The lattice world, quantum foam and the universe as a metamaterial

Crouse, David T.

doi:10.1007/s00339-016-9853-9

Cited by 3 publications

(9 citation statements)

References 10 publications

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“…Although it is naturally difficult to speculate about a nonexistent theory, it is generally believed that such a theory would emerge at a scale comparable to that of the Planck energy [22]. Several theories describe a spacetime made of "quantum foam" which violates Lorentz invariance at very high energy scales [23][24][25], which would imply that the vacuum (which is dominated by these highenergy modes) need not be Lorentz invariant, justifying the abandonment of Assumption 3.…”

Section: Vib Effective Field Theory and Lorentz Invariancementioning

confidence: 99%

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Can the fluctuations of the quantum vacuum solve the cosmological constant problem?

et al. 2018

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The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum mechanics is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. Recently some of the current authors proposed that the stochastic nature of the quantum vacuum can resolve this tension [1]. By treating the fluctuations in the vacuum seriously and allowing fluctuations up to some high-energy cutoff at which Quantum Field Theory is believed to break down, a parametric resonance effect arises that leads to a slow expansion and acceleration. In this work we thoroughly examine the implications of this proposal by investigating the resulting dynamics. Firstly, we improve upon numerical calculations in the original work and show that convergence issues had overshadowed some important effects. Correct calculations reverse some of the conclusions in [1], however the premise that parametric resonance can explain a very slowly accelerating expansion appears to remain sound. After improving the resolution and efficiency of the numerical tests, we explore a wider range of cutoff energies, and examine the effects of multiple particle fields. We introduce a simple model using the Mathieu equation (a prototypical example of parametric resonance), and find that it closely matches numerical results in regimes where its assumptions are valid. Using this model, we extrapolate to find that in a Universe with 28 bosonic fields and a high-energy cutoff 40 times higher than the Planck energy, the acceleration would be comparable to what is observed.

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Section: Vib Effective Field Theory and Lorentz Invariancementioning

confidence: 99%

“…• Many proposals for quantum gravity suppose some discrete spacetime structure arises at a small invariant length scale. Such a length scale must violate Lorentz invariance [22][23][24][25].…”

Section: Cosmological Dynamics Under Semiclassical Stochastic Gravitymentioning

confidence: 99%

Can the fluctuations of the quantum vacuum solve the cosmological constant problem?

et al. 2018

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“…In 2016, upon completing the analysis of the impact of the DST model on Wheeler's quantum foam (Crouse (2016a)), Crouse considered how one could fix the problems with DST. Being at the time unburdened by any knowledge of previous work on DST (besides Weyl's work), or the fact that logical positivism (LP) and the concept of non-absolute space have fallen out of favor with physicists, mathematicians and philosophers, it took little time for us to derive Eq.…”

Section: David Crouse's Distance Formulamentioning

confidence: 99%

“…A more realizable test is described in the next section, namely, analyzing any anomalous motion of black holes and other astronomical bodies or groups of bodies. (Crouse (2016a;b)).…”

Section: Travel At the Speed Of Lightmentioning

confidence: 99%

“…Our interest in discrete space-time (DST) started from a much different topic: a simple exercise where we examined a possible explanation for the observed inertial anomalies of astronomical bodies -anomalies that are normally attributed to dark matter and dark energy (Crouse (2016a)). In that work, we treated John A. Wheeler's quantum foam that ostensibly pervades all space (Wheeler (1957)) as a solid-state material, and then studied the motion of particles and astronomical bodies traveling within this material.…”

Section: Introductionmentioning

confidence: 99%

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On the Nature of Discrete Space-Time: Part 1: The distance formula, relativistic time dilation and length contraction in discrete space-time

Crouse,

Skufca

2018

Preprint

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In this work, the relativistic phenomena of Lorentz-Fitzgerald contraction and time dilation are derived using a modified distance formula that is appropriate for discrete space. This new distance formula is different than the Pythagorean theorem but converges to it for distances large relative to the Planck length. First, four candidate formulas developed by different people over the last 70 years is discussed. Three of the formulas are shown to be identical for conditions that best describe discrete space. It is shown that this new distance formula is valid for all size-scales -from the Planck length upwards -and solves two major problems historically associated with the discrete space-time (DST) model. One problem it solves is the widely believed anisotropic nature of most discrete space models. Just as commonly believed is the second problem -the incompatibility of DST's concept of an immutable atom of space and the length contraction of this atom required by special relativity. The new formula for distance in DST solves this problem. It is shown that length contraction of the atom of space does not occur for any relative velocity of two reference frames. It is also shown that time dilation of the atom of time does not occur. Also discussed is the possibility of any object being able to travel at the speed of light for specific temporal durations given by an equation derived in this work. Also discussed is a method to empirical verify the discreteness of space by studying any observed anomalies in the motion of astronomical bodies, such as differences in the bodies' inertial masses and gravitational masses. The importance of the new distance formula for causal set theory and other theories of quantum gravity is also discussed.

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Reconditioning in Discrete Quantum Field Theory

Gudder

2017

Int J Theor Phys

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We consider a discrete scalar, quantum field theory based on a cubic 4-dimensional lattice. We mainly investigate a discrete scattering operator S(x0, r) where x0 and r are positive integers representing time and maximal total energy, respectively. The operator S(x0, r) is used to define transition amplitudes which are then employed to compute transition probabilities. These probabilities are conditioned on the time-energy (x0, r). In order to maintain total unit probability, the transition probabilities need to be reconditioned at each (x0, r). This is roughly analogous to renormalization in standard quantum field theory, except no infinities or singularities are involved. We illustrate this theory with a simple scattering experiment involving a common interaction Hamiltonian. We briefly mention how discreteness of spacetime might be tested astronomically. Moreover, these tests may explain the existence of dark energy and dark matter.

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The lattice world, quantum foam and the universe as a metamaterial

Cited by 3 publications

References 10 publications

Can the fluctuations of the quantum vacuum solve the cosmological constant problem?

Can the fluctuations of the quantum vacuum solve the cosmological constant problem?

On the Nature of Discrete Space-Time: Part 1: The distance formula, relativistic time dilation and length contraction in discrete space-time

Reconditioning in Discrete Quantum Field Theory

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