Final answer:
To travel far into the future without aging significantly, you can travel at a significant fraction of the speed of light or be in a strong gravitational field, resulting in time dilation. However, neither method allows for travel into the past; only future time travel is theoretically possible.
Step-by-step explanation:
To travel far into the future without aging significantly, you would need to travel at a significant fraction of the speed of light. According to Einstein's theory of relativity, as you approach the speed of light, time dilation occurs. This means the rate at which time passes for you, as the traveler, slows relative to an observer on Earth. Therefore, if you were traveling at near-light speeds, you would age much slower compared to those on Earth, enabling you to travel far into the future without aging very much yourself.
Gravitational time dilation is another phenomenon predicted by general relativity, where time passes at different rates in regions of different gravitational potential; the stronger the gravity, the slower the time. In scenarios with extreme gravity, such as near a black hole, time would slow significantly for an observer close to the object compared to one far away. However, neither traveling near the speed of light nor experiencing strong gravitational fields allows for travel into the past. There is currently no accepted physical theory that permits backward time travel.
So the correct answer to the question is b) Traveling at the speed of light; no, it only allows future time travel.