How Can I Calculate Time Dilation Between Two Observers?

In summary, the question is about two observers, A on earth and B in a spacecraft, setting their watches to the same time and determining how much time must elapse for the watches to differ by 1.00 seconds. The hint is to figure out which variable, T_0 or T_1, is larger. The answer is that after approximately 5.449 seconds of Earth time, the spaceship will be 1 second behind.
  • #1
crazynut52
11
0
I have the attached equation
but when I plug it, I don't get the same answer as in the back of the book...

Here is the question

Two observers, A on earth, B in a spacecraft whose speed is 2.0X10^8 m/s both set their watches to the same time, when the ship is abreast the earth.

How much time must elapse by A's reckoning before the watches differ by 1.00 seconds?
 

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  • #2
What did you plug in? We can't help you if we don't know what you've tried to do.
 
  • #3
crazynut52 said:
I have the attached equation
but when I plug it, I don't get the same answer as in the back of the book...
Here is the question
Two observers, A on earth, B in a spacecraft whose speed is 2.0X10^8 m/s both set their watches to the same time, when the ship is abreast the earth.
How much time must elapse by A's reckoning before the watches differ by 1.00 seconds?
Hint: which one is bigger, [itex]T_0[/itex] or [itex]T_1[/itex]?
 
  • #4
After approx 5.449 secs of Earth time, the spaceship will be 1 sec. behind.
In your thumbnail, Earth time should be on the left of the equation.
 

1. What is the time dilation equation and how does it work?

The time dilation equation is a formula used to calculate the difference in time between two reference frames when one is moving at a constant velocity relative to the other. It is based on Einstein's theory of relativity and takes into account the speed of light and the relative velocity between the two frames. Essentially, it shows that time moves slower for objects in motion compared to those at rest.

2. How is the time dilation equation derived?

The time dilation equation is derived from the Lorentz transformation equations, which describe how physical quantities such as time, length, and mass change between reference frames in special relativity. It is a complex mathematical derivation that involves the speed of light as a constant and the concept of spacetime.

3. Can you provide an example of how the time dilation equation is used in real life?

One example of the time dilation equation in real life is the Global Positioning System (GPS). The satellites that make up the GPS system are moving at high speeds relative to the Earth's surface, which causes time to pass slower for them. This difference in time must be taken into account for the GPS system to accurately calculate positions on Earth.

4. How does the time dilation equation relate to the concept of time travel?

The time dilation equation is often used in science fiction to explain the possibility of time travel. According to the equation, as an object approaches the speed of light, time for that object slows down significantly. This could potentially allow for a traveler to experience less time passing relative to the outside world, effectively "time traveling" to the future.

5. Are there any limitations or exceptions to the time dilation equation?

While the time dilation equation is a fundamental principle of special relativity and has been experimentally verified, it is not applicable in all situations. For example, it does not take into account gravitational effects, which can also cause time dilation. Additionally, it only applies to objects moving at constant velocities, and does not hold true for objects undergoing significant acceleration or deceleration.

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