# What will be the events relative to the ground observer , a time-like or space like?

1. Feb 25, 2012

Please refer to the attached diagram

The train moves in the direction B-A

If the events seen in the ground observer simultaneously, it should be seen at A before B in the train

In special case, the difference in times between A and B according to the train observer could be equal to the time a light signal takes to travel from A to B only if v/c=0.618

However, if the light travel from A to B relative to the train observer, it should do so relative to the ground one as well. But because of the experiment setup, still the ground observer sees the 2 events happen at the same time

So what will be the events relative to the ground observer, a time-like or space like?

Thanks,,,

https://www.physicsforums.com/attachment.php?attachmentid=44367&stc=1&d=1330188385

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2. Feb 29, 2012

Re: what will be the events relative to the ground observer , a time-like or space li

3. Feb 29, 2012

### nitsuj

Re: what will be the events relative to the ground observer , a time-like or space li

seperated spatialy and can be observed as happening simultaniously, spacelike I think.

4. Feb 29, 2012

### Michael C

Re: what will be the events relative to the ground observer , a time-like or space li

If two separate events are simultaneous in a particular frame, they have a space-like separation in all frames.

5. Feb 29, 2012

### nitsuj

Re: what will be the events relative to the ground observer , a time-like or space li

Good point the distinction between spacelike & timelike is invariant.

6. Mar 1, 2012

Re: what will be the events relative to the ground observer , a time-like or space li

OK,,, but according to my calculation attached here, the Δt between A and B for the train observer can be equal to the Δttaken by a light signal from A to B in case of v/c=0.618. This yields a time-like separation !

Last edited: Mar 1, 2012
7. Mar 1, 2012

### Fredrik

Staff Emeritus
Re: what will be the events relative to the ground observer , a time-like or space li

In the first sentence (in the attachment), you're talking about A and B as if they are events. Later you're talking about them as if they are locations in space (specifically in the slice of spacetime that the ground considers space). This makes your argument quite confusing.

If A and B are events, it only makes sense to say that a light signal is sent from A to B if their separation is lightlike, but this would of course immediately contradict the earlier claim that there's an inertial frame in which A and B are simultaneous. Then you start talking about calculating the time it takes the signal to go from A to B. By then you are clearly thinking of A and B as locations, not events. The signal would be sent from an event E on A's world line and received at an event F on B's world line. The separation between E and F is obviously lightlike.

Last edited: Mar 1, 2012
8. Mar 1, 2012

### John232

Re: what will be the events relative to the ground observer , a time-like or space li

The ground observer will see the two "simultanious" events happen at two different times, this is because it will take longer for light to reach the ground observer, but this would only be an illusion since the photon would only be traveling a larger distance from one of the points. Similiar to how we look back in time when we look at the stars, the stars are not younger just because we see them that way. It just takes a certain amount of time for the light to reach the observer since it travels at a limited speed. So then, I would say the seperation of the events is just space like.

9. Mar 1, 2012

### Fredrik

Staff Emeritus
Re: what will be the events relative to the ground observer , a time-like or space li

It has nothing to do with that. When we're talking about what someone "sees" or "experiences", we're not talking about what their eyes or video cameras would pick up. We're talking about the coordinate assignments they would make. An observer on the ground "sees" two events as simultaneous if and only if he assigns the same time coordinate to them.

10. Mar 1, 2012

### nitsuj

Re: what will be the events relative to the ground observer , a time-like or space li

I disagree with that, I can use my head and consider the time that the light has travelled an deduce the star is now older, but from an observed "my reality" perspective what's measureable is all of the information I have ( or could possibly have) regarding that "distant star". The physical reality travels at c. all else is "elsewhere" and sometimes termed unphysical.

That being said, the star is actually "younger" here compared to over "there". not an illusion, a reality. Said differently, at the location here the "distant star" is not old yet, because of the spatial separation more time needs to pass until the star is "old" over here. It would be a safe bet the star is even older over there but that proof does not exist over here, it is not a "reality" here, more an "illusion" of the "mind's eye", specifically an assumption. ( of course physics can predict this future accurately, calculating the age of the star over there, and intuitively is reffered to as "it's age", but comparatively thats relative)

(mumbo jumbo here, but I think it could even be physicaly possible for there to be a "closed timelike curve" (or spacelike? idk) that "transports" the light to the observer location faster than light years)

Last edited: Mar 1, 2012
11. Mar 1, 2012

Re: what will be the events relative to the ground observer , a time-like or space li

I meant A and B as events

If A and B are simultaneous for the ground observer, they must have a spacelike separation for the train observer. This should not permit Δt to be long enough to allow B receiving any light from A. But that may happen if v/c=0.618 !

12. Mar 1, 2012

### Fredrik

Staff Emeritus
Re: what will be the events relative to the ground observer , a time-like or space li

Then your calculation doesn't make much sense. You wrote "AB", meaning "the distance in space between A and B in the ground's(?) rest frame". That's OK, since A and B are by assumption simultaneous in that frame. But then you multiplied AB by $1/\gamma$, expecting to get the distance in space between A and B in the other frame. The concept of distance in space in the train's frame between A and B doesn't make sense, since A and B aren't simultaneous in that frame. What you're calculating this way is the distance in the train's frame between the two points on the ground where A and B occurred. This is not a distance between A and B. It's the distance in the train's frame between A and and an event C on the world line of the point on the ground where B occurred. C would occur significantly later than B, but still not late enough to receive a light signal from A.

13. Mar 2, 2012

Re: what will be the events relative to the ground observer , a time-like or space li

The distance AB for the train observer wont change because he sees the event A happens before B. He always considered A and B simultaneous whenever he measures AB as a distance.
The derivation of Δt according to LT is also based on that assumption and therefore multiplying AB by $1/\gamma$ to yield AB. So multiplication by $1/\gamma$ occurs on both sides of the equations i & ii and it will cancel each other out
And even if you dont want to consider $1/\gamma$, no problem, as the quadratic equation still remains valid because AB will cancel each other out again

Last edited: Mar 2, 2012
14. Mar 2, 2012

### Fredrik

Staff Emeritus
Re: what will be the events relative to the ground observer , a time-like or space li

I don't understand what you're saying here.

$(AB)/\gamma$ isn't the distance between A and B in the train's frame. There's no such thing as a distance between A and B in the train's frame, because A and B are not simultaneous in that frame. $(AB)/\gamma$ is the distance in the train's frame between the points on the ground where events A and B occurred. It's a distance in spacetime along a simultaneity line of the train's frame. There's such a simultaneity line through A, and another one through B, but there's no such simultaneity line through both. So $(AB)/\gamma$ is definitely not the distance in the train's frame between A and B.

I think you need to think about what you're actually calculating using the length contraction formula. You can't plug in the distance between two events and expect to get the distance between those same events in another coordinate system. That's not just wrong, it doesn't make sense. Think about it this way instead: In a spacetime diagram where the axes are the t and x axes of the ground's frame, the world lines of the two points on the ground are vertical lines. A and B are two points on those two lines. Since they are simultaneous, there's a horizontal line that goes through both of them. The length of that line segment from B to A is what you called AB. But $(AB)/\gamma$ is the length that an observer on the train would assign to a line with slope 1/v between two events where such a line intersects the two vertical lines.

15. Mar 2, 2012

### Michael C

Re: what will be the events relative to the ground observer , a time-like or space li

"Won't change" relative to what? The distance between the places where A and B happen will certainly be different when measured in different frames.

If you assign coordinates to the events A and B in the ground frame, you can use the Lorentz transformation to work out the coordinates in the train frame:

THE GROUND FRAME:
Let's say that the distance between the two events in the ground frame is d. To make things easy, we'll put event A at the origin:
Event A: t = 0, x = 0
Event B: t = 0, x = d.

THE TRAIN FRAME:
We define the train frame to have the same origin as the ground frame. It is moving relative to the ground frame along the x axis at a velocity of v. The Lorentz transformation gives us the coordinates of the two events in this frame:
Event A: t' = 0, x' = 0
Event B: t' = -$\gamma$vd/c$^{2}$, x' = $\gamma$d.

Increasing the velocity difference between the two frames will not only increase the time separation between A and B, it will also increase the spatial separation: you can see from the coordinates that the distance in space between the two events has been multiplied by $\gamma$. The space-time interval between A and B stays the same.

16. Mar 2, 2012

### John232

Re: what will be the events relative to the ground observer , a time-like or space li

This may just be too hippy for me. So, if I tied a string around Mars and then held the other side at Earth would their be a reality that exist at the speed of sound?

Shouldn't these be the same two things?

If A and B are not on the train then wouldn't the distance from A to B seen from on the train shorten, since A to B could be "seen" as a single object in motion relative to the train?

17. Mar 2, 2012

### Michael C

Re: what will be the events relative to the ground observer , a time-like or space li

A and B are not objects, they are events.

I'm not sure quite what you mean by saying that "A to B could be "seen" as a single object in motion relative to the train". Are you imagining that a single object could be present at both event A and event B? That won't work, since neither event falls within the light cone of the other.

18. Mar 2, 2012

### Fredrik

Staff Emeritus
Re: what will be the events relative to the ground observer , a time-like or space li

Yes, it obviously doesn't matter if you observe something with your eyes or with a video camera.

You're right, but he wasn't talking about the distance in the train's frame between the points on the ground where A and B occur. That distance changes with speed as $1/\gamma$, i.e. it gets shorter. He was talking about how the coordinate difference $x_A-x_B$ in the train's frame depends on the speed of the train. That difference changes with speed as $\gamma$, i.e. it gets longer.

19. Mar 2, 2012

### John232

Re: what will be the events relative to the ground observer , a time-like or space li

In the orignal post it sounded like A and B where two seperate places outside of the train. So then if you put two objects at a location down the track they would appear to come closer together as the train moved down the track. I was trying to say that the track itself would become shorter from the frame of reference of the train while it was moveing, not longer.

20. Mar 2, 2012

In this occasion, I was not talking about the distance Δx between places where A & B occur, but about the distance between the 2 train ends A and B. Your calculation is right that the Δt=$\gamma$vd/c$^{2}$. OK, so can this time difference allows a timelike separation between A and B if a signal would take off from A to reach B?