# Measuring the Curvature of Space-time Using Time Dilation at Atomic Scale

Jan 02, 2024^{By physicist Dr. Inés Urdaneta and biophysicist William Brown, research scientists at the International Space Federation}

Although quantum mechanics— the physics governing the atomic scale— and general relativity— the physics governing the cosmological scale— are still viewed as disparate regimes within the Standard Model (Haramein's holographic quantum gravitational solution has not reached wide-spread mainstream appeal as of yet), experiments on the quantum scale are reaching the capability of measuring relativistic effects, therefore connecting in practice, what remains seemly disconnected in theory.

Such is the case of the recently observed gravitational Aharonov-Bohm effect—a quantum probe for gravity. In the electromagnetic version of the Aharonov-Bohm effect (in which the highly nonlocal quantum effect was first predicted) an electrically charged particle is affected by an electromagnetic potential, despite being confined to a region in which both the magnetic field and electric field are zero. The underlying mechanism is the coupling of the electromagnetic potential with the complex phase of a charged particle's wave function. A wave function is a complex-valued probability amplitude that describes mathematically the quantum state (given by the observables of the theory, such as speed, position, energy levels, etc) of an isolated quantum system, and the probabilities for the possible results of measurements made on the system can be derived from it, when multiplying this complex function by its complex conjugated to obtain real values, which are the magnitudes related to the physical observables. It is clear that this effect is an entirely quantum mechanical effect. And at this scale, the forces that govern are seemingly mainly electromagnetic in nature.

Given that quantum particles— such as electrons— are described effectively by superposition of states, called wave packets, the original Aharonov-Bohm effect predicts that if an electron beam in a superposition of two wave packets (a combination of wavefunctions) is exposed to a time-varying electrical potential (and no field), it would acquire a phase difference when passing through a pair of metallic tubes. Later the wave packets are recombined, and the phase difference between the wave packets induced by this varying potential leads to a measurable physical effect, an interference pattern.

So, where does the relativistic part come into play? It is known that the theory of gravitation is described by Einstein’s general relativity equations (the Einstein field equations) which explain gravity as the curvature of space and time produced by any mass-energy. This curvature can lead to proper time differences between freely falling, nonlocal trajectories—which means that observer’s clocks in different non-inertial reference frames will not agree, and the observers will disagree on the timing of any event—spacetime curvature results in the relativity of simultaneity as a result of time dilation. Currently, there are no mainstream solutions to the gravity of quantum particles, nor to the origin of their mass; quantum particles mass is so tiny, that the curvature they could produce would be considered negligible (to see the actual solution to these questions see RSF publications like *The Electron and the Holographic Mass Solution).*

But what would happen if we measured the phase difference in quantum particles, produced by the curvature of space time? This is what Mark Kasevich and colleagues at Stanford University have achieved, employing an atom interferometer which uses a series of laser pulses to split, guide and recombine atomic wave packets. The interference pattern obtained from the recombination of these wave packets reveals any change in the relative phase experienced by the waves along the two arms. This is basically the principle of a Michelsen Morley interferometer, but in this experiment the light sources are lasers, which are sources of monochromatic light that enable a much higher resolution.

_{The basic elements of point source interferometry are depicted here. (a) The method starts with a small cloud of ultracold atoms (blue), which is launched upward inside an evacuated enclosure. At the beginning of the trajectory, a laser pulse (red) splits the cloud into two clouds, which both expand as they rise and fall. A second pulse at the top of the trajectory acts as a mirror. (b) When the clouds reach the bottom of the enclosure, a third pulse recombines them. The resulting interference pattern is recorded with two CCD cameras. Image credit and figure description: }_{Philippe Bouyer LP2N, Institut d'Optique d'Aquitaine, 33400 Talence, France August 19, 2013• Physics 6, 92}

As explained in the abstract of the Science paper:

“We measure the gravitational phase shift induced in a matter-wave interferometer by a kilogram-scale source mass close to one of the wave packets. Deflections of each interferometer arm due to the source mass are independently measured. The phase shift deviates from the deflection-induced phase contribution, as predicted by quantum mechanics. In addition, the observed scaling of the phase shift is consistent with Heisenberg’s error-disturbance relation. These results show that gravity creates Aharonov-Bohm phase shifts analogous to those produced by electromagnetic interactions.”

##### Unified Science in perspective -

These results are very important, for several reasons. First, because they enable spacetime curvature (gravitational) measurements at the quantum scale, providing a bridge between quantum theory and relativity. Secondly, this novel methodology can provide a new way of measuring Newton’s gravitational constant with far greater precision than what is currently possible—as the gravitational constant has the least precision in its known value of any measured constant. High precision measurements of G, using techniques like atomic interferometry, will provide an empirical test of Haramein’s highly precise predicted value for G.

Additionally, this is a very clever way of surmounting the difficulties of measuring the dephasing of gravitational waves, which uses the same interferometry principles, but requires arms that are kilometers long!

The connection between electromagnetism and gravity— the so-called grand unification problem, uniting gravity, and EM forces— is a mystery that has baffled scientists for decades. Quantum gravity is supposed to solve this conundrum, which is a way of answering the question on how the phase transition from charges to mass occurs.

Haramein’s generalized holographic theory has proven how mass emerges from the vacuum fluctuations, and therefore, giving a first answer to the source of mass. The connection between gravity and electromagnetism will be completed with his new paper entitled “Scale invariant unification of forces, fields and particles in the quantum vacuum plasma” to come out soon.

Since we already know how to manipulate efficiently EM fields, understanding this connection we can achieve gravitational control. The applications and implications of such understanding are literally ENDLESS.

The unified field theory is already here!