Welcome to Einstein Relatively Easy!
This web site is aimed at the general reader who is keen to discover Einstein's theories of special and general relativity, and who may also like to tackle the essential underlying mathematics.
Einstein's Relativity is too beautiful and too engaging to be restricted to the professionals!
"I have no special talents
I am only passionately curious"
- Category: Dictionary
It should be clear that General Relativity describes gravitation in terms of curvature of spacetime and reduces to Special Theory of Relativity for Local Inertial Frame (LIF). However, it is important to explicitly check that the description reduces to the Newtonian treatment when we select the correct boundary conditions.
These conditions, referred to as the Newtonian limit, are applicable to physical systems exhibiting:
- - objects moving relatively slowly (compared to the speed of light).
- - weak gravitional field.
- - gravitational field does not change with time, ie it is static.
Mathematically, this leads to the following approximations:
- Category: Dictionary
There are traditionally two ways of deriving this equation:
- - first by some informal reasoning by analogy, close to what Einstein himself was thinking (refer to Einstein Tensor and Einstein Field Equations) and which begins with the realization that we would like to find an equation that supersedes the Poisson equation for the Newtonian potential
- - or by starting with an action and deriving the corresponding equations of motion (refer to Einstein-Hilbert action)
- Category: Special Relativity
As we know from the Newton's first law of motion, a free particle in motion travels in a straight line with constant velocity.
In this article our aim is to express this law, sometimes referred to as the law of inertia in the terms of special relativity's concepts. More precisely, we will try to demonstrate that in special relativity's Minkowski flat spacetime, a free particule has the maximum proper time of all possible world lines that connect two events.
As a starting point, let us recall the expression of the Proper Time as measured by a clock between two events A and B in any inertial referential, with t and v correponding respectively to the time and the speed of the clock as measured in this referential - here we assume c=1 for more readability:
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