scholarly journals Time Dilation and the Equivalence of Inertial Frames

2021 ◽  
Author(s):  
Chandru Iyer ◽  
G. M. Prabhu
Keyword(s):  
Inertial Frame ◽  
Time Dilation ◽  
Three Dimensions ◽  
Relativity Theory ◽  
One Dimension ◽  
Dimensional Manifold ◽  
Principle Of Relativity ◽  
Inertial Frames ◽  
Ontological Concept ◽  
The Continuum

Abstract It is well known that simultaneity within an inertial frame is defined in relativity theory by a convention or definition. This definition leads to different simultaneities across inertial frames and the well-known principle of relativity of simultaneity. The lack of a universal present implies the existence of past, present and future as a collection of events on a four dimensional manifold or continuum wherein three dimensions are space like and one dimension is time like. However, such a continuum precludes the possibility of evolution of future from the present as all events exist ‘forever’ so to speak on the continuum with the tenses past, present and future merely being perceptions of different inertial frames. Such a far-reaching ontological concept, created by a mere convention, is yet to gain full acceptance. In this paper, we present arguments in favour of an absolute present, which means simultaneous events are simultaneous in all inertial frames, and subscribe to evolution of future from the present.

Galilean Relativity

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Inertial Frame ◽  
Vertical Component ◽  
Horizontal Component ◽  
The Other ◽  
One Dimension ◽  
Everyday Experience ◽  
Low Speed ◽  
Principle Of Relativity ◽  
Galilean Relativity ◽  
Laws Of Motion

Galilean relativity is a useful description of nature at low speed. Galileo found that the vertical component of a projectile’s velocity evolves independently of its horizontal component. In a frame that moves horizontally along with the projectile, for example, the projectile appears to go straight up and down exactly as if it had been launched vertically. The laws of motion in one dimension are independent of any motion in the other dimensions. This leads to the idea that the laws of motion (and all other laws of physics) are equally valid in any inertial frame: the principle of relativity. This principle implies that no inertial frame can be considered “really stationary” or “really moving.” There is no absolute standard of velocity (contrast this with acceleration where Newton’s first law provides an absolute standard). We discuss some apparent counterexamples in everyday experience, and show how everyday experience can be misleading.

Space-time Transformations in Ether Theories

1991 ◽  
Vol 46 (5) ◽  
pp. 419-425 ◽  
Author(s):  
F. Selleri
Keyword(s):  
Special Relativity ◽  
Relativity Theory ◽  
Absolute Velocity ◽  
Ether Theory ◽  
Velocity Of Light ◽  
Principle Of Relativity ◽  
Inertial Frames ◽  
Special Relativity Theory ◽  
Time Transformations ◽  
Ether Theories

AbstractBy assuming the validity of the principle of inertia and the existence of a privileged frame, the transformation laws (TL) between inertial frames are investigated in ether theories. For onedimensional space the TL's are fixed up to two undetermined functions of absolute velocity, Δ (v) and E(v). If the principle of relativity is finally assumed, these functions acquire their well known Lorentzian expressions ΔL and EL. It is concluded that special relativity theory is "unstable", in the sense that any shift, however small, of Δ away from ΔL and/or of E away from EL leads to an ether theory. In Earth-based experiments one can expect deviations from c of the two-way and one-way velocity of light of the order of 10-12 and 10 -9 respectively

scholarly journals Recovering the Principle of Relativity from the Cosmic Fabric Model of Space

2018 ◽  
Vol 02 (04) ◽  
pp. 1850011 ◽  
Author(s):  
T. G. Tenev ◽  
M. F. Horstemeyer
Keyword(s):  
Reference Frames ◽  
Time Dilation ◽  
Length Scale ◽  
Lorentz Transformations ◽  
Detection Experiment ◽  
Quantum Theories ◽  
Principle Of Relativity ◽  
Length Contraction ◽  
The Continuum ◽  
Negative Outcome

We extend the descriptive power of the Cosmic Fabric model of space developed by Tenev and Horstemeyer [Int. J. Mod. Phys. D 27 (2018) 1850083] to include moving observers by demonstrating that all reference frames are phenomenologically equivalent with one another and transform between each other via the Lorentz transformations. Our approach is similar to that of Lorentz [Versl. Kon. Akad. Wetensch 1 (1892) 74], which was used to explain the negative outcome of the Michelson–Morley æther detection experiment [A. A. Michelson and E. W. Morley, Am. J. Sci. s3–34 (1887) 333], except that we deduce the notions of length contraction and time dilation from the postulates of the Cosmic Fabric model. Our result is valid for the continuum length scale at which, by definition, the cosmic fabric can be described mathematically as a continuum. Herein, we also discuss the length scale-dependent nature of the Cosmic Fabric model as a possible way to relate gravitational and quantum theories.

scholarly journals Symmetries of Thirring Models on 3D Lattices

2022 ◽  
Author(s):  
Andreas Wilhelm Wipf ◽  
Julian Johannes Lenz
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Three Dimensions ◽  
Coupling Phase ◽  
Perturbative Methods ◽  
Dirac Materials ◽  
Recent Developments ◽  
Arbitrary Dimensions ◽  
Relativistic Fermi ◽  
The Continuum

We review some recent developments about strongly interacting relativistic Fermi theories in three spacetime dimensions. These models realize the asymptotic safety scenario and are used to describe the low-energy properties of Dirac materials in condensed matter physics. We begin with a general discussion of the symmetries of multi-flavor Fermi systems in arbitrary dimensions. Then we review known results about the critical flavor number $N_\mathrm{crit}$ of Thirring models in three dimensions. Only models with flavor number below $N_\mathrm{crit}$ show a phase transition from a symmetry-broken strong-coupling phase to a symmetric weak-coupling phase. Recent simulations with chiral fermions show that $N_\mathrm{crit}$ is smaller than previously extracted with various non-perturbative methods. Our simulations with chiral SLAC fermions reveal that for four-component flavors $N_\mathrm{crit}=0.80(4)$. This means that all reducible Thirring models with $\Nr=1,2,3,\dots$ show no phase transition with order parameter. Instead we discover footprints of phase transitions without order parameter. These new transitions are probably smooth and could be used to relate the lattice Thirring models to Thirring models in the continuum. For a single irreducible flavor, we provide previously unpublished values for the critical couplings and critical exponents.

scholarly journals The Yang-Mills heat equation with finite action in three dimensions

2022 ◽  
Vol 275 (1349) ◽  
Author(s):  
Leonard Gross
Keyword(s):  
Heat Equation ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Three Dimensions ◽  
Dimensional Manifold ◽  
Uniqueness Of Solutions ◽  
Reconstruction Procedure ◽  
Content Type ◽  
Yang Mills ◽  
Gauge Functions

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R 3 \mathbb {R}^3 and over a bounded open convex set in R 3 \mathbb {R}^3 . The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation.

scholarly journals Dilation of Time and Newton’s Absolute Time

2019 ◽  
pp. 1-20
Author(s):  
Stefan Von Weber ◽  
Alexander Von Eye
Keyword(s):  
Light Propagation ◽  
Inertial Frame ◽  
Background Radiation ◽  
Frame Of Reference ◽  
Relativity Theory ◽  
Absolute Space ◽  
Light Sources ◽  
Membrane Theory ◽  
Absolute Time ◽  
Microwave Background Radiation

The Cosmic Membrane theory states that the space in which the cosmic microwave background radiation has no dipole is identical with Newton’s absolute space. Light propagates in this space only. In contrast, in a moving inertial frame of reference light propagation is in-homogeneous, i.e. it depends on the direction. Therefore, the derivation of the dilation of time in the sense of Einstein’s special relativity theory, i.e., together with the derivation of the length contraction under the constraint of constant cross dimensions, loses its plausibility, and one has to search for new physical foundations of the relativistic contraction and dilation of time. The Cosmic Membrane theory states also that light paths remain always constant independent on the orientation and the speed of the moving inertial frame of reference. Effects arise by the dilation of time. We predict a long term effect of the Kennedy-Thorndike experiment, but we show also that this effect is undetectable with today’s means. The reason is that the line width of the light sources hides the effect. The use of lasers, cavities and Fabry-Pérot etalons do not change this. We propose a light clock of special construction that could indicate Newton’s absolute time t0 nearly precisely.

Conclusion

2020 ◽  
pp. 224-232
Author(s):  
Aleida Assmann
Keyword(s):  
Temporal Structure ◽  
Three Dimensions ◽  
One Dimension ◽  
Modern Time ◽  
The Past ◽  
The Future ◽  
Time Regime

This concluding chapter poses the question of whether or not we have too much past and too little future. After all, the notion of the past has dramatically increased in its range of meanings, as has the future. The relation between the past, the present, and the future is a three-fold relationship in which one dimension cannot exist for long without the others. Ordering this three-fold temporal structure anew and bringing the three dimensions into a balanced relation, however, continues to be an open adventure. To be sure, it is also the greatest challenge posed by the demise of the modern time regime.

scholarly journals Relativistic Reference Frames in Astrometry

1986 ◽  
Vol 7 ◽  
pp. 101-102
Author(s):  
C A Murray
Keyword(s):  
Coordinate System ◽  
Reference Frames ◽  
Inertial Frame ◽  
Space Time ◽  
Clock Time ◽  
Local Inertial Frame ◽  
Incoming Photon ◽  
Inertial Frames ◽  
Spatial Coordinates

Astrometry can be defined as the measurement of space-time coordinates of photon events. For example, in principle, in classical optical astrometry, we measure the components of velocity, and hence the direction, of an incoming photon with respect to an instrumental coordinate system, and the clock time, at the instant of detection. The observer’s coordinate system at any instant can be identified with a local inertial frame. In the case of interferometric observations, the measurements are of clock times of arrival of a wavefront at two detectors whose spatial coordinates are specified with respect to instantaneous inertial frames.

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