# Time dilation derivation

#### Snip3r

hi all
I was thinking abt the time dilation derivation thought experiment a flash of light shone on a mirror(imagine a window on the left and motion of vehicle towards right), transverse to the direction of motion.according to the derivation the person in the rest frame,P would see the light travelling along the hypotenuse but how? isn't that the speed of light doesnt change with the speed of the source?if i thro a ball from the vehicle perpendicularly then it may appear to go along the hypotenuse cos it wud hv 2 components,the velocity of vehicle&the perpendicular initial velocity with which the ball is thrown but in the case of light it shouldn't have the velocity of vehicle then the light should not hit the mirror in the 1st place according to P,
cos mirror would have moved and the light should escape thro the window isn't it(according to P)?

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#### ghwellsjr

Gold Member
If you think about a cannon aimed upwards and a cannon ball being fired out of it, while the ball is traversing up the inside of the barrel of the cannon, the cannon will be moving to the right and imparting some lateral speed to it so that when it leaves the cannon, it continues on in the same direction it was traveling while inside the barrel, upwards and to the right, don't you agree?

Now lets' say you have a photon gun that creates photons at the bottom of the barrel and guides them to the right as they travel up the barrel of the photon gun. Why would the photon gun be any different that the cannon?

Don't get confused by Einstein's second postulate which states:
light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body
This is really only talking about the speed, c, of light as the emitting body does control the direction of the light.

#### Snip3r

@ ghwellsjr thx fr ur reply
do u mean that the observer at rest would see the photon gun inclined at an angle other than 90degree though according to the observer @ motion the torch is perpendicular to the direction of motion?if not the observer @ rest has no reason to expect the light to travel along the hypotenuse...

#### ghwellsjr

Gold Member
They both will conclude that the gun is pointing straight up at 90 degrees to the direction of travel, but the observer at rest will conclude that a photon has to travel on an angle as it propagates up the barrel and continues on at the same angle toward the mirror.

#### Snip3r

how can the rest observer conclude photon travel at an angle?as he is convinced that the light is fired perpendicularly?what accounts for the horizontal component?

#### Fredrik

Staff Emeritus
Gold Member
how can the rest observer conclude photon travel at an angle?as he is convinced that the light is fired perpendicularly?what accounts for the horizontal component?
The motion of the vehicle. If a car is moving at speed v along a road, and a passenger switches on a laser pointer in the ceiling aimed straight down, the car will have moved a distance vt before the light reaches the passenger's leg (or whatever). So the emission event doesn't occur above the same point on the road as the absorption (or reflection) event.

Edit: Here's an animation: http://www.phys.unsw.edu.au/einsteinlight/jw/text_module4.htm (Click "play" to watch the animation. Use the "step" button repeatedly if you want to watch it slowly).

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#### Janus

Staff Emeritus
Gold Member
how can the rest observer conclude photon travel at an angle?as he is convinced that the light is fired perpendicularly?what accounts for the horizontal component?
Try thinking about it from the opposite direction. The photon gun is "at rest", and you the observer are moving relative to it. It is obvious that the photon goes straight up and down in the frame of the gun. But if you trace the photon's path relative to yourself, it follows a hypotenuse. It is just your relative velocity with respect to the photon gun that accounts for the horizontal component.

This is one of the key ideas of relativity; it doesn't matter which one you consider as "moving", as there is no test that can be made to determine this.

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