Houston we have a problem.
If the human race does not develop starships that can reach other star systems as easily as sea freighters or jetplanes now traverse the Pacific Ocean, it has no long term future. Either an asteroid will eventually smash the planet, or we shall exhaust its natural resources, or the lack of a new frontier will lead to cultural decay. Our star will eventually run out of fuel anyway.
At the time of writing we face only a single obstacle to interstellar travel. Physics as we understand her in the opening years of the twenty first century. We have the technology to sustain life support in space; telemetry and astrogation present no real problems, but propulsion by reaction-thrust (firework) principles remains pathetically inadequate. The billions of dollars expended annually worldwide to improve chemical or even nuclear reaction thrust vehicles cannot in principle yield dividends in fields other than materials science, warfare, orbital astronomy, telecommunications, and a very modest exploration of the local solar system.
Any serious attempt to penetrate interstellar space must come from ideas developed in fundamental physics. No conceivable increment in rocket style technology can possibly get us to anywhere useful. We may as well abandon schemes based on Bussard ramjets, Orions, or Matter-Anti matter reaction thrust vehicles. Such schemes compare to crossing the pacific on surfboards. Whilst they remain just about possible, they would represent a heroic, if not suicidal, waste of effort compared to the quest to develop more useful means of transport.
Even if such drives could achieve a comfortable one gravity of acceleration for a couple of years without an impossible power input, they could achieve relativistic speeds but interstellar gas particles would hit the vessel like hard gamma rays, and dust particles would strike like battleship shells. Thus we have to look within and beyond special and general relativity or quantum physics for some principle which may allow us to 'warp' or 'teleport' across space rather than hammer our way through it.
Some of the ideas on this site may suggest a possible means of moving between star systems without traversing the daunting interstellar voids between them.
Consider the analogy with terrestrial travel. Friction against the solid or liquid surfaces of the planet limits ground and sea vehicles moving around the two dimensional surface to rather modest speeds. However aircraft moving in three rather than two dimensions escape from surface friction and can travel much faster. A tunnel dug right through the planet could provide an exceptionally efficient means of travelling to the antipodes of any point, although no known material could serve as a lining for the tunnel. Simply dive headfirst into the tunnel and freefall to the centre of the earth which you will pass at extreme speed. You will then begin to slow down as you continue, coming, in theory, to a momentary halt at the other end of the tunnel allowing you to just time to grab the lip and clamber out before you fall back again. Elapsed time 42min, fuel required none, g forces nil. In practice you really need to have a vacuum in the tunnel to prevent air friction and a spacesuit to prevent death.
So can we somehow exploit the extra degrees of freedom offered by six dimensions to achieve rapid transit across the universe? Six dimensions seem to offer the higher dimensional equivalents of both aircraft travel and tunnel travel, which for the purposes of this paper we can call Warp1 and Warp 2 respectively.
Now as two dimensions of time lie orthogonal to all points of 4D spacetime, much as the up/down spatial dimension lies orthogonal to every point on a planetary surface, so Warp 1 and 2 journeys can, in principle begin and end anywhere. As with a Tardis, launch from within your garden shed or basement should not present a problem.
Warp 1 craft would basically travel "outside" the hyperspherical three-dimensional "surface" of the observable universe in the "ana" or forward direction of the plane of imaginary time. By analogy with aircraft travel we might expect that such vessels may have to expend energy to resist the spacetime curvature (gravity) of the universe. Warp 2 craft would travel through the "kata" or past direction of imaginary time to any point of equigravitational potential without expending energy, although opening a tunnel may have an energy requirement.
Warp 1. The invention of aircraft required the coming together of two technologies, the technology of aerodynamic lift, and the technology to push persistently against the air. By analogy Warp 1 craft will need something to hold them in imaginary time and something to give them a shove. Now as the plane of imaginary time corresponds in some sense to probability, perhaps we should look at the phenomenon of quantum superposition in which a particle appears to occupy (or to have occupied) an indeterminately large number of possible states simultaneously. At the time of writing, such superpositions only seem to involve small numbers of particles and they seem prone to decohere rapidly back into "normal" states. However perhaps one day we will discover how to place an entire ship into a quantum superposition with a wave function that has a non zero probability at every spatial point in the universe. Then perhaps we will only have to give it the gentlest push, and then allow it to decohere back into "ordinary" reality wherever we want, perhaps trillions of miles away, perhaps almost instantly.
Warp 2. Trying to dig a tunnel through spacetime using general relativity seems less sensible than at first it may appear, and Warp 2 travel does not involve this. Black holes would not consist of "holes" in spacetime; they would consist of impassable "knots". Four dimensional wormhole throats would require titanic amounts of "negative energy" to hold them open for ships to pass, and negative energy seems to have no real meaning or physical reality in this universe. To tunnel across the universe from one point to another we only actually need to penetrate beneath the four dimensional hyperspherical surface of which it consists, to gain the extra degrees of freedom on the "inside" in the kata or past direction of the plane of imaginary time. Warp 2 drive may require essentially the same technology as Warp 1 drive, except that the craft will require a push in the opposite "direction". Neither type of travel requires that the vessel risk ending up in the far past or future probabilities of its destination. Well perhaps it runs no more risk than an air traveller or tunnel diver from London to Australia risks in ending a journey a long way up in the air or some distance underground. (Timecrash- a new sci fi theme perhaps?)
A paper as wildly speculative and analogically based as this would certainly benefit from some supporting maths.