Mar 09, 2022

The way we measure time is via frequency. To measure spatial dimension, we use a ruler. In classical mechanics we assumed that these measurement devices were static and would measure the same time and length no matter how an observer was moving or where they were located. However, in the late 19^{th} century it was discovered that this “common sense” perspective of the world is erroneous, and a new mechanics was necessitated. Hendrik Lorentz and Henri Poincare described how rulers contract and clocks measuring frequency have a dilation in the rate of "ticks" they read depending on the movement of a given frame of reference— which was described in relation to the aether in *Electromagnetic phenomena in a system moving with any velocity smaller than that of light *[1] by Lorentz and *The New Mechanics *[2] by Poincare. These contractions are known as *Lorentz transformations* and were generalized by Einstein in his theory of general relativity to include all accelerating frames of reference and, equivalently, gravitational forces.

_{The Lorentz transformation for calculating time dilation. For a time-interval measured at 20 seconds for a an observer traveling at 200,000 km/s, a stationary observer will measure the same time-interval at 26.85 seconds.}

As Poincare described, and Einstein codified, the effect of time dilation means that the clocks in different moving frames of reference (or equivalently different gravitational field strengths) will not agree on the simultaneity of any event, as the number of “ticks”, or frequency, between the clocks will not be synchronized—they “tick” at different rates due to the differential accelerations of the non-inertial frames of reference.

This results in the *relativity of simultaneity* and deals another shock to our “common sense” view of the world, i.e., time moves at different rates for different observers depending on whether they are accelerating (in a more positively curved region of the gravitational field) or “at rest” relative to an accelerating frame of reference. This means that across the universe there is no uniform reference of time, each local frame has its own reference of time, each has a different “age”. For example, events that occurred in “the past” for observers in a reference frame that is on the surface of a planet will appear as occurring “in the future” world line for observers that are traveling on a spaceship at relativistic speeds (approaching the speed of light).

_{Time dilation as a result of an accelerating frame of reference: An electromagnetic signal emitted by observers on the spaceship and reflected back has a longer distance to travel than a similar signal for “stationary” observers on Earth. The observers are using the light pulse to measure the time of an event, because of the resulting time dilation from acceleration the observers on the spaceship will record the event occurring at a later time (vt) than what is measured for the observers on Earth. For the observers on Earth, it appears that the spaceship’s clock has slowed down, while to the observers on the spaceship it will appear that Earth’s clock will have sped up, which clocks are correct? Both are relative to their frame of reference; the simultaneity of any event is relative. While the clock on the spaceship relative to that on Earth has literally “ticked” more slowly, the moving observer does not experience time slowing down. To the moving observer everything on the ship, the clocks, computers, chemistry, brain signals all seem to be moving along normally at one second per second.}

Thanks to Einstein, we know that these spatial and temporal transformations are the result of the fabric of spacetime literally curving (contracting and expanding) due to mass-energy. Because this relativistic understanding of the nature of our world is so counter to our everyday experience, it can be difficult to fully comprehend or even accept—and that is where experiments that directly measure and demonstrate the effects are important. In a previous article— *Measuring the Curvature of Space-time Using Time Dilation at Atomic Scale*— we described how recent experiments have measured spacetime curvature from mass with atomic precision using atomic wave interferometry, which used the wave-like property of particles to measure the interference produced after a wave-packet was split in two, with one beam directed close to a 1 kilogram mass, and the other traveling unperturbed before the two were recombined.

Now, a second experiment using an atomic clock has observed time dilation by directly measuring the difference in frequency of atoms—the rate at which they vibrate or oscillate— due to their relative positions in Earth’s gravitational field [3]. Moving closer to the center of Earth’s mass causes time to move more slowly (the further into Earth’s gravitational "well" one moves the greater the spacetime curvature, and hence increased time dilation), which can be measured by a slower frequency or rate of oscillation of atomic particles, while “clocks” farther from the center of mass will run faster. Such experiments had already been performed using atomic clocks at different altitudes compared to those on Earth’s surface [4], however the latest experiment has recorded the time dilation effect in a difference of height of a minuscule 0.2 millimeters— roughly twice the width of a piece of paper.

Like the experiment with atomic wave interferometery that is measuring relativistic spacetime curvature in a quantum state of matter [5], the measurement of time dilation with the atomic clock opens the possibility to measure relativistic effects in matter in a quantum state— experimentation that may help to unify our understanding of the quantum mechanical and relativistic regimes, perhaps furthering the development of a theory of quantum gravity, and enabling us to better understand the nature of time.

The atomic clock uses about 100,000 strontium 87 atoms that are cooled to a fraction of a degree above absolute zero. The atoms are arranged in layers using the trapping force of a laser in what is called an optical lattice. By stacking the layers and measuring the frequency of the strontium atoms, which oscillate at a rate of 500 trillion times per second, minute differences in the rate of oscillation can be measured across the stack as a result of time dilation from the different field strengths of Earth’s gravity (going from lower to higher layers in the “stack”). The time measurements are so precise—the atomic pendulum is measuring at a rate of 500 trillion times a second— such that differences in a fraction of a second can be measured out to 19 decimal places [6], so precise that the clock will only lose at most a tenth of second over the entire lifetime of the universe.

_{Laser confinement of atoms in an optical lattice for use as an ultraprecise atomic clock. Layers can be stacked on top of each other to measure differences in atomic oscillatory rates at different heights above Earth’s gravitational center of mass.}

A fascinating possibility is to bring the supercooled strontium atoms into a superposition of state, where their location in the “stack” is undefined. Theoretically, the wave-state of the strontium atom will experience different spacetime curvature all along its wavefunction, it could then be seen if such a condition is permissible or unstable. The preeminent physicist Sir Roger Penrose has predicted that such superpositions of spacetime configurations will be unstable, and result in what he calls objective reduction (as opposed to subjective reduction that seems to rely on measurement or an observer), and if in experiment this is observed to be the case, it may help to explain why large macroscopic objects do not exhibit quantum mechanical states like superpositions—at a certain point gravitational interaction causes objective reduction of the wavefunction.

Interestingly, such a quantum gravitational experiment will also be a test of the unified physics of biology, as Penrose and neuroquantum biologist Stuart Hameroff have utilized a mechanism of orchestrated objective reduction of entangled qubits in neuronal microtubules to explain the mechanism of consciousness [7, 8]. Certainly, such experimentation and others that test relativistic effects in quantum mechanical states of matter will help to further our empirical understanding of a unified physics and come to a truer comprehension of the nature of our universe.

[1] H.A. Lorentz, *Electromagnetic phenomena in a system moving with any velocity smaller than that of light*. Proceedings of the Royal Netherlands Academy of Arts and Sciences, 1904, **6**: 809–831

[2] In French: Poincaré, Henri (1908),* “La dynamique de l’électron”, *Revue générale des sciences pures et appliquées **19**: 386–402. English translation: Poincaré, Henri (1913)*, “The New Mechanics”, *The foundations of science (Science and Method), New York: Science Press, pp. 486-522

[3] A. Mann, “Amazingly precise optical atomic clocks are more than timekeepers,” *Proceedings of the National Academy of Sciences*, vol. 115, no. 29, pp. 7449–7451, Jul. 2018, doi: 10.1073/pnas.1809852115.

[4] Hafele and Keating, Around-the-World Atomic Clocks: Observed Relativistic Time Gains. Science, 177 (1972), 168

[5] Ines Urdenata & William Brown,* Measuring the Curvature of Space-time Using Time Dilation at Atomic Scale, *The Resonance Science Foundation, online 2022

[6] GE Marti, et al., Imaging optical frequencies with 100 μHz precision and 1.1 μm resolution. *Phys Rev Lett* 120, 103201–103207 (2018).

[7] S. Hameroff, “‘Orch OR’ is the most complete, and most easily falsifiable theory of consciousness,” *Cognitive Neuroscience*, vol. 12, no. 2, pp. 74–76, Apr. 2021, doi: 10.1080/17588928.2020.1839037.

[8] William Brown, “Confirmation of Quantum Resonance in Brain Microtubules,” *Resonance Science Foundation*, Feb. 06, 2017. https://resonance8.oldrsf.com/confirmation-quantum-resonance-brain-microtubules/ (accessed Mar. 09, 2022).

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