This neglects the expansion of the universe, the health and safety effects of traveling near to the speed of light, and the fact that we do not know how to do this (you would not be able to bring your own fuel). Nevertheless we do not know why it should be physically impossible.
Alastair Reynolds also does a great job with this in his Revelation Space trilogy, with his lighthuggers.
Humans just aren't wired to consider family members beyond 3 or 4 generations up and down.
Perhaps I'd feel the same general apathy as Pham Nuwen 20 generations down. Then again, he had other familial issues that played a part.
In the other, he'd been resurrected by some godlike AI as a meatspace agent. Millennia after the Qeng Ho era, I think.
The answer is that the 'moving' traveler needs to flip the ship around at some point and thrust back towards the starting point. Whoever turns back around will find that it's their clocks that passed more slowly.
If so, that is not correct. Atomic clocks have measured actual, lasting time differences.
Each should see the other as dilated, no?
An example is the "Plasma Jet Magneto Inertial" 
The main issue that may not be solved by eventual iterative progress is that these kinds of engines create way too much waste heat.
From the point of view of conventional, reductionist models of human biology, the only basic physical health effects, given a reasonably humane spaceship life, would be the risks of collision.
Otherwise, I'd think 1 g would actually make a space journey more livable!
(Velocity is entirely relative, so traveling near the speed of light really doesn't mean much of anything in terms of basic physics/chemistry in the traveling frame. Physics undergrads are told that: light/physics under 1g of acceleration, by the theory of general relativity, is going to behave in exactly the same way as light/physics under 1g of gravity from mass.)
Now, as far as psychological/spiritual/emotional health are concerned, that's another matter. Relativistic effects would extract you from the context of time that gives meaning to all of your relationships with other Earth life, and with Earth itself. It'd be very deep.
Okay but now I'm remembering the article recently shared about Posner molecules and the possibility of meaningful quantum biological organizations in the body.
If our bodies physically depend on, in some yet to be articulated way, quantum information being exchanged/entangled ecologically, and if we depend on the synchronicity of these exchanges (say for example to inform some deeper biological sense of meaningful time)... Well then moving close to the speed of light would take those processes to a different tempo. To what degree are our physical bodies in temporally dependent relationships with their environment or ecologies? How critical are these relationships to basic functioning?
Now I have to agree that we don't know what effects on physical health might be!
You will have had enough time for that before you start moving really fast. (Also, philosophizing is usually a very slow process anyway.)
(Some people don't even believe the Earth is round. They think that their local tangent space is all there is too it! That's how small we are.)
The equivalence principle is the opening from special to general relativity, I don't think ajconway was confusing the two at all!
But then I got to wondering if our bodies aren't critically entangled with our Earth ecologies in various time sensitive ways, and realized that I don't know the answer to this question.
(I.e. https://arxiv.org/abs/quant-ph/0004105 )
So my second question is treating the human body as being meaningfuly physically entangled with it's environment and as being in some sense unified with it. Accelerating a body away from Earth at 1g might be akin to cutting off a limb and expecting it to survive on its own. I don't know if this is the case, but it seems possible.
Almost no fuel needed because its really just a kind of extreme gravity assist that we’ve been doing since what, the 1970s?
I love that you point this out. People are so used to even "hard" science fiction hand-waving this away they often don't realize the magnitude of the problem.
For example, if you use a fusion drive (I_sp = .12 c) and start at 99% fuel (9:1 fuel ratio for initial acceleration and then again for deceleration at the end of the journey, so m_0/m_1 = 10 both times) then you can only travel at .27 c which means time dilation is nearly negligible, only about 4%. Similarly, if you start with 99.99% fuel, you still only achieve 0.5 c, 99.9999% (the payload is now one-millionth of the ship) gives you .68 c, one part per trillion gives you .93 c, etc. We assumed perfect engineering, used a trillion tons of fuel for one ton of payload, and we're still only at Lorentz factor of 2.7. If someone invents an antimatter rocket we can improve the .12 to 1, but that's only a one-order-of-magnitude constant difference. The tyranny of the (relativistic) rocket equation is brutal. This wikipedia article contains the equations used for the above calculations:
Now, you might not have to take all your own fuel with you: Bussard ramjet style designs gather their own fuel as they go once they get up to speed, thereby breaking free of the tyranny of the rocket equation. These are in the realm of science fiction at the moment, but at least they are within the known laws of physics.
Realistic projects like Breakthrough Starshot usually assume (a) an external power source (such as lasers pushing a mirrored object), (b) no deceleration at the end (an order of magnitude savings), (c) very small payloads, and (d) only moderate velocities.
I've been moderately critical of Starshot for other reasons (how can a useful camera or other sensor fit into such a small device? How could it have a directional antenna large enough to focus over 4 light years? How could it contain a power source large enough the send a signal back?) but in terms of just getting a payload a certain distance, it seems workable and is perhaps the best design we have.
So yes, bringing your own fuel is not a good idea if you are trying to get close to light speed!
That kills it for me.
But what kind of specific impulse are we talking about? It has to be quite high, or you're talking about unphysical amounts of reaction mass. Even with photon rockets, we're talking about godlike amounts of energy. Or, we could find clever ways to circumvent the rocket equation.
The most problematic part is likely the fantastic particle and radiation flux that would impinge on the front of the craft.
As far as we know, you always wind up with more drag than you can overcome by using what you scoop as fusion fuel.
Exploiting time dilation would probably be rendered impossible by this.
The observable universe. That one word makes a huge difference.
And if I'm wrong, I apologize and would gladly hear the correct answer.
For these reasons "time slows down for you when you move at relativistic speeds" is really a bad way to think of it (and not how the math of the theory actually works). It's much more proper to say things in the form "To <observer a> it appeared as if the clock of <observer b> was <sped up|slowed down>". E.g.:
To the traveler it appeared as if the clock of Alpha Centauri was sped up.
To Alpha Centauri it appeared as if the clock of the traveler was slowed down.
So if you travel to Centauri from Earth, the fastest you get can get there is 5 years as seen from Earth but to the actual spaceship, it could perceive any arbitrarily small change in time.
Or that, but with a dozen more 9s in it: https://en.wikipedia.org/wiki/Oh-My-God_particle
The beginning of Alastair Reynolds's short story "Weather" (in "Galactic North") addresses this.
Not true. At relativistic speeds, relative velocity is not a simple addition: https://en.wikipedia.org/wiki/Velocity-addition_formula#Spec...
In your example where both parties are moving at 0.6c towards each other, each will perceive the other to be moving at ~0.88c.
In neither your reference frame or the other person's will it appear to be true that your closing speed is faster than c.
However due to the speed of light delay you may perceive the other person as going much faster than c, but this is strictly an illusion. For example, if I were watching a near-light speed ship approaching earth in a telescope, I might see it begin its journey and then see it arrive a few seconds later and my monkey brain would conclude it made the whole trip in the time I was watching it. In reality the light from when it started the trip is a few years old.
Let us say that a ship starts at a distance of 100 ly (lightyears) and moves with 0.95c (speed of light) for all of the distance toward the observer through empty space.
Light will need 100 years to cover the distance. The ship will need ~ 105.26 years (= 100ly/0.95c). The observer can not know that the ship launched before the 100 years passed that it took for light (or any other signal!) to arrive. So it looks like that only 5.26 years later the ship arrives, making it appear that it only took 5.26 years for a distance of 100 ly which appears like a speed of 19 times the speed of light (= 100 ly / 5.26 years).
It's not an equivalent question either, the question is intensity not sum.
However, isn't intensity equal to sum when it comes to light? At least in the visible spectrum, more energy just shifts the wavelength...perceived intensity comes from photon count.