can someone explain this dot point!?! (1 Viewer)

[(^o^)]

Jacaranda around page 82 (it's the old book so not too sure about the new one)
Heading: A constant speed of light

Need help about:
Einstein theory of constant speed of light and a thought experiement that he did: If I were travelling in a train at the speed of light and helf up a miror, would i be able to see my own reflection?

And what is it about "if the traveller in the light-speed train looks at his reflection in the mirror. The observer on the embankment outside the train sees the lights travelling twice at far".

Why is it twice?
What theory/equation does this relate to?

If you tell me to check out your study notes, don't bother, cos it's not detailed enough to make me understand it =/
Sorry school hasn't taught us this yet. So need BOSers' help.

 

[zeropoint]

Hi,

Yep. According to the old train of thought, light travels at a constant speed c relative to the stationary ether. So, imagine yourself sitting inside a train travelling at close to the speed of light. If you hold up a mirror to admire your reflection at a foot's length, you will notice that your reflection appears lagged in time, as though the photons impinging on the mirror are taking less than the usual nanosecond to arrive at the mirror from your face. If you do a little calculation, you will find that the speed of the arriving photons relative to your mirror is reduced from the normal speed of light c, to a value of c - v, where v is the speed of the train. If you imagine the train travelling closer and closer to the speed of light, eventually the relative velocity limits to zero, and you now see nothing but a black image on the mirror surface, since none the photons will ever `catch up' to the receding mirror.

Today of course, this is all known to be incorrect. In fact, the relative speed of light is the same for everyone who travels at constant speed in a straight line. So in reality, your reflection will appear untainted, irrespective of the motion of the train.

If the guy on the embankment watches you through the window. He'll observe the same speed of light c that you do, however the light will have to travel a bit further in his frame due to the receding motion of the mirror. The exact distance can be calculated too if you like. If you set the position of your face at time zero as the origin , you can write down equations for the the position of the mirror and position of the wavefront of light emited by your face.

x_mirror = x_0 + vt
(x_0 is one foot remember?)
and
x_wave = ct

Now we want to find out how long it takes for the light to catch up to the mirror. In other words, when x_mirror = x_wave,

x_0 + vt = ct

subtract vt from both sides

x_0 = ct - vt

take out t and divide by c - v

t = x_0 / (c - v)

Then to get the distance, plug that back into the equation for x_wave and you get

distance covered by light in embankment frame = c x_0 / (c - v)

If you plug in half the speed of light for v, you find that the light path is now 2 ft instead of 1 ft. So that's why it's twice!

 

[(^o^)]

cool... i get most of the stuff you've said. Much more clear.

However what equations are they? --> x_mirror = x_0 + vt
Anything to do with Galilen transformation equations?

or you just made em up to prove the theory??
x_0 looks like a face haha

 

[zeropoint]

cool... i get most of the stuff you've said. Much more clear.

However what equations are they? --> x_mirror = x_0 + vt
Anything to do with Galilen transformation equations?

or you just made em up to prove the theory??
x_0 looks like a face haha

Yep, that equation is just the normal Galilean transformation

x = x' + vt

applied to the moving mirror. The x'-coordinate of the mirror in the moving frame is x_0, so the x-coordinate in the `stationary' frame is

x_mirror = x_0 + vt.

The Galilean transformation is only an approximation for the true Lorentz transformation. In Galiliean relativity, the motion of the light wave would be determined by

x_wave = (c + v)t.

However, the Lorentz transformation preserves the speed of light so that the true equation is

x_wave = ct.

I didn't use the Lorentz transformation for the mirror as the increased complexity of the equations would offset any added illumination. Thus the equation c x_0 / (c - v) is only an approximation for low fractions of the speed of light.

 

[(^o^)]

hmm ok..
I'm getting the equations and the gist of it now, thanks a lot!