If light is relative in speed...

Darg · 12 Jul 2007 at 17:03

Okay, another one of these threads.

Imagine I'm driving in my car past the earth at half the speed of light c/2.

I turn on the headlights. Now since the speed of light is relative to the observer I would see them shining out in front of me like normal.

But to a static observer on the earth they would appear to be going at only half the speed of light relative to my car.

Time for some bad ASCII art to explain better:

According to me in my car (C = Car, O = Earth):

Code:

                    C----------

                    O

According to observer on Earth:

Code:

                    C-----

                    O

The --- indicating the distance the light travels in 1 second in front of the car according to each observer. This is ignoring the time taken for the light from the headlights to reach the static observer. I don't think that would make any difference other then to add confusion.

So what is the actual speed of the light? I cannot understand how it could be going at two different velocities just because it is being observed from two different speeds.

Ex-RoNiN · 12 Jul 2007 at 17:05

There is no "actual" speed of light, it depends on frame of reference.

Just like there is no "outside" reality, it is all a social and mental construct.

Darg · 12 Jul 2007 at 17:07

Ex-RoNiN said:
There is no "actual" speed of light, it depends on frame of reference.

Just like there is no "outside" reality, it is all a social and mental construct.

Don't do that to me when I'm this tired dude..

Indy500 · 12 Jul 2007 at 17:08

Time is relative to the observer, as Einstein said.

Mark47 · 12 Jul 2007 at 17:11

It is kinda like anything really. No measurement really has meaning unless you have something to compare it against.

aardvark · 12 Jul 2007 at 17:12

it might appear that light is traveling at different speeds and it might appear that time runs at different speeds depending on the observer but it only looks that that because its relative - the speed of light is still a constant and doesn't change (in these circumstances)

Darg · 12 Jul 2007 at 17:14

So how long would my headlights look to an observer on earth?

Slam62 · 12 Jul 2007 at 17:14

uh everything will appear normal except the car is going a bit quick

colinuk · 12 Jul 2007 at 17:15

The real question should be if the observer is far enough from the light to only see half the beam, will it last twice as long for him as to the driver in the car?

Darg · 12 Jul 2007 at 17:25

*but* if the light appears the same length to the observer on the planet as it does to the person in the car then the light would appear to the observer on earth to be going at 1.5X the speed of light as you have the speed of the car plus the speed of the light. How is this possible?

aardvark · 12 Jul 2007 at 17:31

Darg said:
*but* if the light appears the same length to the observer on the planet as it does to the person in the car then the light would appear to the observer on earth to be going at 1.5X the speed of light as you have the speed of the car plus the speed of the light. How is this possible?

i assume thats where the time dilation factor comes into play - both are moving at the speed of light so time must be slower for one of the observers??

Inquisitor · 12 Jul 2007 at 17:33

Darg said:
*but* if the light appears the same length to the observer on the planet as it does to the person in the car then the light would appear to the observer on earth to be going at 1.5X the speed of light as you have the speed of the car plus the speed of the light. How is this possible?

Don't think about 'lengths'; think in terms of speed.

The observer on Earth observes the car travelling at half the speed of the light being emitted from his headlights, as you'd expect.

From your car, the light would still appear to be travelling at c relative to you. This is because your perception of time is different to that of the 'static' observer on Earth: time is progressing more slowly for you than it is for the observer. This allows for the apparent difference between speed of light being emitted from your headlights as observed by you and the observer.

Darg · 12 Jul 2007 at 17:37

I should have done astro physics.. you'd have to be stoned to understand all this stuff!

Not that I wasn't anyway.. :rolleyes:

Slam62 · 12 Jul 2007 at 17:43

Darg said:
*but* if the light appears the same length to the observer on the planet as it does to the person in the car then the light would appear to the observer on earth to be going at 1.5X the speed of light as you have the speed of the car plus the speed of the light. How is this possible?

ooh so light can never go above the speed of light, sounds logical but hmm

I suppose light waves are different ie not matter as such but energy and therefore would not gain the additional speed of the car.

Darg · 12 Jul 2007 at 17:47

Slam62 said:
ooh so light can never go above the speed of light, sounds logical but hmm

I suppose light waves are different ie not matter as such but energy and therefore would not gain the additional speed of the car.

But if that were the case then the light would appear to be travelling at half the speed of light to the observer in the car.

Haircut · 12 Jul 2007 at 18:03

Darg said:
But if that were the case then the light would appear to be travelling at half the speed of light to the observer in the car.

No, because you can't just add speeds like that when you get near the speed of light.

0.5c + 0.5c != 1c

You need to use this formula
http://en.wikipedia.org/wiki/Velocity-addition_formula

PinkPig · 12 Jul 2007 at 18:13

This is the central point of special relativity - light travels at the same speed in all frames of reference.

Amleto · 12 Jul 2007 at 18:23

Eurgh, not this again.

I'd rather we wheel out the conveyor belt and put a 'plane on it :mad:

[TR]SweetSpotOz · 12 Jul 2007 at 18:38

Special relativity - not cool.

I just had a lecture about it at Cambridge and I've never been so confused in my whole life.

Really interesting though. Everyone was asking these sorts of questions and there is always a reason why it wouldn't happen.

frying_pan_cat · 12 Jul 2007 at 18:55

The length of the car would be shortened to the observer compared to when they are both in the same inertial reference frame, so I believe that answers your question - the car would be shorter and the light would be less distance from it so they would be in the right proportions.
This probably doesn't make sense but oh well