A design is presented of a laboratory experiment that could test the suitability of relativistic gravity for propulsion of spacecraft to relativistic speeds. The first exact time-dependent solutions of Einstein’s gravitational field equation confirm that even the weak field of a mass moving at relativistic speeds could serve as a driver to accelerate a much lighter payload from rest to a good fraction of the speed of light. The time-dependent field of ultrarelativistic particles in a collider ring is calculated. An experiment is proposed as the first test of the predictions of general relativity in the ultrarelativistic limit by measuring the repulsive gravitational field of bunches of protons in the Large Hadron Collider (LHC). The estimated ‘antigravity beam’ signal strength at a resonant detector of each proton bunch is 3 nm/s2 for 2 ns during each revolution of the LHC. This experiment can be performed off-line, without interfering with the normal operations of the LHC.
Exact payload trajectories in the strong gravitational fields of compact masses moving with constant relativistic velocities are calculated. The strong field of a suitable driver mass at relativistic speeds can quickly propel a heavy payload from rest to a speed significantly faster than the driver, a condition called hyperdrive. Hyperdrive thresholds and maxima are calculated as functions of driver mass and velocity.
In 1924, the influential German mathematician David Hilbert published a paper called “The Foundations of Physics” in which he outlined an extraordinary side effect of Einstein’s theory of relativity.
Hilbert was studying the interaction between a relativistic particle moving towards or away from a stationary mass. His conclusion was that if the relativistic particle had a velocity greater than about half the speed of light, a stationary mass should repel it. At least, that’s how it would appear to a distant inertial observer.
That’s an interesting result and one that has been more or less forgotten, says Franklin Felber an independent physicist based in the US (Hilbert’s paper was written in German).
Felber has turned this idea on its head, predicting that a relativistic particle should also repel a stationary mass. He says this effect could be exploited to propel an initially stationary mass to a good fraction of the speed of light.
The basis for Felber’s “hypervelocity propulsion” drive is that the repulsive effect allows a relativistic particle to deliver a specific impulse that is greater than its specific momentum, thereby achieving speeds greater than the driving particle’s speed . He says this is analogous to the elastic collision of a heavy mass with a much lighter, stationary mass, from which the lighter mass rebounds with about twice the speed of the heavy mass.
What’s more, Felber predicts that this speed can be achieved without generating the sever stresses that could damage a space vehicle or its occupants. That’s because the spacecraft follows a geodetic trajectory in which the only stresses arise from tidal forces (although it’s not clear why those forces wouldn’t be substantial)
The experiment would measure the repulsive gravitational impulses of proton bunches delivered in their forward direction to resonant detectors just outside the beam pipe. This test could provide accurate measurements of post-Newtonian parameters and the first observation of ‘antigravity’, as well as validating the potential utility of relativistic gravity for spacecraft propulsion in the distant future.
A new exact time-dependent field solution of Einstein’s equation is given in Eq. (8) by (Felber, 2008 and 2009).
This exact strong-field solution provides further support for the weak-field results presented in this paper. According to Table 1 and Eq. (9), the exact field solution in Eq. (8) for a mass moving with constant velocity corresponds precisely in the weak-field approximation to the weak-field solution in Eq. (2), for the special case of constant velocity.
A simple Lorentz transformation of the well-known unbound orbit of a payload in a Schwarzschild field gives the exact payload trajectory in the strong field of a relativistic driver with constant velocity, as seen by a distant inertial observer. The calculations of these payload trajectories by this two-step approach, and their animated versions
(Felber, 2006b), clearly show that suitable drivers at relativistic speeds can quickly propel a heavy payload from rest to speeds close to the speed of light.
The strong field of a compact driver mass can even propel a payload from rest to speeds faster than the driver itself – a condition called hyperdrive. Hyperdrive is analogous to the elastic collision of a heavy mass with a much lighter, initially stationary mass, from which the lighter mass rebounds with about twice the speed of the heavy mass.
Hyperdrive thresholds and maxima were calculated and shown in Figure 5 as functions of driver mass and velocity. Substantial payload propulsion can be achieved in weak driver fields, especially at relativistic speeds.
The exact time-dependent gravitational-field solutions of Einstein’s equation in (Felber, 2008 and 2009) for a mass moving with constant velocity, and the two-step approach in (Felber, 2005b, 2006a, 2006b and 2006c) to calculating exact orbits in dynamic fields, and the retarded fields calculated in (Felber, 2005a) all give the same result: Even weak gravitational fields of moving masses are repulsive in the forward and backward directions at source speeds greater than 31/2 c .
The field solutions in this paper have potential theoretical and experimental applications in the near term and potential propulsion applications in the long term. In the near term, the solutions can be used in the laboratory to test relativistic gravity for the first time. Performing such a test at an accelerator facility has many advantages over similar space-based tests of relativity that have been performed and contemplated for the future, including low cost, quickness, convenience, ease of data acquisition and data processing, and an ability to modify and iterate tests in real time. Such a test could provide accurate measurements of post-Newtonian parameters in the extreme relativistic regime and the first observation of ‘antigravity’. Our estimates suggest that each proton bunch in the LHC beam would produce an ‘antigravity beam’ with a signal strength of 3 nm/s2 and a duration of 2 ns at a detector. With a suitable high-Q resonant detector, a typical proton circulation time of 10 hours, and an impulse frequency at peak luminosity of 31.6 MHz, the SPL of the ‘antigravity beam’ at the LHC could be resonantly amplified to exceed 160 dB re 1 μPa.