# What is happening when travelling towards light?

1. Aug 31, 2009

### RogiNicba

When a vehicle is moving while projecting light forward, time slows down inside and the length of the vehicle contracts just enough so that the combination of this two effects make the people inside the vehicle percieve the speed of light projected still be approximetly c no matter the speed of the vehicle, right?

But I was wondering; what makes the people travelling towards a beam of light measure its speed to still be c? I suppose the vehicle in this case should lengthen and the time should be running faster for the passengers to compensate, but that doesn't happen.

Last edited: Aug 31, 2009
2. Aug 31, 2009

### HallsofIvy

It doesn't matter at all whether you are moving toward or away from a light source. In either case, the speed of light (as opposed to "velocity") is c.
If you are moving toward a light source at speed v (velocity -v) relative to the source and light is moving away from the source at speed c, then the speed of light, relative to you, is
$$\frac{-v+ c}{1- vc/c^2}= c\frac{-vc+c^2}{c^2- vc}= c\frac{c^2-vc}{c^2- vc}= c$$
If you are moving away from a light source at speed v( velocity v) relative to the source and light is moving away from the source at speed c, then the speed of light, relative to you, is
$$\frac{v+c}{1+ vc/c^2}= c\frac{vc+ c^2}{c^2+ vc}= c\frac{c^2+ vc}{c^2+ vc}= c$$.

3. Aug 31, 2009

### RogiNicba

I realise that according to special relativity light travells at c for all observers regardless of their speed and direction. The problem is that I can visualise why that is true in the case when something is travelling in the same direction as the light. But I can't understand/visualise how that (the constant speed of light) can also be true when you are travelling towards the source of the light...

To explain what I mean further; suppose you're travelling at a half the speed of light and there are 2 seperate beams of light travelling infront of you, one on the path towards you while the other is travelling away from you(in the sam direction your headed). Now becouse of a combined effect of time dilation and length contraction if one were to measure the speed of the light beam on the path away from you, you would measure(dispite the fact that you're moving at half the speed of light) that the beam is acctualy travelling at c. Becouse even tho Galilean invariance tells us that now the light that is heading away from us shlould be moving away from our vehicle at a distance of c/2 that is not true becouse time dilation takes care that we percieve the beam going a bit faster and length contraction makes sure that our "shortened rullers" measure the length the beam travells to be just enough longer that from the point of view of the driver of the vehicle the light is still travelling at c. Do I understand this correctly so far?

But what troubles me is; wouldn't you now percieve the speed of that other beam(the one headed towards you) to be 1.5c becouse of time moving slower for you and your perception of length being diffrent? How can we percieve both beams of light going at the same speeds at the same time? Didn't Einstein say something along the lines:"If the speed of light is constant for all observers than something else has to change", and so he figured time and length change so that from the observers point of view the speed of light stays the same. But wouldn't than be true that if we wanted to percieve the speed of the beam headed towards us to be c, we should lengthen and time should then be going faster for us? But both time contration and time dilation+length dilation and length contraction is not possible at the same time right?

I appologise for the long post. I just want to make my point clear so you can help me understand. I should also mention that I have been reading/studying up on Special and General relativity for only about 2weeks now and I'm only a highschool graduate 19years of age so I'm not saying Einstein was wrong or anything I'm just clearly missunderstanding/not getting something. But I'm very interested in this and would appreciate it very much if someone could make me understand this. Prefferably in a manner that someone of my education would understand if possible :)

Thanks!

Last edited: Aug 31, 2009
4. Sep 1, 2009

### A.T.

SR doesn't tell you why that is true. It is not a consequence of SR, but an assumption on which SR is based.
Different from what? Knowing how exactly you calculated the 1.5c would be more useful than the long explanation.

5. Sep 1, 2009

### Janus

Staff Emeritus
Part of the problem is that you are putting the cart in front of the horse, so to say.
SR starts with the premise that the speed of light is the same for all observers and because of this, you will measure a clock moving relative to you as ticking slower and being foreshortened, not that they will measure light at c because they are shorter and their clock is running slow. (someone traveling with that clock would say the same about you.)

The other thing is that there is a third effect of Relativity called the Relativity of Simultaneity. What it means is that if you have two clocks separated by a distance and moving parallel to the line joining them, they can read the same time according to someone at rest with respect to them, but will read different times according to someone for which they are moving. According to them the front clock will be ahead of the rear clock. Conversely, if the clocks read the same time to someone for which they are moving, they will not read the same time according to someone at rest with respect to the clocks.

This difference in readings between the clocks according observers is what makes up for what time dilation and length contraction can't alone.