Canada

**THESIS:** The ontology of spacetime should not be modelled as a single universally-shared 4D spacetime manifold.

**THE CONSENSUS SPACETIME ONTOLOGY:** The accepted ontology of classical spacetime is of a 4D differentiable manifold of events. Although different observers may assign different coordinate labels to events, it is conventionally asserted that the underlying reality is that of a single spacetime manifold. 
This single classical manifold ontology prohibits nonlocality, because there is no possibility for any form of physical interaction, except those occurring along paths in the manifold. Consequently, Bell nonlocality (EPR) remains mysterious [1].

**DIAGNOSIS:** The existence of an invariant distance measure (the spacetime interval), and smooth coordinate manifolds has been taken to imply the existence of a universally-shared smooth spacetime manifold. However, this move involves an improper conflation of two different modes of description.
The causal structure possesses invariant properties, but lacks the smooth neighborhood properties required for a manifold, whereas exactly the converse is true of the coordinate manifolds. Manifolds are smooth, but not invariant. We cannot borrow invariance from the causal structure and glue it to coordinate manifolds to create an invariant manifold.

**GR:** The tensor calculus of GR is &quot;coordinate-free&quot; in the sense that it gives consistent results, irrespective of coordinate system. However, the existence of coordinate mappings between spacetime manifolds does not imply the physical existence of a universal shared manifold. By analogy, the existence of an atlas of the human brain (allowing anatomical mapping between individual brains) does not imply the physical existence of a shared `universal brain’. A mathematical mapping does not imply a physical process.

**CONCLUSION:** To move beyond classical GR, it is necessary to abandon the image of spacetime as a single deformable 4D entity, and to replace it with a structure acknowledging the reality of the multiple coordinate manifolds. See [2] for such a `many-spaces’ proposal, including an account of quantum nonlocality.

**REFERENCES**

[1] Nicolas Brunner et al. “Bell nonlocality”. In: Rev. Mod. Phys. 86 (2 Apr. 2014), p. 419.

[2] J. C. Sharp. One Universe, Many Spaces: A Non-Local, Relativistic Quantum Spacetime
https://doi.org/10.20944/preprints201805.0003.v1

CAP Virtual Congress 2021

The Collapse of the Manifold

topology

spacetime

relativity

manifold

This meeting is a great opportunity to explore sessions and workshops designed with your professional development in mind. Present your research and exchange ideas on the latest in teaching and pedagogy. Participate in a wide range of events, activities, plenaries, and so much more, connecting you with peers and colleagues who share your commitment to excellence in physics education.

AAPT WM 22

**THESIS:** The ontology of spacetime should not be modelled as a single universally-shared 4D spacetime manifold.

**THE CONSENSUS SPACETIME ONTOLOGY:** The accepted ontology of classical spacetime is of a 4D differentiable manifold of events. Although different observers may assign different coordinate labels to events, it is conventionally asserted that the underlying reality is that of a single spacetime manifold. 
This single classical manifold ontology prohibits nonlocality, because there is no possibility for any form of physical interaction, except those occurring along paths in the manifold. Consequently, Bell nonlocality (EPR) remains mysterious [1].

**DIAGNOSIS:** The existence of an invariant distance measure (the spacetime interval), and smooth coordinate manifolds has been taken to imply the existence of a universally-shared smooth spacetime manifold. However, this move involves an improper conflation of two different modes of description.
The causal structure possesses invariant properties, but lacks the smooth neighborhood properties required for a manifold, whereas exactly the converse is true of the coordinate manifolds. Manifolds are smooth, but not invariant. We cannot borrow invariance from the causal structure and glue it to coordinate manifolds to create an invariant manifold.

**GR:** The tensor calculus of GR is "coordinate-free" in the sense that it gives consistent results, irrespective of coordinate system. However, the existence of coordinate mappings between spacetime manifolds does not imply the physical existence of a universal shared manifold. By analogy, the existence of an atlas of the human brain (allowing anatomical mapping between individual brains) does not imply the physical existence of a shared `universal brain’. A mathematical mapping does not imply a physical process.

**CONCLUSION:** To move beyond classical GR, it is necessary to abandon the image of spacetime as a single deformable 4D entity, and to replace it with a structure acknowledging the reality of the multiple coordinate manifolds. See [2] for such a `many-spaces’ proposal, including an account of quantum nonlocality.

**REFERENCES**

[1] Nicolas Brunner et al. “Bell nonlocality”. In: Rev. Mod. Phys. 86 (2 Apr. 2014), p. 419.

[2] J. C. Sharp. One Universe, Many Spaces: A Non-Local, Relativistic Quantum Spacetime
https://doi.org/10.20944/preprints201805.0003.v1

technical paper

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Introduction: A great challenge in quantitative dynamic positron emission tomography (PET) imaging is to determine the exact volumes of interest (VOI) with which one wants to work. They have a tremendous impact on the time-activity curves that are used to extract the pharmacokinetic coefficients. Since PET images are functional and not anatomical, using a bijective relationship with a computed tomography (CT) co-image is neither the sole nor the best possibility. In recent years, many publications have come with ingenious methods to work directly with the PET images, ranging from machine learning algorithms to manual toil to define regions. These techniques have different uses, mainly in the hope of enabling easier and more efficient tumor delimitation. In the case of dynamic images, the temporal aspect of the imaging procedure changes the methods that can be implemented. Furthermore, the need to delimitate specific and precise functional sites render the whole operation computationally and physically challenging, especially in the absence of a common and well-established methodology. 
Methodology: In this project, a novel approach using a gradient-based segmentation was used on pre-clinical dynamic PET images on rats. Fourteen different animals were used under similar pre-clinical conditions. The developed segmentation technique uses properties of the image itself, relying on already known properties of the radio-drug used in order to segment automatically the kidney of the animal. The work was conducted using the mini-PET scanner at the Montreal Neurological Institute, according to the ethical guideline from the University of Montréal and the Canadian Tri-Council.
Results: From the preliminary data, the proposed method has a relevant rate of success on clinical images in delimitating the volumes of interest. The respective time-activity curves follow the general pattern of the manual delimitations done by experts, yet with non-negligible differences. So far, the proposed technique offers good result on 8 of the 14 rats, as compared to 12 rats when using a manual segmentation. The greatest strength of the algorithm is its ability to reproduce the same results notwithstanding the operator. The technique can also quantify movement in the organ of interest and work in spite of a great amount of Gaussian noise. 
Keywords: Nuclear Medicine, pre-clinical dynamic PET imaging, pharmacokinetic

On the rationale for a standardized pre-clinical segmentation technique in PET pharmacokinetic

Two dimensional (2D) materials are tempting for nano-electromechanical systems (NEMS), as they are atomically thin, have low mass and high flexibility. 2D materials have tunable optical and electronic properties, and can display other exotic properties, such as superconductivity. Over the last decade, scientists have begun stacking 2D materials into heterostructures that have desirable properties. One heterostructure is twisted bilayer graphene (TBG), which is comprised of two monolayers of graphene stacked at a rotated angle. If the angle of rotation is 1.1 degree, this material can display superconductivity at cryogenic temperatures.

The goal of this work is to model 2D drums, and to prepare sample fabrication techniques for NEMS devices. We developed analytic and numerical approximations for the motion of a 2D drum resonator. We use thin plate solutions due to a non-zero bending rigidity, and assumed low strain . We contrasted these solutions to linear and nonlinear membranes, where tension forces dominate. We consider nonlinearities inherent in the deflection driven by electrostatic forces and where strain dominates over rigidity. We also describe how finite element models can be constructed in Comsol, where the vanishing thinness makes conventional models impractical. These agree with the analytic plate approximations. 

We use flake exfoliation, pick up and placement methods to fabricate heterostructures. We produce graphene flakes via mechanical exfoliation from low residue tape. We detail techniques for optimized cleanliness and monolayer production. The flake pick up is verified via optical and atomic force microscopy (AFM). Our eventual aim is to study a 2D material when it forms the top plate of a capacitor in an LC circuit – allowing a light mass resonator for quantum nanomechanics.

Towards 2D materials as Quantum Nano-Electromechanical Systems

Molybdenum possesses seven stable isotopes and the relative amounts of these isotopes are found to vary in nature. This is because physical and chemical processes can redistribute the isotopes in a system due to the differences atomic masses. Specific processes can leave an “isotopic fingerprint” that may be recorded in the isotopic composition of the element in a given sample. The interpretation of these data can enable one to elucidate source(s) and processes that may have affected the element. An important example of a potential Mo source is petroleum coke (PC). This is a by-product from the extraction of crude oil from the Oil Sands in northern Alberta and although it is employed as a fuel source, it is not used as quickly as it is produced, allowing it to accumulate on site [1]. There is evidence PC dust spread by wind contributes to an increase in polycyclic aromatic hydrocarbons (PAH) and polycyclic aromatic compounds (PAC) accumulating in lichen samples in forests in the Athabasca Oil Sands Region [2]. This could mean that trace metals are deposited in forests or bodies of water. Natural sources of the surrounding oil sands and bitumen seeps mean that the Athabasca River contains relatively high concentrations of metals compared to glacial counterparts. It is vital to distinguish between the natural and anthropogenic inputs so that appropriate procedures can be put in place to minimize human impacts on the region. Concentration measurements of Mo in aqueous environments provide ambiguous results as they do not necessarily distinguish between natural and industrial sources. Isotope abundance data can provide additional information on the source and history of the material. This project measured the isotopic composition of Mo leached from PC. Isotope determination was done using the double spike method measured with a Neptune multi-collector ICP-MS. The δ97/95 values for three oven dried PC leachate samples were determined to be +0.13 ‰, +0.34 ‰, and +0.81 ‰ with a 2σ uncertainty of 0.06 ‰. These samples had concentrations of 3.16, 9.47, and 0.55 µg/L respectively (uncertainty of 5 %). The isotopic composition of samples from this region gives a better understanding of the sources and sinks of Mo and can be combined with snow, lichens, and water to identify potential environmental concerns caused by PC distributed by wind.
1. J. M. Robertson et al. Aqueous- and solid-phase molybdenum geochemistry of oil sands fluid petroleum coke deposits, Alberta, Canada. Chemosphere 217, (2019).
2. M. S. Landis et al. Source apportionment of an epiphytic lichen biomonitor to elucidate the sources and spatial distribution of polycyclic aromatic hydrocarbons in the Athabasca Oil Sands Region, Alberta, Canada. Science of the Total Environment 654, (2019).

Molybdenum stable isotope measurements of petroleum coke in the Athabasca Oil Sands Region

The potential breakdown of the notion of a metric at high energy scales could imply the existence of a fundamental minimal length scale below which distances cannot be resolved. One approach to realizing this minimum length scale is construct a quantum field theory with a bandlimit on the field. We report on an investigation of the effects of imposing a field bandlimit on a curved and compact spacetime. To achieve this operationally, we couple two Gaussian-smeared UDW detectors to a scalar field on a S^2 x R spherical spacetime through Dirac-delta switching. Delta switching allows for a non-perturbative analysis that includes higher order effects due to the bandlimit. The bandlimit is implemented through a cut-off of the allowable angular momentum modes of the field. We find that the detectors are less sensitive to the bandlimit on the spherical spacetime, and observe features similar to flat spacetime. These include the response of the detectors depending on their geometry and that smaller detectors couple in a stronger manner to the field. 
We also explore two squeezed detector setups in both flat and spherical spacetimes, and find notable difference between the two cases. Due to the compact nature of spherical space, the lack of dissipation of any perturbation to the field results in locally excited signals of the field traveling from pole to pole in the spacetime. Quite strikingly, squeezing increases the response of the detectors in flat space but decreases the response on the spherical spacetime. Moreover, we find that squeezing on a sphere introduces extra anisotropies that could be exploited to amplify or weaken the response of the second detector.

Bandlimited UDW detector dynamics on 2+1 flat and spherical spacetimes

Liquid-phase exfoliation (LPE) is a low-cost and scalable technique for producing a wide range of van der Waals nanomaterials that can be incorporated into existing laboratory sample and industrial material production. Liquid-phase exfoliated nanomaterials have the potential to produce devices quickly and at low-cost, with colloidal dispersions easily adaptable to existing production methods. Other methods of nanomaterial production, such as chemical vapour deposition (CVD) and mechanical exfoliation can be costly, time-consuming and require complicated equipment to produce comparatively small area devices. Such methods are excellent for laboratory-scale samples to examine physical properties and produce proof of concept devices. However, LPE can and will bridge the gap towards real-world applications that require faster, easier and more cost-effective production methods. In this work, we investigate the saturable absorption and Kerr nonlinearity of graphene fabricated by LPE and CVD. 

Thin films of LPE graphene were produced on BK7 glass substrates, and compared to CVD graphene transferred onto an identical substrate. Through careful consideration of the concentration of graphene dispersion and deposition methods, very thin films of graphene can be prepared. Atomic force microscopy (AFM) measurements showed effective bi-layer graphene thickness for the LPE samples. Z-scan measurements performed with 180 fs pulses at a wavelength of 1030 nm reveal that both LPE and CVD graphene display strong saturable absorption characteristics, with a nonlinear absorption coefficient (*β*) approaching -104 cm/GW and a Kerr nonlinearity (*n2*) of -1 cm2/GW. Such strong saturable absorption is ideal for devices such as mode-lockers for ultrafast pulsed lasers. The magnitude of the nonlinear absorption coefficient of the LPE graphene increases with pulse duration, *τ*, up to 105 cm/GW at around *τ* = 10 ps. These results pave the way for the use of LPE graphene in nonlinear optical applications such as frequency generation and mode locking.

Nonlinear optical properties of graphene: liquid-phase exfoliation vs chemical vapour deposition

In this research project, I calculated the high-harmonic spectrum from a 1D periodic potential. I investigated numerical methods for solving the 1D time-dependent Schrodinger equation of a particle in a double-well potential, as well as determining its ground state. I used the Crank Nicolson method [1], which is a finite difference method that can be used for numerically solving second-order partial differential equations. Using this method, I calculated the time evolution of an electronic wave function in a harmonic potential. My code was bench-marked against analytic solutions of the harmonic oscillator wave functions. I extended the use of this code by implementing the imaginary time method [2] to determine the ground state of an electron in a double-well potential. The time-independent Schrodinger equation is solved in the Bloch state basis to calculate the band structure of two different 1D periodic potentials. The calculations of dispersion relation are used to calculate the High Harmonic Spectrum and the final results are compared with [3].

[1] Wachter, C. (2017). Numerical Solution of the Time-Dependent 1D-Schrodinger Equation using Absorbing Boundary Conditions (Bachelor Thesis, University of Graz, Austria). Retrieved from https://physik.uni-graz.at/~pep/Theses/BachelorThesis_Wachter_2017.pdf

[2] Williamson, A. (1996). Quantum Monte Carlo Calculations of Electronic Excitations.
Retrieved from http://www.tcm.phy.cam.ac.uk/~ajw29/thesis/node27.html

[3] Wu, M. (2015). Attosecond Transient Absorption in Gases and High Harmonic Generation in Solids (Doctoral dissertation, Louisana State University, USA). Retrieved from https://digitalcommons.lsu.edu/cgi/viewcontent.cgi?article=4320&context=gradschool_dissertations

Calculation of High Harmonic Spectrum from a 1D periodic potential

Blood banks all around the world store blood for several weeks ensuring the availability of blood for transfusion medicine. Although the storage conditions have been optimized for decades it has become evident that red blood cells (RBC) undergo numerous changes when being stored.
We investigated the effect of storage on the nanoscopic bending rigidity of RBC membranes with a combination of Molecular Dynamics simulations, inelastic neutron scattering and diffuse X-ray scattering [1]. Coarse grained (CG) models of RBC membranes were created by matching experimental lipidomic analysis. It was found experimentally that the concentration of fatty acids and cholesterol changes during storage and aged membranes were mimicked by adjusting the lipid composition accordingly. 
Solid supported membrane stacks of fresh and stored RBC samples were prepared. X-ray diffraction experiments were then conducted at high relative humidity allowing to reconstruct the membrane surface fluctuations from diffuse scattering signals using a GPU accelerated workstation. These experiments were complemented by Neutron Spin Echo measurements on RBC vesicles which probe the membrane fluctuations directly. Bending moduli of 1.8 kBT and 15.4 kBT were measured in excellent agreement with the simulation data.
[1] Himbert et al., “The Nanoscopic Bending Rigidity of Red Blood Cell Membranes”, in preparation

THE NANOSCOPIC BENDING RIGIDITY OF RED BLOOD CELL MEMBRANES

Accelerator Science is both a discipline in its own right within modern physics and provides highly powerful tools for discovery and innovation in many other fields of scientific research. Accelerators do support different disciplines of subatomic physics, material sciences, life sciences and applications in research and industry. Accelerator Science Community does perform R&D to improve operational facilities and prepare technologies for new facilities unveiling new opportunities and unprecedented performance parameters. Having delivered nearly five decades of discovery, TRIUMF has a vibrant reputation globally as Canada’s particle accelerator laboratory and a hub for particle accelerator physics and technology with a wide network of international connections. In collaboration with CLS, the Fedoruk Centre and Canadian Universities, we want to grow the impact of Accelerator Science in Canada on the society and the potential to address key issues of the society of today.

Accelerator Science in Canada

Magnetic Resonance Imaging (MRI) is a powerful imaging modality with excellent soft tissue contrast. Contrast agent such as iron oxide nanoparticles can be used to “tag” individual cells, distorting the magnetic field around them and allowing the imaging of single cells. Time-lapse MRI can be used to track the motion of tagged cells, providing insights in the studies of inflammatory diseases and metastasis of cancer. Current methods have a very limited temporal resolution resulting in a detection limit of 1µm/s . In addition, the manual cell counting is time consuming and difficult. 
In this work, a dictionary learning based technique has been developed to accelerate the MRI data acquisition and aid in the task of locating cells. Dictionary learning is a machine learning technique, in which features of an image can be ‘learned’ as atoms. Images can be represented using a sparse combination of atoms. The sparsity property can be used as a constraint in non-linear image reconstruction with data sampled below the Nyquist criteria. The undersampling improved the temporal resolution of the in-vivo measurements by approximately an order of magnitude. The dictionary atom coefficients provided information on the cell locations for feature detection.

Magnetic Resonance Imaging Data Acquisition Acceleration and Feature Detection with Dictionary Learning

The versatility of gamma-ray spectroscopy has given rise to its many applications, from quantification of trace elements in a sample to maintaining nuclear material safeguards. Depending on the application and gamma-ray detector, there is often a compromise made between detection efficiency and energy resolution. While characterizing or quantifying trace radionuclide concentrations in an unknown sample, energy resolution is often the more important property. In these situations, high-purity germanium (HPGe) detectors are the detector of choice as they have a superior energy resolution which significantly reduce measurement uncertainties and improve minimum detection limits.

Applications using HPGe detectors are limited to counting rates on the order of a few tens of thousands of counts per second (cps) before the performance of the detector is severely diminished. The limiting factor for high counting rate measurements comes from the need to shape signals with a relatively long shaping time, on the order of 1-6 μs, to maintain good energy resolution. At higher counting rates however, if a signal is received while a previous signal is still being shaped, pulse-pileup occurs. Pulse-pileup distorts the energy measurement of the previous signal and entirely drops the measurement of the second signal. Traditionally, this situation is usually handled with a pileup rejection method. At ultra high counting rates, on the order of a million cps, the percentage of the pileup rejection is so high that the spectroscopy system suffers from extremely high deadtimes.

In order to solve this critical problem, the present study aims to develop a data acquisition system capable of deconvoluting pileup signals into two or more recovered signals in real-time. This technique has been applied for NaI(Tl) and silicon drift detectors, which showed very promising results. However, applications of this technique for HPGe detectors have been unsuccessful as it relies on a fixed signal rising edge shape, a feature which cannot applied for HPGe detectors due to the variation in the rising shape. Our study has been focused on developing a deconvolution algorithm to identify and recover piled-up signals using a planar HPGe. During this development stage, signal waveforms are analyzed offline, optimizing the algorithm over a range of counting rates while building a library of the rising edge shapes. Once completed, the deconvolution algorithm will be benchmarked for various high-rate measurements. The preliminary result of the pile-up deconvolution performance will be presented.

The Collapse of the Manifold

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