The paths only seem curved because of the warping of spacetime. We can solve for k giving k sqrt ( (1+v/c)/ (1-v/c)) which is the relativistic Doppler shift formula. Matter tells spacetime how to curve Point 1 is actually straightforward to explain: objects simply travel on the straightest possible paths through spacetime, called geodesics. Thus the speed of B according to A is v D/t DA (R)/tA (R) c (kk-1)/ (kk+1). Refer to the article 1907 Equivalence Principle first published expression to read the Einstein's first formulation of this principle. We can now compute the distance of event R from As worldline and time of event R according to A, tA (R). how a local inertial frame (black colour) can be obtained by a general coordinate transformation at any point P of a manifold (blue colour) Refer to the below youtube tutorial to get a good overview of the mathematical expression of the principle, i.e. Refer to the article The Equivalence Principle for more details. ![]() It depends on the fact that all objects fall with exactly the same. The paths of free bodies define what we mean by straight and if we observe an object deviate from constant velocity, it must be because spacetime itself is. Mathematically, this important observation states that in presence of a gravitational field, small enough free falling frames will be inertial, and that in these Local Inertial Frame (LIF), where the metric g μν reduces to η μν, the laws of physics from Special Relativity will hold true. This idea, when stated with greater precision, is called Einsteins principle of equivalence. "The vehicle between flat spacetime and curved spacetime is the Equivalence Principle: the laws of physics are the same in any Local Lorentz frame of curved spacetime as in a global Lorentz frame of flat spacetime" Gravitation (Misner, Thorne, Wheeler) § 8.5. Put in another way, according to this principle, all physic laws wih hold the same form in a free falling Local Inertial Frame (LIF) in presence of the gravitation and in an Inertial Frame in absence of gravitation. The solution only applies to the exterior of a star, where there. Only acceleration can do that, and due to the equivalence principle, it is the same as the effect of a gravitational field. This solution demonstrates how the presence of mass curves at spacetime. Light follows a geodesic, and as the elevator accelerates, photons entering perpendicularly to the elevator sidewalls, those photons' path will be curved. ![]() Note also that as r 1, the metric (6.31) becomes more like Minkowski space this property is known as asymptotic atness. Physically, this principle (sometimes referred as to EEP = Einstein's Equivalence Principle) postulates that there is no experiment done in a small confined space which can tell the difference between a uniform gravitational field and an equivalent acceleration. Note that as M 0, we recover Minkowski space, as expected. The equivalence principle states that the 'force' you feel, for example, when youre pushed into your seat in an accelerating vehicle is the same thing as gravity.
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