This deduction is possible because our physical world obeys strict laws of cause and effect. Theoretically, if we knew the position and velocity of every object in the universe, we could play the laws of physics backward to see where all of those objects came from. Of course this is a massive simplification, given problems like quantum uncertainty, but the argument holds for all classical objects in the universe. If you agree that in theory we can do this, then it's a simple matter of engineering to obtain the data and do the computations needed to make an observation of the past.
Large-scale computation of atomic motion on the earth is clearly far beyond our current capabilities of observation and computation. Therefore, researchers have had to come up with clever ways to find traces of the object or process of interest. Several examples you are probably already familiar with:
- Counting the rings in a tree can tell you when the tree was born and what kinds of weather it has lived through.
- Fossils can tell us what life forms lived on the earth long before any humans existed
- Observations of today's stars and galaxies allows us to determine the life cycle of these objects and the universe as a whole.
New methods of reasoning about the past and observing its evidence have appeared in the last decade or two. One notable example of this is population genetics. Researchers can use observations made today (markers in people's DNA) to determine where and when human migrations occurred, and where certain traits first developed. This new tool allows historians to piece together huge migration patterns that occurred tens of thousands of years ago. See http://www.newworldencyclopedia.org/entry/Human_migration for an article and map of human migration. This is an amazing example of going far back in time, all over the earth.
Even when not using a may fly strategy, astronomy is a field where looking back in time is quite commonplace. This is possible (mandatory, in fact) because light has a finite speed and the universe is very large. So when we look at a galaxy that's 20 million light years away, we must be seeing it as it appeared 20 million years ago, when the light our telescopes detect first left its source on its long journey to us. Many of the objects we look at are probably no longer existing, but we can't see this directly until the light from the object's later life stages reach us, many years hence.
This is why astronomers want bigger and bigger telescopes, to look further and further back in time. Is there a limit to how far back we can look using this approach of just looking further away? Well, there is if we're limited to visible light, because when the universe was less than 100,000 years old, it was still so dense that light could not escape to begin its journey toward us (http://curious.astro.cornell.edu/question.php?number=84). However, what about other types of astronomical investigations? Recent developments in neutrino detectors have allowed us to use these mysterious particles as our messengers from the past. The main benefit of this is that neutrinos have no charge and a very low mass, so they interact very seldom with ordinary matter. Usually, they shoot right through the empty space between an atom's nucleus and its electrons. This helps us see things we normally can't see using electromagnetic radiation (such as visible light or radio waves). For instance, the core of a star is normally inaccessible to us because the light from the outer layers obscures what's going on inside. But neutrinos from the core reactions in a star would have no trouble travelling unimpeded through the outer layers of the star and heading towards our detectors. See http://www.phys.hawaii.edu/~jgl/nuastron.html for more information on neutrino astronomy.
While there are huge technical hurdles to seeing the early history of the universe or human events of past millenia, I don't see any reason why it shouldn't be possible in principle. This makes it a simple matter of engineering. Given the amazing things we're able to deduce about the past now, I expect we'll continue to discover new means of traveling back in time, as long as human curiosity remains alive.
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