Constancy of speed of light and galiliean transformation

[jablonsky27]

Hi,

I'm reading up on special relativity and it is pointed out that the galilean transformation dictates that if a light source were moving at velocity v wrt to an observer in another inertial frame of reference, then this observer would calculate the speed of light to be either (c-v) or (c+v) depending upon the source's direction of motion.

Since this is untrue, the galilean transformation is wrong.

My question is why was this a surprising result(inapplicability of galilean transformation to light)?
This is equally true of sound as well isn't it - the speed of sound is independent of the speed of the source.

 

[harrylin]

Hi,

I'm reading up on special relativity and it is pointed out that the galilean transformation dictates that if a light source were moving at velocity v wrt to an observer in another inertial frame of reference, then this observer would calculate the speed of light to be either (c-v) or (c+v) depending upon the source's direction of motion.

Since this is untrue, the galilean transformation is wrong.

My question is why was this a surprising result(inapplicability of galilean transformation to light)?
This is equally true of sound as well isn't it - the speed of sound is independent of the speed of the source.

What was surprising, is that at the same time the relativity principle holds: no motion relative to the ``light medium'' can be detected, the speed of light is measured as c with respect to any inertial reference system. That may seem to be, as Einstein put it, irreconcilable with the postulate that the speed of light in empty space is c, independent of the motion of the source.

- http://www.fourmilab.ch/etexts/einstein/specrel/www/

Note: all observers are in all inertial frames of reference.

 

[jablonsky27]

the speed of light is measured as c with respect to any inertial reference system. That may seem to be, as Einstein put it, irreconcilable with the postulate that the speed of light in empty space is c, independent of the motion of the source.

the relativity principle states that all physical phenomena have the same form in all inertial reference frames.
applying the galilean transformation to light and any inertial frame results in an incompatibility.

similarly, doesn't applying the galilean transformation to sound also result in the same incompatibility? so i guess my question is, why wasnt it realized wrt to sound itself that there was a problem with galilean transformation and Newtonian mechanics in general?

 

[Janus]

the relativity principle states that all physical phenomena have the same form in all inertial reference frames.
applying the galilean transformation to light and any inertial frame results in an incompatibility.

similarly, doesn't applying the galilean transformation to sound also result in the same incompatibility?

No, it doesn't, becuase the the speed of sound is relative to the medium through which it is traveling. Thus the speed of sound relative to receiver depends on the velocity of the receiver with respect to the medium. For light, no movement by source or receiver will result in the receiver measuring a difference in the speed of light with respect to himself.

 

[GTOM]

And isn't the speed of light relative to the local space-time curvature, or gravity field?
Ok, it is constant in 4 dimensional spacetime, but does that mean, it is always the same in 3 dimensional space?

 

[DrGreg]

And isn't the speed of light relative to the local space-time curvature, or gravity field?
Ok, it is constant in 4 dimensional spacetime, but does that mean, it is always the same in 3 dimensional space?

You probably have in mind that in a non-inertial frame (for example if the observer is accelerating, or in the realm of general relativity when gravity or cosmological expansion is accounted for) it is possible for the speed of light at some distance away from the observer might not equal the constant c.

But in all cases if you measure the speed of light in vacuum as it passes right next to you, using local clocks and local rulers, you always get the same answer c no matter where you are or how you are moving or accelerating (or how the source moved).

The same does not apply to sound because your speed relative to the medium (e.g. air) makes a difference.

 

[GTOM]

"But in all cases if you measure the speed of light in vacuum as it passes right next to you, using local clocks and local rulers, you always get the same answer c no matter where you are or how you are moving or accelerating (or how the source moved)."

I heard, that they measure speed that they compare the wave amplitudo at the start, and at the end.
So how do you make a difference, that Doppler effect only changed frequency, because you move with c/2 or the light speed relative to you is only c/2?
How can you say, the high speed doesn't effect the measuring instrument?

Sorry but i really don't get it. :(
Light travels through space. How should it know, what speed do i have, so it will hit me with a speed of c, no matter what?

Maybe we could get similar results to sound, if our instruments would use sound waves.
We measure things with EM waves, and light is an EM wave. What effects light, also effects our instruments.

 

[harrylin]

"But in all cases if you measure the speed of light in vacuum as it passes right next to you, using local clocks and local rulers, you always get the same answer c no matter where you are or how you are moving or accelerating (or how the source moved)."

I heard, that they measure speed that they compare the wave amplitudo at the start, and at the end.
So how do you make a difference, that Doppler effect only changed frequency, because you move with c/2 or the light speed relative to you is only c/2?
How can you say, the high speed doesn't effect the measuring instrument?

Sorry but i really don't get it. :(
Light travels through space. How should it know, what speed do i have, so it will hit me with a speed of c, no matter what?

Maybe we could get similar results to sound, if our instruments would use sound waves.
We measure things with EM waves, and light is an EM wave. What effects light, also effects our instruments.

It would be inconsistent to claim that a high speed does not affect our instruments. So, that thing you did get!
However, we could not get similar results with sound, because our instruments are not at all made of sound waves (they can be thought of made of some kind of electromagnetic waves, see http://en.wikipedia.org/wiki/Matter_wave).

Harald