QUESTION: I understood that the Muons live long enough to strike earth. According to their own clocks they are following their decay time. But according to our clocks they bypass decay time, My question is if I were a muon, What would I see?
Would I see the world getting really fast and lab time going crazy?
ANSWER: Almost right. You would see the world going by very fast. But the world clocks would be going very slow, because with respect to (w.r.t.) you, they are whizzing by at the same speed that you are whizzing by w.r.t. the world.
That is a puzzle for the student of relativity. The muom clock runs slow w.r.t. the world AND the world clocks run slow w.r.t. the muon. Clocks run at a rate that depnds on their speed w.r.t. an observer. Different observers will measure the speed (and rate) of a moving clock differently according to the speed of the clock at their (different) frames of reference.
In other words, the rate of a clock is not the same w.r.t. differently moving observers. The time rate of a clock is unique only with respect to itself. We call that its "proper" rate.
That what is meant by saying that time rates are relative, not absolute.
[an error occurred while processing this directive]---------- FOLLOW-UP ----------
QUESTION: Thank you sir, But I really couldn't understand this.
Let us assume an example.
Let us take Alex and Bob. Alex is having an event(A light clock--- records the time taken by light ray to go 24e8m and hit a mirror and come back) which takes 16 seconds to occur.
Now Bob, is watching Alex and he finds that Alex is whizzing at 0.6c.
Hence Bob calculates the time taken for that event to occur, he sees that the light ray has to travel 60e8m to complete the event.
Now Bob says that the event took place in 20 seconds. And that Alex's watch is slower.
Now my question arises that if Alex is unaware of his speed and he sees Bob now, his 16seconds are bobs 20 seconds. So does Alex see that Bob's clock is speeding? I mean, he has to see the 20 seconds. Now, where am I wrong? Because I cannot see how they both see each other slowing?
If possible sir, then could you solve above discussion with help of Lorentz transformation? That is how the times would vary if I were Alex or Bob. Thanks in advance.
Ron, I am not surprised that you have trouble understanding time dilation. Everybody finds that a mystery. But experiment verifies this behavior.
Suppose you are in a space ship and I am on Earth. Your clocks run fine with respect to (w.r.t.) you and mine run fine w.r.t. me. But yours run slow w.r.t. me and mine run slow w.r.t. you. We describe that by saying that time is not absolute but is relative to the frame of reference w.r.t. which it is measured.
If it were not this way, and if your clocks run slow with respect to everyone, then we would have a way to measure absolute motion: We would all agree that you are in motion but I am not. Relativity says this cannot be. Motion is not absolute. Earth is moving relative to your spaceship. Each of us finds that the other's clock runs slow relative to ourselves.
Nature does not care whether we understand her or not! Experiment is the only way to find out what goes on in nature, and experiments say that time is relative, whether we understand it or not.
Sorry about that, but relativity gives right answers, even if we cannot understand why.