Periodically it seems that the subject comes up regarding human colonization of space and then all manner of problems and difficulties are discussed with various people taking their respective sides on the physics that's possible and what isn't.
However, I would offer a different perspective on this and argue that it isn't a physics problem. This isn't about speed, about time, or about energy, although these are problems. The problem is about biology.
More specifically, the problem is about the passengers we have to take. Not humans, not embryos, or not some cryogenically preserved individuals. The problem is bacteria.
We often hear about transporting the human genome, as if that's all that is needed for human life, but this overlooks the reality that our bodies are populated by an a whole order of magnitude more life than is accounted for by our cells. We are unequivocally dependent on this life and where we go, it goes.
More importantly, the same relationship exists for anything we might consider to be a food source, whether it be plant or animal that is supposed to accompany us on this trip. In short, we would have to construct a completely self-contained, viable biosphere to engage in any colonization efforts, at any level.
The simplistic comparisons to the exploration of North America overlook that aspect of things, since that occurred within the same biosphere, despite some rather significant, and unexpected consequences for some of the inhabitants [i.e. smallpox].
The real unknown aspect of this problem is that it must also take natural selection into account, since we are not in control of this biosphere and its inhabitants. While we may entertain notions about genetically controlling plants, animals, and even ourselves, we can do nothing about the millions and billions of microbes that will tag along. More importantly, we can't even begin to speculate what would happen if any should die off because of the trip, or if some should mutate or even become pathogenic.
Basically we are clueless as to the effect of natural selection on this significant part of the biosphere and the role it would have in determining the future relationship we have with this entourage.
More to the point, we have no idea what would happen if we simply unleashed this biosphere onto a new planet. If there was already life present, the consequences likely would be catastrophic [probably to the colonists]. If no life is present, then we would be attempting to duplicate a particular ecology, which is something that has never played out the same way twice in a row [again, probably catastrophic for the colonists]. We simply can't assume that commensual or symbiotic relationships hold in a new habitat.
In my view, I think these particular problems are intractable, however for those that might have a more optimistic take, consider then that we don't need to focus on solving the energy problems of transportation or the effect on humans. Those problems are trivial compared to the accommodations we will have to reach to support our microbial partners. Without them, there is no trip and there is no future.
Some references to consider:
"Bacteria are needed for life"
"Humans Have Ten Times More Bacteria than Human Cells: How Do Microbial Communities Affect Human Health?"
"DNA of Good Bacteria Drives Intestinal Response to Infection"