Breakthrough Propulsion Physics Program
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The Breakthrough Propulsion Physics Project (BPP) was a research project funded by NASA from 1996 through 2002, to study various proposals for "revolutionary" methods of spacecraft propulsion which would require breakthroughs in physics before they could be realized, hence the name. During its six years, this program was funded with a total investment of $1.2 million.
The diametric drive was a speculative proposal for an "engine" which would create a non-conservative gravitational field with non-zero curl. It was argued that in such circumstances, the side of the field which creates more force on the spacecraft will accelerate the spacecraft in the direction of the force.
One idea for realizing this concept involved hypothetical particles with negative mass, originally proposed by Robert Forward and Jamie Woodward. If one were to construct a block of negative mass, and then attach it to a normal "positive" mass, the negative mass would fall towards the positive as does any mass toward any other. On the other hand, the negative mass would generate "negative gravity", and thus the positive mass (the spaceship itself generally) would fall away from the negative mass. If arranged properly, the distance between the two would not change, while they continued to accelerate forever. It has been argued that stability issues might arise.
The concept is illustrated according to Millis by :
- is the gravitational scalar potential
- is normal mass
- is distance
By disjunction is meant the separation of the source of a field from matter to which interaction would be with under normal physical states.  According to a summary of speculative propulsion ideas on NASA's website
|“||This concept entertains the possibility that the source of a field and that which reacts to a field can be separated. By displacing them in space, the reactant is shifted to a point where the field has a slope, thus producing reaction forces between the source and the reactant. Although existing evidence strongly suggests that the source, reactant, and inertial mass properties are inseparable, any future evidence to the contrary would have revolutionary implication to this propulsion application.||”|
The concept is expressed in math  as :
Pitch and bias
One proposed method of achieving a diametric drive, or possibly a disjunction drive, which was studied in the BPP was called the pitch drive. This has been described as involving a hypothetical disjoint field which would eliminate the need for the field to be generated on the spacecraft itself.
One specific proposal for such a pitch drive was called the bias drive. According to this proposal, if it were possible to locally alter the value of the gravitational constant G in front of and behind the craft, one could create a bias drive. While the gravitational constant is a fundamental physical constant in general relativity, the Brans–Dicke theory of gravitation does in a sense allow for a locally varying gravitational constant, so the notion of a locally varying gravitational constant has been seriously discussed in mainstream physics. It has been claimed[by whom?] that one problem with the concept of a bias drive was that it might create a singularity in the field's gradient located inside the vehicle.
The bias drive and pitch drive is expressed qualitatively in mathematics  as :
- is the Gaussian distribution over dimensionless
- is the magnitude of hypothetical pitch drive effect
- is the magnitude of hypothetical bias drive effect
The Alcubierre drive, also called the warp drive, is a proposal, originally due to the physicist Miguel Alcubierre, which consists of a toy model of a Lorentzian spacetime with properties somewhat reminiscent of the fictional "warp drive" from the science fiction series Star Trek.
The differential sail was another speculative proposal, which appealed to the zero-point energy field. As the Heisenberg uncertainty principle implies that there is no such thing as an exact amount of energy in an exact location, vacuum fluctuations are known to lead to discernible effects such as the Casimir effect. The differential sail was a speculation that it might be possible to induce differences in the pressure of vacuum fluctuations on either side of sail-like structure—with the pressure being somehow reduced on the forward surface of the sail, but pushing as normal on the aft surface—and thus propel a vehicle forward. 
After funding for research ended, the Project's founder and manager, Marc G. Millis, was supported by NASA to complete the documentation of results. The culmination of that work is the book, Frontiers of Propulsion Science, which was published in February 2009, by the American Institute for Aeronautics and Astronautics (AIAA). Chapter 3 (Prerequisites for Space Drive Science) provides refinements and deeper explanation of the following hypothetical "space drive" propulsion methods: diametric drive, pitch drive, bias drive, disjunction drive, and three variations of differential sails.
After the BPP was canceled in 2002, some former members, including manager Marc G. Millis, founded the Tau Zero Foundation (named after the novel of the same name), an organization that advocates research into interstellar travel. The new organization is not affiliated with NASA. Millis retired from NASA on February 3, 2010, and continues to pursue similar research via Tau Zero.
- Marc G. Millis, The Challenge To Create The Space Drive, 1997, Journal of Propulsion and Power.
- Marc G. Millis & Eric W. Davis (editors): Frontiers of Propulsion Science. American Inst. of Aeronautics and Astronautics, Reston VA, 2009, ISBN 978-1-56347-956-4 (739 pages), Summary.
- Breakthrough Propulsion Physics Project. (Marc Millis explains on this page that NASA has not sponsored this project since 2002, but he apparently hopes to reinstate funding.)
- "Breakthroughs" commonly submitted to NASA - These are ideas that do *not* work, but are often submitted to NASA anyway. (Apparently offline, available here or through Archive.org at )
- Tau Zero Foundation