Galilei proposed the principle of relativity, but not the “Galilean transformation”

2020 ◽  
Vol 88 (3) ◽  
pp. 207-213
Author(s):  
K. M. Browne
Keyword(s):  
Galilean Transformation ◽  
Principle Of Relativity

Gluing Solutions

2017 ◽  
Author(s):  
Philip Isett
Keyword(s):  
Stress Tensor ◽  
Compact Support ◽  
Smooth Solution ◽  
Continuous Solution ◽  
Total Momentum ◽  
Frame Of Reference ◽  
Galilean Transformation ◽  
Hölder Continuous ◽  
Pressure Form ◽  
Original Frame

This chapter deals with the gluing of solutions and the relevant theorem (Theorem 12.1), which states the condition for a Hölder continuous solution to exist. By taking a Galilean transformation if necessary, the solution can be assumed to have zero total momentum. The cut off velocity and pressure form a smooth solution to the Euler-Reynolds equations with compact support when coupled to a smooth stress tensor. The proof of Theorem (12.1) proceeds by iterating Lemma (10.1) just as in the proof of Theorem (10.1). Applying another Galilean transformation to return to the original frame of reference, the theorem is obtained.

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.

FRACTALS AND THE QUANTUM THEORY OF SPACETIME

1989 ◽  
Vol 04 (19) ◽  
pp. 5047-5117 ◽  
Author(s):  
LAURENT NOTTALE
Keyword(s):  
Fractal Dimension ◽  
Heavy Ion ◽  
Space Time ◽  
Curvilinear Coordinates ◽  
Fractal Structures ◽  
Ion Collisions ◽  
Principle Of Relativity ◽  
First Results ◽  
Fractal Space ◽  
Dimension 2

We review in this paper the first results obtained in an attempt at understanding quantum space-time based on a new extension of the principle of relativity and on the geometrical concept of fractals. We present methods for dealing with the nondifferentiability and the infinities of fractals, as a first step towards the definition and intrinsic description of a fractal space. After having recalled that the Heisenberg relations imply a transition of spatial coordinates of a particle to fractal dimension 2 about the de Broglie length λ = ħ/p, it is suggested that a similar transition occurs for temporal coordinates about the de Broglie time τ = ħ/E. We then investigate the hypothesis that the microstructure of space-time is of fractal nature, and that the observed properties of the quantum world at a given resolution result from the smoothing of curvilinear coordinates of such a spacetime projected into classical spacetime. Along this road, we successively study the link of fractal dimension 2 to spin, we give first hints on the expected behavior of families of fractal geodesics, and we exhibit a general class of fractal structures which is assumed to yield a lowest order description of the quantum vacuum. The links between the new approach and both special and general relativity are touched upon. We finally suggest that the anomalous peaks recently observed in the spectra of positrons from supercritical heavy ion collisions may be understood in this context.

scholarly journals Discussion on Relativity of Time Interval in the Theory of Relativity

2019 ◽  
Vol 11 (5) ◽  
pp. 41
Author(s):  
Zhonggang Li
Keyword(s):  
Experimental Evidence ◽  
Light Source ◽  
Vertical Line ◽  
Time Interval ◽  
Theory Of Relativity ◽  
Principle Of Relativity

Einstein's principle of relativity is an important fundamental of relativity. It can also be said that relativity is based on the assumption of the principle of relativity. This assumption can be represented by a diagram of "relativity of time interval", as shown in Fig.  a . According to the theory of relativity, a flash emits from the light source in the moving car and returns to the light source after being reflected by the mirror on the roof. The person in the train thinks that the flash returns to the light source along a vertical line, and the person off the train thinks that the flash returns to the light source along the AMB  curve. The time taken in the two routes is inconsistent. In fact, it is a preconception. Einstein believes that the flash will undoubtedly return to the light source, which is a matter of course and need not be discussed. Therefore, he did not think more and immediately carried out the next research on the time taken inside and outside the train. Here's where the problem arose. Is there an experimental evidence? If the flash does return to the light source, then the next analysis carried out by Einstein is correct and impeccable. However, if the flash does not return to the light source, then Einstein's next analysis and the whole theory of relativity make no sense.

scholarly journals Evidence for an Invalidity of the Principle of Relativity

2011 ◽  
Vol 02 (11) ◽  
pp. 1247-1249 ◽  
Author(s):  
Janusz Drożdżyński
Keyword(s):  
Principle Of Relativity

The relativistic quantum mechanics of the elementary particles

1949 ◽  
Vol 45 (2) ◽  
pp. 263-274 ◽  
Author(s):  
H. S. Green
Keyword(s):  
Quantum Mechanics ◽  
Density Matrix ◽  
Relativistic Quantum ◽  
Difficult Problem ◽  
Dynamical Variable ◽  
Elementary Particles ◽  
Relativistic Quantum Mechanics ◽  
Principle Of Relativity ◽  
The One ◽  
Real Linear

The search for a theory of the elementary particles which is founded on the well-established principles of quantum mechanics and conforms at the same time with the requirements of the principle of relativity has, in recent years, taken several divergent directions. On the one hand, the second quantization of wave fields derived from a Lagrangian by a variational procedure(1) has succeeded in accounting for the existence and most of the properties of the electron, the photon, and the meson. On the other hand, many generalizations of the Dirac wave equation of the electron(2) have been attempted, with applications to the meson(3) and the proton(4). Heisenberg(5) has considered the much more difficult problem of the interaction between different particles, and has found that the key to the situation is the so-called ‘scattering matrix’, which is nothing other than a limiting form of the relativistic density matrix, as defined in § 2 of this paper. It seems probable that the relativistic density matrix ρ; or statistical operator, as it may be called without reference to representation, will play an important part in relativistic quantum mechanics in the future. It satisfies the same equation as the wave function, but differs from it in being a real linear operator, or a dynamical variable, in the terminology of Dirac.

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