Difference between the Shapiro Delay and time dilation?

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I recently listened to The Origins Podcast with Lawrence Krauss and he had on the 94 year old physicist Irwin Shapiro. It was interesting and went into some of the details regarding the history of his work. In it he brings up how he first calculated what we now call the Shapiro Delay. It is a measure of light's deflection caused by a large mass such as the sun. It sounds very similar to time dilation. Does anyone here know the difference between the Shapiro Delay and time dilation and why it was only in 1964 that was discovered? It seems like a natural deduction from GR.
 
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It's more than just time dilation; it's measurably affected by the curvature of Schwarzschild spatial planes.

Why it wasn't thought of before is an imponderable. But there are a number of factors that may be relevant.

People tend to think in terms of tests you can do. To measure Shapiro delay you need to measure flight time, which depends on knowing the launch time of the light. The only ways I can think of doing it is radar (low power sets were developed in World War II), sending a space probe to the far side of the Sun (space exploration took off in the 1960s), or tracking pulsars (not discovered until the 1960s). It couldn't have been done much before it was. In fact, the radar set they tested it with was built in the early 60s, so may have stimulated research itself (people were looking for applications for it).

Also, I seem to recall that there was relatively little theoretical interest in GR between the 1920s and the 1960s, when there was a resurgence because new mathematical tools were brought to bear. So maybe there just wasn't much work in that field.
 
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