Model Of Spacetime Foam Research Articles

On properties of the distribution of virtual wormholes in a vacuum

A model of spacetime foam in the form of an arbitrary distribution of spherical Euclidean wormholes is considered. A method for constructing the exact solution of Einstein’s Euclidean equations for the metric corresponding to this model is proposed. In the framework of our model, we obtain the expression for the Euclidean action and its dependence on the parameters of wormholes in the explicit form. It is shown how the solutions obtained makes it possible to determine all possible correlation functions associated with the parameters of virtual wormholes in the vacuum state.

Lorentz and CPT breaking in gamma-ray burst neutrinos from string theory

Previous studies on high-energy gamma-ray burst neutrinos from IceCube suggest a neutrino speed variation at the Lorentz violation (LV) scale of ~6.4 × 1017 GeV, with opposite velocity variances between neutrinos and antineutrinos. Within a spacetime foam model, inspired by string theory, we develop an approach to describe the suggested neutrino/antineutrino propagation properties with both Lorentz invariance and CPT symmetry breaking. A threshold analysis on the bremsstrahlung of electron-positron pair (ν → νee+) for the superluminal (anti)neutrino is performed. We find that, due to the energy violation caused by the quantum foam, such reaction may be restricted to occur at sufficient high energies and could even be kinematically forbidden. Constraints on neutrino LV from vacuum ee+ pair emission are naturally avoided. Future experiments are appealed to test further the CPT violation of cosmic neutrinos and/or neutrino superluminality.

Lorentz- and CPT-violating neutrinos from string/D-brane model

We show that the space-time foam model from string/D-brane theory predicts a scenario in which neutrinos can possess linearly energy dependent speed variation, together with an asymmetry between neutrinos and antineutrinos, indicating the possibility of Lorentz and CPT symmetry violation for neutrinos. Such a scenario is supported by a phenomenological conjecture from the possible associations of IceCube ultrahigh-energy neutrino events with the gamma-ray bursts. It is also consistent with the constraints set by the energy-losing decay channels (e.g., e+e− pair emission, or neutrino splitting) upon superluminal neutrino velocities. We argue that the plausible violations of energy-momentum conservation during decay may be responsible for the stable propagation of these neutrinos, and hence for the evasion of relevant constraints.

Probing Spacetime Foam with Extragalactic Sources of High-Energy Photons

Quantum fluctuations can endow spacetime with a foamy structure. In this review article, we discuss our various proposals to observationally constrain models of spacetime foam. One way is to examine if the light wave-front from a distant quasar or GRB can be noticeably distorted by spacetime-foam-induced phase incoherence. As the phase fluctuations are proportional to the distance to the source but inversely proportional to the wavelength, ultra-high energy photons (>1 TeV) from distant sources are particularly useful. We elaborate on several proposals, including the possibility of detecting spacetime foam by observing “seeing disks” in the images of distant quasars and active galactic nuclei. We also discuss the appropriate distance measure for calculating the expected angular broadening. In addition, we discuss our more recent work in which we investigate whether wave-front distortions on small scales (due to spacetime foam) can cause distant objects become undetectable because the phase fluctuations have accumulated to the point at which image formation is impossible. Another possibility that has recently become accessible is to use interferometers to observe cosmologically distant sources, thereby giving a large baseline perpendicular to the local wave vector over which the wave front could become corrugated and thus distorted, reducing or eliminating its fringe visibility. We argue that all these methods ultimately depend on the availability of ways (if any) to carry out proper averaging of contributions from different light paths from the source to the telescope.

Ultrahigh-energy photons from LHAASO as probes of Lorentz symmetry violations

The Large High Altitude Air Shower Observatory (LHAASO) is one of the most sensitive gamma-ray detector arrays currently operating at TeV and PeV energies. Recently the LHAASO experiment detected ultra-high-energy (UHE; ${E}_{\ensuremath{\gamma}}\ensuremath{\gtrsim}100\text{ }\text{ }\mathrm{TeV}$) photon emissions up to 1.4 PeV from twelve astrophysical gamma-ray sources. We point out that the detection of cosmic photons at such energies can constrain the photon self-decay motivated by superluminal Lorentz symmetry violation (LV) to a higher level, thus can put strong constraints to certain LV frameworks. Meanwhile, we suggest that the current observation of the PeV-scale photon with LHAASO may provide hints to permit a subluminal type of Lorentz violation in the proximity of the Planckian regime, and may be compatible with the light speed variation at the scale of $3.6\ifmmode\times\else\texttimes\fi{}{10}^{17}\text{ }\text{ }\mathrm{GeV}$ recently suggested from gamma-ray burst (GRB) time delays. We further propose detecting PeV photons coming from extragalactic sources with future experiments, based on LV-induced threshold anomalies of ${e}^{+}{e}^{\ensuremath{-}}$ pair-production, as a crucial test of subluminal Lorentz violation. We comment that these observations are consistent with a D-brane/string-inspired quantum-gravity framework, the space-time foam model.

Light speed variation in a string theory model for space-time foam

We revisit a supersymmetric string model for space-time foam, in which bosonic open-string states, such as photons, can possess quantum-gravity-induced velocity fluctuations in vacuum. We argue that the suggestion of light speed variation with lower bound from gamma-ray burst photon time delays can serve as a support for this string-inspired framework, through connecting the experimental finding with model predictions. We also derive the value of the effective quantum-gravity mass in this framework, and give a qualitative study on the model-dependent coefficients. Constraints from birefringent effects and/or photon decays, including the novel γ-decay constraint obtained here from the latest Tibet ASγ near-PeV photon, are also found to be consistent with predictions in such a quantum-gravity scheme. Future observation that can testify further the theory is suggested.

On the Physical Implications of Hawking's Spacetime Foam

AbstractHawking's spacetime foam model predicts that due to quantum fluctuations, spacetime is filled with black hole like objects. We argue that Hawking's model implies a cosmological constant of the observed order and that it also solves the problem of time in quantum gravity.

Novel foamy origin for singlet fermion masses

We show how masses for singlet fermions can be generated by interactions with a D-particle model of space-time foam inspired by brane theory. It has been shown previously by one of the authors (N.E.M.) such interactions may generate generate dynamically small masses for charged fermions via the recoils of D-particle defects interacting with photons. In this work we consider the direct interactions of D-particle with uncharged singlet fermions such as right-handed neutrinos. Quantum fluctuations of the lattice of D-particles have massless vector (spin-one) excitations that are analogues of phonons. These mediate forces between the singlet fermions, generating large dynamical masses that may be communicated to light neutrinos via the seesaw mechanism.

Virtual black holes in a third quantized formalism

In this paper, we will analyse virtual black holes using the third quantization formalism. As the virtual black hole model depends critically on the assumption that the quantum fluctuations dominate the geometry of spacetime at Planck scale, we will analyse the quantum fluctuations for a black hole using third quantization. We will demonstrate that these quantum fluctuations depend on the factor ordering chosen. So, we will show that only certain values of the factor ordering parameter are consistent with virtual black holes model of spacetime foam.

NEW CONSTRAINTS ON QUANTUM GRAVITY FROM X-RAY AND GAMMA-RAY OBSERVATIONS

One aspect of the quantum nature of spacetime is its "foaminess" at very small scales. Many models for spacetime foam are defined by the accumulation power $\alpha$, which parameterizes the rate at which Planck-scale spatial uncertainties (and thephase shifts they produce) may accumulate over large path-lengths. Here $\alpha$ is defined by theexpression for the path-length fluctuations, $\delta \ell$, of a source at distance $\ell$, wherein $\delta \ell \simeq \ell^{1 - \alpha} \ell_P^{\alpha}$, with $\ell_P$ being the Planck length. We reassess previous proposals to use astronomical observations ofdistant quasars and AGN to test models of spacetime foam. We show explicitly how wavefront distortions on small scales cause the image intensity to decay to the point where distant objects become undetectable when the path-length fluctuations become comparable to the wavelength of the radiation. We use X-ray observations from {\em Chandra} to set the constraint $\alpha \gtrsim 0.58$, which rules out the random walk model (with $\alpha = 1/2$). Much firmer constraints canbe set utilizing detections of quasars at GeV energies with {\em Fermi}, and at TeV energies with ground-based Cherenkovtelescopes: $\alpha \gtrsim 0.67$ and $\alpha \gtrsim 0.72$, respectively. These limits on $\alpha$ seem to rule out $\alpha = 2/3$, the model of some physical interest.

Stringy models of modified gravity: space-time defects and structure formation

Starting from microscopic models of space-time foam, based on braneuniverses propagating in bulk space-times populated by D0-branedefects (``D-particles''), we arrive at effective actions used by alow-energy observer on the brane world to describe his/herobservations of the Universe. These actions include, apart from themetric tensor field, also scalar (dilaton) and vector fields, thelatter describing the interactions of low-energy matter on the braneworld with the recoiling point-like space-time defect(D-particle). The vector field is proportional to the recoil velocityof the D-particle and as such it satisfies a certain constraint. Thevector breaks locally Lorentz invariance, which however is assumed tobe conserved on average in a space-time foam situation, involving theinteraction of matter with populations of D-particle defects. In thispaper we clarify the role of fluctuations of the vector field onstructure formation and galactic growth. In particular we demonstratethat, already at the end of the radiation era, the (constrained)vector field associated with the recoil of the defects provides theseeds for a growing mode in the evolution of the Universe. Such agrowing mode survives during the matter dominated era, provided thevariance of the D-particle recoil velocities on the brane is largerthan a critical value. We note that in this model, as a result ofspecific properties of D-brane dynamics in the bulk, there is no issueof overclosing the brane Universe for large defect densities. Thus, inthese models, the presence of defects may be associated withlarge-structure formation. Although our string inspired models dohave (conventional, from a particle physics point of view) dark mattercomponents, nevertheless it is interesting that the role of``extra'' dark matter is also provided by the population of massivedefects. This is consistent with the weakly interacting character ofthe D-particle defects, which predominantly interact onlygravitationally.

Using observations of distant quasars to constrain quantum gravity

Aims. The small-scale nature of spacetime can be tested with observations of distant quasars. We comment on a recent paper by Tamburini et al. (A&A, 533, 71) which claims that Hubble Space Telescope observations of the most distant quasars place severe constraints on models of foamy spacetime. Methods. If space is foamy on the Planck scale, photons emitted from distant objects will accumulate uncertainties in distance and propagation directions thus affecting the expected angular size of a compact object as a function of redshift. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We also address the mechanics of carrying out such a test. We draw upon our previously published work on this subject (Christiansen et al. 2011), which carried out similar tests as Tamburini et al. and also went considerably beyond their work in several respects. Results. When calculating the path taken by photons as they travel from a distant source to Earth, one must use the comoving distance rather than the luminosity distance. This then also becomes the appropriate distance to use when calculating the angular broadening expected in a distant source. The use of the wrong distance measure causes Tamburini et al. to overstate the constraints that can be placed on models of spacetime foam. In addition, we consider the impact of different ways of parametrizing and measuring the effects of spacetime foam. Given the variation of the shape of the point-spread function (PSF) on the chip, as well as observation-specific factors, it is important to select carefully -- and document -- the comparison stars used as well as the methods used to compute the Strehl ratio.

No quantum gravity signature from the farthest quasars

Context: Strings and other alternative theories describing the quantum properties of space-time suggest that space-time could present a foamy structure and also that, in certain cases, quantum gravity (QG) may manifest at energies much below the Planck scale. One of the observable effects could be the degradation of the diffraction images of distant sources. Aims: We searched for this degradation effect, caused by QG fluctuations, in the light of the farthest quasars (QSOs) observed by the Hubble Space Telescope with the aim of setting new limits on the fluctuations of the space-time foam and QG models. Methods: We developed a software that estimates and compares the phase variation in the interference patterns of the high-redshift QSOs, taken from the snapshot survey of HST-SDSS, with those of stars that are expected to not be affected by QG effects. We used a two-parameter function to determine, for each test star and QSO, the maximum of the diffraction pattern and to calculate the Strehl ratio. Results: Our results go far beyond those already present in the literature. By adopting the most conservative approach where the correction terms, that describe the possibility for space-time fluctuations cumulating across long distances and partially compensate for the effects of the phase variations, are taken into account. We exclude the random walk model and most of the holographic models of the space-time foam. Without considering these correction terms, all the main QG scenarios are excluded. Finally, our results show the absence of any directional dependence of QG effects and the validity of the cosmological principle with an independent method; that is, viewed on a large scale, the properties of the Universe are the same for all observers, including the effects of space-time fluctuations.

D-foam-induced flavor condensates and breaking of supersymmetry in free Wess-Zumino fluids

Recently we argued that a particular model of string-inspired quantum space-time foam (D-foam) may induce oscillations and mixing among flavoured particles. As a result, rather than the mass-eigenstate vacuum, the correct ground state to describe the underlying dynamics is the flavour vacuum, proposed some time ago by Blasone and Vitiello as a description of quantum field theories with mixing. At the microscopic level, the breaking of target-space supersymmetry is induced in our space-time foam model by the relative transverse motion of brane defects. Motivated by these results, we show that the flavour vacuum, introduced through an inequivalent representation of the canonical (anti-) commutation relations, provides a vehicle for the breaking of supersymmetry (SUSY) at a low-energy effective field theory level; on considering the flavour-vacuum expectation value of the energy-momentum tensor and comparing with the form of a perfect relativistic fluid, it is found that the bosonic sector contributes as dark energy while the fermion contribution is like dust. This indicates a strong and novel breaking of SUSY, of a non-perturbative nature, which may characterize the low energy field theory of certain quantum gravity models.

Limits on spacetime foam

Plausibly spacetime is "foamy" on small distance scales, due to quantum fluctuations. We elaborate on the proposal to detect spacetime foam by looking for seeing disks in the images of distant quasars and AGNs. This is a null test in the sense that the continued presence of unresolved "point" sources at the milli-arc second level in samples of distant compact sources puts severe constraints on theories of quantized spacetime foam at the Planckian level. We discuss the geometry of foamy spacetime, and the appropriate distance measure for calculating the expected angular broadening. We then deal with recent data and the constraints they put on spacetime foam models. While time lags from distant pulsed sources such as GRBs have been posited as a possible test of spacetime foam models, we demonstrate that the time-lag effect is rather smaller than has been calculated, due to the equal probability of positive and negative fluctuations in the speed of light inherent in such models. Thus far, images of high-redshift quasars from the Hubble Ultra-Deep Field (UDF) provide the most stringent test of spacetime foam theories. While random walk models ($\alpha = 1/2$) have already been ruled out, the holographic ($\alpha=2/3$) model remains viable. Here $\alpha \sim 1$ parametrizes the different spacetime foam models according to which the fluctuation of a distance $l$ is given by $\sim l^{1 - \alpha} l_P^{\alpha}$ with $l_P$ being the Planck length. Indeed, we see a slight wavelength-dependent blurring in the UDF images selected for this study. Using existing data in the {\it Hubble Space Telescope (HST)} archive we find it is impossible to rule out the $\alpha=2/3$ model, but exclude all models with $\alpha<0.65$. By comparison, current GRB time lag observations only exclude models with $\alpha<0.3$.

Stringy Space-Time Foam and High-Energy Cosmic Photons

In this review, I discuss briefly stringent tests of Lorentz-violating quantum space-time foam models inspired from String/Brane theories, provided by studies of high energy Photons from intense celestial sources, such as Active Galactic Nuclei or Gamma Ray Bursts. The theoretical models predict modifications to the radiation dispersion relations, which are quadratically suppressed by the string mass scale, and time delays in the arrival times of photons (assumed to be emitted more or less simultaneously from the source), which are proportional to the photon energy, so that the more energetic photons arrive later. Although the astrophysics at the source of these energetic photons is still not understood, and such non simultaneous arrivals, that have been observed recently, might well be due to non simultaneous emission as a result of conventional physics effects, nevertheless, rather surprisingly, the observed time delays can also fit excellently the stringy space-time foam scenarios, provided the space-time defect foam is inhomogeneous. The key features of the model, that allow it to evade a plethora of astrophysical constraints on Lorentz violation, in sharp contrast to other field-theoretic Lorentz-violating models of quantum gravity, are: (i) transparency of the foam to electrons and in general charged matter, (ii) absence of birefringence effects and (iii) a breakdown of the local effective lagrangian formalism.

Ultrahigh-Energy Photons as Probes of Lorentz Symmetry Violations in Stringy Space-Time Foam Models

The time delays between γ rays of different energies from extragalactic sources have often been used to probe quantum gravity models in which Lorentz symmetry is violated. It has been claimed that these time delays can be explained by or at least put the strongest available constraints on quantum gravity scenarios that cannot be cast within an effective field theory framework, such as the space-time foam, D-brane model. Here we show that this model would predict too many photons in the ultrahigh energy cosmic ray flux to be consistent with observations. The resulting constraints on the space-time foam model are much stronger than limits from time delays and allow for Lorentz violation effects way too small for explaining the observed time delays.

Implications of Space-Time Foam for Entanglement Correlations of Neutral Kaons

The role of CPT invariance and consequences for bipartite entanglement of neutral (K) mesons are discussed. A relaxation of CPT leads to a modification of the entanglement which is known as the ω effect. The relaxation of assumptions required to prove the CPT theorem are examined within the context of models of space-time foam. It is shown that the evasion of the EPR type entanglement implied by CPT (which is connected with spin statistics) is rather elusive. Relaxation of locality (through non-commutative geometry) or the introduction of an environment do not by themselves lead to a destruction of the entanglement. One model of the environment, which is based on non-critical strings and D-particle capture and recoil, leads to a specific momentum dependent stochastic contribution to the space-time metric and consequent change in the neutral meson bipartite entanglement. Although the class of models producing the omega effect is non-empty, the lack of an omega effect is demonstrated for a wide class of models based on thermal like baths which are often considered as generic models appropriate for the study of space-time foam.

Flavor condensates in brane models and dark energy

In the context of a microscopic model of string-inspired foam, in which foamy structures are provided by brany pointlike defects (D-particles) in space-time, we discuss flavor mixing as a result of flavor nonpreserving interactions of (low-energy) fermionic stringy matter excitations with the defects. Such interactions involve splitting and capture of the matter string state by the defect, and subsequent re-emission. As a result of charge conservation, only electrically neutral matter can interact with the D-particles. Quantum fluctuations of the D-particles induce a nontrivial space-time background; in some circumstances, this could be akin to a cosmological Friedman-Robertson-Walker expanding-universe, with weak (but nonzero) particle production. Furthermore, the D-particle medium can induce an Mikheyev-Smirnov-Wolfenstein-type effect. We have argued previously, in the context of bosons, that the so-called flavor vacuum is the appropriate state to be used, at least for low-energy excitations, with energies/momenta up to a dynamically determined cutoff scale. Given the intriguing mass scale provided by neutrino flavor mass differences from the point of view of dark energy, we evaluate the flavor-vacuum expectation value (condensate) of the stress-energy tensor of the $1/2$-spin fields with mixing in an effective-low-energy quantum field theory in this foam-induced curved space-time. We demonstrate, at late epochs of the Universe, that the fermionic vacuum condensate behaves as a fluid with negative pressure and positive energy; however, the equation of state has ${w}_{\mathrm{fermion}}g\ensuremath{-}1/3$ and so the contribution of the fermion-fluid flavor vacuum alone could not yield accelerating universes. Such contributions to the vacuum energy should be considered as (algebraically) additive to the flavored boson contributions, evaluated in our previous works; this should be considered as natural from (broken) target-space supersymmetry that characterizes realistic superstring/supermembrane models of space-time foam. The boson fluid is also characterized by positive energy and negative pressure, but its equation of state is, for late eras, close to ${w}_{\mathrm{boson}}\ensuremath{\rightarrow}\ensuremath{-}1$, and hence overall the D-foam universe appears accelerating at late eras.

Time delays of strings in D-particle backgrounds and vacuum refractive indices

Using standard techniques in string/D-brane scattering amplitude computations, we evaluate the scattering of open strings off D-particles in brane world scenarios. The D-particles are viewed as D3 branes wrapped up around three cycles, and their embedding in brane worlds constitutes a case of intersecting branes, among which strings are stretched, representing various types of excitations of the Standard Model (SM) particles in the low-energy limit. Our analysis, reveals interesting and novel selection rules for the resulting causal time delays, proportional to the energy of the incident matter state, from the processes of splitting, capture and re-emission of the latter by the D-particles. There are relatively large time delays only for excitations that belong to the Cartan subalgebra of the SM gauge group, which notably includes photons. We discuss the possible relevance of these results to models of space time foam with non-trivial vacuum refractive index for photons and demonstrate how current astrophysical observations can be used to discriminate low- from high-string-scale models in this context.