Synchronized Clocks: Time Dilation and Lorentz Transformations

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In summary, the conversation discusses a scenario where a person A with a watch is standing on a train station and a train passes by with a speed of 3/5c. Person B on the front of the train synchronizes their watch with person A and sends a light signal to person C on the back of the train. Person C synchronizes their watch when they receive the signal, taking it -100ms back to adjust for light travel. The question is what will the watches of person A and C show when C passes A. This scenario involves the use of Lorentz transformations.
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Homework Statement



A person "A" with a watch is standing on a train station. A train (which proper length is 100ms*c) passes him with a speed of 3/5c. A person "B" sitting on the front of the train synchronizes his watch with the "A" (both set to 0) when he passes him. At the same time he sends a light signal to another passenger "C" who is on the back of the train. Once "C" receives the signal, he synchronizes his watch (taking it -100ms back to adjust for light travel).
What "A" and "C" watches are going to show when "C" passes "A"?

Homework Equations


Lorentz transformations
 
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  • #2
What happened to part 3 of the template? Where is your attempt at a solution? You must provide this, site rules require it.

Also, this isn't advanced physics: thread moved.

You have two events here:
1. Person B passes Person A.
2. Person C passes Person A.

What is the time interval (##\Delta t##) between these two events according to the observer (person A) on the track? What is the time interval (##\Delta t^\prime##) according to the observers (persons B and C) on the train? How are these two related to each other?
 

FAQ: Synchronized Clocks: Time Dilation and Lorentz Transformations

What is the purpose of synchronized clocks?

Synchronized clocks are used to ensure that different clocks are displaying the same time at any given moment. This is important in situations where precise timing is necessary, such as in scientific experiments, transportation systems, and communication networks.

What is the difference between A and C synchronized clocks?

The main difference between A and C synchronized clocks is the method they use to synchronize. A synchronized clocks use atomic clock technology, which is based on the natural vibrations of atoms, while C synchronized clocks use network time protocol (NTP), which synchronizes time using a network server.

How accurate are synchronized clocks?

Both A and C synchronized clocks are highly accurate, with a margin of error of only a few nanoseconds. However, atomic clocks are considered to be slightly more accurate than NTP synchronized clocks.

What are the benefits of using synchronized clocks?

Using synchronized clocks can prevent confusion and discrepancies caused by differences in time between different devices. It also ensures that events and processes can be accurately timed and coordinated.

How are synchronized clocks used in everyday life?

Synchronized clocks are used in a variety of everyday applications, such as in banking and financial transactions, traffic signals, and GPS systems. They are also used in industrial processes, such as in manufacturing and power plants, to ensure precise timing and coordination.

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