Sunday 25 October 2020

special relativity - A relative time dilation paradox.


Let us assume that there are two astronauts A and B who are floating in space. A sees B passing by and vice versa. A sends signals to B every minute. According to A since B is moving his clock will be slower. So B will receive the signals prior to the appointed minute. The same argument can be applied for B who will conclude A's clock is running slow. Who is right?



Answer




Both are right. Any moving clock is slower than a clock at rest, from the perspective of the frame at rest.


Maybe this simplified freehand graphic (apologies for its lack of precision) helps to see that both A and B feel the same about each other's time dilation:


enter image description here


Let's say that the red axis represents A and its proper time measured in minutes (first eight minutes are showed). Green axis and its numbers represents B observer.


Light or radio signals from A to B, represented in red oblique lines, are fired on a minute basis. Six of them are showed, that took six minutes of A proper time. However, these six signals from A to B take some eight minutes in B proper time. B concludes that A clock is slower. The same holds if we invert the situation (green lines from B to A). Well, almost the same (the last green line is intended to go from green 6 to red 8, blame my trembling fingers).


No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...