An introductory question about special relativity

In summary, the conversation discussed the arrival of two lightning flashes at different distances (x=0 and x=12) and the simultaneous arrival of the two flashes at x=9. The equation t_3=t_1+9/c and t_4=t_2+3/c were derived, leading to the conclusion that t_2-t_1=6/c. This information was used to find the time difference for an assistant observing the flashes at x=3. Finally, the speaker suggests other ways to approach the problem, but commends the summarizer for their thorough and detailed work.
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Homework Statement
I can understand that the lightning coming from x=0 will reach to the assistant earlier, However, the question also asks for the time difference of the assistant receiving the lightning and this is the point I'm not sure about. My answer is 12km/c (c is the speed of light) Is this correct?
Relevant Equations
t=s/v
1639101926912.png


The way I was doing is that I list events
1. lightning hits x=0 this is (x_1=0,t_1)
2. lightning hits x=12 (x_2=12,t_2)
3. left lightning reaches "me" (x_3=9,t_3)
4. right lightning reaches "me" (x_4=9,t_4=t_3) t_4=t_3 since "I" see the lightning at the same time

Then the equation can be :
t_3=t_1+9/c
t_4=t_2+12-9/c=t_2+3/c

and since t_4=t_3 this implies t_2-t_1=6/c
Then it's possible to suppose t_1=0 and t_2=6/c

Then for the assistant:
1. lightning hits x=0 this is (x_1=0,t_1)
2. lightning hits x=12 (x_2=12,t_2)
3. left lightning reaches "me" (x_3'=3,t_3')
4. right lightning reaches "me" (x_4'=3,t_4'=t_3')

and t_3'=t_1+3/c=3/c
t_4'=t_2+12-3/c=6/c+9/c=15/c

The difference for the assistant is : 15/c-3/c=12/c
 
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  • #2
That all looks good. Your work is nicely and carefully done.

Once you work it out, you can sometimes step back and see other ways to get to the answer a little quicker.

For example, Let E be the event of the simultaneous arrival of the two flashes at x = 9 km.

It is clear that the flash from x = 0 must have passed x = 3 km at some time earlier than the occurrence of E. How much earlier? That's easy to write down in terms of ##c## and the distance between x = 3 km and x = 9 km.

Likewise, the flash from x = 12 km will pass x = 3 km at some time later than the occurrence of E. How much later is again easy to write down in terms of ##c## and the distance between x = 3 km and x = 9 km.

Then, the time difference between the arrival of the flashes at x = 3 km follows.

However, I like the way you explicitly wrote out the space and time coordinates (x, t) of the relevant events. When you get to more complicated problems where you are dealing with various events as observed in different frames of reference, you will find that writing out what you know about (x, t) for each event in each frame of reference will really help a lot.
 
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Related to An introductory question about special relativity

1. What is special relativity?

Special relativity is a theory proposed by Albert Einstein in 1905 to explain the relationship between space and time. It states that the laws of physics are the same for all observers in uniform motion, and the speed of light is constant for all observers regardless of their relative motion.

2. How does special relativity differ from classical mechanics?

Special relativity differs from classical mechanics in that it takes into account the effects of high speeds and the constancy of the speed of light. In classical mechanics, time and space are considered absolute, while in special relativity they are relative and can be affected by the speed of an observer.

3. What are the key concepts of special relativity?

The key concepts of special relativity include the principle of relativity, the constancy of the speed of light, and the equivalence of mass and energy (expressed in Einstein's famous equation E=mc^2). It also introduces the idea of time dilation and length contraction, where time and space appear to change for observers in different frames of reference.

4. What are some real-world applications of special relativity?

Special relativity has many real-world applications, including the development of GPS technology, which relies on precise time measurements and takes into account the effects of relativity. It also plays a crucial role in particle accelerators and the study of subatomic particles.

5. Can special relativity be proven?

Special relativity has been extensively tested and confirmed through numerous experiments and observations. However, like all scientific theories, it is subject to potential revisions or modifications as new evidence is discovered. So while it cannot be definitively proven, it has withstood rigorous testing and is widely accepted by the scientific community.

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