GALILEO AND THE PRINCIPLE OF RELATIVITY '
In his "Dialogue concerning the system" Galileo Galilei gives a very clear description of the "principle of relativity Galilean. " He imagines an experimenter, who was imprisoned in the hold of a ship, running a series of observations on falling bodies. Galileo explains, very clearly, as in any way possible to make this observation any indication on the speed of motion (uniform) of the vessel by experiments that take place exclusively inside. The Galileo's original formulation, however, is descriptive and marks the entrance of the concept in modern physics of relativity: "It 's impossible to bring out the absolute motion of an object and you can only talk about relative speed of two objects." The principle of relativity is verifiable in the life of every day, sitting in the compartment of a train is leaving the station with another train on the side, we find it hard to understand if we are moving us or the other train. Galilean relativity is in perfect agreement with the mechanics of Newton and the law of universal gravitation. It is therefore not possible to determine the state of absolute motion by measuring the gravitational force between bodies. The relativistic world can be encoded by an infinite number of potential observers, called inertial, and in relative uniform motion. None of these takes precedence over others and the laws of physics are written in the same way for everyone. In special relativity observers are not allowed in non-uniform motion and would indeed be possible to detect the motion of the ship in rough seas. The existence of observers Inertia is an empirical fact and when it does not follow from any higher principle. The Galilean relativity has remained in good agreement with the observed data until the end of the nineteenth century, and continues to be used successfully to treat relativistic phenomena, namely those that take place at speeds much lower than that of light (c = 299,792.458 km / s). At speeds approaching ac - called relativistic - it proves to be invalid and need to use Einstein's relativity.
The Galilean principle of relativity states then the absolute physical equivalence of all inertial reference systems: no experiment performed within a given reference system can highlight the rectilinear uniform and the same system, or, in other words, the physical laws discovered by investigators working in laboratories in uniform rectilinear relative motion must have the same shape. The challenge now is to derive formulas that link the time-space coordinates of the same event viewed from two different references, and to prove that the laws of physics are invariant in form, the transition from a reference to another, it is a question of translating formulas in the content of this principle. Consider two references in order (ie, two systems of orthogonal axes):
Galilean relativity is perfectly valid to explain the covariance of mechanical laws of nature in the transition from an inertial system to another, fell into default when you consider the phenomena of electromagnetic nature. These phenomena are summarized in qualitative terms, the following laws:
1. Coulomb's law (the electric field of a point charge);
2. The magnetic field lines are continuous and have no beginning or end;
3. A time-varying magnetic field produces an electric field (electromagnetic induction);
4. A magnetic field can be produced by a flow of current from a variable electric field.
Well, the equations that govern these phenomena - the equations of Maxwell (James Clerk Maxwell, 1831-1879) - are not covariant with respect the Galilean transformations: if they were universally valid, an inertial observer who performs an experiment of electromagnetic nature, would notice and be at rest or in motion with respect to another inertial observer, depending on the outcome of a similar experiment, conducted by this second observer.
RELATIVITY 'Einstein
The Galilean transformations ensure the covariance of physical laws, the variation of inertial systems, only with regard to mechanical phenomena, but they fall in default when you take into account the phenomena of nature Electromagnetic. Is due to Albert Einstein (1879-1955) a considerable extension of the formulas of Galileo, which ensures the covariance of all physical laws, the variation of inertial systems. Suppose, next to each other, the formulas of Galileo and Einstein, to examine the similarities and differences. We refer to the figure of Part 1 , assuming, for simplicity, that the relative motion of the two systems occurs in the direction of x, common to both.
Einstein Galileo
formulas down (Galilean transformations), in which the spatial coordinates are strictly independent of time, involve that the two observers, moving relative to each other, have synchronized clocks. The formulas above (Lorentz transformations, which were adopted by Einstein), in which the spatial coordinates and the time they imply one another, imply that the two observers, moving relative to each other, have asynchronous clocks. The Lorentz transformations give good results, whenever the velocity v with which a system moves to the other, c is comparable to that of light - about 300,000 miles per second - while, as noted immediately, if the relationship is negligible, is reduced substantially to those of Galileo. The speed of light, and any other electromagnetic phenomenon, are to varying covariates inertial systems, like the mechanical laws of nature, if we assume as valid the Lorentz transformations.
In 1916, Einstein extended the principle of relativity to all reference systems, including non-inertial, using formulas that guarantee the covariance of all the laws of nature, the variation of observers (General Relativity). In particular, every observer measures in its own space-time (generally non-Euclidean), the distance between two events in space-time, using a metric whose coefficients are functions of the distribution of matter and energy in space itself. This implies that space and time are no longer, as Newton , two empty containers, where you can admire the natural phenomena, but a construction of the same phenomena (see Descartes ). Gravitational effects, such as tides , find place in this beautiful theoretical construction, which remain valid, with some correction, but the formula Newton . But it is to be noted that this formula, in the context of general relativity, does not express ghostly action at a distance, but spontaneous movements or natural LINEEA along the minimum length (geodesic) space-time. According to the evocative words of Max Jammer (contained in History of the concept of space ): "[...] the gravitation does not own, in General Relativity, the characteristics of a force, but reduces to a property of space-time. The program Descartes (ie the geometrization of physics), has finally been realized by Einstein. " One might add that the validity in this context, the formula for gravitational Newton produce also, somehow, a synthesis of Cartesian ideas and those of Newton himself.
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