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- Even applying the time dilation formula (Lorentz's equation) my calculations on Special Relativity seem to be wrong. the speed of light doesn't seem to be constant.

Hello!

I am trying to make some calculations on the Special theory of relativity over a practical example, considering the time dilation, but I may (more than likely..) be doing something wrong (probably with my assumptions). I would appreciate any comment on it.

The example is that of a rocket travelling at half the speed of light, so let´'s say at 150.000 km/s.

I am assuming that for those who are inside the rocket to measure the speed of light as that of 300.000 km/s (because it is a constant for all observers), this means that they see the light (its photons) 300 km ahead of the rocket, when a second (counted from inside the rocket) has passed (because, as relativity says, speed of a moving object related to another moving object is the difference between the two speeds). Light has travelled 300km more than the rocket (from the point of view of the guys inside the rocket) after a second.

Then my calculations are as follow:

. When a second within the rocket has passed, they have actually advanced 173 kms, since, due to the time dilation, that second is slower than in a stationary clock and is the equivalent to 1.1547 stationary-clock seconds (as a result of the time-dilation formula: t'= ϒ t, where ϒ would be 0.866 for a speed of 150km/s). So, travelling at 150 km/s during 1.1547 secs means you travel 173 kms in a second.

. And the light will reach 346,42 kms, going at 300 kms during 1.1547 secs.

But then, 346,42 - 173 is less than 300. How come the guys in the rocket measure a speed of light of 300km/s (or what seems to be the same: that they see the light at 473km, 300 ahead of them)??

Thank you in advance,

Regards,

Jose

I am trying to make some calculations on the Special theory of relativity over a practical example, considering the time dilation, but I may (more than likely..) be doing something wrong (probably with my assumptions). I would appreciate any comment on it.

The example is that of a rocket travelling at half the speed of light, so let´'s say at 150.000 km/s.

I am assuming that for those who are inside the rocket to measure the speed of light as that of 300.000 km/s (because it is a constant for all observers), this means that they see the light (its photons) 300 km ahead of the rocket, when a second (counted from inside the rocket) has passed (because, as relativity says, speed of a moving object related to another moving object is the difference between the two speeds). Light has travelled 300km more than the rocket (from the point of view of the guys inside the rocket) after a second.

Then my calculations are as follow:

. When a second within the rocket has passed, they have actually advanced 173 kms, since, due to the time dilation, that second is slower than in a stationary clock and is the equivalent to 1.1547 stationary-clock seconds (as a result of the time-dilation formula: t'= ϒ t, where ϒ would be 0.866 for a speed of 150km/s). So, travelling at 150 km/s during 1.1547 secs means you travel 173 kms in a second.

. And the light will reach 346,42 kms, going at 300 kms during 1.1547 secs.

But then, 346,42 - 173 is less than 300. How come the guys in the rocket measure a speed of light of 300km/s (or what seems to be the same: that they see the light at 473km, 300 ahead of them)??

Thank you in advance,

Regards,

Jose