Solving Problems on Time Dilation | Special Relativity | Physics problems

This video takes the viewers through a series of interesting and challenging problems on the topic of Time Dilation in Einstein's Special Relativity. One of the important effects of Albert Einstein's 1905 Special theory of relativity is the time dilation. Time dilation refers to the effect by which moving clocks slow down. This implies that when compared to stationary clocks at rest, clocks moving at a relative speed slow down. If two clocks are synchronised on earth and one of them is taken on a journey, the clock that traveled would show less time on arriving back to earth. The importance of time dilation becomes clear when we realise that even all biological processes such as heart beat or pulse rate slow down while traveling in comparison to when at rest. In fact, the very famous Twin Paradox of Special theory of Relativity arises from the dilation of time. We have posted a video on the concept of time dilation on this channel. In continuation of our efforts, this video provides a series of problems on time dilation which are solved in clear steps with a thorough and detailed explanation of each of the steps involved. Students preparing for various Physics exams at the undergraduate level as well as competitive exams at the post-graduate level could find these problems very useful. This video forms part of a series of videos on Special Relativity and also of videos on problems in special relativity. For people interested in solving physics problems, i earnestly believe that this video should be quite interesting and engaging.

[shrivatsa]

Hello sir,

In this thought experiment, we have a spaceship with infinite fuel that accelerates constantly. According to the observer inside the spaceship, the acceleration is constant, and they calculate that they will reach the speed of light in let's say 60 seconds of their own time. For this to be possible, the spaceship must be accelerating at a rate of approximately 50, 000 kilometer per second squared in their frame of reference.

However, from the perspective of an external observer (in the rest frame), the situation is quite different. As the spaceship approaches the speed of light, the relativistic effects come into play. The external observer sees the spaceship’s acceleration decrease dramatically as it approaches light speed due to the relativistic increase in mass. Therefore, in the external frame, it would take an infinite amount of time for the spaceship to actually reach the speed of light. Consequently, the spaceship will never actually reach 60 seconds of acceleration in the external frame; it will asymptotically approach this point.

When the observer inside the spaceship reaches 60 seconds of their own time, the Lorentz factor, which describes time dilation and length contraction, becomes extremely large, suggesting infinite length contraction in the direction of motion. This results in a paradox: the universe appears to contract to zero length in the direction of the spaceship's motion from the perspective of the observer inside. This extreme contraction suggests that the physics as understood in relativistic terms starts to break down.

In this scenario, after the 60th second of acceleration in the observer’s frame, the concept of time and space as experienced by the accelerating observer becomes problematic. The external frame perceives an infinite amount of time having passed, and the observer’s frame would experience infinite length contraction, making conventional measurements and concepts seem meaningless.

So my question is, how will the accelerating frame perceive its 61st second or 62nd second? Mathematically, the gamma factor gives us imaginary numbers. Does that mean the accelerating frame shall approach a higher dimension of somewhat? Or is it simply saying that mathematics is not operatable? Because its frame is free to experience time beyond 60 seconds, doesn't it? Or does the fuel itself become empty and in the accelerating frame, it's no more an accelerating frame as there is zero fuel to push it further from the speed of light?

[favourfriday]

Good day sir.
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