# Why does time slow down when traveling at high speeds [duplicate]

One of the effects of traveling at high speeds is slowing down of clocks. I can understand gravity time dilation effect but not how would velocity affect clock speeds.

How correct it is, if I say that higher the speed, more object travels through space dimension therefore less it travels through time dimension; therefore slowing down of time?

## marked as duplicate by Jim, Kyle Kanos, Brandon Enright, John Rennie, JamalSNov 29 '14 at 10:27

• possible duplicate of What are the mechanics by which Time Dilation and Length Contraction occur? – Jim Nov 28 '14 at 19:36
• Your question must mention two reference frames, otherwise the notion of ‘slower than’ wouldn’t make sense. – Berrick Caleb Fillmore Nov 28 '14 at 19:55
• As Berrick Fillmore says, you have to specify the frames of coordinates. You say "more the object travels through space dimension ..." From whose point of view, of the observer at rest, or of the one who travels? – Sofia Nov 28 '14 at 21:44
• (cont.) Maybe the interval conservation can help. For a traveler, his 20th and his 21th birthday occur in the same place. The relativistic interval between the events is -c^2 t^2, where t is 1 year. But for his family on the earth the interval is X^2 - (cT)^2, X being the distance between the positions of the spacecraft at the two events, and T the time ON EARTH between them. Since the interval is conserved, you get t^2 = T^2 - (X/c)^2 . So, from the family, the bigger is the rocket velocity, the bigger is X (MORE he travels in space), and therefore the bigger is T (MORE he travels in time). – Sofia Nov 28 '14 at 21:54
• How were you able to understand Gravitational Time Dilatation without understanding it? – Schrödinger's Cat Nov 29 '14 at 5:49

Imagine, for example, that two different inertial observers, one sitting on a train moving through a station with uniform velocity $v$ with respect to ground. The experiment will consist of turning on a flashlight aimed at a mirror directly above on the ceiling and measuring the time it takes the light to travel up and be reflected back on its starting point. The observer sitting on the train see that the light ray follow a strictly vertical path (as fig. a)from $A$ to $B$ to $C$ and the ground observer see that the light ray travel from $A$ to $B$ to $C$ as fig. b. Both the observer see the light back to the starting point but it is clear from the two fig. that they traveling different distances. If ground observer think that the time taken by the light for the experiment is $\Delta t$ and the train observer claim that the time taken is $\Delta t'$ then
$\Delta t' ={\frac{2BC}{c}}$ and $\Delta t ={\frac{AB+BC}{c}}$. And hence it can be proved that ${\frac{\Delta t'}{\Delta t}}={\sqrt{1-{\frac{v^2}{c^2}}}}$ This indicates that the train passenger's clock runs slow but it seems to the ground observer. Actually both observer's clock moving at the same rate.

A couple of things first...

1) Time dilation is not a consequence of high speeds, but of ANY speed - it just the effects grow large rapidly within about 10% the speed of light. Low speeds can have measurable consequences as is the case with magnetic fields for example.

2) All identical clocks "tick" away at the same rate under all circumstances,** metering out their proper-time distances, so be careful using expressions like "time slowing down" as if "time" were a thing itself that moved or flowed. This will help keep in mind that "time" is component, like space, used to locate a point in spacetime. It's a subtle distinction but one worth bearing in mind.

**Clocks in relative motion and various points in a gravitational field move along worldlines that are not necessarily parallel and thus project different time intervals (coordinate times) onto the other clock's worldlines. This effect is time dilation.

That said, your "How correct is" part of your question is not too far off. That is, the greater the motion of some other object through your space (greater spatial component) the less the other object moves through your time (smaller temporal component) because the spacetime interval ($ds^2 = dt^2 - dx^2$) is an invariant quantity - is what I think you meant to say.

If you haven't done so already I recommend reading Sofia's comment as she works through the arithmetic and this may aid your understanding.