Relativistic Pendulum Time Dilation: A Glimpse into Einstein's World

What is true about the time measurements of the oscillating pendulum in a relativistic rocket?

A) TA>TB B) TA=TB C) TA

Final answer:

In terms of relativistic physics, time appears to move slower in a frame moving relative to an observer. Therefore, the oscillation period of the pendulum as measured by an observer stationary relative to the rocket (TA) is actually longer than that measured by an observer moving along with the rocket (TB), meaning TA > TB.

Explanation:

The subject matter of this question concerns relativistic physics, specifically the concept of time dilation according to the Special Theory of Relativity from Albert Einstein.

When Observer A sees a pendulum oscillating back and forth in a relativistic rocket and measures its period to be TA and Observer B moves along with the rocket and measures the period of the pendulum to be TB, the correct relationship between these two measurements is that TA > TB.

Time dilation essentially means that time moves slower in a frame moving relative to an observer, and this is a consequence of the constant speed of light for all observers.

The pendulum in the relativistic rocket, therefore, appears to oscillate slower (meaning a longer period, TA) to an observer stationary relative to the rocket (Observer A) than to an observer moving with the rocket (Observer B) who measures the proper time, TB.

As a result, TA is indeed greater than TB. This phenomenon also implies that all clocks, including our biological clocks such as aging, appear to run slower in a moving frame compared to a stationary frame.