Inertial frame in the context of Rindler coordinates

⭐ Core Definition: Inertial frame

In classical physics and special relativity, an inertial frame of reference (also called an inertial space or a Galilean reference frame) is a frame of reference in which objects exhibit inertia: they remain at rest or in uniform motion relative to the frame until acted upon by external forces. In such a frame, the laws of nature can be observed without the need to correct for acceleration.

All frames of reference with zero acceleration are in a state of constant rectilinear motion (straight-line motion) with respect to one another. In such a frame, an object with zero net force acting on it, is perceived to move with a constant velocity, or, equivalently, Newton's first law of motion holds. Such frames are known as inertial. Some physicists, like Isaac Newton, originally thought that one of these frames was absolute — the one approximated by the fixed stars. However, this is not required for the definition, and it is now known that those stars are in fact moving, relative to one another.

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👉 Inertial frame in the context of Rindler coordinates

Rindler coordinates are a coordinate system used in the context of special relativity to describe the hyperbolic acceleration of a uniformly accelerating reference frame in flat spacetime. In relativistic physics the coordinates of a hyperbolically accelerated reference frame constitute an important and useful coordinate chart representing part of flat Minkowski spacetime. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion, for which a uniformly accelerating frame of reference in which it is at rest can be chosen as its proper reference frame. The phenomena in this hyperbolically accelerated frame can be compared to effects arising in a homogeneous gravitational field. For general overview of accelerations in flat spacetime, see Acceleration (special relativity) and Proper reference frame (flat spacetime).

In this article, the speed of light is defined by $c = 1$ , the inertial coordinates are $(X, Y, Z, T)$ , and the hyperbolic coordinates are $(x, y, z, t)$ . These hyperbolic coordinates can be separated into two main variants depending on the accelerated observer's position: If the observer is located at time $T = 0$ at position $X = 1/α$ (with $α$ as the constant proper acceleration measured by a comoving accelerometer), then the hyperbolic coordinates are often called Rindler coordinates with the corresponding Rindler metric. If the observer is located at time $T = 0$ at position $X = 0$ , then the hyperbolic coordinates are sometimes called Møller coordinates or Kottler–Møller coordinates with the corresponding Kottler–Møller metric. An alternative chart often related to observers in hyperbolic motion is obtained using Radar coordinates which are sometimes called Lass coordinates. Both the Kottler–Møller coordinates as well as Lass coordinates are denoted as Rindler coordinates as well.

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⭐ Core Definition: Inertial frame
👉 Inertial frame in the context of Rindler coordinates
Inertial frame in the context of Center-of-momentum frame
Inertial frame in the context of Preferred frame
Inertial frame in the context of Lorentz covariance
Inertial frame in the context of Covariant formulation of classical electromagnetism

Inertial frame in the context of Center-of-momentum frame

A special case of the center-of-momentum frame is the center-of-mass frame: an inertial frame in which the center of mass (which is a single point) remains at the origin. In all center-of-momentum frames, the center of mass is at rest, but it is not necessarily at the origin of the coordinate system. In special relativity, only when the system is isolated is the COM frame necessarily unique.

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Inertial frame in the context of Preferred frame

In theoretical physics, a preferred frame or privileged frame is usually a special hypothetical frame of reference in which the laws of physics might appear to be identifiably different (simpler) from those in other frames.

In theories that apply the principle of relativity to inertial motion, physics is the same in all inertial frames, and is even the same in all frames under the principle of general relativity.

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Inertial frame in the context of Lorentz covariance

In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same for all observers that are moving with respect to one another within an inertial frame. It has also been described as "the feature of nature that says experimental results are independent of the orientation or the boost velocity of the laboratory through space".

Lorentz covariance, a related concept, is a property of the underlying spacetime manifold. Lorentz covariance has two distinct, but closely related meanings:

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Inertial frame in the context of Covariant formulation of classical electromagnetism

The covariant formulation of classical electromagnetism refers to ways of writing the laws of classical electromagnetism (in particular, Maxwell's equations and the Lorentz force) in a form that is manifestly invariant under Lorentz transformations, in the formalism of special relativity using rectilinear inertial coordinate systems. These expressions both make it simple to prove that the laws of classical electromagnetism take the same form in any inertial coordinate system, and also provide a way to translate the fields and forces from one frame to another. However, this is not as general as Maxwell's equations in curved spacetime or non-rectilinear coordinate systems.
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Inertial frame in the context of Rindler coordinates

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⭐ Core Definition: Inertial frame

👉 Inertial frame in the context of Rindler coordinates

Inertial frame in the context of Center-of-momentum frame

Inertial frame in the context of Preferred frame

Inertial frame in the context of Lorentz covariance

Inertial frame in the context of Covariant formulation of classical electromagnetism