Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: jim on 05/04/2008 16:50:20

Hi,
This may be a silly question, but I think it will help me understand a whole lotta other things...
I understand that the speed of light (C) is the ultimate speed limit in the universe. Now, if Im driving along at 100km /h and I switch on my lights will the speed of the light emitted from my headlights be c or c+100km/h ? If its just C then what is the factor that causes this limits and what happens if I watch a spaceship travelling at c  100km/h with its headlights on??
Thanks!
Jim

Special relativity says that, however fast you may be going, relative to anywhere else, you will measure the speed of light as c. So two people, traveling at different speeds will measure the speed of the same beam of light as being the same.
How can this happen? Well, time and distance become distorted is such a way as to make both measurements give the same answer.
One of the basics of SR is that you must be in an inertial frame  not accelerating or in a gravitational field. Under these conditions there is no way of 'knowing' which of you is stationary and which is moving  or whether you are both moving it's all relative  hence the name.
Even in General Relativity, whatever you are doing (including accelerating) you will measure c as the same.
Everything else hangs on this.

Yup.. Speed of light would just be C.. Because it's just like a torch, and if it's left on the table, switched on, the speed of light would be C.. But if you're running with a torch, it would have no difference to the running, as the light would travel FROM the source (the torch) and would also be C.. Me thinks!

Indeed. This may seem counter intuitive to anyone who does not know the theory of relativity. It does lead to a good deal of other strange effects that are also counter intuitive. But most of these strange phenomena are not things we experience in everyday life but have been shown to be true in various experiments.

Your spaceship could never reach the speed of C because doing so would take infinite energy, however lets say the spaceship was travelling 100km's per hour less than the speed of light. To an observer inside the spaceship, would it seem the light was only travelling 100km's an hour? No. In fact, it would still travel at C as far as they could tell. This is because at speeds close to the speed of light time itself is warped, so a clock in the ship will run much slower than one stationary relative to the ship. So to the stationary observer, an hour after they have turned the lights on, the light will seem 100 kilometres ahead. But to the people in the spaceship, when they have measured the light is 100km's ahead, it will only have taken the tiniest fraction of a second to them, not one hour. So time itself changes in order to keep the speed of light constant, it seems.
Hope that makes it easier to understand

But most of these strange phenomena are not things we experience in everyday life
There are a lot of phenomena which we take for granted as being fairly humdrum and strictly classical yet they can be explained very well in terms of relativistic effects  for instance, the socalled magnetic force between two currentcarrying wires can be explained quite satisfactorily by the relativistic effects on conduction electrons moving at speeds a a few mm per second.

Yup.. Speed of light would just be C.. Because it's just like a torch, and if it's left on the table, switched on, the speed of light would be C.. But if you're running with a torch, it would have no difference to the running, as the light would travel FROM the source (the torch) and would also be C.. Me thinks!
But the speed would still be c even if the torch is running towards you or away from you at c.
V = (v_{1} + v_{2})/(1 + v_{1}v_{2}/c^{2}).

First, when you talk about traveling at a certain speed, you have to say
what you are traveling that speed relative to. Relativity tells us that
there is no fixed reference frame, so you can equally well think of being in
a spaceship moving away from a stationary planet at speed c100km/h as
being a stationary spaceship and with the planet moving away at c100km/h;
these two situation have identical physical laws from the point of view
of the person in the spaceship. This includes the speed of light
being the same; light will always travel away at the same speed.
Where it get complicated in when you think about somebody on the planet
and somebody on the spaceship both viewing the light from the
headlights. They both view the speed of light being the same. Intuitively,
this is inconsistent. Just one example of this is that light waves
oscillate at a given frequency and so at different points in space
are in a different phase; naively the two viewers would see these oscillations
spread out differently in space, which isn't possible.
To make these facts consistent requires the really weird bits of
special relativity: if you view somebody moving relative to you
at great speed, it will look to you like time moves slower for that
person (also, they will be heavier and smaller). While really weird,
the constancy of the speed of light, and timedilation effects
have been measured experimentally to good accuracy. In fact, the
GPS satellites (which rely on very accurate clocks) are moving fast
enough that they have to account for timedilation to work.

How can this happen? Well, time and distance become distorted is such a way as to make both measurements give the same answer.
_{<Mod edit  Removed spam>}

Just a comment:
There's no universal frame of reference but for any change to occur there must be a frame of reference for the change to be compared to, to be established as a change.