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The space R 3 is endowed with a scalar product , . Time is a scalar which is the same in all space E 3 and is denoted as t. The ordered set { t} is called a time axis. Motion (also path or trajectory) is a function r : Δ → R 3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R 3.
is the time between two events as measured in the moving reference frame in which they occur at the same place (e.g. two ticks on a moving clock); it is called the proper time between the two events; t is the time between these same two events, but as measured in the stationary reference frame;
The action of the Einstein-aether theory is generally taken to consist of the sum of the Einstein–Hilbert action with a Lagrange multiplier λ that ensures that the time vector is a unit vector and also with all of the covariant terms involving the time vector u but having at most two derivatives.
The field equations of general relativity are not parameterized by time but formulated in terms of spacetime. Many of the issues related to the problem of time exist within general relativity. At the cosmic scale, general relativity shows a closed universe with no external time. These two very different roles of time are incompatible. [4]
Presentism is a view about temporal ontology, i.e., a view about what exists in time, that contrasts with eternalism—the view that past, present and future entities exist (that is, the ontological thesis of the 'block universe')—and with no-futurism—the view that only past and present entities exist (that is, the ontological thesis of the ...
Temporal finitism is the doctrine that time is finite in the past. [clarification needed] The philosophy of Aristotle, expressed in such works as his Physics, held that although space was finite, with only void existing beyond the outermost sphere of the heavens, time was infinite.
These equations specify how the geometry of space and time is influenced by whatever matter and radiation are present. [5] A version of non-Euclidean geometry, called Riemannian geometry, enabled Einstein to develop general relativity by providing the key mathematical framework on which he fit his physical ideas of gravity. [6]
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive where and when events ...