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Chapter 33: Problem 6

If you're in a spaceship moving at \(0.95 c\) relative to Earth, do you perceive time to be passing more slowly than it would on Earth? Think! Is your answer consistent with the relativity principle?

Short Answer

Expert verified
Yes, time would indeed be perceived as passing more slowly on the spaceship moving relative to Earth at 0.95c in accordance with the time dilation concept in special relativity. This is consistent with the Principle of Relativity as it confirms that the laws of physics hold true in all inertial frames of reference.

Step by step solution

01

Understand time dilation

Time dilation is a difference in the elapsed time measured by two observers, due to a relative velocity between them or to a difference in gravitational potential between their locations. In the case of special relativity, only the relative velocity affects the time measurements. In this problem, the observer in the spaceship will be measuring time that appears to be passing more slowly compared to the observer on Earth.
02

Compare the time measurements

The time dilation equation provides us with the quantitative relationship between the time measurements for moving and stationary observers. However, we don't need to compute any specific values for this exercise. Instead, we just need to use our understanding of the principle. Since the spaceship is moving relative to the Earth at a significant fraction of the speed of light, the observer in the spaceship would experience time as passing more slowly compared to Earth.
03

Test consistency with the Principle of Relativity

The Principle of Relativity srates that the laws of physics are the same in all inertial frames of reference. In this case, by observing slower time while on the spaceship compared to on Earth, the moving observer is still functioning under the same laws of physics as the stationary observer on Earth. Therefore, yes, this scenario is consistent with the relativity principle.

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Most popular questions from this chapter

What's special about the special theory of relativity?

Find the speed of an electron with kinetic energy (a) 100 eV, (b) \(100 \mathrm{keV},\) (c) \(1 \mathrm{MeV},\) and (d) \(1 \mathrm{GeV} .\) Use suitable approximations where possible.

A spaceship travels at \(0.80 c\) from Earth to a star 10 light years distant, as measured in the Earth-star reference frame. Let event A be the ship's departure from Earth and event B its arrival at the star. (a) Find the distance and time between the two events in the Earth-star frame. (b) Repeat for the ship's frame. (Hint: The distance in the ship frame is the distance an observer has to move with respect to that frame to be at both events-not the same as the Lorentz-contracted distance between Earth and star.) (c) Compute the square of the spacetime interval in both frames to show explicitly that it's invariant.

Event A occurs at \(x=0\) and \(t=0\) in reference frame \(S .\) Event \(B\) occurs at \(x=3.8\) light years and \(t=1.6\) years in \(S .\) Find (a) the distance and (b) the time between \(A\) and \(B\) in a frame moving at \(0.80 c\) along the \(x\) -axis of \(S.\)

Time dilation is sometimes described by saying that "moving clocks run slow." In what sense is this true? In what sense does the statement violate the spirit of relativity?
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