scholarly journals Time Dilation and the Equivalence of Inertial Frames

2021 ◽  
Author(s):  
Chandru Iyer ◽  
G M Prabhu
Keyword(s):  
Time Dilation ◽  
Uniform Motion ◽  
Relative Speed ◽  
Addition Formula ◽  
Inertial Frames ◽  
Velocity Addition

We have compared the data of three clocks A, B and D moving in relative uniform motion with relative speed/velocity between A and B set at 0.6c, relative speed/velocity between A and D set at 0.8c and relative speed between B and D set at (5c/13) = 0.3846c as per the velocity addition formula (0.8-0.6)/(1-0.8*0.6). We have compared the time readings of the clocks when they meet at three events. Event 1 meeting of A and B, Event 2 meeting of A and D, Event 3 meeting of B and D.

scholarly journals Time Dilation and the Equivalence of Inertial Frames

2021 ◽  
Author(s):  
Chandru Iyer ◽  
G M Prabhu
Keyword(s):  
Time Dilation ◽  
Uniform Motion ◽  
Relative Speed ◽  
Addition Formula ◽  
Inertial Frames ◽  
Velocity Addition

We have compared the data of three clocks A, B and D moving in relative uniform motion with relative speed/velocity between A and B set at 0.6c, relative speed/velocity between A and D set at 0.8c and relative speed between B and D set at (5c/13) = 0.3846c as per the velocity addition formula (0.8-0.6)/(1-0.8*0.6). We have compared the time readings of the clocks when they meet at three events. Event 1 meeting of A and B, Event 2 meeting of A and D, Event 3 meeting of B and D.

The four basic errors of special theory of relativity and the solution offered by extended Galilean relativity

2020 ◽  
Vol 33 (2) ◽  
pp. 211-215 ◽  
Author(s):  
Shukri Klinaku
Keyword(s):  
Special Theory ◽  
Theory Of Relativity ◽  
Special Theory Of Relativity ◽  
Speed Of Light ◽  
Addition Formula ◽  
Principle Of Relativity ◽  
Galilean Relativity ◽  
Velocity Addition ◽  
Basic Equations ◽  
Tycho Brahe

Is the special theory of relativity (STR) a “simple” or “tricky” theory? They who think that it is a simple theory say (i) that its postulates are simple, that Nature is such, (ii) that the mathematics of STR is perfect, and (iii) that experiments support it. I consider its two postulates to be very true, whereas the mathematics of the STR has a shortcoming, and, as for the experiments, the question must be posed: which theory do they support best? The problem for STR lies in the transition from its postulates to its basic equations, i.e., Lorentz transformation and the velocity addition formula. The passage from the principle of relativity and the constancy of the speed of light to the basic equations of the STR is affected by four fundamental errors—three physical and one mathematical. Continuous attempts to reconcile these latent mistakes have made STR increasingly tricky. As a result, it is in a similar situation to Ptolemy's geocentric model after “improvements” thereto by Tycho Brahe. However, the “Copernican solution” for relative motion—offered by extended Galilean relativity—is very simple and effective.

Recasting the Lorentz Velocity Addition Formula

2010 ◽  
Vol 48 (1) ◽  
pp. 4-4
Author(s):  
John Mallinckrodt
Keyword(s):  
Addition Formula ◽  
Velocity Addition

scholarly journals The Nature of Time

2017 ◽  
Vol 9 (2) ◽  
pp. 21 ◽  
Author(s):  
Sydney Baldwin Self
Keyword(s):  
Time Dilation ◽  
Frame Of Reference ◽  
Point Of View ◽  
Uniform Motion ◽  
Physical Event ◽  
Absolute Time ◽  
Physical Time ◽  
Multiple Observations ◽  
Planck Time ◽  
Nature Of Time

I.    Special relativity does not address the fact that time must exist on lifeless worlds. It only addresses time that is observed, which requires that observers be present.II.    The time that exists on lifeless worlds can be termed physical time.III.    The failure to recognize the existence of physical time has resulted in a view of time that is contrived, overly simplistic and contains irrational conclusions which are not experimentally supported.IV.    On worlds where conscious life exists, both physical time and observed time exist. The characteristics of physical time and of observed time are very different.V.    Physical time has the following attributes:a.    Each physical event is associated with physical time.b.    The attributes of absolute time, ‘now’ and time dilation are associated with every physical event.c.    All physical events occur during ‘now’. d.    A physical event results in a change to physical reality.e.    The frame of reference associated with a physical event is universal.f.    In order to be observed, a physical event must have an associated observed event.VI.    Observed time has the following attributes.a.    Every observed event is associated with observed time.b.    An observed event can only occur as the result of a physical event.c.    Multiple observations can be associated with a single physical event.d.    The attribute of ‘now’ and a frame of reference are associated with every observed event.VII.    The duration of physical ‘now’ is a Planck time which is also the unit of measure for absolute time and time dilation.VIII.    Time dilation is computed using the Lorentz transformation.IX.    The statement regarding time dilation “When two observers are in relative uniform motion and uninfluenced by any gravitational mass, the point of view of each will be that the other's (moving) clock is ticking at a slower rate than the local clock” is mathematically, experimentally and logically wrong.X.    During physical ‘now’ a particle may move through space or it may move through time; which it does is a probability based on the speed of the particle expressed as a percentage of the speed of light.

Special Relativity via Modified Bessel Functions

2000 ◽  
Vol 55 (9-10) ◽  
pp. 745-753 ◽  
Author(s):  
B. H. Lavenda
Keyword(s):  
Doppler Effect ◽  
Bessel Functions ◽  
Average Distance ◽  
Jump Process ◽  
Momentum Conservation ◽  
Modified Bessel Functions ◽  
Addition Formula ◽  
Hyperbolic Cosine ◽  
Inertial Frames ◽  
Energy And Momentum

The recursive formulas of modified Bessel functions give the relativistic expressions for energy and momentum. Modified Bessel functions are solutions to a continuous time, one-dimensional discrete jump process. The jump process is analyzed from two inertial frames with a relative constant velocity; the average distance of a particle along the chain corresponds to the distance between two observers in the two inertial frames. The recursion relations of modified Bessel functions are compared to the 'k calculus' which uses the radial Doppler effect to derive relativistic kinematics. The Doppler effect predicts that the frequency is a decreasing function of the velocity, and the Planck frequency, which increases with velocity, does not transform like the frequency of a clock. The Lorentz transformation can be interpreted as energy and momentum conservation relations through the addition formula for hyperbolic cosine and sine, respectively. The addition formula for the hyperbolic tangent gives the well-known relativistic formula for the addition of velocities. In the non-relativistic and ultra-relativistic limits the distributions of the particle's position are Gaussian and Poisson, respectively.

scholarly journals Direct calculation of length contraction and clock retardation

2015 ◽  
pp. 49-58 ◽  
Author(s):  
D.V. Redzic
Keyword(s):  
Electromagnetic Field ◽  
Causal Effect ◽  
Direct Calculation ◽  
Equation Of Motion ◽  
Uniform Motion ◽  
Correct Equation ◽  
Length Contraction ◽  
Inertial Frames ◽  
Electromagnetic Models ◽  
Dynamical Change

For simple electromagnetic models of a rod and a clock, a change of shape of a rod and of the rate of clock when they are set in uniform motion is calculated exactly, employing the correct equation of motion of a charged particle in electromagnetic field and the universal boostability assumption. Thus it is demonstrated that, for the simple system considered, the length contraction and clock retardation can be interpreted as dynamical cause-and-effect phenomena, and not as kinematical effects as usually construed in conventional presentations of Special Relativity. It is argued that the perspective relativistic change of an object (corresponding to observations from two inertial frames), while certainly being an a causal effect, has a dynamical content in the sense that it is tantamount to an actual dynamical change of the object in one frame.

The field of a moving charge

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Radiation ◽  
Lorentz Transformation ◽  
World Line ◽  
Uniform Motion ◽  
Special Cases ◽  
Inertial Frames ◽  
A Charge

This chapter begins the study of electromagnetic radiation by calculating the field created by a single moving charge, first when in uniform motion, and then when it is accelerated. It reveals the potential created by a charge in uniform motion starting from the Coulomb expression for the potential in the frame where it is at rest, and then by making a Lorentz transformation. The chapter then follows the exact reasoning for any type of motion by introducing inertial frames tangent to the charge world line. In this way, it obtains the retarded Liénard–Wiechert potential created by a charge in any type of motion. After studying some special cases of the field of a moving charge, the chapter defines the asymptotic, radiation, part of the field.

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