Einstein's Elevator: World Lines, Michelson-Morley Experiment and Relativistic Paradox

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation, and for the first time the worldlines equations are given. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, especially the experiment with the accelerated Michelson-Morley interferometer is solved, and we described an experiment where a new relativistic paradox appears --- a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

World Lines in Einstein's Elevator

We all have in mind Einstein's famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are semi-ellipses with the center on the event horizon. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, such as the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears — a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical. The concepts of metric, coordinated velocity and horizon are discussed, and the analogy with the black hole is made.

Opposing hypotheses of the reflection of light applied to the Michelson interferometer with a particular geometry

The derivation of light paths in the Michelson interferometer is based on the hypothesis that the incident speed and reflected speed of the wavefront of a ray of light are equal in the frame at absolute rest. In this case, the Michelson‐Morley experiment predicts a fringe shift of <mml:math display="inline"> <mml:mrow> <mml:mo> </mml:mo> <mml:mn>0.40</mml:mn> </mml:mrow> </mml:math> . With the hypothesis that the incident speed and reflected speed of the wavefront of a ray of light are equal in the inertial frame of a mirror at the instance of collision, the Michelson interferometer with a particular geometry predicts zero fringe shift, which is in agreement with the result of the Michelson‐Morley experiment.

Opposing hypotheses of the reflection of light applied to the Michelson interferometer

The derivation of light paths in the Michelson interferometer is based on the hypothesis that the incident speed and reflected speed of the wavefront of a ray of light are equal in the frame at absolute rest. In this case, the Michelson‐Morley experiment predicts a fringe shift of 0.40. With the hypothesis that the incident speed and reflected speed of the wavefront of a ray of light are equal in the inertial frame of a mirror at the instance of collision, the Michelson‐Morley experiment predicts a fringe shift of 0.40 × 10−4, which is in agreement with the experimental result.

World Lines in Einstein's Elevator

We all have in mind Einstein&rsquo;s famous thought experiment in the elevator where we observe the free fall of a body, and then the trajectory of a light ray. Simply here, in addition to the qualitative aspect, we carry out the exact calculation. We consider a uniformly accelerated reference frame in rectilinear translation, and we show that the trajectories of the particles are ellipses centered on the event horizon. The frame of reference is non-inertial, the space-time is flat, the metric is non-Minkowskian, and the computations are performed within the framework of special relativity. Some experimental consequences are discussed, such as the deviation of trajectories, the desynchronization of a falling clock, the accelerated Michelson-Morley experiment, and, finally, an experiment where a paradox appears &mdash; a particle of matter seems to go faster than light. The differences, compared to the classical case, are important at large scale and close to the horizon, but they are small in the lift where the interest is above all theoretical and pedagogical. The study helps the student to become familiar with the concepts of metric, coordinate velocity, horizon, and, to do the analogy with the black hole.

Aether Integration

In this paper we investigate into the possible resurrection for the aether and it&rsquo;s compatibility with the theory of relativity. We revisit the Michelson-Morley experiment and expose some of the major inadequacies. In this regard, we have presented the true/corrected form of the Michelson-Morley experiment. We have tried to revise the interpretational aspect of the mathematical formalism regarding the metric of Minkowskian space-time in addendum with it&rsquo;s relationship to the two theories of time. We herein have also tried to restrain some of the quantum mechanical issues arising from the mainstream understanding of the mathematical formalism of the Minkowskian manifold. Essentially, we have argued in favour of aether to be incorporated into our mathematical formalism as well the physical understanding of the universe.

The Law of Conservation of Time and Its Applications

Time is a complex category not only in philosophy but also in mathematics and physics. In one thought about time, the author accidentally discovered a new way to explain and solve problems related to time dilation, such as solving the problem of Muon particle when moving from a height of 10 km to the earth’s surface, while the Muon’s lifespan is only 2.2 microseconds, or explaining Michelson-Morley experiment using the new method. In addition, the author also prove that the speed of light in vacuum is the maximum speed in the universe, and discovered the red shift effect while there is no increase in distance between objects. To do this, the author has built two axioms based on the discontinuity in the motion of the object and draw two consequences along with the law of conservation of time.

Reflection of Light as a Mechanical Phenomenon Applied to a Particular Michelson Interferometer

Derivation of light paths in the Michelson interferometer is based on the hypothesis that the speed of light does not change after reflection by a mirror in motion. The Michelson-Morley experiment predicts a fringe shift of 0.40. The same fringe shift is predicted for a particular Michelson interferometer in which the beam splitter of the interferometer makes an angle of 45&deg; with the direction of light from the source. Light behaves like a wave and also as a particle. Thus, it is reasonable to consider the reflection of light as a mechanical phenomenon. With this hypothesis, the speed of light changes after reflection, and the predicted fringe shift for the particular Michelson interferometer is zero which is in accordance with the result of the Michelson-Morley experiment. Apparently, light travels in any inertial frame as if this particular interferometer belongs to a fixed frame. The velocity of light is considered independent of the velocity of its source, which is in accordance with astronomers&rsquo; observations of the binary stars, and the experiment performed at CERN, Geneva, in 1964.