Why Does Time Dilation Seem Asymmetrical?

[Ahmed Abdullah]

At first I must admit that I am a novice, know a little about physics. The analysis below most probably full of flaws.
We know that t=t0/{1-(v/c)^2}, t0 is the time experienced by a person traveling at v speed in a space ship, t is the time that is experienced by a stationary observer on the earth.
None of the reference frame is more fundamental than other. So we can assume the spaceship to be stationary and the planet Earth is in motion( i.e -v). So easily opposite of the formula can be proven. That is : t0=t/{1-(v/c)^2},
In the first case time is dilated for the spaceman. And in the second it is true for the person on the earth. Which one is the truth? If both, How possible!

Let's think of a particular case, a vehicle can travel at such speed that it can dilate time, 5 fold than a stationary observer (relative to the earth). So for every ticking of second in a clock placed inside the vehicle, there will be 5 on the clock of a stationary observer. Let's place two stationary clock along the path of the vehicle. Say, the vehicle meet the first clock when both clock gave the same reading. Let it be 00:00. When the vehicle rider reached the second clock his clock showed that one second has passed( i.e 00:01). So the reading on the stationary clock would be 00:05.
This strongly shows that time ONLY dilated for the vehicle rider.
Further examples are those when an austraunaut departs at nearby speed of light, when he returns he returns to a different earth. Many years passes when he spent some hours at a speed of 99% that of light.This also shows that time ONLY dilated for the austraunaut, not for the dwellers on the earth. WhY?? Why time dilation is preferred for someone in relative motion to earth. When a reference frame is in motion relative to other frame, we can assume any of them to be in motion and other stationary. So there is a symmetry and we can expect simmilar result in both of the frame.
I know I am wrong, sillyish. But I can't get it. :'-(

 

[Galileo]

Hi Ahmed, don't worry, this is one of the difficult concepts to grasp in relativity.
It all depends from which reference frame you are observing. The Earth observer will observe the spaceman's clock going slower than his own and the spaceman will see the earthman's clock going slower than his own.

Putting synchronized clocks along the path of the spaceship which are stationary relative to the Earth person is exactly how time is measured in the Earth frame, so naturally the clock will read 5 seconds when the ship's clock reads 1. Continuing the trip it means that when the ship's clock reads 00:05 it will pass an Earth clock reading 00:25, right?

Let's see how that would look from the spaceman's point of view (i.e lengths and times measured in his frame). He would not only observe the clocks moving, they are not synchronized properly (as viewed from his frame)! Simultaneity is relative, so two clocks ticking at the same time are not ticking at the same time as seen by someone moving relative to the clocks.
Besides that, he would also notice the clocks going slower than his own and the distances at which they are placed are shorter due to Lorentz contraction.
So when the spaceman has traveled for 5 seconds, the clock's lined on the Earth will have passed only 1 second. From this we can conclude that the particular clock he passes at that moment read 00:04 at the time the ship left the origin.

 

[Galileo]

Further examples are those when an austraunaut departs at nearby speed of light, when he returns he returns to a different earth. Many years passes when he spent some hours at a speed of 99% that of light.This also shows that time ONLY dilated for the austraunaut, not for the dwellers on the earth. WhY?? Why time dilation is preferred for someone in relative motion to earth. When a reference frame is in motion relative to other frame, we can assume any of them to be in motion and other stationary. So there is a symmetry and we can expect simmilar result in both of the frame.

This is a different case. The two viewpoints are not equivalent and there is no symmetry here. It is the astronaut which has to accelerate (turn around) and go back to earth. Changing your velocity means switching between inertial frames, that's where the difference comes from. If the spaceship's engines were off all the time and you'd put a big rocket thruster on the Earth and make a round trip with the whole earth, then the situation will be reversed.

 

[Ahmed Abdullah]

Thnk you very much for you sensible response.