## Regis petit – relativity electricity drinking game

• Historical background• Einstein equations• Solution of Einsteins equations• Solution of Einsteins equations with Schwarzschild metric• Solution of Einsteins equations with Friedmann-Lemaitre-Robertson-Walker metric• Spectral shifts• Definition of concepts• Bibliography 1. What is Relativity ? ( Paragraph Previous / Next ) 1.1. The three stages of relativity ( Previous / Next Subparagraph )

Imagine two observers O and O’ in relative movement with respect to each other, who wish to set their watches by exchange of optical signals. grade 6 electricity quiz Suppose that the two watches are synchronized by any means so that they indicate the same time at the same initial instant. At this instant each observer sends a signal to the other. What time does each watch indicate when each observer receives the signal from the other ? It is obvious that this is not the same time.

And Poincaré explains : " The transmission duration is not the same in both directions since the observer O, for example, goes ahead of the optical propagation emanating from O’, while the observer O’ flees the propagation emanating from O. The watches will indicate what can be called local time of each observer, so that one of them will delay on the other. It does not matter since we have no way of seeing it…" [POI L’Etat, p.311]

In 1975 Jean-Marc Levy-Leblong published an article on Restricted Relativity presented in a modern form deduced only from the properties of space and time (Poincaré’s postulates), without need for reference to electromagnetism [LEV One_more]. Einstein’s postulate on the invariance of the light speed in all reference frames then appears as a simple consequence of the Lorentz-Poincaré transformation describing Restricted Relativity.

For black holes the singularity r = r * can be eliminated by a suitable choice of the coordinate system. On the other hand, the singularity r = 0 is a singularity of the Metric tensor g which shows the limit of the black holes description by the General Relativity and probably requires the use of a quantum theory of gravitation which does not really exist to date.

We finally write and solve the equations of Geodesics which describe the movement of free particles in the space considered, that is when these particles (material systems or photons) are not subjected to an external force other than gravitation in the context of General Relativity. See Geodesic of a material body and Geodesic of a photon.

6.3. gas block dimple jig Singular case : when Λ equals Λ F, with positive k, the relation (Q5) induces that the curve a(t) has a point with horizontal tangent (a’ = 0) that coincides with the inflection point I. electricity year 4 This model has two types of possible behavior : a static model (Einstein static universe) for which a(t) = constant (curve C3), and an open model with an inflection point for which a’ = a" = 0 at the point a I = a F (curve C4).

6.4. When Λ is less than Λ F, with positive k, the relation (Q5) induces that the curve a(t) has two extremums (a’ = 0 ; points M1 and M2). This model has two types of possible behavior : a closed model (a" 0) with a minimum point in M2 (curve C5), the respective inflection points I1 and I2 being fictitious and rejected in the forbidden band (a1 θ, as if the light received by the mobile observer concentrated on its movement direction.

The general covariance of a physical law has nothing to do with the Covariance of the tensor components. The word "covariance" does not refer to the covariant index of a Tensor but only indicates a writing of the physical law which remains form-invariant under any coordinates transformation (invariance by diffeomorphism) [AMI Initiation_aux_Tenseurs, p.18].

The Newtonian limit is to do : E0/m b crit, the photons coming from infinity will approach the central body and return to infinity. The trajectory looks like a hyperbola for the large values of b (see Figure 1 above) and can make several rounds of the central body before starting again for the values of b near b crit (see Figure 2 above).

– For b b crit : there are three real roots, one of which is negative. The largest positive root corresponds to the periastron r per which is reached continuously from a photon arriving from infinity. Given the particular conditions : p > b crit and at first order of r*/b, the deflection δφ of the light ray from a straight line path (see Figure 1 above) is then as follows [GOU Relativité_Générale, p.86, 87] :

This effect was described for the first time by Einstein in 1905 in the following form : "If at point A there are two synchronized clocks and we move one of them at a constant speed v according to a closed curve which amounts to A, the displacement being completed in t seconds, then the mobile clock will delay by (1/2) t (v/c) 2 seconds on the immobile clock when it arrives at A (neglecting the fourth order of v/c and higher orders) [EIN Sur_electrodynamique, para.4]".

Thus, two clocks associated with distinct Universe lines will generally be desynchronized when they intersect. electricity in india voltage More precisely, two perfect clocks (that is, never deregulating) and ideally synchronized clocks will shift if they are separated before reuniting them again. The number of seconds counted will differ between the two clocks, the cumulative time depending on the trajectory followed by each clock. If the reference frame is not Inertial, the offset will be an advance or a delay.

– Henri Bergson, French philosopher, explains : "We are told that if two identical and synchronous clocks are in the same place in the reference system, if one is moved and brought back close to the other at the end of time t (time of the system), this one will delay on the other clock. In reality, it would be necessary to say that the moving clock exhibits this delay at the precise instant when it touches, still moving, the immobile system, and where it will go in. electricity vancouver wa But as soon as it goes in, it will indicate the same time as the other…" [BER Durée, p.208].

The metric of Karl Schwarzschild is a Relativistic metric corresponding to the static gravitational field with central symmetry. This is the case of the Sun and many stars. The central body is spherically symmetrical and not necessarily static (for example, a pulsating star that oscillates radially or a star that collapses into a black hole while maintaining its spherical symmetry). The gravitational field must be static even if it is not static in the area where the matter is located. Note that the gravitational field is necessarily static in spherical symmetry and in vacuum (Birkhoff theorem).

Measurements are made by fixed clocks in their reference frame and whose internal mechanism is generally insensitive to the reference frame movement. An atomic clock is an ideal clock because the time it provides does not depend very much on accelerations undergone which are very low compared to the centripetal acceleration of an electron around its atomic nucleus (about 10 23 m.s -2).

In Restricted Relativity, for a given reference frame, the proper duration (d0) is the time interval that separates two events occurring at the same place in this reference frame. gas block install In any other reference frame, the duration is greater than the proper duration and is called apparent duration (d). Some authors speak of Dilation of apparent durations.

In the twin paradox, one of the twins stays on Earth while his brother makes a space journey at a speed close to the light speed and then goes back to Earth. We must then consider three Inertial references frames : the twin "at rest", the traveling twin on outward journey and the traveling twin on return journey. m power electricity To date it is no longer disputed that the clocks of the two successive reference frames of the traveling twin indicate a total duration shorter than the one of the twin at rest ( Multiplicity of proper times) and there is no longer a paradox. However few authors produce a demonstration of this phenomenon that is physically acceptable, with non-infinite Quadri-accelerations at the rupture points of the spatio-temporal trajectory of the traveling twin [GOU Relativité_Restreinte, p.41].

Note that the Principle of equivalence combined with the Multiplicity of proper times predicted by Restricted Relativity leads us to predict a multiplicity of proper times where there is a multiplicity of gravitational potentials. Two perfect clocks placed in places of different gravitational potentials will not record identical cumulative times. We can speak of "Twin paradox bis": two twins living at different altitudes will not record the same duration.

– Thibault Damour, Phycisien of Relativity, asserts that even if the traveling twin goes back to Earth younger than the sedentary twin, he will not live any longer. The best image is cryogenics : instead of sending one of the twins into space, he was put in an ice block and then delivered. The proper time of the traveling twin is actually shorter than the one of the sedentary twin but he does not acquire an additional "biological time", for example the number of heartbeats.