Galilean

In physics , an inertial frame, or inertial, is a repository in which a single object (which is exercised no force or on which the net force is zero) is moving in translation uniform rectilinear (immobility is a special case of uniform motion). This means that the principle of inertia , which is set out in the first Newton's law , applies.

An inertial frame is named in honor of Galileo , and more particularly to the Galilean relativity.

The search for an inertial frame is a delicate subject, the actual determination of such a repository is always approximate.

In a non-inertial reference frame , which is driven by an accelerated motion relative to an inertial frame, it must involve the forces of inertia.

Definition

In classical physics as relativity , the space of the observer is deemed to affine space of three dimensions which is associated a time used to set the body movements observed.

An inertial frame and in which a body free (not influenced by a force ) is imparted with a uniform motion, immobility being a special case.

• In Newtonian mechanics , Galilean all benchmarks are equivalent: if two observers O and O 'are driven in a uniform translational motion relative to one another, then the same laws of motion apply to each of them, that O is the reference supposed to be "stationary" (in which case O is in motion) or it is assumed that O 'and O still moving. In the framework of Newtonian mechanics, time passes, by assumption, at the same rate for all observers means that a clock calibrated in a reference will continue to measure the same periods in any other framework, that it is Galilean or not. Time is said Newtonian.

• In relativity , the equivalence of inertial frame is also assumed valid. Cons by assuming Newtonian absolute time is inconsistent with the hypothesis of the invariance of the speed of light by changing the inertial frame: it is the same in any inertial frame. Relativity leads observers to define time and distance from the speed of light is identical in each of their respective benchmarks. These measures relate to the repository of the observer: observers in different repositories will achieve a separation in time and space differ between the same two events. By cons of space-time interval will be unchanged: it is independent of inertial frame chosen is one invariant.

The Newtonian mechanics allows reasoning in any repository, but it usually favors the use of Galilean reference to simplify the analysis. In contrast, special relativity applies only in the inertial frame, the other repositories are studied in general relativity.

Examples

• Is the center of mass of a satellite and the direction of "fixed" (the furthest stars, quasars, "appear" to be fixed): This defines a quasi-Galilean referential because in the space capsule objects float in weightlessness. The repository can be considered related geocentric - roughly - as Galileo: the experience shows that every body has launched a movement that is the addition of a uniform motion and the motion imparted by the force of gravity (neglecting friction air, axifuge effect due to rotation of the earth on its axis, and the differential tidal forces due to the stars essentially the Sun and the Moon).

• Examples of non-inertial reference systems: the repository of a vehicle speeding from the road, objects tend to move in the opposite direction of acceleration, force and this without any "real" does being applied to them, in a rotating frame around a point (vehicle during cornering), objects tend to move outwards from the corner.

Confrontation with experiment

In practice, a system related to real bodies can be approximately locally and momentarily Galilean.

Compared to a system of any reference, the space is physically non-homogeneous and anisotropic, and time not uniform, and in this case the description of a single phenomenon even can take a very complicated shape. For example, when we place ourselves in a rotating carousel, we can see that objects tend to move outside the arena: the movement observed shows that in the reference frame related to the armory, there is a physical difference gradual and going from the center to the periphery (the space is not physically homogeneous).

However, experience teaches us that we can always find an inertial frame: the space is (approximately) homogeneous and isotropic, and uniform time. In practice it merely a repository of approximately inertial approximation satisfactory for the experiment considered. Thus, the ground reference can be assumed Galilean, unless the effects of the rotation of the Earth are not negligible: for experience short-term laboratory, we generally accept, to calculate the trajectory of a missile ballistics , no.

Principle of Relativity

Galilean repositories are used in Newtonian mechanics and special relativity. In both theories, inertial frames are supposed to use uniform motion against each other, over the principle of relativity states that:

• Two experiments of Newtonian mechanics or classical, made identically in two different inertial frames take place the same way. Resteinte relativity, these are all types of physical experiments (except gravity , which is not defined), not just mechanics.

For example, in classical mechanics, considering the earth's surface as an inertial frame in which the body does not undergo the influence of gravity (first approximation), the system related to a train passing at constant speed relative to the ground is also inertial (also under the influence of gravity). Suppose two people respectively motionless to the ground and land for a relative to train for the other. Suppose two people each have in hand an object identical in all respects and let go of each object one meter above the ground. These two people then watch every drop of their object: each observed falls (vertical) perfectly identical to the other's observations (measurements made by one and the other person are the same).

• Experience observed for two separate repositories Galilean (supposedly moving on rectilinear uniform) follows a written identically in the two repositories. The difference between the two laws is only the numerical value of a parameter (vector form, in general) that changes from one repository to another because of the relative speed of two frames. This setting changes the observations and measurements made of the experience from one or other landmark.

In the example above, if a person looks at the fall of the object on the other, she will not see a drop similar: in addition to vertical motion, it will see a horizontal uniform linear motion, all forming in his eyes a path to the parabolic shape.

Invariances

Emmy Noether showed, by its symmetry theorems , the significant relationship between the homogeneity of time and conservation of energy , the homogeneity of space and the conservation of momentum , the isotropy of the space and conservation of angular momentum.

Change repository

A change of reference is the set of laws to apply to convert physical quantities from one repository to another. In the case where the conversion is on the distances and times, we talk about transformation.

Classical mechanics

In the framework of Newtonian mechanics, if a repository is driven by a relative motion of rectilinear uniform compared to an inertial frame, then this reference is itself inertial, the bodies are also free subject to the "inertial motion". So there are an infinity of inertial frames in uniform rectilinear against each other, and it is assumed that all inertial frames are .

If For i = 1, 2, denote the two inertial frames of respective origins , And denote the vectors joining the origin to the point Body observed, time homogeneous in each repository, and the relative velocity of versus The vector formula of change of reference is:

, Taking because of the first equality.

If the axes of reference are pairwise parallel and the relative velocity is parallel to the axis of Yields:

Relativity

In this theory, too, we accept the assumption that all repositories are Galilean translational spatial rectilinear uniformly relative to each other. The difference with classical physics is that they are repositories of the Minkowski space to four dimensions and that the time axis is specific to each repository.

The Lorentz transformations coincide with the Galilean transformation for velocities small compared to the speed of light.

In general relativity

In general relativity , any weight and any kinetic energy imply a curvature of spacetime and thus a deviation of possible trajectories in the environment of the earth: this is the gravitation. In the vicinity of any mass of space is homogeneous and isotropic, so there can be no true inertial frame in the sense that it is included in special relativity or classical physics.

However, a reference free-fall in a gravitational field is locally inertial: according to the principle of equivalence , in the immediate vicinity of a geodesic whole body follows a geodesic parallel and at the same speed, so in that directory, and very locally (mathematically: at one point), while body checks the inertial motion. Of course, you have to accept this talk of virtual body virtual energy and masses too small to have a noticeable effect on space-time.

Similarly, far from any mass (mathematically: an infinite distance) is an inertial reference frame.

In this theory, because of the equivalence principle , the inertial frame are not all in uniform rectilinear against each other, and strictly speaking, space is curved, this notion of "rectilinear uniform" does may have the same meaning as in an affine space. One use of benchmarks is that the equalities Galilean tensor are easier to establish than in the general case of any repository, and once established for a type of referential tensor equality is true for any kind of repository ( therefore is always true).

Criticism by Henri Poincare

Henri Poincare in his book Science and Hypothesis (1902) stressed that the principles of physics are based on any logical necessity.

Already, this scholar put into question the a priori that the physical space is a three-dimensional Euclidean space, although he found "no experience will never be in contradiction with the postulate of Euclid, however no experiments will never be in contradiction with the postulate of Lobachevsky " .

Poincare articulates his thinking as follows. An inertial frame is defined as a Cartesian reference , assumed affine space, where the movement of any body not influenced by a force in a straight uniform must know what a force before applying this definition. A force can be measured-so-defined by the fact that it makes the movement non-uniform rectilinear : the concept of force presupposes that of Galilean is well defined. Force and the inertial frame are defined by one another. What looks like when a circular definition is rooted in experience: observing systems almost isolated (that is to say away from the body can significantly influence), we always come to define repositories in which the movements of the centers of gravity systems are almost rectilinear and uniform . Finally, Henri Poincare insists mechanics is an experimental science where nature is irrelevant concepts used, only count the fact that these concepts are "convenient" in terms of their mathematical formulation, they are measurable and predict results of experiments repeated.

Notes

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