Listen terrestrial intelligent species: WeirdSciences is going to delve into a new idea of making interstellar travel feasible and this time no negative energy is to be used to propel spacecraft. Though implementing negative energy to make warp drive is not that bad, but you need to refresh your mind.
By Eric Baird
Alcubierre’s 1994 paper on hyperfast travel has generated fresh interest in the subject of warp drives but work on the subject of hyper-fast travel is often hampered by confusion over definitions — how do we define times and speeds over extended regions of spacetime where the geometry is not Euclidean? Faced with this problem it may seem natural to define a spaceship’s travel times according to round-trip observations made from the traveller’s point of origin, but this “round-trip” approach normally requires signals to travel in two opposing spatial directions through the same metric, and only gives us an unambiguous reading of apparent shortened journey-times if the signal speeds are enhanced in both directions along the signal path, a condition that seems to require a negative energy density in the region. Since hyper-fast travel only requires that the speed of light-signals be enhanced in the actual direction of travel, we argue that the precondition of bidirectionality (inherited from special relativity, and the apparent source of the negative energy requirement), is unnecessary, and perhaps misleading.
When considering warp-drive problems, it is useful to remind ourselves of what it is that we are trying to accomplish. To achieve hyper-fast package delivery between two physical markers, A (the point of origin) and B (the destination), we require that a package moved from A to B:
||. . . leaves A at an agreed time according to clocks at A,
||. . . arrives at B as early as possible according to clocks at B, and, ideally,
||. . . measures their own journey time to be as short as possible.
From a purely practical standpoint as “Superluminal Couriers Inc.”, we do not care how long the arrival event takes to be seen back at A, nor do we care whether the clocks at A and B appear to be properly synchronised during the delivery process. Our only task is to take a payload from A at a specified “A time” and deliver it to B at possible “B time”, preferably without the package ageing excessively en route. If we can collect the necessary local time-stamps on our delivery docket at the various stages of the journey, we have achieved our objective and can expect payment from our customer.
Existing approaches tend to add a fourth condition:
||. . . that the arrival-event at B is seen to occur as soon as possible by an observer back at A.
This last condition is much more difficult to meet, but is arguably more important to our ability to define distant time-intervals than to the actual physical delivery process itself. It does not dictate which events may be intersected by the worldline of the travelling object, but can affect the coordinate labels that we choose to assign to those events using special relativity.
If we introduce an appropriate anisotropy in the speed of light to the region occupied by our delivery path, a package can travel to its destination along the path faster than “nominal background lightspeed” without exceeding the local speed of light along the path. This allows us to meet conditions 2(a) and 2(b), but the same isotropy causes an increased transit time for signals returning from B to A, so the “fast” outward journey can appear to take longer when viewed from A.
This behaviour can be illustrated by the extreme example of a package being delivered to the interior of a black hole from a “normal” region of spacetime. When an object falls through a gravitational event horizon, current theory allows its supposed inward velocity to exceed the nominal speed of light in the external environment, and to actually tend towards vINWARDS=¥ as the object approaches a black hole’s central singularity. But the exterior observer, A, could argue that the delivery is not only proceeding more slowly than usual, but that the apparent delivery time is actually infinite, since the package is never actually seen (by A) to pass through the horizon.
Should A’s low perception of the speed of the infalling object indicate that hyperfast travel has not been achieved? In the author’s opinion, it should not — if the package has successfully been collected from A and delivered to B with the appropriate local timestamps indicating hyperfast travel, then A’s subsequent opinion on how long the delivery is seen to take (an observation affected by the properties of light in a direction other than that of the travelling package) would not seem to be of secondary importance. In our “black hole” example, exotic matter or negative energy densities are not required unless we demand that an external observer should be able to see the package proceeding superluminally, in which case a negative gravitational effect would allow signals to pass back outwards through the r=2M surface to the observer at the despatch-point (without this return path, special relativity will tend to define the time of the unseen delivery event as being more-than-infinitely far into A’s future).
Negative energy density is required here only for appearances sake (and to make it easier for us to define the range of possible arrival-events that would imply that hyperfast travel has occurred), not for physical package delivery.
- Hyperfast Return Journeys and Verification
It is all very well to be able to reach our destination in a small local time period, and to claim that we have travelled there at hyperfast speeds, but how do we convince others that our own short transit-time measurements are not simply due to time-dilation effects or to an “incorrect” concept of simultaneity? To convince observers at our destination, we only have to ask that they study their records for the observed behaviour of our point of origin — if the warpfield is applied to the entire journey-path (“Krasnikov tube configuration”), then the introduction and removal of the field will be associated with an increase and decrease in the rate at which signals from A arrive at B along the path (and will force special relativity to redefine the supposed simultaneity of events at B and A). If the warpfield only applies in the vicinity of the travelling package, other odd effects will be seen when the leading edge of the warpfield reaches the observer at B (the logical problems associated with the conflictng “lightspeeds” at the leading edge of a travelling warpfield wavefront been highlighted by Low, and will be discussed in a further paper). Our initial definitions of the distances involved should of course be based on measurements taken outside the region of spacetime occupied by the warpfield.
A more convincing way of demonstrating hyper-fast travel would be to send a package from A to B and back again in a shorter period of “A-time” than would normally be required for a round-trip light-beam. We must be careful here not to let our initial mathematical definitions get in the way of our task — although we have supposed that the speed of light towards B was slower while our warpdrive was operating on the outward journey, this artificially-reduced return speed does not have to also apply during our subsequent return trip, since we have the option of simply switching the warpdrive off, or better still, reversing its polarity for the journey home.
Although a single path allowing enhanced signal speeds in both directions at the same time would seem to require a negative energy-density, this feature is not necessary for a hyper-fast round trip — the outward and return paths can be separated in time (with the region having different gravitational properties during the outward and return trips) or in space (with different routes being taken for the outward and return journeys).
- Caveats and Qualifications
Special relativity is designed around the assumption of Euclidean space and the stipulation that lightspeed is assumed to be isotropic, and neither of these assumptions is reliable for regions of spacetime that contain gravitational fields.
If we have a genuine lightspeed anisotropy that allows an object to move hyper-quickly between A and B, special relativity can respond by using the round-trip characteristics of light along the transit path to redefine the simultaneity of events at both locations, so that the “early” arrival event at B is redefined far enough into A’s future to guarantee a description in which the object is moving at less than cBACKGROUND.
This retrospective redefinition of times easily leads to definitional inconsistencies in warpdrive problems — If a package is sent from A to B and back to A again, and each journey is “ultrafast” thanks to a convenient gravitational gradient for each trip, one could invoke special relativity to declare that each individual trip has a speed less than cBACKGROUND, and then take the ultrafast arrival time of the package back at A as evidence that some form of reverse time travel has occurred , when in fact the apparent negative time component is an artifact of our repeated redefinition of the simultaneity of worldlines at A and B. Since it has been known for some time that similar definitional breakdowns in distant simultaneity can occur when an observer simply alters speed (the “one gee times one lightyear” limit quoted in MTW ), these breakdowns should not be taken too seriously when they reappear in more complex “warpdrive” problems.
Olum’s suggested method for defining simultaneity and hyperfast travel (calibration via signals sent through neighbouring regions of effectively-flat spacetime) is not easily applied to our earlier black hole example, because of the lack of a reference-path that bypasses the gravitational gradient (unless we take a reference-path previous to the formation of the black hole), but warpdrive scenarios tend instead to involve higher-order gravitational effects (e.g. gradients caused by so-called “non-Newtonian” forces ), and in these situations the concept of “relative height” in a gravitational field is often route-dependent (the concept “downhill” becomes a “local” rather than a “global” property, and gravitational rankings become intransitive). For this class of problem, Olum’s approach would seem to be the preferred method.
In order to be able to cross interstellar distances at enhanced speeds, we only require that the speed of light is greater in the direction in which we want to travel, in the region that we are travelling through, at the particular time that we are travelling through it. Although negative energy-densities would seem to be needed to increase the speed of light in both directions along the same path at the same time, this additional condition is only required for any hyperfast travel to be “obvious” to an observer at the origin point, which is a stronger condition than merely requiring that packages be delivered arbitrarily quickly. Hyperfast return journeys would also seem to be legal (along a pair of spatially separated or time-separated paths), as long as the associated energy-requirement is “paid for” somehow. Breakdowns in transitive logic and in the definitions used by special relativity already occur with some existing “legal” gravitational situations, and their reappearance in warpdrive problems is not in itself proof that these problems are paradoxical.
Arguments against negative energy-densities do not rule out paths that allow gravity-assisted travel at speeds greater than cBACKGROUND, provided that we are careful not to apply the conventions of special relativity inappropriately. Such paths do occur readily under general relativity, although it has to be admitted that some of the more extreme examples have a tendency to lead to unpleasant regions (such as the interiors of black holes) that one would not normally want to visit.
[Ref: Miguel Alcubierre, "The warp drive: hyper-fast travel within general relativity," Class. Quantum Grav. 11 L73-L77 (1994), Michael Spzir, "Spacetime hypersurfing," American Scientist 82 422-423 (Sept/Oct 1994), Robert L. Forward, "Guidelines to Antigravity," American Journal of Physics 31 (3) 166-170 (1963). ]