Visualizing the Doppler Effect

After having shown that the formula which describes the Doppler effect in the general case holds only in the case of the "very high" frequency assumption, we derive free of assumptions Doppler formulas for two scenarios presented in the revisited paper.

We present the special theory of relativity taking the Doppler effect as the starting point, and derive several of its main effects, such as time dilation, length contraction, addition of velocities, and the mass-energy relation, and assuming energy and momentum conservation, we discuss how to introduce the 4-momentum in a natural way. We also use the Doppler effect to explain the "twin paradox", and its version on a cylinder. As a by-product we discuss Bell's spaceship parad...

Visualizations that adopt a first-person point of view allow observation and, in the case of interactive simulations, experimentation with relativistic scenes. This paper gives examples of three types of first-person visualizations: watching objects that move at nearly the speed of light, being a high-speed observer looking at a static environment and having a look-around near a compact object. I illustrate and explain the main aspects of the visual observations, outline thei...

Special Relativity is often seen as a conceptually difficult topic, which in turn is difficult to effectively teach. This work focuses on the role of visualizations as a tool in teaching Special Relativity at the secondary or university level. The Theory Of Conceptual Fields proposed by G\'erard Vergnaud is used to analyze the conceptualization process in learning Special Relativity so that the "breakpoints" in this process can be identified. Visualizations as a didactic tool...

The Special Theory of Relativity, introduced by Albert Einstein in the early 20th century, marked a radical shift in our understanding of space and time. Nevertheless, the theory's non-intuitive implications continue to pose conceptual challenges for novice physicists. In this thesis, we propose a virtual reality solution based on the development of a Unity package capable of simulating the effects of relativity in a digital environment. The current implementation includes th...

This paper will attempt to show that the Doppler principle was of major relevance to Einstein for the genesis of the special theory of relativity.

In order to describe natural phenomena, science develops sophisticated models that use mathematical and formal languages which seem, and often are, very far from common experience. When a phenomenon is not accessible to our senses, its description is indirect and understanding can be difficult for those who are not trained to understand the consequences of formal languages used by scientists. When one succeed to obtain a direct visualization of a phenomenon inaccessible to se...

The principles of the special theory of relativity are extremely simple. A knowledge of the Pythagorean theorem and an ability to perform the simplest algebraic operations are sufficient to be conversant with the kinematics of the special theory of relativity, as well as the time dilation and contraction of the longitudinal dimensions of moving bodies that are associated with relative motion. However, the simplicity of the fundamentals of the theory of relativity are in surpr...

This paper shows as the relativistic Doppler effect can be extended also to time and space associated to moving bodies. This extension derives from the analysis of the wave-fronts of the light emitted by a moving source in inertial motion in the empty space, as viewed from the stationary reference. Indeed, time and space can be represented by the same vector quantities, which appear asymmetrical in forward and back direction along the path of the moving body. Consequently, th...

Many formalisms of special relativity are shown in various textbooks. However, even in those where the underlying geometry of Minkowski space is emphasized, the visualisations are lacking. This article aims to remedy this by expressing relativistic concepts in a visual manner, using the full power of hyperbolic trigonometric functions. Minkowski diagrams in energy-momentum space are used and then augmented in comparison with previous uses in literature by direct usage of tria...