Is light travel time for event time calculation usually implicit?

[DocZaius]

I am beginning a textbook on SR and I have come across the introductory example of disagreement regarding simultaneity.

John is in a lab and Mary flies through the lab's corridor on a rocket. The rocket has an antenna. The antenna strikes John's pen in his shirt pocket and creates a spark. 2 meters down the corridor, the rocket's antenna strikes the fire extinguisher and creates a spark.

Now the book immediately says that John's span of time between each spark is different than Mary's span of time between each spark.

The book says that John calculated a certain time between each spark. Does that time represent John's measurement between each spark's light arriving at his eyeballs? Or does it instead represent John's measurement between each spark's light arriving at his eyeballs with him correcting for signal latency and considering how long it took for each spark's light to reach his eyeball?

In other words, did John set t=0 for the time the first spark's light reached his eyeball and t=36 nanoseconds for the time the second spark's light reached his eyeball and leave it at that? Or did he instead set t=0 for the time the first spark's light reached his eyeball minus the amount of time it took for light to travel 0.1 meters from the shirt pocket to his eyeball, with the same correction for the fire extinguisher?

Basically, my question is: Is it standard in SR problems for such declarations of time lapses between events from an observer's point of view to implicitly correct for light distance travel, or merely (and crudely) base them on when light of such events reached the observer?

I am very surprised and disappointed that the textbook did not make it clear which method John used to calculate the time lapse between each event.

 

[JesseM]

I am beginning a textbook on SR and I have come across the introductory example of disagreement regarding simultaneity.

John is in a lab and Mary flies through the lab's corridor on a rocket. The rocket has an antenna. The antenna strikes John's pen in his shirt pocket and creates a spark. 2 meters down the corridor, the rocket's antenna strikes the fire extinguisher and creates a spark.

Now the book immediately says that John's span of time between each spark is different than Mary's span of time between each spark.

The book says that John calculated a certain time between each spark. Does that time represent John's measurement between each spark's light arriving at his eyeballs? Or does it instead represent John's measurement between each spark's light arriving at his eyeballs with him correcting for signal latency and considering how long it took for each spark's light to reach his eyeball?

In other words, did John set t=0 for the time the first spark's light reached his eyeball and t=36 nanoseconds for the time the second spark's light reached his eyeball and leave it at that? Or did he instead set t=0 for the time the first spark's light reached his eyeball minus the amount of time it took for light to travel 0.1 meters from the shirt pocket to his eyeball, with the same correction for the fire extinguisher?

Basically, my question is: Is it standard in SR problems for such declarations of time lapses between events from an observer's point of view to implicitly correct for light distance travel, or merely (and crudely) base them on when light of such events reached the observer?

I am very surprised and disappointed that the textbook did not make it clear which method John used to calculate the time lapse between each event.

Which book of SR are you using? Most textbooks make it clear that each observer uses local clocks to assign times to events, clocks which are at rest in their system and which have been "synchronized" using the Einstein synchronization convention. For example, John could have a clock next to his pen and a clock next to the fire extinguisher, and he could judge the time of each spark based on the reading of the clock that was right next to it at the moment the spark occurred. Since the Einstein synchronization convention says that the clocks should be synchronized using the assumption that light travels at c speed in all directions in that frame--in other words, I can synchronize two clocks by setting off a flash at their midpoint, and setting them to read the same time when the light hits them--this method is functionally equivalent to noting the time the light reaches your eyes and subtracting the time for the light to travel from the event to your eyes, under the assumption it travels at c. But it's a bit "cleaner" conceptually, since you're always assigning coordinates based on local measurements where you don't have to worry about signal delays.

Either way, yes, in your textbook you should assume John is basing his assignment of times based on either the "local synchronized clocks" method or the "correcting for signal latency" method (which, again, will lead to identical answers), not basing it on when he actually sees the light from events.

 

[DocZaius]

Which book of SR are you using? Most textbooks make it clear that each observer uses local clocks to assign times to events, clocks which are at rest in their system and which have been "synchronized" using the Einstein synchronization convention. For example, John could have a clock next to his pen and a clock next to the fire extinguisher, and he could judge the time of each spark based on the reading of the clock that was right next to it at the moment the spark occurred. Since the Einstein synchronization convention says that the clocks should be synchronized using the assumption that light travels at c speed in all directions in that frame--in other words, I can synchronize two clocks by setting off a flash at their midpoint, and setting them to read the same time when the light hits them--this method is functionally equivalent to noting the time the light reaches your eyes and subtracting the time for the light to travel from the event to your eyes, under the assumption it travels at c. But it's a bit "cleaner" conceptually, since you're always assigning coordinates based on local measurements where you don't have to worry about signal delays.

Either way, yes, in your textbook you should assume John is basing his assignment of times based on either the "local synchronized clocks" method or the "correcting for signal latency" method (which, again, will lead to identical answers), not basing it on when he actually sees the light from events.

Thank you SO much for this very clear answer. I am using "Spacetime Physics" by Edwin F. Taylor and John Archibald Wheeler

This textbook did not make it clear that John was using a clock system that was synchronized using the Einstein synchronization convention. I wish it did make that clear. By the way, how sure are you that my textbook is implicitly using locally synchronized clocks for its measurements? 99%?

 

[JesseM]

Thank you SO much for this very clear answer. I am using "Spacetime Physics" by Edwin F. Taylor and John Archibald Wheeler

This textbook did not make it clear that John was using a clock system that was synchronized using the Einstein synchronization convention. I wish it did make that clear.

What page is the John/Mary example on? If you look on pages 37-44 they do make it very clear that each inertial observer is using a "latticework of meter sticks and clocks" to assign coordinates to events, with the clocks synchronized using light flashes (p. 37-38).

 

[DocZaius]

Page 5. (I have the second edition)

 

[JesseM]

Page 5. (I have the second edition)

Ah, OK, it looks like they're trying to introduce the basic idea of the "spacetime interval" in relativity without explaining the full context of what the coordinates that each observer assigns to events actually means physically. But they do supply the missing details fairly soon.