Why is length contracted but time is dilated? I've just started special relativity and have a quick question on the terminology. From a stationary frame, lorentz transformation gives both length and time of moving frame scaled by the same factor:
$$\Delta x = \gamma \Delta x'\\\Delta t = \gamma \Delta t'$$
Then why does my textbook say length is contracted but time is dilated? From the equations, both the length and time are contracted. What am I missing?
 A: Suppose a rocket going from Earth to Alpha Centauri.
From the rocket frame, the distance between these two locations is shorter than the 4 light years that an Earth observer measures. That is length contraction.
And when the rocket arrives in Alpha Centauri, the clocks of the star (if synchronized to the Earth) will show more time passed than the rocket clocks. That is time dilation.
The logic is to measure the trip distance and duration, and compare with the other frame measurements.
A: Velocity implies equal distance, but either shorter or longer time, so to a person in a car driving on land, and seeing the road as a kilometer would be a contraction of length, but actually the road is 2 kilometers long, dilation of time is also inferred into contraction of distance such that whatever distance we see may take longer time to cover if the velocity of the moving vehicle is constant, and this greatly defines the ideology of spacetime, for example, the sun viewed from the earth seems like the sun is just outside the earth, probably around the same distance as the moon, but in reality, it is millions of miles away from the moon and earth.
In essence,it all depends on the way light behaves and how our eyes can intercept and our brain can interpret the concept of space time.
A: I'm not particularly conversant in special relativity, but I think your first equation is incorrect. Assuming prime designates the moving frame, I believe gamma in the first equation should be in the denominator. Then, given $γ>1$
$$\Delta x=\frac{\Delta x^{'}}{γ}$$
$$\Delta t=γ\Delta t^{'}$$
Where, 
$\Delta x^{'}$ is the length of the moving object as measured in the moving frame (proper length), and $\Delta x$ is the length of the moving object as measured in the stationary frame (contracted length).
$\Delta t^{'}$ is the elapsed time of the moving clock as measured in the moving frame (proper time), and $\Delta t$ is the elapsed time of the moving clock as measured in the stationary frame (dilated time).
Hope this helps.
A: Length is contracted because we're talking about the length of the object, and time is dilated because we are talking about the scale of the measuring device (length between tics).
It could just have well been "ruler dilation" and "interval contraction".
