The reason light from the most distant known galaxy, GN-z11, has taken around 13.4 billion years to reach us is due to the expansion of the universe. While light travels at a finite speed, the fabric of space itself can also stretch or expand.
When astronomers observe distant galaxies, they are effectively looking back in time. The light emitted by GN-z11 started its journey towards us around 13.4 billion years ago. However, during that time, the universe has been expanding, causing space to stretch. This expansion causes the wavelength of the light to increase, which in turn reduces its energy.
As a result of the expansion, the light from GN-z11 has had to travel through an increasingly stretched space, which has effectively increased the distance it had to cover to reach us. So even though light travels at a constant speed, the expansion of the universe has caused the distance between GN-z11 and us to increase over time.
This phenomenon is often referred to as "cosmological redshift." The light from distant galaxies, including GN-z11, gets stretched as it travels through expanding space, leading to a shift of its wavelength towards longer, redder wavelengths. By analyzing this redshift, astronomers can estimate the distance and age of the observed galaxies.
Therefore, when we say that GN-z11 is around 13.4 billion light-years away, we are referring to the time it took for the light to reach us, taking into account the expansion of the universe during that period.