According to the principles of special relativity, time dilation does not affect light itself. From the perspective of a photon, which is a particle of light, time does not pass at all. This means that, for a photon, its journey from Betelgeuse to Earth would be instantaneous.
However, from our perspective as observers on Earth, we experience time and are subject to time dilation effects. When we observe light from a distant object like Betelgeuse, we are indeed seeing it as it was in the past.
In the case of Betelgeuse, which is approximately 640 light-years away, when we observe light from that star, we are seeing it as it was about 640 years ago according to Earth time. The light emitted from Betelgeuse takes approximately 640 years to travel through space and reach us on Earth. Thus, the image we see is a snapshot of the star's state as it appeared 640 years ago.
This concept is often referred to as the "lookback time" or "light travel time." It means that when we observe distant objects in space, we are essentially observing them as they were in the past, with the amount of time corresponding to the distance in light-years.
So, when we observe light from Betelgeuse, we are seeing the star as it appeared 640 years ago, not another span of time.