Generic warp drives violate the null energy condition (2105.03079v2)

Abstract: Three very recent articles have claimed that it is possible to, at least in theory, either set up positive energy warp drives satisfying the weak energy condition (WEC), or at the very least, to minimize the WEC violations. These claims are at best incomplete, since the arguments presented only demonstrate the existence of one set of timelike observers, the co-moving Eulerian observers, who see "nice" physics. While these observers might see a positive energy density, the WEC requires all timelike observers to see positive energy density. Therefore, one should revisit this issue. A more careful analysis shows that the situation is actually much grimmer than advertised -- all physically reasonable warp drives will violate the null energy condition, and so also automatically violate the WEC, and both the strong and dominant energy conditions. While warp drives are certainly interesting examples of speculative physics, the violation of the energy conditions, at least within the framework of standard general relativity, is unavoidable. Even in modified gravity, physically reasonable warp drives will still violate the purely geometrical null convergence condition and the timelike convergence condition which, in turn, will place very strong constraints on any modified-gravity warp drive.

• The paper establishes that generic warp drive solutions inherently violate the null energy condition, necessitating exotic matter for any superluminal travel concept.
• It examines several configurations—including Alcubierre, Natário, and Lentz drives—by computing stress-energy tensors to reveal consistent energy condition breaches.
• The analysis implies that without breakthroughs in modified gravity or quantum theories, practical warp drive realization remains speculative within classical physics.

Violation of Energy Conditions in Warp Drive Spacetimes

The paper under discussion investigates the feasibility of warp drives—a hypothetical concept in general relativity that allows for faster-than-light travel—and their compatibility with the energy conditions. Specifically, the authors focus on whether these concepts can exist without violating fundamental energy conditions, such as the Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC), and the Null Energy Condition (NEC).

Key Findings

1. Energy Condition Violations: Analyzing recent claims of positive energy warp drives, the paper argues and establishes that these solutions inherently violate the NEC. Consequently, violations of WEC, SEC, and DEC also occur. This reinforces the long-standing theoretical position that superluminal travel necessitates exotic matter with properties not compatible with all observers seeing only positive energy density.
2. General Overview of Warp Drives: The paper revisits several known warp drive configurations, including Alcubierre, Natário, and Lentz/Fell-Heisenberg zero-vorticity drives. It thoroughly examines their stress-energy tensors, establishing conditions under which all proposed configurations violate established energy conditions.
3. Detailed Analysis: Extensive technical evaluation is presented, dissecting the mathematical formulations and consequences of warp drives. The curvature, Riemann, Ricci, and Einstein tensors are calculated for generic spacetimes within Natário's framework, showing that despite potential configurations suggested in recent literature, these models do not fulfill the necessary criteria to abide by conventional energy conditions.

Implications

• Theoretical Considerations: Without adherence to energy conditions, any warp drive concept remains speculative under classical physics principles. The need for exotic matter and energy configurations extends beyond minor modifications, suggesting that either our understanding of gravity or matter-energy interactions must evolve for warp drives to be viable.
• Practical Impact: There is no current practical mechanism or technology to create or control the exotic matter necessary for such constructs. The paper suggests an inherent impossibility within the framework of general relativity without appealing to speculative physics or significantly revised theoretical models.

Future Directions

Given the impossibility of achieving warp drives under contemporary physics, several potential research avenues have been discussed:

1. Modified Theories of Gravity: Investigating extensions of general relativity, including quantum gravity theories, may yield frameworks where energy conditions can be locally violated without the paradoxical implications found in classical theories.
2. Quantum Considerations: Exploring macroscopic quantum effects might provide a loophole to bypass current restrictions, though the practical realization remains far from reach.
3. New Forms of Matter: The pursuit of exotic states of matter that inherently violate energy conditions continues to be a far-off frontier, necessitating breakthroughs in particle physics and materials science.

The paper underlines the critical nature of sticking to established scientific methods while exploring the boundaries of physics, emphasizing the need for rigorous checks against established principles before claiming feasible configurations of theoretical constructs like warp drives.