Relativity-Finding the time of an event

[tmlfan_17]

For the problem below, I understand how to solve it using numbers, but I am having trouble understanding the physics/logic behind the solution. More specifically, I do not understand how the time of seeing the light flash is different compared to the actual arrival of light. Any assistance would be very helpful. Thanks.

Experimenter A in reference frame S stands at the origin looking in the positive x-direction. Experimenter B stands at x = 900 m looking in the negative x-direction. A firecracker explodes somewhere between them. Experimenter B sees the light flash at t = 3.0 ms. Experimenter A sees the light flash at t = 4.0 ms. What are the spacetime coordinates of the explosion?

 

[tiny-tim]

hi tmlfan_17!

… I do not understand how the time of seeing the light flash is different compared to the actual arrival of light.

they are the same: you do see the light when it arrives at your eye

(but what does this have to do with relativity? the observers are at rest relative to each other )

 

[tmlfan_17]

I think that this problem relates to relativity because frame of references are possibly important to the understanding of relativity. From my understanding, light takes 1.0 μs to reach experimenter B (as light travels at 300 m/μs). However, he/she sees it at 3.0 μs. I don't understand why they are not seeing it at 1.0 μs.

 

[tiny-tim]

i think i don't understand the original question

what is S ?​

 

[tmlfan_17]

S is the standing reference frame for which both Experimenter A and B are within. I will post the solution to the problem below in (.jpg format). Hopefully this will help clarify my concerns.

 

[tiny-tim]

S is the standing reference frame for which both Experimenter A and B are within. I will post the solution to the problem below in (.jpg format). Hopefully this will help clarify my concerns.

ah, that clears up what was puzzling me about what you originally posted …

Experimenter B sees the light flash at t = 3.0 ms. Experimenter A sees the light flash at t = 4.0 ms.

… that should have been 3.0 µs and 4.0 µs ​

ok, so light would take 3 µs to go from A to B

so if the flash takes a µs to reach A and b µs to reach B, then a + b = 3

and also a - b = 1 (because when the flash reaches B, it stil has 1 µs to go before it reaches A)

so a = 2, b = 1 ​

From my understanding, light takes 1.0 μs to reach experimenter B (as light travels at 300 m/μs). However, he/she sees it at 3.0 μs. I don't understand why they are not seeing it at 1.0 μs.

yes, b = 1 µs

so since the question tells you that the time on the clock when it reaches B is 3 µs (and for A, a = 2 µs, and the arrival time is 4µs), that means it must have started at 2 µs

(and yes, there's no relativity in all of that! )

 

[tmlfan_17]

I apologize for the copy and paste mishap. From my understanding the time on the clock that the light reaches Experimenter B is 3 µs, but the actual time of travel for the light is 1 µs (making the time of the incident at t=2 µs). The 3 µs is almost like a "false time". Does that look correct?

 

[tiny-tim]

hi tmlfan_17!

(just got up :zzz:)

From my understanding the time on the clock that the light reaches Experimenter B is 3 µs, but the actual time of travel for the light is 1 µs (making the time of the incident at t=2 µs). The 3 µs is almost like a "false time". Does that look correct?

yes that's correct

the flash happens at 2, the light takes 1 to reach B at 3, and 2 to reach A at 4

but i don't understand your worry about "false time" …

what do you think "real time" is??

time is what we want it to be, i may set my watch at zero at a totally different time to when you set yours at zero

if we live in different time zones, that's obvious

but even the same person may use different clocks: if you're timing an experiment, you're very likely to start a stop-watch at zero, to make calculation easier (ie to avoid having to subtract the "real start time" from every reading)