The Platform by Robert P. Fitton

A young woman (Rosey Bradley) in 1947 begins seeing images in a mirror found in the Dresden bombing in World War II. When she is contacted in the mirror through time by Buddy Powell, a member of a highly classified project in 2027, Rosey begins to think she has lost her mind. It is only when Buddy physically returns to Rosey's time of the big bands, big automobiles, and big dreams- post World War II- that he and Rosey fight to make the project also transported back to 1947 operational again. Buddy meets with important scientists of the day including Vannevar Bush as he is pursued by traitors from 2027 who want the project to control the world. In a weird twist in New Mexico, they learn the true importance of the project for mankind.