How can I get rid of Abs?

In the following code, the functions WP[t] and WS[t] are real. Time also is a positive parameter. As you can see, MATHEMATICA enters Abs in the calculations. Including Abs only complicates the next parameters and calculations that cause the program to not run. In order not to complicate the calculations, how should I correct the code so that MATHEMATICA does not include Abs in the calculations??

m = {{0, WP[t], 0}, {WP[t], 0, WS[t]}, {0, WS[t], 0}};
q = Eigenvectors[m];
p1 = Normalize[q[[1]]]
p2 = Normalize[q[[2]]]
p3 = Normalize[q[[3]]]


{-(WS[t]/(Sqrt[1 + Abs[WS[t]/WP[t]]^2] WP[t])), 0, 1/Sqrt[
 1 + Abs[WS[t]/WP[t]]^2]}

{WP[t]/(Sqrt[1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*WS[t]), 
-(Sqrt[WP[t]^2 + WS[t]^2]/(Sqrt[1 + Abs[WP[t]/WS[t]]^2 + 
   Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*WS[t])), 
  1/Sqrt[1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]}


 {WP[t]/(Sqrt[1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*WS[t]), 
   Sqrt[WP[t]^2 + WS[t]^2]/
   (Sqrt[1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*WS[t]), 
   1/Sqrt[1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]}

m = {{0, WP[t], 0}, {WP[t], 0, WS[t]}, {0, WS[t], 0}};
q = Eigenvectors[m];
p1 = Normalize[q[[1]]] /. Abs -> RealAbs // Simplify
p2 = Normalize[q[[2]]] /. Abs -> RealAbs // Simplify
p3 = Normalize[q[[3]]] /. Abs -> RealAbs // Simplify

{-(WS[t]/(Sqrt[1 + Abs[WS[t]/WP[t]]^2] WP[t])), 0, 
   1/Sqrt[1 + Abs[WS[t]/WP[t]]^2]} /. Abs -> RealAbs // Simplify

{WP[t]/(Sqrt[
       1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*
      WS[t]), -(Sqrt[
       WP[t]^2 + 
        WS[t]^2]/(Sqrt[
         1 + Abs[WP[t]/WS[t]]^2 + 
          Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*WS[t])), 
   1/Sqrt[1 + Abs[WP[t]/WS[t]]^2 + 
      Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]} /. 
  Abs -> RealAbs // Simplify


{WP[t]/(Sqrt[
       1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*
      WS[t]), Sqrt[
     WP[t]^2 + 
      WS[t]^2]/(Sqrt[
       1 + Abs[WP[t]/WS[t]]^2 + Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]*
      WS[t]), 1/
    Sqrt[1 + Abs[WP[t]/WS[t]]^2 + 
      Abs[Sqrt[WP[t]^2 + WS[t]^2]/WS[t]]^2]} /. 
  Abs -> RealAbs // Simplify