Galactic Relativistic Travel, in Theory
Standard physical ideas of galactic travel imagine an earth only effort. But there is the science fiction of an advanced galactic Empire (Foundation), and that would have set up an advanced galactic system of travel. Let’s imagine what that could be.
The Galaxy is vast. It is 100,000 light years across, with 100 billion stars and probably many of them with planetary systems, with perhaps one planet in the habitable zone.
The relativistic calculation imagines a space ship which accelerates with a comfortable 1 g earth like gravity acceleration, eventually reaching close to the speed of light, and then turning the ship around, and decelerating at 1 g, until the destination is reached. Even traveling from one side of the galaxy to the opposite side could be done in a few decades.
There are two ways to look at how that happens, with the traveler, and the stationary observer. The observer sees the time dilatation or slowing factor on the space ship, which is larger than 1,
gamma = 1/√ (1-v^2/c^2) ,
and time (spaceship) = time (observer)/ gamma,
And gamma goes to infinity as the velocity v approaches the speed of light c.
The space traveler sees the steady galactic space contract, so instead of a vast distance, it seems to shrink by the factor 1/gamma, and make it appear feasible to cross in a few decades at relativistic speeds.
A simple non-relativistic estimate of how long it takes to reach v = c at acceleration g is given from v = g t to be
t = c/g = 3 x 10^8 meters/sec / 9.8 meters/ sec^2 = 3 x 10^7 sec.
With 86,400 seconds in a day, this would take naively 347 days, or about a year.
Just to inform warping Star Trek and Star Wars fans, that burst of acceleration to light speed with the stars zooming past in about three seconds, would leave you much much flatter than a pancake, and your ship as well. The acceleration g_warp is:
G_warp = c / 3 sec = 3 x 10^8 m / sec/ 3 sec = 10^8 m / sec^2 = 10^7 g.
So, in Foundation, as Hari Seldon travels 50,000 years from the center of the galaxy, Trantor, to the galactic edge, to a stationary observer, the cloned Empire also goes through 50,000 years, or 500 centuries, or 2,500 generations of clones generated every 20 years. The TV series misses this point, only alloting one generation.
Here is the link to the Wikipedia article on Galactic Travel, which contains the exact 1-g acceleration and deceleration equation result also.
Here is the graph for a relativistic 1-g voyage and return. For the one-way trip, just divide the time in half. The formulas hold for everybody, not just twins.
We see that a round trip from Earth to the Galactic center would take about 40 years. So the one way trip would be about 20 traveler’s years, and 25,800 light years in Earth years.
The flights have to be express to get them done in a lifetime. A Local that stops and starts would not get the advantage of the time dilation. So, likely, all Express flights go to the Transportation Terminal at the center of the Galaxy, which is called Trantor for short. Then you change Express vehicles and directions to do the outward journey to your destination. Hence, who controls Trantor controls the Galaxy.
Presumably the Sturbridge is the hypothetical building that reaches up to orbiting altitude, to save expending that much energy by a rocket.
Anyway, here is my advanced galactic civilization acceleration scheme. You have a sequence of pony express type lasers with giant batteries, located along a straight Galactic Highway. As a spaceship passes, you hit its reflecting stern with the laser light, and give it a continuous boost, until it reaches the next boosting station. The express boost facilities can be charged with fusion reactors.
The reflecting stern prevents the ship from heating up, and by reflecting light gets twice the momentum boost than just absorbing the laser light.
Slowing the spaceship down is done by the same method, but you turn the space ship around to keep the effective gravity still on the stern, with the remaining lasers pointed to slow the ship down.
This scheme only seems to have a Redshift flaw. To cross the 100,000 light year galaxy, say in 50 years, gamma has to reach 2,000. But the laser light from the spaceship point of view has been redshifted down by a factor of 1/2000, and contains only this fraction of the momentum generated by the lasers. However, if the accelerating lasers are equally spaced from the reference frame of the galaxy at rest, from the space ship, they will be compressed in separation and encountered gamma or 2,000 times more rapidly, cancelling out the redshift effect and keeping a constant rate of momentum input.
The decelerating lasers, on the other hand, are blue shifted to provide 2,000 times the decelerating momentum. I’m still working on the consequences off this.
In high energy particle physics, our accelerators work by providing an electromagnetic wave, and putting the accelerating charged particles on a wavefront, like surf boarding. As the particles increase in relativistic speed, the speed of the electromagnetic wave also increases in step. Trying to do this in space, means continuous tubes, and highly charging the spacecraft.
One good thing about the Galactic Express, is that they supply the compatible spacecraft, so we don’t have to figure out how to make one. They also run shuttle services, which keeps the cost down if you only have a small crew to transport, and can join other crews from nearby stars or planets. One hangup, is that we are used to the earth gravity acceleration of g. Beings from another planet may have a much greater or much lower gravity. That means that you might have to run several shuttles with given ranges of acceleration.
Note that we all inhabit the Galaxy, and calling them aliens will become ridiculous.
Since information is not transported more rapidly despite all the effort, it is not clear that the system is really needed. Maybe it will end up just the show-off destination by the richest, such as those that fly to the edge of outer space for a few minutes now.
