# How Does Shapiro Delay Work?

*Most recent answer: 08/25/2012*

Q:

I've read about the Shapiro delay. Why does light appear to slow down or as I understood it, light takes longer to travel the same distance in different circumstances. Wasn't the speed of light in a vacuum constant? Or is that only in special relativity?

- The Burst (age 18)

- The Burst (age 18)

A:

Funny you should ask. My wife says her mom just got a very sweet note from Irwin Shapiro, an old friend.

The rule about the speed of light being constant only applies locally to patches of spacetime small enough to be effectively flat, i.e. ones which can be described by special relativity. On a bigger scale, with gravity involved, phrases like "the same distance" become ambiguous.

Let's think of light from some distant star. There's an extra delay in how long it takes to reach us when the light happens to pass near the sun on its way. How come? We can describe it in a particular choice of coordinates, the Schwarzschild coordinates. Two things happen to the light as it goes near the sun:

1) Close to the sun, the effective rate at which time passes is slowed. According to local clocks there, the light is traveling at the usual speed, c, but we think those clocks are slow so from our point of view the light is going slower.

2. As it approaches and departs from the vicinity of the sun, the light travels extra distance, more than what you would calculate if you drew a big circle around the sun and took the diameter to be its circumference over 2pi. Space isn't Euclidean- the diameter of that circle is bigger than it should be based on the circumference. So the light has farther to go (as measured by local rulers) than it would if it weren't going near the sun.

These effects add up to give the Shapiro delay.

Should you say that under these circumstances the light travels farther? In our coordinate choice, that does account for half the effect. However, there are lots of different coordinate choices. Whichever one you like, the effect is real.

Mike W.

The rule about the speed of light being constant only applies locally to patches of spacetime small enough to be effectively flat, i.e. ones which can be described by special relativity. On a bigger scale, with gravity involved, phrases like "the same distance" become ambiguous.

Let's think of light from some distant star. There's an extra delay in how long it takes to reach us when the light happens to pass near the sun on its way. How come? We can describe it in a particular choice of coordinates, the Schwarzschild coordinates. Two things happen to the light as it goes near the sun:

1) Close to the sun, the effective rate at which time passes is slowed. According to local clocks there, the light is traveling at the usual speed, c, but we think those clocks are slow so from our point of view the light is going slower.

2. As it approaches and departs from the vicinity of the sun, the light travels extra distance, more than what you would calculate if you drew a big circle around the sun and took the diameter to be its circumference over 2pi. Space isn't Euclidean- the diameter of that circle is bigger than it should be based on the circumference. So the light has farther to go (as measured by local rulers) than it would if it weren't going near the sun.

These effects add up to give the Shapiro delay.

Should you say that under these circumstances the light travels farther? In our coordinate choice, that does account for half the effect. However, there are lots of different coordinate choices. Whichever one you like, the effect is real.

Mike W.

*(published on 08/25/2012)*