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An experiment has been performed to demonstrate the relativistic time dilation as a large effect, using only comparatively simple equipment. μ-mesons incident on top of Mt. Washington, New Hampshire, were selected to have speeds in the range between 0.9950 c and 0.9954 c. The number of these which survived to reach sea level was measured in Cambridge, Massachusetts. The number expected without time dilation was calculated from the distribution of decay times of these μ-mesons (i.e., the mean life as measured in both this experiment and others) and from the known distance of descent. The observed time dilation factor is 8.8±0.8 to be compared with the effective time dilation factor calculated for mesons of these speeds in our detection geometry 1/(1 − v2/c2)12 = 8.4 ± 2.

The circular arc swept out by the angular displacement of a clock indicator (or its equivalent representation) measuring time is shown to be a Lorentz invariant, representing “universal” time. The concepts of time dilation and transverse Doppler effect are accordingly not physically observable. The experiments on these effects when examined critically are found to be inconclusive. Length contraction, also experimentally unconfirmed, and kinematic temporal phase, both consequences of the Lorentz transformations, are as a matter of logical consistency also physically unobservable.

It is shown that, contrary claims notwithstanding, apparently no one before Einstein in 1905 ventured the idea that all clocks in motion might go slow. And thus, however logical it would have been, there never existed a theory based on the axioms of length contraction and time dilation relative to the ether.

Frequency shifts that occur between objects moving in gravitational fields are a merger of classical Doppler shift and relativistic time dilation. The way to obtain relativistic Doppler formulas by multiplying together classical and relativistic quantities is shown to be false. An exact formula for the general-relativistic effect does not exist; but approximations of a sufficient accuracy are procurable.

The problem of observing a collision between two spaceships is utilized to illustrate the misuse of time dilation and length contraction, and the incorrect description of space-time coordinates in special relativity. By emphasizing the equivalence of all inertial frames, students can be guided to correct descriptions of space-time coordinates and to proper applications of time dilation and length contraction.

The ellipsoid theory Is a modification of the ether theory coupled with time dilation. It is not in conflict with any known observational evidence. Certain astronomical evidence, which conflicts with relativity theory, supports the ellipsoid theory. The moon laser experiment will serve as a direct test of the validity of both theories.

Doppler effects for time-varying inhomogeneous media are considered. The ray path is represented in terms of a two-parameter function, this takes into account its time evolution. Time dilation along the path is discussed. This provides, in a systematic way, an alternative derivation to a heuristic expression previously given by Gill. The phase function is integrated along the ray path and yields the various Doppler effects in a straightforward way. It is shown that the generalized Doppler effect is produced by the relative motion of source and receiver with respect to the medium, and the cumulative rate of change of frequency and propagation vector along the path.

A very accurate evaluation of the Schwarzschild constants is now possible from continuous observation of the spin axes of coupled gyroscopes, because the angular velocities of these axes can be more than 100000 times greater than the better known precession velocity of a single gyro in orbit around the Earth. This enormous increase in velocity is a consequence of a gravo-magnetic effect in gravitational interaction that resembles the electro-magnetic effect in electrical interaction.

In connection with another article by the author, we show how it might be possible to travel faster than the speed of light. We show that for clocks and rods moving faster than the speed of light, we get instead of “time dilation” and “Lorentz contraction,” respectively, “time contraction” and “Lorentz expansion,” respectively. It is shown that this paper is in confirmation with earlier articles dealing with this subject.

New radar observations yield a more stringent test of the predicted relativistic increase in echo times of radio signals sent from Earth and reflected from Mercury and Venus. These "extra" delays may be characterized by a parameter $\ensuremath{\lambda}$ which is unity according to general relativity and 0.93 according to recent predictions based on a scalar-tensor theory of gravitation. We find that $\ensuremath{\lambda}=1.02$. The formal standard error is 0.02, but because of the possible presence of systematic errors we consider 0.05 to be a more reliable estimate of the uncertainty in the result.

The anomalous magnetic momenta≡1/2 (g−2) of the muon has been measured in the CERN muon storage ring. The result is (116 616±31)·10−8 compared with the theoretical value (116 588±2)·10−8 showing agreement to (240±270) parts per million. The lifetime of muons moving in a circular orbit with γ=12 was found to agree with the time dilation predicted by special relativity to within 1.1%. Details are given of the storage ring magnet, the instrumentation and the data analysis. The theoretical implications of the result are discussed.

An investigation of the propagation of light, assuming absolute spacial distances, the veracity of the principle of causality, and that the average speed of light measured over a closed path is a constant C, shows that the speed of light may have values between C/2 and is a function of direction. Generalized Lorentz transformations are found which are shown to be equivalent to those conventionally adopted. That an absolute simultaneity cannot be established electromagnetically is shown to follow. The arbitrary nature of indirect observables such as time dilation is discussed.

The ages of twins who travel along intersecting orbits in a central gravitational field are studied using general relativity. It is shown to order v2 / c2 that even though neither twin experiences acceleration, the aging is asymmetric.