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Frame of reference

reference frameframes of referencereference frames
An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.
Sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference.

Special relativity

special theory of relativityrelativisticspecial
An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.
1) The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference).

Lorentz transformation

boostboostsLorentz boosts
Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). However, because special relativity postulates that the speed of light in free space is invariant, the transformation between inertial frames is the Lorentz transformation, not the Galilean transformation which is used in Newtonian mechanics.
Frames of reference can be divided into two groups: inertial (relative motion with constant velocity) and non-inertial (accelerating, moving in curved paths, rotational motion with constant angular velocity, etc.).

Accelerometer

accelerometersG-sensoracceleration sensor
All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration.
Put another way, at any point in spacetime the equivalence principle guarantees the existence of a local inertial frame, and an accelerometer measures the acceleration relative to that frame.

Non-inertial reference frame

accelerated reference framenon-inertialnon-inertial frame
In a non-inertial reference frame in classical physics and special relativity, the physics of a system vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces.
A non-inertial reference frame is a frame of reference that is undergoing acceleration with respect to an inertial frame.

General relativity

general theory of relativityrelativitygeneral relativity theory
In general relativity, in any region small enough for the curvature of spacetime and tidal forces to be negligible, one can find a set of inertial frames that approximately describe that region. Einstein’s general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature.
Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames.

Coriolis force

Corioliscoriolis effectCoriolis forces
The physics must account for the Coriolis effect—in this case thought of as a force—to predict the horizontal motion.
Newton's laws of motion describe the motion of an object in an inertial (non-accelerating) frame of reference.

Newton's laws of motion

laws of motionNewton's second lawNewton's second law of motion
In an inertial frame, Newton's first law, the law of inertia, is satisfied: Any free motion has a constant magnitude and direction. Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed.
Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames.

Fictitious force

inertial forcefictitious forcesinertial
In a non-inertial reference frame in classical physics and special relativity, the physics of a system vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces.
1) Figure 1 (center panel). To an observer at rest on an inertial reference frame (like the ground), the car will seem to accelerate. In order for the passenger to stay inside the car, a force must be exerted on the passenger. This force is exerted by the seat, which has started to move forward with the car and is compressed against the passenger until it transmits the full force to keep the passenger moving with the car. Thus, the forces exerted by the seat are unbalanced,so the passenger is accelerating in this frame.

Euclidean vector

vectorvectorsvector addition
with F the net force (a vector), m the mass of a particle and a the acceleration of the particle (also a vector) which would be measured by an observer at rest in the frame.
In these cases, each of the components may be in turn decomposed with respect to a fixed coordinate system or basis set (e.g., a global coordinate system, or inertial reference frame).

Rotating reference frame

rotating frame of referencerotating framerotating coordinate system
In contrast, Newton's second law in a rotating frame of reference, rotating at angular rate Ω about an axis, takes the form:
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame.

Quantum reference frame

When quantum effects are important, there are additional conceptual complications that arise in quantum reference frames.
An inertial reference frame (or inertial frame in short) is a frame in which all the physical laws hold.

Expansion of the universe

expanding universeexpandingexpansion of space
Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to expansion of the universe, and partly due to peculiar velocities.
General relativity necessarily invokes a metric in four dimensions (one of time, three of space) because, in general, different reference frames will experience different intervals of time and space depending on the inertial frame.

Force

forcesattractiveforce vector
Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton's first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed.
The laws of physics are the same in every inertial frame of reference, that is, in all frames related by a Galilean transformation.

Mach's principle

Machiandistant masses of the universeMach principle
A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach's principle).
The idea is that the existence of absolute rotation (the distinction of local inertial frames vs. rotating reference frames) is determined by the large-scale distribution of matter, as exemplified by this anecdote:

Centrifugal force

centrifugalcentrifugal accelerationcentrifugal effect
Another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force.
It does not exist when a system is described relative to an inertial frame of reference.

Speed of light

clight speedvelocity of light
However, because special relativity postulates that the speed of light in free space is invariant, the transformation between inertial frames is the Lorentz transformation, not the Galilean transformation which is used in Newtonian mechanics.
regardless of the motion of the source or the inertial reference frame of the observer.

Inertial navigation system

inertial guidanceINSinertial navigation
Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space.
Gyroscopes measure the angular velocity of the sensor frame with respect to the inertial reference frame.

Classical mechanics

classicalNewtonianNewtonian physics
Today the notion of "absolute space" is abandoned, and an inertial frame in the field of classical mechanics is defined as:
These special reference frames are called inertial frames.

Minkowski space

flat spacetimelightlikespacelike
Einstein’s general theory modifies the distinction between nominally "inertial" and "noninertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature.
In mathematical physics, Minkowski space (or Minkowski spacetime) is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

Preferred frame

privileged reference framespreferred reference frameprivileged
Some theories may even postulate the existence of a privileged frame which provides absolute space and absolute time.
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 general principle of relativity.

Galilean invariance

Galilean invariantGalilean relativityPrinciple of relativity
Galilean invariance
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames.

Milky Way

galaxyMilky Way Galaxyour galaxy
Those that reside in the Milky Way turn with the galaxy, exhibiting proper motions.
Although special relativity states that there is no "preferred" inertial frame of reference in space with which to compare the Milky Way, the Milky Way does have a velocity with respect to cosmological frames of reference.

Relativity of simultaneity

simultaneitylocal timerelative simultaneity
The invariance of the speed of light leads to counter-intuitive phenomena, such as time dilation and length contraction, and the relativity of simultaneity, which have been extensively verified experimentally.
In physics, the relativity of simultaneity is the concept that distant simultaneity – whether two spatially separated events occur at the same time – is not absolute, but depends on the observer's reference frame.

Lorentz covariance

Lorentz invariantLorentz invarianceLorentz covariant
Lorentz invariance
In relativistic physics, Lorentz symmetry, named for 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.