Teleporting or quickly moving a telescope 4,900 parsecs in a short period of time would allow you to get a glimpse of the past.
The Earth and our solar system are emitting a constant stream of light into the void of space. Just as we can see other planets and stars, that light makes the observation of Earth possible from other locations.
Space is huge, and out there are photons containing images of Earth going back to the formation of the planet. That light and the images contained within are traveling away from Earth in all directions at the speed of light.
Because of all this, it is possible (theoretically) to see the earth as it was when dinosaurs lived. How? The same way you would see the earth as it is today: position yourself in space at a distance from the Earth and allow the photons to hit your eyes, revealing the image of present-day Earth. Technically speaking, the image you would see is always outdated because a photon reflecting off an apple three feet away still takes a tiny amount of time to travel from the apple to your eye.
To see Earth in the past, you will need to position yourself in space at a point farther away than the distance that the photons you wish to observe have travelled. Picture a calm lake. Gently dip your finger into the water. A stone is thrown into the lake a short distance away, causing a ripple. The ripples reach your finger, giving you a sense of what happened: a stone was thrown. That is equivalent to viewing earth from the moon. The stone’s splash represents all matter on earth and its position and appearance. The ripple represents the photons being emitted into space in all directions which describe that matter.
Now imagine if you wanted to experience the ripple a second time. You would need to very quickly move farther away from the splash point, outpacing the ripples, and dip your finger in the water once more. If you are quick enough, your finger will again feel the ripple and give you a sense of what caused it.
The tricky bit is that light travels faster than ripples on a lake, requiring that you move faster than the speed of light to observe photons a second time. Einstein didn’t believe this was possible, because nothing could travel faster than the speed of light. How could you outrun something if you could only match its speed?
The recent observation of neutrinos moving faster than the speed of light, if confirmed, open up some interesting possibilities. What if we can figure out how to move matter faster than the speed of light? If that secret were unlocked, I propose that we send a telescope into distant space to observe earth in the past.
In order to capture images of the earth as it was 8,000 years ago, we would need to position a telescope more than 47 quadrillion miles (~2,451 parsecs) away, capture the images of earth, and recall the telescope in a reasonable amount of time. In order to accomplish this particular mission over the course of 10 years, we must discover a way to travel about 800 times the speed of light. As either the duration of the experiment increases or the amount of time back into the past you want to see decreases, the speed faster than light you would need the telescope to travel decreases.
Imagine how cool it would be to look at an ancient earth. You could create a time-lapse movie showing the formation of the planet, the changes of terrain and atmosphere, and the development of civilizations. However, it is worth noting that the universe would explode in this type of experiment.