"in" and "out" states in Weinberg's QFT In Weinberg's QFT Page 109, he defines the "in" and "out" states as

the 'in' and 'out' states* $\Psi_{\alpha}^{+}$ and $\Psi_{x}^{-}$ will be found to contain the particles described by the label $\alpha$ if observations are made at $t \rightarrow-\infty$ or $t \rightarrow+\infty$, respectively.

And then he claims that

Note how this definition is framed. To maintain manitest Lorentz invariance, in the formalism we are using here, state-vectors do not change with time $-$ a state-vector $\Psi$ describes the whole spacetime history of a system of particles. (This is known as the Heisenberg picture, in distinction with the Schrödinger picture, where the operators are constant and the states change with time.) Thus we do not say that $\Psi_{\alpha} \pm$ are the limits at $t \rightarrow \mp \infty$ of a time-dependent state-vector $\Psi(t)$


However, implicit in the definition of the states is a choice of the inertial frame from which the observer views the system; different observers see equivalent state-vectors, but not the same state-vector. In particular, suppose that a standard observer $\mathcal{O}$ sets his or her clock so that $t=0$ is at some time during the collision process, while some other observer $\mathcal{O}^{\prime}$ at rest with respect to the first uses a clock set so that $t^{\prime}=0$ is at a time $t=\tau ;$ that is, the two observers' time coordinates are related by $t^{\prime}=t-\tau .$ Then if $\mathcal{O}$ sees the system to be in a state $\Psi, \mathcal{O}^{\prime}$ will see the system in a state $U(1,-\tau) \Psi=\exp (-i H \tau) \Psi .$ Thus the appearance

Now my question is: as we are talking about a state-vector $\Psi$ in the Heisenberg picture, which do not evolve over time. Why does the state vector change under the change of observers with different setting of time.
 A: I think I got the point.
In Heisenberg's picture, the state-vectors do not change according to the Schodinger's equation governing the time evolution of the state. Since different pictures are defined in how operators and state vectors are changing with $\textbf{time evolution equation}$.
But the state vectors $\textbf{do}$ change under symmetry transformations such as Lorentz transformation. And one Lorentz transformation is "time translation", which coincides with time evolution operator of the schdinger equation but the physical meaning is different.
Now let's do a "change of inertial frame of observing the system", what we are doing here is doing a "Lorentz transformation" rather than doing a "time evolution", so the state vectors do change and it changes with the same way of time evolution incidentally.
A: 
a state-vector $\Psi$ describes the whole spacetime history of a system of particles.

Think of $\Psi$ heuristically as corresponding to the worldlines of a system of particles. (Obviously there are no actual worldlines, because we're doing quantum mechanics.) The worldlines describe the entire spacetime history of the particles, but the worldlines are not Lorentz invariant. Different observers in different inertial frames will see different worldlines. Of course this is just the classical picture, but the basic idea that the state of the system is not Lorentz invariant carries over to the quantum case.
