Gravitational Beamsplitter

A beamsplitter is a fundamental tool in optics that prepares a photon of light into two coherent states by dividing a parallel beam of light into two separate beam paths, A and B as in the figure. Usually a beamsplitter is a partially silvered mirror inside of a cube of otherwise transparent material and passes 50% of its light while reflecting the other 50% providing two possible futures for every single matter wave of light. This of course ignores the reflections and losses that occur at the other surfaces.

There are two interpretations for the action of a beamsplitter that represent two fundamentally different world views; ballistic and deterministic or relational and probabilistic. In a ballistic and deterministic worldview, the beamsplitter simply diverts each photon of light in the source beam onto either path A or path B. If you observe a photon at A, that means that that photon followed path A and that is why it was not seen at B.

In the second relational and probabilistic worldview, light actually follow both paths as matter waves and the beamsplitter introduces a coherence or relation between the two possible futures or states for each of two matter waves within the original source beam. In this relational worldview, light from the source propagates along both coherent paths A and B, but still an observer at A sees only 50% of the light waves as photons and does not see the other 50%, but now it is because of constructive and destructive interferences along both paths. Thus, a relational matter wave propagates from a source, the beamsplitter, along both relational paths A and B as a coherent superposition of paths A and B.

In a ballistic and deterministic worldview, seeing a photon at A means that that photon was always on path A and never on path B and that is why that photon as a particle did not appear at B. This is very intuitive and is largely what we experience in our macroscopic ballistic reality. In a relational and probabilistic worldview, though, seeing a photon at A does not mean that the light wave was only on path A. Even though that light wave did not appear as a photon at B, the light wave of that photon propagated on both A and B up until it was observed at A. So it was possible to have seen that photon at B up until actually seeing it at A. In essence, seeing A means not seeing B and the two events are coherent and related to each other instantaneously despite their separation in space and time.

This confusing superposition of quantum states A and B means that it is not a lack of knowledge that precludes knowledge of path A or B, it is rather an intrinsic superposition of matter waves that makes the precise path fundamentally unknowable. The result is not dependent on the nature of the observer and the photon can be absorbed by any object with the same result. The existence of unknowable paths is even more confusing to understand given the nature of our intuitive ballistic reality where all objects are located in unique places. It is difficult for us to imagine an object as a matter wave emanating from a source on more than one possible coherent and symmetric path. It is even more difficult for us to imagine any number of objects existing in the same place at one time. We only imagine single objects with single ballistic Cartesian trajectories and those paths are ultimately knowable even if we might not know them at the moment.  We find it difficult to imagine an object as a matter wave whose exact path is fundamentally uncertain.

The way that light waves interfere with themselves and with each other shows the truth of the relational worldview for light as matter waves. It is therefore true that objects behave as matter waves, including photons of light or people or planets, and an object as a matter wave can exist everywhere in the universe even though we only experience the object in one place. Each matter wave can have coherent relational states superimposed with different phases on other Cartesian worldlines. When a matter wave dephases or decoheres, it behaves like the ballistic and deterministic objects of our intuition. We can cause that dephasing or other objects can dephase a matter wave as well in the single object of our ballistic intuition.

We imagine a macroscopic reality that has objects on ballistic trajectories and for this reality, objects as matter waves have long since lost any other possible futures. When two incoherent objects collide, they collide in a ballistic reality. Two coherent objects, though, can pass through each other as matter waves given a gravity or charge mediated matter wave coherence and that coherence confuses our innate ballistic worldview.

In principle, a gravity beamsplitter as shown in the figure at right can prepare small objects like atoms or molecules into coherent gravity states. Two massive spheres like the earth and moon are in a binary orbit with each other as in the figure. Two much smaller and identical objects, A and B, are in orbits that intersect at the gravitational Lagrange point between the the earth and moon.

For quantum gravity, the identical Lagrange objects A and B can take on a superposition of coherent futures, one orbiting earth and the other in a complementary orbit around the moon and those two orbits interfere with each other. For any macroscopic object emitting and absorbing radiation, there is a fairly short time of dephasing and the object matter waves A and B will quickly dephase into either A or B ballistic orbits and the two incoherent objects may then collide at the orbit crossing.

For cold microscopic matter, though, a matter wave can persist for a much longer time as a superposition of two possible futures, orbits around the earth and moon. The result will be that the objects A and B can occupy the same space and will pass through each other and interfere with each other but not collide in the ballistic sense. As a result of this coherence, there is an extra binding energy for A and B due to the quantum exchange force between those paths.

Essentially, a coherent matter wave that includes both orbits and appears to act simultaneously across arbitrary separations, either appearing as an object or as a matter wave in orbits around earth and moon. The coherent identical objects {A, B} are part of an oscillating orbital state between earth and moon. If these two objects {A, B} are coherent, they will interfere with each other along a coherent trajectory back onto themselves. The gravity actions of coherent matter waves have many unexpected and nonintuitive effects.

For example, there is only a collisional future for {A, B} particles at the Lagrange orbital crossing in general relativity, while for quantum gravity there is also a wavelike exchange future for matter waves of properly phased objects {A, B}. Quantum gravity predicts an additional attractive force beyond just simple gravitational or charge forces for coherent matter as a result of exchange of identical particles. This additional gravity binding force due to quantum exchange and is what science now calls dark matter.

Quantum exchange forces are coherent relational actions that appear to act instantaneously over arbitrary separation. As a result, even though the exchange correction for the gravity of a galaxy is actually locally quite small compared to Newtonian gravity, over arbitrary separation, quantum gravity exchange can seem like a large amount of dark matter as an equivalent Newtonian gravity action within a galaxy.

A superposition state of hydrogen molecules that begins from a stationary ground state involves excitation with several quanta of infrared photons. Such an excitation has sufficient energy to accelerate a pair of neutral H₂ molecules into low earth orbit at 8 km/s as shown.

As long as the two H₂ molecules remain coherent, they do not collide in the classical sense despite being on the same orbit trajectory. Rather, they form a superposition state of the counterpropagating molecules that in effect interfere with each other. As soon as the hydrogens dephase, they experience a classical collision with any number of possible futures.

Note that the inverse process where heat is emitted from two molecules results in bonding states that we call gravity. Instead of bonding by displacement of charge, gravity bonding occurs as a result of displacement of neutral particles and emission of heat as photon pairs as quadrupoles. Typically science interprets the heating of a matter accretion as caused by gravity, but in matter time, it is the emission of heat as photon quadrupoles that causes gravity.

There is a very large number of gravity states for a matter accretion and therefore a very large entropy as well.