Gravitational Length Contractions?
Special Relativity basic premises are that the speed of light is constant for all observers, and that time dilation effects occur for clocks moving with respect to each other. To keep the speed of light constant, SR lays claims to length contractions effects. This is described in various sources.
General relativity lays claim to time dilation effects in gravitational fields, but it makes no claims for length contraction effects. However, length contraction effects are present particularly because of the way that the units (meter and second) are defined.
Since the speed of light in vacuum is constant, and because gravity slows down clocks; this would mean that clocks can mark seconds faster at distances far away from Earth’s surface. A shorter second would mean that light travels a smaller distance in outer space that on Earth. At first it may seem that the speed of light is not constant, but because the length (meter) is defined in terms of the speed of light, the result is length contractions.
Let’s start with some definitions:
The meter is defined as “the length of the path traveled by light in vacuum in 1⁄299,792,458 of a second”.
The official definition of a second is “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”
Multiplying these two terms we can define the meter in terms of the distance light travels in 30.66 periods of a cesium 133 atom (approximately.)
Let’s say that we construct a bar with ultra stable materials with a length equals to 1 meter as defined above. The speed of light is constant regardless of the presence of gravitational fields, but the “periods of the radiation of cesium 133 atom” are not so immune; a second in outer space is shorter than a second on Earth. Light would travel slightly farther in one second on Earth than on one second in outer space, and our bar (all other things being equal) would seem shorter on Earth.
Of course we have two other
options, but neither is
good: Light slows down in the
presence
of gravitational fields or the bar expands proportionally to
remain at
a
constant length.