Studying Relativity: Speed Limit of c in All Inertial Frames?

[mmmboh]

How I studied relativity, we postulated that a particle traveling at c in one inertial frame travels at c in all inertial frame. But now looking through a book, I see that they just postulate that all laws of physics are same in all inertial frames, and that there is a speed limit (c). However then I don't quite get the reasoning on why if an object travels at c in one inertial frame, it follows that it must travel at c in all inertial frames...Is there a contradiction I'm not seeing that if you measure a particle traveling at c, someone moving much faster than you doesn't necessarily have to? This wouldn't change the speed limit in their frame.
(I know this is wrong, I'm just trying to deduce it from how the book did it).

 

[Aimless]

In special relativity, velocities are not additive. If Observer A sees Observer B moving to the right at .9 c, and Observer B sees Observer C moving to the right at .9c, this does not mean that Observer A sees Observer C moving to the right at 1.8c. Rather, velocity obeys something known as the Lorentz Transformation, which in this case leads Observer A to see Observer C traveling at a mere .994c.

These Lorentz transformation rules guarantee that everyone sees light (or any other energetic massless particle) traveling at exactly c no matter how fast each Observer might be moving with respect to other Observers.

 

[mmmboh]

I know that, but those laws are derived based on the postulate that an object traveling at c in one reference frame travels at c in all reference frames. I want to know if you can get that based on the postulates:

1. All laws of physics are the same in all inertial frames.
2. There is a speed limit.

 

[Aimless]

Someone else is probably better equipped to answer this than I, but from a naive first inspection the two rules you name don't seem sufficient to uniquely define a transformation law.

"Objects observed to be traveling at c in one reference frame will be observed to be traveling at c in all reference frames" is usually taken to be one of the postulates. After all, that was one of the first observations that touched off the whole subject.

 

[Janus]

I know that, but those laws are derived based on the postulate that an object traveling at c in one reference frame travels at c in all reference frames. I want to know if you can get that based on the postulates:

1. All laws of physics are the same in all inertial frames.
2. There is a speed limit.

Number 2 is not one of the postulates.

The second postulate is that the speed of light is constant for all inertial frames. The speed limit is a conclusion arrived at from the postulates.