Why does time dilation affect all clocks equally?

[NoahsArk]

"How exactly would John use his ship as a clock? Withthe light and ball, he measures how long it takes for them to travel a fixed distance in the Y direction relative to him, but the ship has no relative motion with respect to John. "

I meant that Alex could use John's ship as a clock. My main question, though, relates to what we've been discussing about only needing to use the vertical speed to calculate time dilation when the clock is perpendicular to the ship. Many sites on the net that introduce special relativity use the light clock example and explain time dilation by saying that the stationary frame sees the moving frame's time go slower because the stationary frame sees the beam of light going up a longer path. Based on what we've been discussing, the longer path has nothing to do with why the stationary observer sees the clock on the ship tick slower. The lengrh of the path (which is the height of the light clock) is the same for both, it's just that for the stationary observer the light goes up that path slower. True, the stationary observer also views the beam going in a sideways direction, but we only use the length of its vertical path to calculate time dilation. Am I correct about this?

PAllen thank you for that resource. I have not heard of aberration before and will read about it.

 

[Doc Al]

The lengrh of the path (which is the height of the light clock) is the same for both,

No, the length of the path taken by the light beam is not the same. In one frame, the light travels just vertically; in the other frame, the light travels diagonally over a longer path.

but we only use the length of its vertical path to calculate time dilation.

That's just a calculational convenience. Note that when you do that you only use the vertical component of the velocity.

 

[NoahsArk]

But is it true that the longer path in these examples is not a factor in the time dilation?

 

[Doc Al]

But is it true that the longer path in these examples is not a factor in the time dilation?

No, that's not true. That longer path allows you to immediately deduce time dilation (for a light clock).

 

[NoahsArk]

No, that's not true. That longer path allows you to immediately deduce time dilation (for a light clock).

The longer the voyage is that the ship goes on, the longer the diagonal path will be. But the length of the journey is not affecting gamma, only the speed of the ship is?

 

[Doc Al]

The longer the voyage is that the ship goes on, the longer the diagonal path will be. But the length of the journey is not affecting gamma, only the speed of the ship is?

The speed of the ship determines both gamma and the length of the diagonal path. (They are all connected.)