Perhaps, such a mirror already really exists somewhere at a distance of a billion light years to see the reflection of dinosaurs in the past. In fact, it may not be a mirror, but rather a topology of space that performs the same function.
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In topology, you can begin to move forward and then return to the starting point of the path. A similar result is trivial for curved space, for example, the surface of the Earth.
This approach can work for a flat space that exists in three dimensions. This means that, on a large scale, light moves in straight lines, not in curves.
Theoretically, in the Hubble photographs, one of the galaxies in deep space could be ours. It does not look like today, but as it was billions of years ago.
Even if such a theory is fundamentally wrong, is it possible to see the past by looking through a telescope at a certain distance from the planet?
Due to the limited speed of light, we see the past by looking at the sky at night. The brightest star Sirius is located at a distance of 8.6 light years from Earth. The light that we see has been traveling for 8.6 years, that is, we see Sirius as it was 8.6 years ago.
The effect increases with distant objects. Ursa Major stars are located at a distance of 60 to 125 light years from Earth. When we look at the star Dubhe, we see the light that emanated even before our birth.
The Andromeda Galaxy is the most distant object visible to the naked eye. Today, we see the Andromeda galaxy long before the advent of modern humans. At that time, our distant ancestors Australopithecus inhabited the Earth.
Galaxy NGC 4980 is located in 80 million light-years, and about the same number of years ago, dinosaurs lived.
The final speed of light has the same effect in all directions. If there are intelligent aliens in the galaxy NGC 4980, theoretically they can see the Milky Way in the time of dinosaurs, including our planet.
Unfortunately, it is unlikely to be able to see the dinosaurs themselves from such a great distance. Using modern technology, our astronomers cannot determine any details on the largest planets orbiting nearby stars.
Anyway, in the reflection of the mirror, or through a telescope located at some distance from the celestial body, it is possible to see its past.
But such a man-made mirror will require tremendous resources and a rigorous installation up to the atom. And using a telescope, it is impossible to see the smallest details without the use of technologies that are far beyond human comprehension.