# Time dilation simple derivation

In a special theory of relativity we have a phenomenon known as time dilation. There is a simple explanation of this, with a thought experiment with a train and a flash light:

We flash a light in a moving train and it hits the top of the train and comes back again. What is the time needed for a light beam to do this in a moving train frame and in a still frame glued to the tracks?

In short, seen from a frame of a moving train there is no problem, because light simply moves straight up and deflects from the top of the train and then comes back again and is detected.

My question is this: If a train moves a bit, should not light hit the top a bit behind the spot directly ortogonal to the flash light on the floor? But then again, what is the fundamental difference between the moving train and one that is still? None! So light could not care less about this. And it will do exactly the same, hit the top directly orthogonal to the floor. But it is not from the same argument that you would use if we were talking about a bullet instead, right? Light is not a bullet, it is not safely placed inside of a barrel of a gun so it does not get the extra velocity component.

The only argument left is that it simply has to do it that way because there is no fundamental difference if the train moves with the constant velocity or just stands still. And now of course, as seen from a track-frame, emission and detection happen in two different places, so we have to assume that light traveled diagonally, moving on a triangle. This took it a bit longer because of a distance as seen from the track.

Could you please, if you understood this reasoning, tell me, is it correct and, if needed, give some insight?

• tnx :-) man.... Commented Dec 28, 2014 at 15:45
• Your reasoning seems fine, but note that this type of reasoning should be regarded as providing evidence that time dilation must exist, but not an explanation of it. For a more thorough explanation see The real meaning of time dilation or search this site for similar questions. Commented Dec 29, 2014 at 7:32
• Well, in many text books you only have mathematical derivations of Lorentz transformations. In my book, that is good enough explanation. Or? Commented Dec 29, 2014 at 7:59
• The only really satisfactory explanation is to derive the time dilation from the invariance of the line interval. You will never achieve an intuitive understanding unless you appreciate that all the weird effects in SR stem from this symmetry principle. Commented Dec 29, 2014 at 8:11
• cool...one thing...if you put yourself in one reference frame which is still and your friend in other, which is moving, and and then emit spherical wave in exact moment when your friend passes through, you should both see a spherical wave, regardless of his movement. But now everything else needs to be adjusted to this fact. What about this? So you have equation for a sphere in both coordinate systems :-) Commented Dec 29, 2014 at 8:33