# Light goes this path with c

1. Feb 18, 2010

### teodorakis

Hello, i am studyig the special relativity for a while and actually mathematics isn't so difficult but cenceptually it's very unnatural to me.Anyway, first i want to ask about michelson morley experiment, in that experiment light beam which goes in a zigzag path, it's assumed that light goes this path with c, speed of light.But isn't this the use of constant speed of light postulate which is not known yet? Or if we accept the galilean transformation this speed should be c+u(speed of the apparatus)(vectorally), like if you're in a train moving with speed of u in +x direciton you throw the ball with c in +y direction and the speed of the train is u in x direction, to the person in an inertial reference frame outside the train the speed of the ball is u+c(vectorally), but in case of light we can't do that? Light travels at speed c to all observers, but in michelson morley experiment this is not known yet, what do i missing?

2. Feb 18, 2010

### yuiop

Re: basics

If you use the assumption that light travels with speed c+u, when you do the calculations the signals do not arrive back at the centre at the same time. Since the signals did arrive back at the same time they had to change the assumptions. Assuming a constant speed of light seemed reasonable, because this was hinted at by Maxwell's equations for the propagation of an electromagnetic signals, which were already known at the time. Even this assumption is not enough to explain the observations and Lorentz made the further assumption of length contraction, which could explain the observations. The observations of the MMX experiment were not expected and they had to find an explanation for it. So far no one has found a better explanation, that agrees with all other known experiments and observations.

Another experiment, measuring the aberration of light from distant stars, also confirmed that light does not travel according to c+u and that observation was made by Bradley in 1725 which was a long time before the MMX experiment (1887).

Also, you should note that there is not one set of rules for the velocity of light and another set of rules for particles like trains and balls. All velocities add according to the same formula:

$$\frac{(u+v)}{(1+u^2v^2/c^2)}$$

For example u could be the train and v could be the ball. If v happens to be a light particle traveling at c, then the combined velocity is also c for any u. Light is just one extreme of the addition equation that applies to all particles at all velocities. The Newtonian addition of velocities (u+v) is simply an aproximation that is aproximately correct at everyday velocities.

Last edited: Feb 18, 2010
3. Feb 18, 2010

### I_am_learning

Re: basics

The whole of relativity lies in the experimental result that light's velocity is constant. Should it be found some day that there was a serious mistake in the experiment, the whole of relativity would go down. But be sure as hell that it won't happen. Also many more experiments have directly confirmed the results of relativity, such as time dilation.

4. Feb 18, 2010

### teodorakis

Re: basics

so in the mmx experiment one of the psotulates of relativity is used?

5. Feb 18, 2010

### I_am_learning

Re: basics

I hope you mean Michaelson Morley Experiment, my mmx experiment;
One of the postulate isn't used there, but verified instead (that the velocity of light is invariant)

6. Feb 19, 2010

### grav-universe

Re: basics

Actually they would but Maxwell's equations show that light should travel at a constant speed in every direction, so always measured at c. As you mentioned, aberration of starlight also indicates it. The belief that light travels ballistically with the source at c-v and c+v was still continued to be held by many for a long time until the Ives-Stilwell experiment was performed where the sum of the results of the Doppler effect of light travelling in the forward direction and back from atoms was measured and found to clearly not indicate ballistic motion for Doppler but matching Relativistic Doppler instead. Also, with ballistic motion, length contraction and time dilation are not necessary, but are observed with the decay of muons. Relativity also provides a good explanation for the interaction of electric and magnetic fields with relative motion as well as subatomic processes.

Last edited: Feb 19, 2010
7. Feb 20, 2010

### teodorakis

Re: basics

another question:
about time dilation, when we derive the time dilation formula we use a simple clock which the light goes up and back in the vertical direction, and we compare the time between a stationary clock and a moving clock and derive the formula. But we always take the clock vertical to the motion. Now i know once we evaluate the formula it's true for all proceses, including mechanical and other.So we don't need to analyze other types of clocks which can be in all other directions(am i right?), but mathematically i can't derive the same formula, for example when we set the clock in horizontal position(along the motion) i can't derive the time dilation formula.Is there any way of doing this?
Thank you.

8. Feb 20, 2010

### teodorakis

Re: basics

i got an answer for my question above now another one:)
in mm experiment the null result is verified by the fact that the distance in the direction of motion of light is shrunk by lorentz factor. But they still accept that the velocity of light towards the observer is c+u(u:speed of observer), so until einstein the constantness of the speed of light wasn't known yet or was it?And even after einstein if we use the lorentz factor and add the velocities as i metioned we still get the correct result(time dilation for example) but with mistaken assumption?
I hope i could explain what i mean.

9. Feb 20, 2010

### teodorakis

Re: basics

i want to add something, if we accept the constantness of light than we say light takes more distance or less distance according to the position of the source to the motion,we conclude the same solution by accepting the galilean transformation and use the ordinary vector algebra in mm experiment?

10. Feb 20, 2010

### grav-universe

Re: basics

The speed of light is considered always to be c in the frame of an observer in the M-M experiment also. The thing is, though, that while the light is travelling at c, the apparatus is travelling at v as well, so it may look like the speed of light is figured at c+v and c-v but it is really just the combination of c only for the light and v for the apparatus. For example, let's say that according to some reference frame, the apparatus is travelling away from the observer at v while light travels in the same direction along an arm of the apparatus from one end to the other with a length of d as measured in the reference frame. So the light pulse starts at one end of the arm and travels to the other end of the arm at c, but while this is happening, the arm itself is moving away from the observer at v, so the end point is moving away at v.

The distance the observer sees the light pulse travel is just x = c t. The other end of the apparatus was originally at a distance of d from the end that the light pulse started, but during the time that the light pulse was travelling from one end to the other along the arm, the end it was travelling to was also moving away at v, so in a time of t, that end has travelled a distance of v t, making the distance the light has to travel a total of x = d + v t, therefore x = c t = d + v t. The time the light takes to travel this distance according to that reference frame, then, is c t = d + v t, (c - v) t = d, t = d / (c - v). Similarly, for a light pulse travelling from the furthest end to the closest end, the closest end will be moving toward the light pulse at v while the light pulse also moves toward the closest end at c, so less time elapses to travel the arm, with a time travelling back of t = d / (c + v). So the c - v and c + v there have nothing to do with the speed of light itself, being just c always in any direction, but have to do with the time it takes to travel along an arm while the arm is also moving to the frame of reference.

11. Feb 20, 2010

### yuiop

Re: basics

Your right. Thanks for the correction. Silly mistake on my part.

12. Feb 21, 2010

### teodorakis

Re: basics

gray-universe thanks for the reply, now i got it, kev thank you for your replies too. You didn't make a mistake, the equations come to a conclusion wihich looks like adding/subtracting the speed of light with the speed of reference frame.

13. Feb 21, 2010

### edpell

Re: basics

New physics does not invalidate old physics it extends it. If there are new effects they will need to be added to a new theory.