Special Relativity with Three reference frames

AI Thread Summary
The discussion revolves around solving a physics problem related to special relativity with three reference frames. Participants are analyzing the positions and times of two events in different rocket frames, using the equation s² = c²Δt² - Δx² to find relationships between them. There is confusion regarding the separation of events versus frames, with emphasis on using the correct events to determine the speed of rocket frame C. The key point is that rocket C must be moving at a speed that allows it to observe both events occurring at the same location. Clarifications are provided on how to approach the calculations and the importance of maintaining consistent reference points.
scienceLilly75
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Homework Statement


In the laboratory frame, event 1 occurs at x = 0 light-years, t = 0 years. Event 2 occurs at x = 6 light-years, t = 10 years. In all rocket frames, event 1 also occurs at the position 0 light-years and the time 0 years. The y- and z- coordinates of both events are zero in all frames.
a) In rocket frame A, event 2 occurs at time t’ = 14 years. At what position x’ will event 2
occur in this frame?
b) In rocket frame B, event 2 occurs at position x’’ = 5 light-years. At what time t’’ will
event 2 occur in this frame?
c) How fast must rocket frame C move if events 1 and 2 occur at the same place in this
rocket frame?

Homework Equations


s^2 = c^2Δt^2-Δx^2
t = (1/√1-v^2/c^2)t'

The Attempt at a Solution


For part A, I did c^2Δt^2-Δx^2 = c^2Δt'^2-Δx'^2. Because the everything in the rocket frames start at 0, then the entire left side becomes 0 and I get. √c^2 * (14)^2 = Δx' which is 4.2*10^9 or 14c.
I did the same thing for part B. The c^2Δt^2-Δx^2 = c^2Δt''^2-Δx''^2 and ended up with √5/c = 1.29*10^-4 = Δt''.
For part c, I know that I need to use t = (1/√1-v^2/c^2)t' . However, if I set t=0, then I get v rocket = c ---which shouldn't be right. It should be some fraction of c. My question is if if I am looking at a third reference frame, then do I use the values for time and position from the one before it? So to find the v in rocket frame C, I need to only use the data from rocket frame B?
 
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Hi scienceLilly75! Welcome to PF! :smile:

(try using the X2 button just above the Reply box :wink:)
scienceLilly75 said:
In the laboratory frame, event 1 occurs at x = 0 light-years, t = 0 years. Event 2 occurs at x = 6 light-years, t = 10 years. In all rocket frames, event 1 also occurs at the position 0 light-years and the time 0 years. The y- and z- coordinates of both events are zero in all frames.
a) In rocket frame A, event 2 occurs at time t’ = 14 years. At what position x’ will event 2
occur in this frame?

For part A, I did c^2Δt^2-Δx^2 = c^2Δt'^2-Δx'^2. Because the everything in the rocket frames start at 0, then the entire left side becomes 0 and I get. √c^2 * (14)^2 = Δx' which is 4.2*10^9 or 14c.

No …

i] if x is in light-years, and t is in years, then c = … ? :wink:

ii] the separation (c2t2 - x2) has to be between events 1 and 2, so it isn't 0 ! :smile:
 
But at the beginning the time and position of the event is 0, so the left side has to be zero right?

Or do I need to find spatial separation between A and B, then spatial separation between B and C?
 
Hi scienceLilly75! :smile:

(just got up :zzz:)
scienceLilly75 said:
But at the beginning the time and position of the event is 0, so the left side has to be zero right?

Or do I need to find spatial separation between A and B, then spatial separation between B and C?

sorry, but that doesn't even make sense …

A B and C are frames, and there's no separation between frames (spatial or otherwise)

separation is between two events

so which two events are you going to use? :smile:

(oh, and c = … ? :wink:)
 
I am confused. I understand that there is no separation between frames but between events in frames. In that case, I am stuck. The only thing I know about the frame C is that event one occurs at t=0, x=0. If the events occur on the same place on the rocket, then x' also equals 0. But then that will leave me with t' = 0 using the spatial relativity equation. if t'=0, then it is not moving. Where am I going wrong?
 
Hi scienceLilly75! :smile:
scienceLilly75 said:
I understand that there is no separation between frames but between events in frames.

Why do you say "in frames"? Separation is between two events, period. :wink:

Use event 1 and event 2. :smile:
 
So to find the speed, I have to use info from event 1 and 2 how they appear in frame c? then I can use v = x/t?
 
Make up a table. Label the rows Laboratory, Rocket A, Rocket B, Rocket C. Label the columns Event 1 Time, Event 1 Distance, Event 2 Time, Event 2 distance. Fill in the table with any information you have available. If there is information missing, fill in any algebraic variable name that you choose. Add a 5th column to the table in which you calculate the following quantity

((Event 2 Time) - (Event 1 Time))2 - ((Event 2 Distance) - (Event 1 Distance))2. This quantity must be the same for all rows of the table.
 
scienceLilly75 said:
So to find the speed, I have to use info from event 1 and 2 how they appear in frame c? then I can use v = x/t?

why do you need for speed for part (a) ? :confused:

what is the separation between events 1 and 2 ?​
 
  • #10
Question 3 is a little ambiguous. I guess it is asking how fast rocket C is traveling relative to the laboratory frame of reference. The key to answering this question is recognizing that rocket C is physically present at both events.
 
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