If A & C are stationary with each other but distanced apart, B is in the middle of them. If B is moving towards C with certain velocity V closer to light with respect to A. Will magnitude of velocity of B w.rt. C be equal to V?
The reason I asked this because:
If I am correct, We see object when light from object reaches to us. When object moves away from one point to another, the distance travelled is measured in our reference frame and is not affected by the speed of object. So the speed of the object can calculated as the distance between the two position travelled by the object divided by the difference in the time taken by the light( emmited when they reach to both the position) to reach to us. Right?
If this is true then the speed should be different when object moves towards B or away from A in my case because at any particular position light is emitted in both the direction i.e. towards A & B travelling with velocity C and when object moves to another location to get closer to B, the light which will travel towards A will have longer span then the one travelling towards B and so the time taken by both should be different and so the speed.
I know this is not what theory of relativity says. So, please correct me where I am wrong.
Dear D.N.Shrimali,
Please see the first few pages of my work ' Lorentz Transformation Via Minkowskian ........,DOI10.13140/RG,2.224338.86723, Jan 19,where the equation of a line in four dimensional space-time is defined.This will help you to resolve your problem. Even then, if you are unable to resolve your problem, kindly let me know.
Regards
Ramesh Chandra
The distance traveled by B as measured by A or C is done after correcting for the light travel time from B to A (or C). When this is done, the magnitude of the velocity whether A measures or C, will turn out to be V.
There is another way to measure the velocity. If B carries a source of monochromatic light whose rest wavelength is lambda, then C will measure a wavelength shorter than lambda, while A will measure it to be longer. From the change in the wavelength one can infer the speed. It can be easily shown that the speed is V for both A and C.
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