scholarly journals Generalised Kochen–Specker Theorem in Three Dimensions

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Václav Voráček ◽  
Mirko Navara
Keyword(s):  
Unit Sphere ◽  
Hidden Variables ◽  
Three Dimensions ◽  
Quantum Theories

AbstractWe show that there is no non-constant assignment of zeros and ones to points of a unit sphere in $$\mathbb{R}^3$$ R 3 such that for every three pairwisely orthogonal vectors, an odd number of them is assigned 1. This is a new strengthening of the Bell–Kochen–Specker theorem, which proves the non-existence of hidden variables in quantum theories.

PROBING BELL'S INEQUALITY WITH CLASSICAL SYSTEMS

2010 ◽  
Vol 09 (04) ◽  
pp. 395-402 ◽  
Author(s):  
D. K. FERRY
Keyword(s):  
Quantum Mechanics ◽  
Bell Inequality ◽  
Hidden Variables ◽  
Optical Polarization ◽  
Bell’S Inequality ◽  
Epr Paradox ◽  
Quantum Theories ◽  
Considerable Evidence ◽  
Classical Systems ◽  
Quantum Behavior

From the early days of quantum mechanics, there has been a discussion on the concept of reality, exemplified by the EPR paradox. To many, the idea of the paradox and the possibility of local hidden variables was dismissed by the Bell inequality. Yet, there remains considerable evidence that this inequality can be violated even by classical systems, so that experiments showing quantum behavior and the violation of the inequality must be questioned. Here, we demonstrate that classical optical polarization experiments can be shown to violate the Bell inequality. Hence, such experiments cannot be used to distinguish between classical and quantum theories.

The Avoidance of Collisions for Newtonian Bodies with Hidden Variables

1992 ◽  
Vol 45 (1) ◽  
pp. 52-59 ◽  
Author(s):  
B. D. Bramson
Keyword(s):  
Collision Avoidance ◽  
Relative Motion ◽  
Hidden Variables ◽  
Rate Of Change ◽  
Three Dimensions ◽  
Current Range ◽  
Collision Avoidance System ◽  
Moving Bodies

The collision avoidance of a pair of uniformly moving bodies is considered in three dimensions. The relative motion of the bodies yields an expression relating the time to closest approach, the minimum range, the current range and its rate of change, other variables being unobservable. A Boolean relation is then proposed that is satisfied whenever the minimum range and time to closest approach simultaneously fall below given thresholds. The relation is further studied, in particular with regard to the issue of false and premature alarms. An airborne collision avoidance system is a possible application.

scholarly journals Midpoint sets contained in the unit sphere of a normed space

2011 ◽  
Vol 48 (2) ◽  
pp. 180-192
Author(s):  
Konrad Swanepoel
Keyword(s):  
Unit Ball ◽  
Unit Sphere ◽  
Normed Space ◽  
Higher Dimensions ◽  
Three Dimensions ◽  
Closed Unit Ball ◽  
Facial Structure ◽  
Finite Dimensional ◽  
Dimensional Normed Space

The midpoint set M(S) of a set S of points is the set of all midpoints of pairs of points in S. We study the largest cardinality of a midpoint set M(S) in a finite-dimensional normed space, such that M(S) is contained in the unit sphere, and S is outside the closed unit ball. We show in three dimensions that this maximum (if it exists) is determined by the facial structure of the unit ball. In higher dimensions no such relationship exists. We also determine the maximum for euclidean and sup norm spaces.

scholarly journals New interpretation and thought experiment in quantum mechanics

2018 ◽  
Author(s):  
John joseph Taylor
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Thought Experiment ◽  
Hidden Variables ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Interpretation Of Quantum Mechanics ◽  
Multiple Dimensions ◽  
Non Local ◽  
New Interpretation

An interpretation of quantum mechanics involving multiple dimensions is proposed, as well as a thought experiment that in principle if performed correctly could either prove or disprove quantum randomness. All outcomes, of a particle’s wave function manifest but manifest in more than three dimensions, and when the wave function collapses, we see the outcome of the wave function, which only exist in three dimensions. Furthermore, a particle is a much larger object, and exists physically as a wave across more than three dimensions and our best description of this is the Schrodinger wave, because it only describes it in three dimensions. We cannot observe the particle as a wave because it is spread out as an object in which most of it exists in more than three dimensions, but when we observe the part or outcome of a wave function that does exist in three dimensions, which is when collapse occurs it leads to particle like properties, due to not being able to interact with the rest of the wave because it is confined to just interacting on a three dimensional scale because we are observing it in three dimensions. Furthermore we cannot observe the part of the wave function that exists in more than three dimensions, in three dimensions because of the principle that in order to observe an object in it's entirety it needs to be observed in all of it's dimensions. Strange phenomenon in quantum mechanics such as tunneling, can be explained by saying that there is a probability of finding the part of wave function that exists in three dimensions on the other side of the barrier, which has travelled over that barrier classically and the probability of it travelling over the barrier decreases expontentially to the width of the barrier increasing. Whether the quantum world is random, or is determined by non-local hidden variables, can be determined by a simple deductive thought experiment as outlined in this article.

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

3-D reconstruction and analysis of mammalian mitotic spindle structure

1992 ◽  
Vol 50 (1) ◽  
pp. 578-579
Author(s):  
Kent McDonald ◽  
David Mastronarde ◽  
Rubai Ding ◽  
Eileen O'Toole ◽  
J. Richard McIntosh
Keyword(s):  
Cross Sections ◽  
Mitotic Spindle ◽  
Experimental Studies ◽  
Video Camera ◽  
Three Dimensions ◽  
Mitotic Spindles ◽  
Black And White ◽  
Reconstruction Methods ◽  
Spindle Structure ◽  
Tissue Culture Line

Mammalian spindles are generally large and may contain over a thousand microtubules (MTs). For this reason they are difficult to reconstruct in three dimensions and many researchers have chosen to study the smaller and simpler spindles of lower eukaryotes. Nevertheless, the mammalian spindle is used for many experimental studies and it would be useful to know its detailed structure.We have been using serial cross sections and computer reconstruction methods to analyze MT distributions in mitotic spindles of PtK cells, a mammalian tissue culture line. Images from EM negatives are digtized on a light box by a Dage MTI video camera containing a black and white Saticon tube. The signal is digitized by a Parallax 1280 graphics device in a MicroVax III computer. Microtubules are digitized at a magnification such that each is 10-12 pixels in diameter.

Five-Dimensional Microscopy using Widefield-Deconvolution: Practical Considerations and Biological Applications

1996 ◽  
Vol 54 ◽  
pp. 268-269
Author(s):  
W.F. Marshall ◽  
K. Oegema ◽  
J. Nunnari ◽  
A.F. Straight ◽  
D.A. Agard ◽  
...  
Keyword(s):  
Confocal Microscopy ◽  
High Speed ◽  
Laser Scanning ◽  
Ccd Camera ◽  
Image Plane ◽  
Time Lapse ◽  
Laser Scanning Confocal Microscopy ◽  
Three Dimensions ◽  
Excitation Light ◽  
Cooled Ccd

The ability to image cells in three dimensions has brought about a revolution in biological microscopy, enabling many questions to be asked which would be inaccessible without this capability. There are currently two major methods of three dimensional microscopy: laser-scanning confocal microscopy and widefield-deconvolution microscopy. The method of widefield-deconvolution uses a cooled CCD to acquire images from a standard widefield microscope, and then computationally removes out of focus blur. Using such a scheme, it is easy to acquire time-lapse 3D images of living cells without killing them, and to do so for multiple wavelengths (using computer-controlled filter wheels). Thus, it is now not only feasible, but routine, to perform five dimensional microscopy (three spatial dimensions, plus time, plus wavelength).Widefield-deconvolution has several advantages over confocal microscopy. The two main advantages are high speed of acquisition (because there is no scanning, a single optical section is acquired at a time by using a cooled CCD camera) and the use of low excitation light levels Excitation intensity can be much lower than in a confocal microscope for three reasons: 1) longer exposures can be taken since the entire 512x512 image plane is acquired in parallel, so that dwell time is not an issue, 2) the higher quantum efficiently of a CCD detect over those typically used in confocal microscopy (although this is expected to change due to advances in confocal detector technology), and 3) because no pinhole is used to reject light, a much larger fraction of the emitted light is collected. Thus we can typically acquire images with thousands of photons per pixel using a mercury lamp, instead of a laser, for illumination. The use of low excitation light is critical for living samples, and also reduces bleaching. The high speed of widefield microscopy is also essential for time-lapse 3D microscopy, since one must acquire images quickly enough to resolve interesting events.

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