I am a little confused by the quoted text is worth mentioning.

[rgtr]

Homework Statement

"
There is always a difference between the time that an event happens and the time that
someone sees the event happen, because light takes time to travel from the event to the
observer.
"

Relevant Equations

No equation

Hi I am reading a book and I am confused why some text is mentioned. Could someone help explain.

https://scholar.harvard.edu/files/david-morin/files/relativity_chap_1.pdf
page 14
"
There is always a difference between the time that an event happens and the time that
someone sees the event happen, because light takes time to travel from the event to the
observer.
"

I am a little confused by the quoted text is worth mentioning. Can someone go into a little more detail?

Thanks

 

[Orodruin]

There is not much more to it.

If you are not colocated with the event, light will take some time to travel to you from the event. Therefore you will receive the light from the event later than the event occurred.

Which part of it is unclear to you?

 

[rgtr]

Do they mean if you were located at exactly the location of the event the time would be accurate vs if you are farther away it takes longer to reach your eye. Also isn't your location important when doing calculations? When would I be exactly near the event? Won't most scenarios be a distance away?

 

[Orodruin]

Accurate is the wrong word. It is about observational delay, not accuracy.

Also isn't your location important when doing calculations?

No. The coordinates are of the actual events, not about when they are observed. The observational time delay needs to be accounted for when assigning coordinates to observations but is not relevant to the calculations themselves.

 

[PeroK]

Note also that events are not always observed using light. Bats, for example, navigate by echo-location and must process the time delay from emitting a signal to receiving it. They cannot have the simple view of the world that we have given the almost instantaneous transmission time of light on everyday scales.

Furthermore, the time delay of light signals was used to give an early estimate of the speed of light by measuring how far out of sync the orbit of one of Jupiter's moons appeared to be depending on the distance between Jupiter and Earth:

https://en.wikipedia.org/wiki/Speed_of_light#First_measurement_attempts

 

[robphy]

"There is always a difference between
the time that an event happens and
the time that someone sees the event happen, because light takes time to travel from the event to the
observer."

A spacetime diagram might help clarify.

Consider the inertial observer BOB along worldline SR and a distant event P [i.e. not on SR].

According to BOB, who uses his wristwatch and light-signals to assign coordinates to events,
P has BOB(t,x)-coordinates $( (t_R+t_S)/2, (t_R-t_S)/2 )$.
Events R and S are the intersections of the light-cone of P with the inertial worldline along SR.

According to BOB, event P is simultaneous with the local event when BOB's wristwatch reads $t_{P_{sim}}$, the midpoint of events S and R. This wristwatch-time is when BOB would say that "P happens".

But BOB doesn't see (i.e. receive a maximum-speed signal from) the event P until local event R,
when his wristwatch reads $t_R$.

Update:
It might also help to say that
“$P_{sim}$ and $P$ are spacelike-related… in fact, purely spatial according to BOB”
and
“$R$ and $P$ are lightlike related”.

 

[rgtr]

A spacetime diagram might help clarify.
View attachment 301461

Consider the inertial observer BOB along worldline SR and a distant event P [i.e. not on SR].

According to BOB, who uses his wristwatch and light-signals to assign coordinates to events,
P has BOB(t,x)-coordinates $( (t_R+t_S)/2, (t_R-t_S)/2 )$.
Events R and S are the intersections of the light-cone of P with the inertial worldline along SR.

According to BOB, event P is simultaneous with the local event when BOB's wristwatch reads $t_{P_{sim}}$, the midpoint of events S and R. This wristwatch-time is when BOB would say that "P happens".

But BOB doesn't see (i.e. receive a maximum-speed signal from) the event P until local event R,
when his wristwatch reads $t_R$.

Update:
It might also help to say that
“$P_{sim}$ and $P$ are spacelike-related… in fact, purely spatial according to BOB”
and
“$R$ and $P$ are lightlike related”.

Can I just summarize the diagram tell me if I made any mistakes.
Does the diagram take place at S ? Also I assume this has 3 different frames. The ground frame and Bob who is moving which is S and R path and the line S and P is where Bob sends the light beams from his eye for events 1 + R is where the light beam returns to his eye.

Also I am confused by this line "According to BOB, event P is simultaneous with the local event when Bob's wristwatch reads tpsim' , the midpoint of events S and R? "

Also what how are Psim and P spacelike? Could light not like reach them. I think the definition of spacelike means light or slower light can reach them.

Would the diagram in this scenario always happen where Bob starts to see the event?

 

[robphy]

Can I just summarize the diagram tell me if I made any mistakes.
Does the diagram take place at S ? Also I assume this has 3 different frames. The ground frame and Bob who is moving which is S and R path and the line S and P is where Bob sends the light beams from his eye for events 1 and R is where the light beam returns to his eye.

Also I am confused by this line "According to BOB, event P is simultaneous with the local event when Bob's wristwatch reads tpsim' , the midpoint of events S and R? "
Also what how are Psim and P spacelike. Could not like reach them. I think the definition of spacelike means light cannot reach them.
Would the diagram in this scenario always happen where Bob starts to see the event?

This is a position-vs-time diagram (where, by convention, time runs upwards),
as drawn by an inertial observer (Alice) [not shown as a vertical "worldline" representing an inertial observer at rest],
where inertial observer Bob is moving [with velocity (3/5)c].

All events occur in all frames.
However, these observers may have different coordinate-descriptions of these events.

SP is an outoging light signal (Event-S is the event Bob must use to reach event-P with a light-signal),
and PR is a reflected (echo) light-signal
(where event-R is the reception event [when Bob's eye sees the signal reflected by P]).
Neither SP nor PR is along a frame of reference (since light-signals have no meaningful frame of reference).

According to Bob, P_sim and P have the same t-coordinate. So Bob says that they are simultaneous.
According to Alice, however, P_sim occurs before P... so, Alice says that P_sim happens before P.

(Bob says, according to his wristwatch,
the time-interval from S-to-P is equal to that of P-to-R [using the above method of assigning coordinates to P]
Alice, however, says, according to her wristwatch [using an analogous method],
the S-to-P time interval is longer than the P-to-R time-interval.)

That P_sim and P are spacelike means that no signal (neither light nor a slower signal [a baseball]) can be sent between them. It can also impy that there is an inertial frame of reference where those events occur "at the same time in that frame".

(Note that S and P_sim cannot be signaled by a light-signal, but can be signaled by a slower-signal.
S and P_sim are said to be timelike-related (and are thus NOT "spacelike-related").)

 

[rgtr]

So this is a space-time diagram That switches between Alice and Bob's frame using a Lorentz transform?
I have prior read a little about spacetime diagram with lorentz transform but have not gotten to them yet in the book.