A recent post on a forum I visit got me thinking about this idea.
First, imagine you are on board a high speed train and you have a gun. This isn’t Murder on the Orient express though, this is an experiment.
Say the train is moving at the same speed as the gun can fire a bullet (assuming this speed is the initial velocity of the bullet and the train is moving in a vaccuum, so air resistance is negligible), call this 500 m/s.
Now, fire the bullet out of the window directly ahead. What happens?
Well, without air resistance the bullet isn’t limited by terminal velocity, so the bullet is moving at 500 m/s before it is fired, then gains an extra 500 m/s once it is fired. The bullet is moving at 1000 m/s. Or, with respect to the passenger on the train, the bullet is moving at 500 m/s.
Now, point the gun directly backwards, away from the direction of motion and fire. Again, relative to the passenger the bullet travels at 500 m/s, but relative to an observer standing by the tracks, the bullet appears to be falling straight down.
Then that got me thinking about a similar problem that is all too common in Physics classes.
Imagine you are on board a spacecraft travelling at the speed of light.
You have a torch, you point it in the direction you are moving and turn it on.
What happens?
Well, the light travels away from you at the speed of light.
Now, what about a stationary observer? (that is, the spacecraft is moving relative to the observer)
Nothing can travel faster than light, right?
Right.
Well, the observer also sees the light travel at the speed of light in the direction the craft is travelling.
But then the observer would see the light moving at the same speed as the craft, yet the craft sees the light moving away at the speed of light.
A contradiction?
That’s where Einstein comes in with the Special Theory of Relativity.
This states that light moves at a constant velocity relative to all observers, irrelevant of their velocity or direction.
This is allowed to happen by a phenomena known as time dilation. That is, time slows down the faster you get.
This then leads to the famous ‘twin’ thought experiment.
Take a set of twins, give them identical clocks, leave one on Earth and set one off on a journey round the Universe at very, very high velocity.
When the travelling twin comes back, his clock will be lagging behind the stationary twin on Earth. Thus, he has aged less.
Time dilation is a very interesting concept of both Special and General Relativity, and has had a profound impact on modern Physics, even modern life. In fact, GPS satellites orbitting Earth must take into account relativistic effects, something called gravitational time dilation, when sending positioning data.
