be easier to visualize if you imagine the lightning strike to happen in the air on the sides of the train and understand that the lady moves away/towards these points in the air.

That answer is correct, and the easiest way to see this is to solve the problem in the reference frame in which the train and the lady and the scorch mark on the train are all at rest. That's what "according to the people on the train" means.

(and I just lost a bet with myself - I was expecting you to start disagreeing at question 3)

 

[salzrah]

Nugatory! Yes, the scorch mark is at rest in the reference frame of the train and lady. BUTTTT the position of the origin of the light is NOTTTTTTTTTTTT. The lady-train are moving relative to the origin of the light-- the scorch marks don't mean anything. ahhhhhhhhh my head's going to explode. lol

Nuggatory, do you think that the time it takes for the light to travel to the train-lady is the same for both lights?

 

[ghwellsjr]

Sorry to spam posts but can whoever answer this question.
Let's say I am standing between two light bulbs and they both turn on at the same time.

You should always get in the habit of saying which frame you mean when you say two remote events happen at the same time, even if you think it is obvious. And you should state clearly that you are half way between the two light bulbs, if that is what you mean. Otherwise your scenario is ambigous. You should say, I am standing halfway between two light bulbs and they both turn on at the same time in my rest frame.

At that instant, I begin to run towards the light bulb on the right at a speed .5c.

Now you have introduce a third event, that of you starting to run. So all three events happen at the same time.

Will I see the light from the right bulb before the light from the left bulb?

Yes, you will see the light from the right bulb before the light from the left one.

Now if you had said that it was in the frame in which you are at rest while you are traveling at 0.5c that the light bulbs turned on at the same time, both being equidistant from you at that moment, then you would see light from them both at the same time.

Can everyone please please please read this explanation about the relativity of simultaneity by HowStuffWorks.
http://science.howstuffworks.com/science-vs-myth/everyday-myths/relativity13.htm

There's a little confusion on this website because of this sentence:

If Garret rides his skateboard in the same fashion as he did with the cannonballs, when he reaches the halfway mark, he sees the light bulb he is moving towards turn on first and then he sees the light bulb he is moving away from turn on last.

It's hard to tell if the author meant for the phrase "when he reaches the halfway mark" to apply to the preceding phrase and the preceding sentence and the preceding paragraph, meaning that when he reaches the halfway mark, the lights turn on, which would be correct for what he says later. But, it would more likely be interpreted by someone who is just learning SR that he meant for that phrase to apply to the next phrase, meaning when he reaches the half way mark he immediately sees the light he is moving towards turn on and then later sees the other bulb come on, which would be incorrect.

Now, just because Garett (the guy on the skateboard) SEES the light at different times does not mean they actually occurred at different times in his frame of reference. He can use his relative velocity with respect to Meagan OR with respect to the origin of the light source, which is a point in space that is at rest in Meagan's frame, and calculate how much extra distance the light on the left had to travel. He will then determine that the two light bulbs in fact turned on at the same time.

You have to understand that the issue of "did the lights come on at the same time" is a matter of definition. Nature does not disclose to us whether two remote events happen at the same time. So we must agree on a definition to be able to talk sensibly about remote events.

And we have all agreed to use Einstein's definition of simultaneity which is if you are halfway between two events in your rest frame and you see them at the same time, then they happened at the same time in your rest frame.

So if you say that Garret is halfway between the two bulbs in his rest frame and he does not see them turn on at the same time then they did not turn on at the same time in his rest frame. But you are correct, he can see when and where he was when he saw each light bulb come on and do a calculation to see if the light bulbs came on at the same time in Meagan's rest frame.

 

[salzrah]

Yes, you will see the light from the right bulb before the light from the left one.

Now if you had said that it was in the frame in which you are at rest while you are traveling at 0.5c that the light bulbs turned on at the same time, both being equidistant from you at that moment, then you would see light from them both at the same time.

You say, "...while you are at rest while you are traveling at .5c" is that a typo?
Did you mean to say something like-- "Now if you had said that it was in the frame in which you are at rest with respect to the light origins that the light bulbs turned on at the same time, both being equidistant from you at that moment, then you would see light from them both at the same time." ? If yes, okay I agree.

There's a little confusion on this website because of this sentence:


It's hard to tell if the author meant for the phrase "when he reaches the halfway mark" to apply to the preceding phrase and the preceding sentence and the preceding paragraph, meaning that when he reaches the halfway mark, the lights turn on, which would be correct for what he says later. But, it would more likely be interpreted by someone who is just learning SR that he meant for that phrase to apply to the next phrase, meaning when he reaches the half way mark he immediately sees the light he is moving towards turn on and then later sees the other bulb come on, which would be incorrect.

I took that sentence to mean the former way -- the correct way.

So if you say that Garret is halfway between the two bulbs in his rest frame and he does not see them turn on at the same time then they did not turn on at the same time in his rest frame. But you are correct, he can see when and where he was when he saw each light bulb come on and do a calculation to see if the light bulbs came on at the same time in Meagan's rest frame.

As I have said earlier. Just because "he does not see them turn on at the same time" does NOT mean "they did not turn on at the same time in his rest frame". Just because he SEES something at a certain time does not mean it HAPPENED at that time. Garret can calculate the extra distance/short distance the lights traveled and figure out that in fact the two flashes occurred at the same time in his reference frame. Meagan can also conclude both flashes occurred at the same time because she SEES the light travel to her at the same time AND the relative velocity between her and the origin of the light is zero, unlike Garret.

 

[levytate]

levytate, I have never tried to account for length contraction when solving these problems of relativity of simultaneity. But after reading your post, which may explain a lot to me, can you tell me why we should apply the principle of length contraction to Garrett's reference frame? That will help me justify what you are saying is correct.

As far as I know it has to do with the constancy of c (the speed of light). That is, the speed of light is the same for all observers irrespective of their motion relative to the source of the light.

The scenario you are proposing, where Garret is traveling at a velocity v towards one bulb (lets call that B) and away from the other (let's call that A), and he sees the light from B first, and then A, but is able to calculate that both lights flashed simultaneously, by calculating the distance the light has traveled when he meets it, would be true under Galilean relativity. It would, however, mean that Garret would measure the speed of light to be c+v.

He could calculate that the speed of light with respect to its source is c, but the constancy of the speed of light says that the speed of light is c for every observer, irrespective of their motion relative to the source.

 

[pervect]

Pervect, can you explain to me why the answer to that question is no. (btw I agree with you, I just want to see how you justify your answer).

The Einstein synchronization convention says that if you emit a signal at the midpoint of two points, clocks are synchronized if and only if the two clocks have the same reading when the signal arrives at their location.

We can draw the space-time diagrams for a stationary frame, in which case we see that a horizontal line represents the line of simultaneity.

If we draw the space-time diagram for Einstein synchronization in a moving frame, we can see that it's not horizontal, and hence that the notion of simultaneity is different.

The threads in which I first drew these diagrams might also be of some interest.
It appears the second one is more complete, one of the diagrams went missing in the first thread.

https://www.physicsforums.com/showpost.php?p=3447152&postcount=5
https://www.physicsforums.com/showpost.php?p=3451900&postcount=26

 

[salzrah]

As far as I know it has to do with the constancy of c (the speed of light). That is, the speed of light is the same for all observers irrespective of their motion relative to the source of the light.

The scenario you are proposing, where Garret is traveling at a velocity v towards one bulb (lets call that B) and away from the other (let's call that A), and he sees the light from B first, and then A, but is able to calculate that both lights flashed simultaneously, by calculating the distance the light has traveled when he meets it, would be true under Galilean relativity. It would, however, mean that Garret would measure the speed of light to be c+v.

He could calculate that the speed of light with respect to its source is c, but the constancy of the speed of light says that the speed of light is c for every observer, irrespective of their motion relative to the source.

First, I'm glad you actually understand my argument and reason that it does make sense [except for afterwards when you disprove it =p]. Second, your explanation seems sound and almost makes complete sense to me. But let me go through it and see if I really understand what you are saying. I believe you are saying that the distances (measured by Garret) the two light waves travel to hit Garret (who is in a frame moving with respect to the light origins) can NOT be used to calculate the actual time when the flashes occur. This is because by using these distances, the relative speed (measured in Garret's frame) between Garret and the light would be greater than c. This makes sense because if he measures a distance D1 that the light he is traveling towards has to move through to hit him and a time T1 it takes for that to happen (both measured in his frame of reference), he will get a value NOT equal to c for the relative speed between him and the light. This is because D1 accounts for the movement of Garret to the light relative to Meagan (in rest frame of light origin) AND the movement of the light to Garret relative to Meagan. This value of D1, measured by Garret in his frame, will cause the relative speed between Garret and the light to be higher than c. This conclusion itself means that D1 or T1 must change.

Now, you're saying we can chose for D1 to change, applying "length contraction". Okay, so now we get new values of D1. This new distance value will ensure D1/t = c. Likewise, we can say T1 has to change and apply "time dilation". We apply time dilation and get a new time T1 for the time measured by Garret in his frame -- this value will make d/T1 = c.

Next, we can apply either one of these techniques for the other light wave that Garret is moving away from in his frame. Now that we have all of our new D1/D2 OR T1/T2 values what can we conclude? We can conclude that Meagan will either
a) see the light waves travel different distances (to reach Garret) in her frame than what Garret measures in his frame.
or
b) see the light waves travel different time intervals (to reach Garret) in her frame than what Garret measures in his frame.

Is everything I have said above correct? I feel like I kind of understand where length contraction and time dilation come from now. If yes, how does any of that relate to or prove that two events that are simultaneous in one FoR are not simultaneous in another FoR that is moving relative to the other frame (relativity of simultaneity)? The only way I imagine that it proves the relativity of simultaneity is by observing that when you calculate the ACTUAL time the front lightning flash [that Garret moves towards] occurs in Garret's frame using the new D1 or T1, it will be different then the ACTUAL time you calculate that the back lightning flash [that Garret moves away from] occurs in Garret's frame using the new D2 or T2. Essentially, both events MUST occur at different times in Garret's frames to keep the integrity of Einstein's second postulate.

If everything stated above is correct, then my last request is for someone to prove this mathematically, by using the Lorentz factor, for any random situation such as the train/lightning one we discussed in this thread-- for the sake of me and other people who are reading that need this last bit of justification for the relativity of simultaneity.

After asking for that mathematical proof I have one last question -- 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?*** the ACTUAL time is when the event occurs in a reference frame accounting for (subtracting) the time it takes for light to travel to the object/Garret's eyes
***FoR = frame of reference

 

[Erland]

Yes, that is true. But the point of the light origin IS NOT MOVING with the train. It stays at the position where it was. So while the train moves relative to the point, even though the x-axis is at rest wrt the train, the x-axis is not at rest with respect to the point. Okay, can you tell me if you can represent the point of where the light originates as a ball? Or any object? It will help me in making an example if you agree with that...

Let us represent the x-axes as two very long rulers, with ordinary marks on them, one at rest relative to the ground-frame and the other one at rest relative to the train-frame. These rulers are physical, made of wood, metal, plastic, or anything.
Now, suppose that a beam of light suddenly begins its journey at a point whose x-coordinate is (say) x=4 on the ground-ruler and (say) x=7 on the train-ruler. These coordinates are physical marks on the rulers. At this event these two marks at the rulers lie next to each other, with effectively no distance between the marks.

As time goes by, these two marks on the rulers move away from each other. Yet, you are convinced that the "point of the light origin", which we may think of as a ball if you want to, all the time stays at the x=4-mark on the ground-ruler, not at the x=7-mark on the train-ruler. For you say that "the point of the light origin IS NOT MOVING with the train". Why not? Why can't I with the same right say that the point of the light origin (ball) IS NOT MOVING with the ground, but is at rest relative to the train?
For this "ball" is entirely abstract. We cannot see it, or detect it with any experiment. It only exists in our imagination. (If you don't agree with this, please design such an experiment!)
And then there is no compelling reason to say that it is at rest in the ground-frame and moves in the train-frame, and not the other way round.

The only reason I can think of is that you consider the ground as actually at rest, and the train as actually moving. But, by the Special Principle of Relativity, we have precisely the same right to say that the train (with its ruler) is at rest, and that the ground (with its ruler) is moving. Thus, this reasoning contradicts the Special Principle of Relativity, and this why I say that you deny this principle.

 

[salzrah]

Okay Erland, I finally understand what you are saying. You can say that the origin of light is at rest with either the ground-frame or the train-frame. But that's not the point. The point is that at least one of the frames will NOT be at rest relative to the origin of light, and the other WILL be at rest relative to the light origin. This still doesn't answer the statements I expressed earlier. However, I am glad we got that cleared up. This entire time I thought you were arguing that there is no relative motion between the ground-frame and the light origins AND no relative motion between the train-frame and the light origins.

 

[Erland]

Okay Erland, I finally understand what you are saying. You can say that the origin of light is at rest with either the ground-frame or the train-frame. But that's not the point. The point is that at least one of the frames will NOT be at rest relative to the origin of light, and the other WILL be at rest relative to the light origin.

OK, we can express it in this way if you want to. And I am also glad that we agree on this.

It must be emphasized, however, that when we say that one of the two frames in question is at rest relative to "the origin of light" and that the other one is not at rest relative to "the origin of light", this is a completely arbitrary choice. We can with equal right make the opposite choice.

And it follows from this arbitrariness of choice, by an argument that is familiar by now (in the video, for example), that there are pairs of events which are considered as simultaneous in one of the frames but not simultaneous in the other frame.

 

[ghwellsjr]

Okay Erland, I finally understand what you are saying. You can say that the origin of light is at rest with either the ground-frame or the train-frame. But that's not the point. The point is that at least one of the frames will NOT be at rest relative to the origin of light, and the other WILL be at rest relative to the light origin. This still doesn't answer the statements I expressed earlier. However, I am glad we got that cleared up. This entire time I thought you were arguing that there is no relative motion between the ground-frame and the light origins AND no relative motion between the train-frame and the light origins.

I hate to burst your bubble but the issue of simultaneity has nothing to do with the rest state of the "origin of light". That is why Einstein uses lightning instead of light bulbs. When you use light bulbs you can easily get hung up by this irrelevant side issue of being concerned about the rest state of the bulbs both before and after they come on. If we think of lightning as being a single instantaneous event, meaning that it has no motion in any frame, then you can get away from your fixation on the "origin of light".

Also, your request for a proof of the relativity of simultaneity cannot be fulfilled. If you don't accept Einstein's second postulate and his definitions that lead to the concept of a reference frame, but rather take the viewpoint of those prior to Einstein's theory that there exists an ACTUAL time, as you put it, then you will never be satisfied with Einstein's theory. Even if you believe that nature operates on a universal absolute time, which is the same as promoting an absolute ether rest state, but you acknowledge that that absolute ether rest state can never be identified, then it's not a matter of finding a proof for the relativity of simultaneity, but rather of realizing that Einstein's second postulate and his theory of Special Relativity is a simpler theory than any other theory that supports the idea of an ACTUAL time and because it is consistent with the facts of nature, it can be accepted without any proof whatsoever, which is a good thing because there is no such proof.

 

[Erland]

In order to simplify the discussion, so that people don't need to repeat the same arguments again and again, and to avoid misunderstandings, let me clarify this about salzracs posiition, if I understand him correctly (salzrac may correct me if I am wrong):

1. With "origin of light", he does not mean "light source" but - something else.
2. He accepts both the fundamental postulates of SR.
3. He accepts time dilation.
4. He does not accept the relativity of simultaneity.

 

[salzrah]

I hate to burst your bubble but the issue of simultaneity has nothing to do with the rest state of the "origin of light". That is why Einstein uses lightning instead of light bulbs. When you use light bulbs you can easily get hung up by this irrelevant side issue of being concerned about the rest state of the bulbs both before and after they come on. If we think of lightning as being a single instantaneous event, meaning that it has no motion in any frame, then you can get away from your fixation on the "origin of light".

So you're saying there can be no relative motion between the light origin and another object? Look, the origin of light is the position where the light comes from. Why can you not have motion relative to this origin? It does't matter if it's lightning or a light bulb -- they BOTH have an origin from which they emit light. How can you deny I cannot move away from where a light originates? That's absurd. As for motion relative to light itself, the ideas of length contraction and time dilation were added to Einstein's relativity to ALLOW motion with respect to light. So whether you say you cannot have motion relative to the origin of light, or if you say you cannot have motion relative to light itself -- I say you're wrong.
You said, "If we think of lightning as being a single instantaneous event, meaning that it has no motion in any frame," how does that make sense? Just because an event is instantaneous does not mean we cannot move relative to that event. Instantaneous means it happens in an insignificant amount of time... I'm not trying to nit pick what your saying, but without a better explanation on your part I can't understand where you're coming from.

Also, your request for a proof of the relativity of simultaneity cannot be fulfilled. If you don't accept Einstein's second postulate and his definitions that lead to the concept of a reference frame, but rather take the viewpoint of those prior to Einstein's theory that there exists an ACTUAL time, as you put it, then you will never be satisfied with Einstein's theory. Even if you believe that nature operates on a universal absolute time, which is the same as promoting an absolute ether rest state, but you acknowledge that that absolute ether rest state can never be identified, then it's not a matter of finding a proof for the relativity of simultaneity, but rather of realizing that Einstein's second postulate and his theory of Special Relativity is a simpler theory than any other theory that supports the idea of an ACTUAL time and because it is consistent with the facts of nature, it can be accepted without any proof whatsoever, which is a good thing because there is no such proof.

I accept the relativity of simultaneity I just wanted a mathematical proof of the particular situation I mentioned. And I DO accept Einstein's second postulate. You're confusing what I mean by "ACTUAL time" , the ACTUAL time is when the event occurs in a reference frame accounting for the time it takes for light to travel to your eyes. I am not at all saying that there exists some right time for both reference frames or some "universal absolute time" for when the lightning strikes. In the manner I speak of ACTUAL time it DOES EXIST -- you simply confused what I mean by it.

Either way, in the end I completely understand the relativity of simultaneity and the solution to the problem I had with it has NOTHING to do with relative motion, "ACTUAL time", motion wrt the light origins, or any other argument that was placed. I understood the concepts completely and understood both of Einstein's postulates. The solution to the problem came from levytate who led me to find out that length contraction and time dilation are the solutions to the problems I was presenting in the relativity of simultaneity. Now it all makes sense. However, I will still greatly appreciate it if someone answered the last question I proposed in post #81 =). Thanks to everyone for the great discussions we had so far on this thread!

 

[salzrah]

In order to simplify the discussion, so that people don't need to repeat the same arguments again and again, and to avoid misunderstandings, let me clarify this about salzracs posiition, if I understand him correctly (salzrac may correct me if I am wrong):

1. With "origin of light", he does not mean "light source" but - something else.
2. He accepts both the fundamental postulates of SR.
3. He accepts time dilation.
4. He does not accept the relativity of simultaneity.

1. The origin of light is the POSITION of where the light source originally emits light.
4. I do NOW accept it, just needed the right proof =)

Look at post #81 and the end of post #87

 

[harrylin]

[..] You may also have gotten the impression that light itself plays some fundamental role in relativity. The modern point of view is that it doesn't. The fact that Einstein's 1905 postulates referred to light was just an artifact of people's limited understanding of fundamental particles and fields in 1905.

That has nothing to do with "people's limited understanding in 1905". The original view was that light itself doesn't play a fundamental role in relativity - it's simply a kind of boundary condition that allows to obtain in a simple and straightforward manner the Lorentz transformations.

how can we theoretically prove that time measuring techniques that do not rely on light still have special relativistic effects? [...]

One can never theoretically prove that a theory cannot be disproved. By the time of inception of SR, there was ample evidence that no matter how one measured, the relativity principle was upheld for mechanical and electromagnetic effects; and Maxwell's theory of light propagation was also firmly established.
If other time measuring techniques do not have relativistic effects, then the relativity principle can be broken; but there is to my knowledge no reason to expect such a possibility.

 

[harrylin]

[..] I have one last question -- Let's say there are two FoR moving relative to each other. If I am 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 assume that you mean that you are in rest in FoR1. Event A occurs in both frames. And obviously, since an event that happened did so in both frames, it also happened in the other frame at that point. However, due the disagreement about clock synchronisation it is different at another point far away. FoR1 ascribes for example to FoR2 that its clocks there are behind - 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.
You can easily see that for yourself if you make a sketch with two X-axes for S and S' to which you add clock times, and on which you for simplicity place the event at point x=x'=0 and with both clock times t=t'=0, as is habitual with the Lorentz transformations.

 

[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.