Is Widely Separated in Relativity About Space or Perception?

[Physic lover]

Hello
Can you please help understand the following statement

This proposition sounds at first extremely unusual, but does it look unusual to you if I say that, having your dinner on a train, you eat your soup and your dessert in the same point of the dining car, but in widely separated points of the railway track? However, this statement about your dinner in the train can be formulated by saying that two events happening at different times at the same point of one system of reference will be separated by a definite space interval from the point of view of another system
Thanks in advance

 

[Doc Al]

This proposition sounds at first extremely unusual, but does it look unusual to you if I say that, having your dinner on a train, you eat your soup and your dessert in the same point of the dining car, but in widely separated points of the railway track? However, this statement about your dinner in the train can be formulated by saying that two events happening at different times at the same point of one system of reference will be separated by a definite space interval from the point of view of another system

That statement makes sense to me. What part(s) don't you understand?

Realize that observers in the train and observers alongside the track are each perfectly entitled to measure things from their own frame of reference. Relative to the train, the two events happen at different times, but at the same position (your seat in the dining car). Relative to the tracks, the two events happen at different positions. (Since the train has moved while you were eating.)

 

[jedishrfu]

you have two frames of reference:
- standing on the ground
- riding in the train

when you eat your dinner on the train, your friend on the train would say you ate your meal at event #0 and then drank your soup a few moments later at event #1 (train observer sees time separation)

but for the person on the ground would say you ate your meal at event #0 when the train was here and then drank your soup at event #1 when the train traveled a few hundred meters down the tracks. (ground observer sees space and time separation)

 

[nitsuj]

Hello
Can you please help understand the following statement

This proposition sounds at first extremely unusual, but does it look unusual to you if I say that, having your dinner on a train, you eat your soup and your dessert in the same point of the dining car, but in widely separated points of the railway track? However, this statement about your dinner in the train can be formulated by saying that two events happening at different times at the same point of one system of reference will be separated by a definite space interval from the point of view of another system
Thanks in advance

What's misunderstood? I see nothing SR/GR here either.

I "move along" with Earth around the sun, the speed is generally constant, so the time as marked on the calendar could be shown as a distance traveled measurement instead. Simple as that.

 

[Physic lover]

you have two frames of reference:
- standing on the ground
- riding in the train

when you eat your dinner on the train, your friend on the train would say you ate your meal at event #0 and then drank your soup a few moments later at event #1 (train observer sees time separation)

but for the person on the ground would say you ate your meal at event #0 when the train was here and then drank your soup at event #2 when the train traveled a few hundred meters down the tracks. (ground observer sees space and time separation)

Thank you

 

[ghwellsjr]

Hello
Can you please help understand the following statement

This proposition sounds at first extremely unusual, but does it look unusual to you if I say that, having your dinner on a train, you eat your soup and your dessert in the same point of the dining car, but in widely separated points of the railway track? However, this statement about your dinner in the train can be formulated by saying that two events happening at different times at the same point of one system of reference will be separated by a definite space interval from the point of view of another system
Thanks in advance

I hope you're not getting confused by that term "space interval" and thinking it is the same as "spacetime interval". The latter term is invariant in different Inertial Reference Frames (IRF's) and will always be time-like, while the first term is not. So in an IRF in which the dining car is at rest, the difference in the spatial coordinates between when you ate your soup and when you ate your dessert will be zero but in an IRF in which the railway track is at rest, it will be non-zero (assuming the train is moving).

 

[tade]

you have two frames of reference:
- standing on the ground
- riding in the train

when you eat your dinner on the train, your friend on the train would say you ate your meal at event #0 and then drank your soup a few moments later at event #1 (train observer sees time separation)

but for the person on the ground would say you ate your meal at event #0 when the train was here and then drank your soup at event #2 when the train traveled a few hundred meters down the tracks. (ground observer sees space and time separation)

a somewhat non intuitive consequence of RoS

 

[ghwellsjr]

you have two frames of reference:
- standing on the ground
- riding in the train

when you eat your dinner on the train, your friend on the train would say you ate your meal at event #0 and then drank your soup a few moments later at event #1 (train observer sees time separation)

but for the person on the ground would say you ate your meal at event #0 when the train was here and then drank your soup at event #2 when the train traveled a few hundred meters down the tracks. (ground observer sees space and time separation)

There are not three events involved here--just two. Your event #1 and #2 are the same event and should not be given different names, they are both event #1, they just have different coordinates in the two frames (as you correctly pointed out).

 

[ghwellsjr]

What's misunderstood? I see nothing SR/GR here either.

I "move along" with Earth around the sun, the speed is generally constant, so the time as marked on the calendar could be shown as a distance traveled measurement instead. Simple as that.

Nothing SR here? You imply that we could take the distance traveled in the ground frame and divide it by the time interval in the train frame and get the relative speed between the two. Are you sure you don't want to rethink this?

 

[jedishrfu]

There are not three events involved here--just two. Your event #1 and #2 are the same event and should not be given different names, they are both event #1, they just have different coordinates in the two frames (as you correctly pointed out).

Sorry my typo the event #2 is really #1. you are right there are only two events. I've corrected the original post.

 

[nitsuj]

Nothing SR here? You imply that we could take the distance traveled in the ground frame and divide it by the time interval in the train frame and get the relative speed between the two. Are you sure you don't want to rethink this?

[STRIKE]Sorry if you feel I implied any calculations[/STRIKE],Oh yea I did imply that, I was trying to "show" the difference is relative motion. You sure you don't want to rethink the op/

I re-read the post and still see nothing SR, (relativistic "effects")

So yea the way the op reads, you could take train frame time and ground frame distance to calculate the speed. Are we considering the minute differences in the different frames measures of time/length?

 

[nitsuj]

a somewhat non intuitive consequence of RoS

Can you point out the RoS in this scenario? I can't see it.

 

[Doc Al]

I re-read the post and still see nothing SR, (relativistic "effects")

I agree. Every word in that statement would equally apply in Galilean relativity.

 

[nitsuj]

I agree. Every word in that statement would equally apply in Galilean relativity.

phew, as merely a layman of SR I sometimes lack confidence in my conclusion.

 

[Doc Al]

So yea the way the op reads, you could take train frame time and ground frame distance to calculate the speed. Are we considering the minute differences in the different frames measures of time/length?

I wouldn't make any such assumption (which goes beyond the statement). After all, this is the SR forum, so presumably we are setting up a situation to analyze things relativistically.

 

[ghwellsjr]

[STRIKE]

Nothing SR here? You imply that we could take the distance traveled in the ground frame and divide it by the time interval in the train frame and get the relative speed between the two. Are you sure you don't want to rethink this?

Sorry if you feel I implied any calculations[/STRIKE],Oh yea I did imply that, I was trying to "show" the difference is relative motion. You sure you don't want to rethink the op/

I re-read the post and still see nothing SR, (relativistic "effects")

So yea the way the op reads, you could take train frame time and ground frame distance to calculate the speed. Are we considering the minute differences in the different frames measures of time/length?

Let's suppose the train is traveling at 0.6c and let's suppose you eat your soup at the common origin of the two reference frames (the first event) and you eat your dessert 8 minutes later according to the Proper Time on your own clock (the second event). In the frame of the railway track, this occurs at the widely separated point of 6 light-minutes away from the first event. Here is a spacetime diagram for the railway track's rest frame:

You are shown on the train in red and the dots indicate the one-minute Proper Time ticks on your clock. I end the scenario at the event where you have your dessert.

Now the calculation you propose is to take the railway track's space interval of 6 light-minutes between the two events and divide it by your Proper Time interval of 8 minutes between the two events and calculate a relative speed of 0.75c but this is incorrect. The correct calculation is to use the railway track's Coordinate Time of 10 seconds and divide that into the railway track's Coordinate Distance of 6 light-minutes to arrive at the correct speed of 0.6c.

 

[jedishrfu]

Well the OP quote came from the book Mr Thompkins in Wonderland:

http://books.google.com/books?id=xb...es at the same point of one system of&f=false

and based on the paragraph following the quote it certainly seems the quote is a precursor to a discussion on SR.

 

[nitsuj]

Let's suppose the train is traveling at 0.6c and let's suppose you eat your soup at the common origin of the two reference frames (the first event) and you eat your dessert 8 minutes later according to the Proper Time on your own clock (the second event). In the frame of the railway track, this occurs at the widely separated point of 6 light-minutes away from the first event. Here is a spacetime diagram for the railway track's rest frame:

You are shown on the train in red and the dots indicate the one-minute Proper Time ticks on your clock. I end the scenario at the event where you have your dessert.

Now the calculation you propose is to take the railway track's space interval of 6 light-minutes between the two events and divide it by your Proper Time interval of 8 minutes between the two events and calculate a relative speed of 0.75c but this is incorrect. The correct calculation is to use the railway track's Coordinate Time of 10 seconds and divide that into the railway track's Coordinate Distance of 6 light-minutes to arrive at the correct speed of 0.6c.

Yup, Just didn't see any mention of speeds, so I didn't assume the scenario was about an idealized train going unrealistically fast.

With that said and to Doc Als point this is a scenario posted in an SR/GR forum, so the analysis should be from a relativistic perspective, for me the OP read as if it asking about relative motion, not specifically relativistic effects.

 

[ghwellsjr]

Yup, Just didn't see any mention of speeds, so I didn't assume the scenario was about an idealized train going unrealistically fast.

With that said and to Doc Als point this is a scenario posted in an SR/GR forum, so the analysis should be from a relativistic perspective, for me the OP read as if it asking about relative motion, not specifically relativistic effects.

What do you think the phrase "widely separated" was intended to convey?

But it doesn't matter what the speed is, we live in a relativistic world, not a Galilean world and my answer is still correct no matter what the speed is, unrealistically fast or realistically fast.

 

[nitsuj]

What do you think the phrase "widely separated" was intended to convey?

But it doesn't matter what the speed is, we live in a relativistic world, not a Galilean world and my answer is still correct no matter what the speed is, unrealistically fast or realistically fast.

Yes, you are right

Widely separated means far apart, I can't "read" beyond it's actual meaning.