# Time and Relativity

laforge
Ok in my class we just started reviewing relativity and I had a really hard time grasping it. My teacher says that time moves slower as you get closer to light speed, which I understand because time is kind of a made up variable (right?).

The one thing I really have a hard time understanding is this. Imagine two clocks, one on Earth and one in a spaceship. The spaceship travels at 0.5 x the speed of light and travels far out into space and comes back. Why when the clock in the spaceship comes back it becomes unsynchronized with the clock that was stationary on Earth.

From my understanding the physical mechanics in the clock stay the same no matter how fast or far it travels. So even if it goes the speed of light for a really long time the second hand of the clock will still move forward every second. So even when it comes back, taking out any variable of part failures, the distance the hands of the clock moved should be the same. My teacher says different though.

Can anyone help?

Dalgo
You are thinking of time as 2 fold instead of one. You are saying that time is universal and individual (One overall and one for the clock) this is not the case. The hands on the clock are slowed proportionally to the closeness to light speed. So when you arive back on Earth your clock had had less time to move so actually the counterpart is different then the one in space.

laforge
So I should be thinking of the experiment in one reference frame? And not a separate one for each?

My teacher also said it had something to do with the deceleration of the ship for it to turn around and come back. He said that relativity laws don't work during that time interval. Is that correct?

phyti
an event is 'o'
a tick is '|'

earth clock ticks:
o o o o|o o o o|o o o o|o o o o|

spacecan clock ticks (@ .6c) :
o o o o o|o o o o o |o o o o o|

the rate of ticks decreases with speed.

Mentor
From my understanding the physical mechanics in the clock stay the same no matter how fast or far it travels. So even if it goes the speed of light for a really long time the second hand of the clock will still move forward every second. So even when it comes back, taking out any variable of part failures, the distance the hands of the clock moved should be the same. My teacher says different though.
Actually, both you and your teacher are correct. One of the key ideas that comes out of relativity is the idea that space and time are not separate things, they are just different directions in a combined thing called spacetime. A correctly functioning clock always correctly measures proper time along its own path through spacetime, but some paths are different lengths than others.

Here is an analogy, a clock measures the distance of a path through spacetime in the same way that an odometer in a car measures the distance of a path through space. If you and a buddy both drive from LA to NY, but you drive through Denver and your buddy drives through Dallas then when you meet up at NY your odometers will have different readings. Both odometers correctly measured the distance along two different paths to the same location. This causes no great intellectual effort to understand because we are used to the fact that "north" and "east" are not really separate things but just different directions in the same space. In a similar way seconds and meters are not really separate things but just different directions in the same spacetime.

The only real difference is that the odometer going straight from A to B reads the shortest distance possible and the clock going straight from A to B reads the longest proper time possible. Thus a "moving" clock accumulates less time than a "resting" clock and therefore can be said to be slow, when all that is really happening is that the "moving" clock is taking a shortcut through spacetime. So both you and your teacher are right in some sense.