Bluemofia
F=ma
That's very hypothetical.
If we did create a spaceship that can travel at c, assuming our laws of physics still hold, the ship will be massless. So if the technology is advanced enough, you can just beam people and things and use the information to regenerate it on the other side. Need a dedicated facility though.
Assuming that we just got special relativity wrong (it depends on *how wrong*, more on this later), it depends on how much energy it takes to actually get it to c to determine what size to make the ship, as well as what other technologies we have available.
If it takes a lot of energy (probably will), it will probably be a small ship to minimize the mass. It is more difficult to build and design a large ship than a small one, simply because of the scaling of mass/strength/size ratios. Not to mention the material strengths of the things involved.
The advantages of a larger ship will be that it can have more shielding against interstellar dust and particles, to avoid damage in general, assuming we don't have stuff like star wars shielding.
Now for the trip, if special relativity is utter garbage (ie, using Newtonian Physics), the trip will take a bit more than 50 years (give time to accelerate to c safely), setting some size for the ship required to hold a self-sustaining ecosystem. How large it needs to be is up for debate, and again determined by how efficient we are at recycling materials and readily available power supplies.
If special relativity is wrong in a weird way, such that you can somehow go faster than light with positive mass, but everything else works the same way, you can't do it without making your ship and everyone and everything in it out of dark matter (matter that only interacts with gravity and possibly the weak force; I'm not well versed enough in weak and strong interactions to judge this one well) to stop the microwave background radiation from being blue-shifted to infinite energies due to the motion of the ship at c and photo-disintegrating the atoms of the ship.
If you had shielding to deal against that somehow, it will still take a significant amount of time (a few years) such that the acceleration process is non-lethal. This allows you to make a far smaller ship, but still one larger than the ones we have now.
If we also have technology to deal with acceleration processes, we can just ignore it and make the ship however large of stuff it needs to carry, plus the engine and stuff. It will take zero time in your reference frame to get from Earth to 50 light years away because of time dilation causing you to stop in time. How you control where to drop back to normal space is another question, as your computers can't tell where to stop if every single point in your trajectory is associated with the same time to stop. Easily avoided by going slightly slower than light speed, though kinda defeats the point of a light speed ship.
For several ships at once, depends on materials science to see how easy it is to build a large vessel, and if we have constraints such as ecosystems, power, recycling, etc.
Ok, and now for the radio question. Assuming the signals are non-beamed, the signal strength will drop off as 1/r^2 as you get further and further from Earth. Depending on how strong we send out the signals (I don't know how strong, and how weak of signals we can detect, and how they compare to background sources), they might not even be able to pick up radio from Earth because it is too weak, and not beamed. If it is specifically beamed to them, or if they are strong enough to be detected from where they are, they will receive signals from the day they left Earth, assuming they traveled there at c instantly. They traveled at the same speed as the radio waves, so that they will be receiving the same ones that traveled with them as they arrive (in zero time in their frame, remember). Looking back at Earth, they will see it the day they left Earth also, with the same reasoning. However, if they were to turn around and travel to Earth, they will see 100 years pass by, as it took 50 years for them to get to Earth on Earth's reference frame, and another 50 years to get back. For them, they will pass through the light waves emitted from the 100 years all compacted together, with Earth apparently rapidly aging 100 years.
) about this, is because I'm writing a short story, and I want a way to describe it so that it can enable the reader to easily visualize in his head what it would look like if he looked at it with his own eyes.
