scholarly journals Proper Time Operator and its Uncertainty Relation

Author(s):  
Hou Ying Yau
2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Alexander R. H. Smith ◽  
Mehdi Ahmadi

Abstract At the intersection of quantum theory and relativity lies the possibility of a clock experiencing a superposition of proper times. We consider quantum clocks constructed from the internal degrees of relativistic particles that move through curved spacetime. The probability that one clock reads a given proper time conditioned on another clock reading a different proper time is derived. From this conditional probability distribution, it is shown that when the center-of-mass of these clocks move in localized momentum wave packets they observe classical time dilation. We then illustrate a quantum correction to the time dilation observed by a clock moving in a superposition of localized momentum wave packets that has the potential to be observed in experiment. The Helstrom-Holevo lower bound is used to derive a proper time-energy/mass uncertainty relation.


2003 ◽  
Vol 8 (4) ◽  
pp. 4-5
Author(s):  
Christopher R. Brigham ◽  
James B. Talmage

Abstract Permanent impairment cannot be assessed until the patient is at maximum medical improvement (MMI), but the proper time to test following carpal tunnel release often is not clear. The AMA Guides to the Evaluation of Permanent Impairment (AMA Guides) states: “Factors affecting nerve recovery in compression lesions include nerve fiber pathology, level of injury, duration of injury, and status of end organs,” but age is not prognostic. The AMA Guides clarifies: “High axonotmesis lesions may take 1 to 2 years for maximum recovery, whereas even lesions at the wrist may take 6 to 9 months for maximal recovery of nerve function.” The authors review 3 studies that followed patients’ long-term recovery of hand function after open carpal tunnel release surgery and found that estimates of MMI ranged from 25 weeks to 24 months (for “significant improvement”) to 18 to 24 months. The authors suggest that if the early results of surgery suggest a patient's improvement in the activities of daily living (ADL) and an examination shows few or no symptoms, the result can be assessed early. If major symptoms and ADL problems persist, the examiner should wait at least 6 to 12 months, until symptoms appear to stop improving. A patient with carpal tunnel syndrome who declines a release can be rated for impairment, and, as appropriate, the physician may wish to make a written note of this in the medical evaluation report.


2020 ◽  
Author(s):  
Konstantin B. Yushkov ◽  
Vladimir Ya. Molchanov ◽  
E.A. Khazanov

Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan

This chapter discusses the kinematics of point particles undergoing any type of motion. It introduces the concept of proper time—the geometric representation of the time measured by an accelerated clock. It also describes a world line, which represents the motion of a material point or point particle P, that is, an object whose spatial extent and internal structure can be ignored. The chapter then considers the interpretation of the curvilinear abscissa, which by definition measures the length of the world line L representing the motion of the point particle P. Next, the chapter discusses a mathematical result popularized by Paul Langevin in the 1920s, the so-called ‘Langevin twins’ which revealed a paradoxical result. Finally, the transformation of velocities and accelerations is discussed.


Author(s):  
David M. Wittman

This chapter shows that the counterintuitive aspects of special relativity are due to the geometry of spacetime. We begin by showing, in the familiar context of plane geometry, how a metric equation separates frame‐dependent quantities from invariant ones. The components of a displacement vector depend on the coordinate system you choose, but its magnitude (the distance between two points, which is more physically meaningful) is invariant. Similarly, space and time components of a spacetime displacement are frame‐dependent, but the magnitude (proper time) is invariant and more physically meaningful. In plane geometry displacements in both x and y contribute positively to the distance, but in spacetime geometry the spatial displacement contributes negatively to the proper time. This is the source of counterintuitive aspects of special relativity. We develop spacetime intuition by practicing with a graphic stretching‐triangle representation of spacetime displacement vectors.


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