What does it mean to “travel through time?” We already travel through time at a rate beyond our control, no matter what we do. So let’s say that what we mean by time travel is that the subjective rate of passage of time for the “time traveler” is very different from the rate of time passage in the external world: we get to another time faster than the muggles do (slower is boring). And of course it would be nice if it were perfectly safe.
In the interests of practicality, I shall neglect the possibility of traveling backward in time: this seems to work conceptually only on the level of individual quantum particles, which is very inconvenient if you happen to consist of more than one particle. So let us concentrate on moving forward through time at variable and controllable rates. Since it is vastly harder to control the external world than it is to change our subjective experience, our search for practicality must concentrate on what we can do to ourselves, individually, to get our ticket to ride.
The first thing that comes to mind is cryogenic stasis, often referred to as “cold sleep”. We freeze ourselves and cool our corpsicles down to liquid helium temperatures. That should put an end to destructive oxidation reactions, shouldn’t it? All motions, and all chemical reactions, stop at absolute zero, right? Wrong! Quantum mechanics assures us that there is residual zero-point energy that keeps everything in motion even at zero degrees absolute. (This follows from the uncertainty principle: the product of the uncertainty in momentum (Δp) times the uncertainty of position (Δx) of each particle is a constant. If any particle were absolutely at rest (Δp = 0), then Δx would be infinite: we wouldn’t know where in the Universe the particle was.) This has interesting ramifications for the rate of chemical reactions in our bodies as we chill down toward absolute zero. All the reactions that can damage our cells do slow down dramatically with decreasing temperature, up to the point at which quantum tunneling effects become more important than classical chemical kinetics. Thereafter, further cooling has virtually no effect on the rates of “bad” reactions. This means you cannot stop oxidative damage to your cells (and your DNA) even at absolute zero. This is a real concern: you don’t want to arrive in 5,002,016 AD with a wrecked, poisoned, and embarrassingly oxidized body.
Given this concern, then we need to identify what causes these destructive reactions and get rid of the cause. Well, first of all, our bodies contain three biologically essential elements that have radioactive isotopes; tritium, carbon-14, and potassium-40; whose decay reactions produce energetic charged particles. These particles, both gamma rays and beta radiation-- high-speed electrons and positrons-- tear apart water molecules to make atomic oxygen, hydroxyl radical, hydroperoxyl radical and even molecular oxygen, all of which are deadly poisons to a wide variety of essential biochemicals. We have several ways to suppress this kind of damage: filling ourselves with antioxidants that sop up the damaging oxidative chemicals, and getting rid of the three offending radioisotopes. The antioxidants you get from eating a flat of blueberries, even if they succeed in entering your blood stream, are bulky molecules that are immobilized at low temperatures: they can’t move to the site of the problem. You could eat yourself blue in the face, enough to qualify for Avatar citizenship, without making yourself much safer. (Happier, perhaps, but not safer.)
Of course, we could raise people on radioisotope-free nutrients to avoid the problem altogether. We could get our drinking water from deep aquifers where the tritium content is essentially zero (70,000-year-old groundwater has survived 10,000 half-lives of tritium decay). We can source our carbon from Carboniferous coal (450 million years is about 100,000 half-lives of carbon-14). Potassium is a much worse problem because it has a billion-year half-life. There is no potassium in nature that is old enough to have had the radioisotope decay away. We would have to separate the isotopes of natural potassium to get rid of the dangerous potassium-40. This requires huge mass spectrometers or other dedicated equipment and great expense, but could be done.
Assuming success with potassium, we would next have to deal with biologically non-essential elements that sneak into our bodies because of their chemical similarity to things we really need, such as radioactive uranium and thorium masquerading as calcium atoms in our bones. We could deal with this problem only if all the calcium entering our bodies during life were scrupulously cleaned of undesirable radioactive trace elements. Again, this is very expensive but achievable.
But we live on a planet in a galaxy: the crust of the planet contains radioactive potassium, uranium and thorium whose radiation strikes us from outside, even if our bodies are completely clean inside. And of course we are struck by cosmic rays rather often, both primary cosmic ray protons and, more importantly, cascades of charged secondary particles such as muons that are made by the impact of cosmic ray primaries on atoms in our atmosphere. So we hide our corpsicle deep underground and store it in the bottom of a mine shaft, where the effects of cosmic rays can’t reach. Then we have to shield ourselves from radioisotopes in the surrounding rock by lining our hobbit hole with a thick layer of lead. Once again, all this is expensive but achievable.
Have we overlooked anything? What about those pesky neutrinos? Shielding against them is simply impossible; a layer of lead light-years thick would be required. But neutrinos are uncharged and interact very poorly with matter. Is there any reason to fear them? Not normally, but we have gone to such extraordinary lengths to reduce risks that this is now the #1 problem remaining. It happens that the natural and non-radioactive isotope chlorine-37 has a tiny probability of capturing a neutrino, which converts it into argon-37, which unfortunately is radioactive, emitting an energetic charged agent of destruction, an 813 keV beta particle. We can’t just swear off of chlorine: every human body contains cellular fluid that resembles the early oceans where the first cell originated, endowing us all with sodium chloride in every cell. Well, at great expense we could separate the chlorine isotopes and use only chlorine-35…
Or maybe the desire to achieve perfect guaranteed safety is actually insane…