I know these two versions of the same postulate is saying the same thing. But I failed to connect them. Please help me understand the links between them.
version1
The laws of physics are the same in all inertial reference frames.
version2
The speed light is traveling at is the same no matter what the constant velocity of the observer (inertial frame reference) looking at the light is.
If I am not mistaken, the observer, whether stationary or traveling at constant velocity, is the inertial reference frame, to which the speed that light is traveling at is relative.
If that is correct, the version 1 is contradicting what Einstein said about speed of light being always constant. Because the "traditional" law of physics clearly says that there has to be some change in the observed speed of light as the speed of the observer varies.
Best Answer
That motion was relative was realized by Galileo, so there was a theory of relativity -- Galilean relativity -- long before Einstein. That the speed of light should be the same according to all observers is indeed inconsistent with the Galilean relativity. This is because in Galilean relativity time is absolute. But it is not mathematically inconsistent to have a universal speed of light. We "just" have to give up the idea that time is absolute. (That's a very big "just" - a Nobel prize "just"!) From On the Electrodynamics of Moving Bodies:
The Galilean relativity says that if Alice moves at a velocity $v$ relative to Bob, their space and time coordinates are related by \begin{align} t_A & = t_B \\ x_A & = x_B + vt_B \end{align} and it follows from this that if Alice emits a signal with velocity $w$, Bob will observe its velocity to be $v+w$. This is why Einstein says that the postulates are apparently irreconcilable, as you have found.
But in the Einsteinian relativity, Alice's and Bob's space and time coordinates are instead related by \begin{align} t_A & = \gamma(t_B - v x_B/c^2) \\ x_A & = \gamma(x_B + \frac{v}{c} t_B) \end{align} where $$\gamma = 1/\sqrt{1 - \frac{v^2}{c^2}}$$ and $c$ is some constant with the units of velocity -- at this point we haven't related $c$ to physical phenomena like light yet. Now it turns out that when space and time are related like this, because Alice does not agree with Bob what time is, velocities add differently. If Alice emits a signal with velocity $w$, the velocity measured by Bob is $$v\oplus w = \frac{v + w}{1 + vw/c^2}.$$
Now there are two interesting things about this formula. First of all, if $v, w < c$ then $v\oplus w$, and -- as the resolution to the conundrum -- if $w = c$, then regardless of $v$, $v\oplus w = c$. So under this theory of relativity, signals moving at $c$ are special: everyone will agree that they move at $c$.
To relate this to light, one of Maxwell's equations -- the equations that govern electricity and magnetism -- is $$\nabla\times\mathbf B = \mu_0 \mathbf J + C^{-2} \frac{\partial \mathbf E}{\partial t}$$ where $C$ is a constant with units of velocity -- it is the speed of electromagnetic waves, that is, light. It turns out that Maxwell's equations are never consistent with Galilean relativity, but they are consistent with Einsteinian relativity, under the condition that $c = C$. So the $c$ that enters into the coordinate transformation is indeed the speed of light. (You can do the math to make absolutely certain that it is like this, but you can also think of it like this: under Einsteinian relativity $c$ is the only speed that everyone agrees on. So if everyone is to agree on the form of the equation, the only velocity that can show up is $c$.)