Minimizing time dilation shift in Penning trap atomic clocks

Time dilation and remote non-simultaneity are two of the most famous predictions derived from the Lorentz transformation. As a simple example, consider two lightning strikes which occur at different positions in space. According to Einstein’s special theory, the time differences Δt and Δtꞌ measured by two observers between the two strikes must satisfy a strict proportionality relation (time dilation): Δtꞌ=XΔt. However, it is also claimed, by virtue of the corresponding prediction of remote non-simultaneity, that the two events can occur simultaneously for one of them (Δt=0) without doing so for the other (Δtꞌ≠0). It is pointed out that it is impossible to satisfy both of the above conditions because that would mean having to violate the algebraic axiom which states that multiplication of any finite number, in this case X, by zero (Δt) must have a product (Δtꞌ) of zero as well. Only by violating this axiom is it possible to avoid a direct contradiction of the prediction of remote non-simultaneity. As a result, the Lorentz transformation itself is shown to be invalid since it is responsible for both of the above predictions. A different space-time transformation is therefore presented which also satisfies both of Einstein’s postulates of relativity without requiring that space and time be mixed. The Hafele-Keating experiments with atomic clocks carried onboard circumnavigating airplanes confirm that time dilation is a real effect, but they also show that the prediction of Einstein’s theory that observers can disagree in principle which of two clocks runs slower is not correct. The Global Positioning System makes use of the observed proportionality relationship between elapsed times to adjust the rates of atomic clocks carried onboard its satellites so that they run at the same rate as identical clocks located on the earth’s surface. This practice also serves as a confirmation that remote non-simultaneity has no basis in fact. Otherwise, it would make no sense to have the two clocks running at the same rate in order to measure elapsed times for laser beams to travel between the satellite and the ground position.

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The Theories of Relativity and Bergson's Philosophy of Duration and Simultaneity During and After Einstein's 1922 Visit to Paris

10.20944/preprints202001.0273.v1 ◽

2020 ◽

Author(s):

CS Unnikrishnan

Keyword(s):

Empirical Data ◽

Albert Einstein ◽

Universal Time ◽

Time Dilation ◽

Henri Bergson ◽

Atomic Clocks ◽

Time Duration ◽

Main Text ◽

Made In

In 1922, Albert Einstein visited Paris and interacted extensively with an illustrious section of the French academia. In overfilled sessions at the Coll\`{e}ge de France and the Sorbonne, Einstein explained his theories of relativity, and prominent physicists, mathematicians and philosophers listened, debated, questioned and explored facets of relativity. The 1922 visit had its echoes in the life and works of many who participated, particularly decisive for Einstein and the philosopher Henri Bergson. This essay examines that eventful visit, focusing on the physical and logical aspects of Bergson's critique, with physics commentaries, linking prominent French physicists and mathematicians Langevin, Painlev\'{e}, Hadamard, Becquerel, Sagnac, and Kastler. I give particular attention to the logical and empirical accuracy of the physics issues involved, delineating Bergson's exact reasoning for his philosophical enthusiasm in Einstein's theory and for the ensuing critique. Bergson's philosophical stand on duration and simultaneity is reassessed in the context of later developments in cosmological physics as well as the wealth of empirical data involving comparison of atomic clocks. Finally we are led naturally to a surprising completion of the philosopher's program on universal time, duration and simultaneity, in harmony with the time of the physicist. In the appendices after the main text I also give the physics background and easily verifiable proofs for the assertions made in the text, pertaining to relativity, simultaneity and time dilation, clearly distinguishing beliefs and facts.

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Mass spectrometry for future atomic clocks

Nature ◽

10.1038/d41586-020-01251-6 ◽

2020 ◽

Vol 581 (7806) ◽

pp. 35-36

Author(s):

Marianna S. Safronova

Keyword(s):

Mass Spectrometry ◽

Atomic Clocks

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Atomic clocks

Journal of the Institution of Electrical Engineers ◽

10.1049/jiee-3.1958.0318 ◽

1958 ◽

Vol 4 (48) ◽

pp. 647-653

Author(s):

L. Essen

Keyword(s):

Atomic Clocks

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Estimation of Thermal and Stochastic Variations of Chip Scale Atomic Clocks for Navigation of a Lunar CubeSat

Proceedings of the 51st Annual Precise Time and Time Interval Systems and Applications Meeting ◽

10.33012/2020.17302 ◽

2020 ◽

Author(s):

Margaret M. Rybak ◽

Penina Axelrad ◽

Jill Seubert ◽

Todd Ely

Keyword(s):

Atomic Clocks

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Improved Temperature Compensation of Atomic Clocks and INS Instruments using Multivariate Model-based Design Optimized for Real-world Operating Conditions.

Proceedings of the 49th Annual Precise Time and Time Interval Systems and Applications Meeting ◽

10.33012/2018.15601 ◽

2018 ◽

Author(s):

Andrew V. Dowd

Keyword(s):

Real World ◽

Temperature Compensation ◽

Multivariate Model ◽

Operating Conditions ◽

Atomic Clocks ◽

Model Based

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The Equivalence Principle

10.1093/oso/9780199658633.003.0013 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

General Relativity ◽

Special Relativity ◽

Equivalence Principle ◽

Time Dilation ◽

Gravitational Redshift ◽

Coordinate Systems ◽

Spacetime Metric

The equivalence principle is an important thinking tool to bootstrap our thinking from the inertial coordinate systems of special relativity to the more complex coordinate systems that must be used in the presence of gravity (general relativity). The equivalence principle posits that at a given event gravity accelerates everything equally, so gravity is equivalent to an accelerating coordinate system.This conjecture is well supported by precise experiments, so we explore the consequences in depth: gravity curves the trajectory of light as it does other projectiles; the effects of gravity disappear in a freely falling laboratory; and gravitymakes time runmore slowly in the basement than in the attic—a gravitational form of time dilation. We show how this is observable via gravitational redshift. Subsequent chapters will build on this to show how the spacetime metric varies with location.

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Energy and Momentum

10.1093/oso/9780199658633.003.0012 ◽

2018 ◽

Author(s):

David M. Wittman

Keyword(s):

Time Dilation ◽

Speed Of Light ◽

Massless Particles ◽

The Everyday ◽

Low Speeds ◽

Energy And Momentum ◽

Deep Relationship ◽

Insight Into ◽

Momentum Relation

Tis chapter explains the famous equation E = mc2 as part of a wider relationship between energy, mass, and momentum. We start by defning energy and momentum in the everyday sense. We then build on the stretching‐triangle picture of spacetime vectors developed in Chapter 11 to see how energy, mass, and momentum have a deep relationship that is not obvious at everyday low speeds. When momentum is zero (a mass is at rest) this energy‐momentum relation simplifes to E = mc2, which implies that mass at rest quietly stores tremendous amounts of energy. Te energymomentum relation also implies that traveling near the speed of light (e.g., to take advantage of time dilation for interstellar journeys) will require tremendous amounts of energy. Finally, we look at the simplifed form of the energy‐momentum relation when the mass is zero. Tis gives us insight into the behavior of massless particles such as the photon.

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