Archimedes force on Casimir apparatus

Shevchenko, V.; Shevrin, E.

doi:10.1142/s0217732316501662

“…Thus the trace corresponds to summing over all possible loops of this kind. This construction has been proposed in [38,39]. After incorporating the zero-point length correction from quantum gravity, the trace of the thermal heat kernel reads as follows…”

Section: Thermodynamic Dimensionmentioning

confidence: 99%

Ultraviolet dimensional reduction of spacetime with zero-point length

Mondal

2021

Preprint

0

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Among the many disparate approaches towards quantum gravity, the reduction of spacetime dimension in the ultraviolet regime is expected to be a common thread. The dimensionality of spacetime can be defined in various contexts. The spectral dimension of spacetime is defined in the context of diffusion processes on a manifold. We show that a spacetime with zero-point length has spectral dimension 3.5 when the characteristic diffusion time has the size of the zero-point length. The spectral dimension (negatively) diverges for an even shorter diffusion time, thus preventing any reliable physical interpretation in the deep ultraviolet regime. The thermodynamic dimension is defined by realizing that the free energy F (β) of a free field or ideal gas at finite temperature (β −1 ) in D dimensions scales as F ∼ β −D . Using Schwinger's proper time formalism at finite temperature, we show that for spacetime incorporating a zero-point length, the thermodynamic dimension reduces to 1.5 near the Planck scale and then to 1 in the deep ultraviolet regime. This signifies a "phase-transition" in which a (massless) bosonic ideal gas in four dimensions essentially behaves like radiation (w = 1/3) at low energies, whereas near the Planck scale, it behaves equivalently to having an equation of state parameter w = 2. Furthermore, dimension can be deduced from the potential VD(r) of interaction between two point-like sources separated at a distance r as its scaling depends on D. Comparing with the scaling behavior of conventional Yukawa-like potentials at short distances, we show that the zero-point length spacetime's ultraviolet dimension appears to be either 2 or 3 depending on the use of massive or massless force carriers as probes.

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“…In various papers [23,24], the force exerted by the gravitational field on a rigid Casimir cavity at rest on Earth has been calculated: it is directed upward and it is equal to:…”

Section: General Scheme Of the Experimentsmentioning

confidence: 99%

“…From an experimental point of view, it is important to note that in the recent past the scientific community focused on the possibility of verifying or discarding the various hypotheses by measuring the effects of the gravitational field on a Casimir cavity [16][17][18][19][20][21], in particular by performing a weighing measurement on a rigid Casimir cavity [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Progress in a Vacuum Weight Search Experiment

Avino

¹

,

Calloni

²

,

Caprara

³

et al. 2019

Physics

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We present the status of the art of the Archimedes experiment, devoted to measuring the debated interaction of quantum vacuum fluctuations and gravity. The method is essentially the weighing of the transition energy of a layered superconductor where the contribution of vacuum energy to the transition energy is expected to be relevant. The transition is obtained by modulating the temperature of the superconducting sample at a frequency of about 10 mHz and the expected change of weight is measured with a suitably designed high sensitivity cryogenic beam balance. In this paper, we present an overview of the experiment, discussing the expected signal to be measured, and presenting in particular the result of a prototype balance operated in our present laboratory. In the frequency range of the measurement, the sensitivity is affected mainly by seismic, thermal, sensor, and control noise. We discuss these points showing in particular the design of the cryogenic apparatus, the final balance, and the quiet seismic site that will host the final measurement.

show abstract

Ultraviolet dimensional reduction of spacetime with zero-point length

Mondal

¹

2022

View full text Add to dashboard Cite

Among the many disparate approaches towards quantum gravity, the reduction of spacetime dimension in the ultraviolet regime is expected to be a common thread. The spectral dimension of spacetime is defined in the context of diffusion processes on a manifold. We show that a spacetime with zero-point length has spectral dimension 3.5 when the characteristic diffusion time has the size of the zero-point length. The spectral dimension (negatively) diverges for an even shorter diffusion time, thus preventing reliable physical interpretation in the deep ultraviolet regime. The thermodynamic dimension is defined by realizing that the free energy $$F(\beta )$$ F ( β ) of a free field or ideal gas at finite temperature ($$\beta ^{-1}$$ β - 1 ) in D dimensions scales as $$F\sim \beta ^{-D}$$ F ∼ β - D . Using Schwinger’s proper time formalism, we show that for spacetime incorporating a zero-point length, the thermodynamic dimension reduces to 1.5 near the Planck scale and then to 1 in the deep ultraviolet regime. This signifies a “phase-transition” in which a (massless) bosonic ideal gas in four dimensions essentially behaves like radiation ($$w=1/3$$ w = 1 / 3 ) at low energies, whereas near the Planck scale, it behaves equivalently to having an equation of state parameter $$w=2$$ w = 2 . Furthermore, dimension can be deduced from the potential $$V_D(r)$$ V D ( r ) of interaction between two point-like sources separated at a distance r as its scaling depends on D. Comparing with the scaling behavior of conventional Yukawa-like potentials at short distances, we show that the ultraviolet dimension appears to be either 2 or 3 depending on the use of massive or massless force carriers as probes.

show abstract

Archimedes force on Casimir apparatus

Cited by 3 publications

References 22 publications

Ultraviolet dimensional reduction of spacetime with zero-point length

Ultraviolet dimensional reduction of spacetime with zero-point length

Progress in a Vacuum Weight Search Experiment

Ultraviolet dimensional reduction of spacetime with zero-point length

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