Proper acceleration

physical acceleration
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object.wikipedia
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Accelerometer

accelerometersG-sensoracceleration sensor
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object.
An accelerometer is a device that measures proper acceleration.

Acceleration (special relativity)

three-acceleration in special relativityacceleration within special relativityaccelerations
Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers (see three-acceleration in special relativity).
One can derive transformation formulas for ordinary accelerations in three spatial dimensions (three-acceleration or coordinate acceleration) as measured in an external inertial frame of reference, as well as for the special case of proper acceleration measured by a comoving accelerometer.

Weightlessness

zero gravityzero-gravityzero-g
This state is also known as "zero gravity" ("zero-g") or "free-fall," and it produces a sensation of weightlessness.
This acceleration which is not due to gravity is called "proper acceleration".

Four-acceleration

acceleration vector4-acceleration
In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant.
Therefore, the magnitude of the four-acceleration (which is an invariant scalar) is equal to the proper acceleration that a moving particle "feels" moving along a worldline.

Proper velocity

ccelerityProper speed
In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time.
Proper acceleration at any speed is the physical acceleration experienced locally by an object.

G-force

gg-forcesGs
In an accelerating rocket after launch, or even in a rocket standing at the gantry, the proper acceleration is the acceleration felt by the occupants, and which is described as g-force (which is not a force but rather an acceleration; see that article for more discussion of proper acceleration) delivered by the vehicle only. Such geometric (or improper) forces include Coriolis forces, Euler forces, g-forces, centrifugal forces and (as we see below) gravity forces as well.
His weight (a downward force) is 725 N. In accordance with Newton’s third law, the plane and the seat underneath the pilot provides an equal and opposite force pushing upwards with a force of 725 N. This mechanical force provides the 1.0 g-force upward proper acceleration on the pilot, even though this velocity in the upward direction does not change (this is similar to the situation of a person standing on the ground, where the ground provides this force and this g-force).

Fictitious force

inertial forcefictitious forcesinertial
This weight, in turn, is produced by fictitious forces or "inertial forces" which appear in all such accelerated coordinate systems, in a manner somewhat like the weight produced by the "force of gravity" in systems where objects are fixed in space with regard to the gravitating body (as on the surface of the Earth).
The physical acceleration a A due to what observers in the inertial frame A call real external forces on the object is, therefore, not simply the acceleration a B seen by observers in the rotational frame B, but has several additional geometric acceleration terms associated with the rotation of B.

Rapidity

rapidities
For constant unidirectional proper-acceleration, similar relationships exist between rapidity η and elapsed proper time Δτ, as well as between Lorentz factor γ and distance traveled Δx.
Proper acceleration (the acceleration 'felt' by the object being accelerated) is the rate of change of rapidity with respect to proper time (time as measured by the object undergoing acceleration itself).

Proper reference frame (flat spacetime)

momentarily comoving reference frame'' (MCRF)proper reference frameproper reference frames
Proper reference frame (flat spacetime): accelerated reference frame in special relativity (Minkowski space)
(For the representation of accelerations in inertial frames, see the article Acceleration (special relativity), where concepts such as three-acceleration, four-acceleration, proper acceleration, hyperbolic motion etc. are defined and related to each other.)

Proper time

proper-time
Here a single reference frame of yardsticks and synchronized clocks define map position x and map time t respectively, the traveling object's clocks define proper time τ, and the "d" preceding a coordinate means infinitesimal change.
Proper acceleration

Acceleration

decelerationacceleratem/s 2
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers (see three-acceleration in special relativity). When holding onto a carousel that turns at constant angular velocity you experience a radially inward (centripetal) proper-acceleration due to the interaction between the handhold and your hand.
Proper acceleration, the acceleration of a body relative to a free-fall condition, is measured by an instrument called an accelerometer.

Theory of relativity

relativityrelativisticrelativity theory
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object.

Free fall

free-fallfreefallhighest fall without a parachute
It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured.

Coordinate system

coordinatescoordinateaxis
Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers (see three-acceleration in special relativity).

Lorentz covariance

Lorentz invariantLorentz invarianceLorentz covariant
In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant.

Weight

gross weightweighingweigh
In situations in which gravitation is absent but the chosen coordinate system is not inertial, but is accelerated with the observer (such as the accelerated reference frame of an accelerating rocket, or a frame fixed upon objects in a centrifuge), then g-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems.

Angular velocity

angular speedangular velocitiesangular velocity tensor
When holding onto a carousel that turns at constant angular velocity you experience a radially inward (centripetal) proper-acceleration due to the interaction between the handhold and your hand.

Rotating reference frame

rotating frame of referencerotating framerotating coordinate system
This cancels the radially outward geometric acceleration associated with your spinning coordinate frame.

Geodesic

geodesicsgeodesic flowgeodesic equation
This outward acceleration (from the spinning frame's perspective) will become the coordinate acceleration when you let go, causing you to fly off along a zero proper-acceleration (geodesic) path.

Affine connection

connectionaffineconnections
Note that geometric accelerations (due to the connection term in the coordinate system's covariant derivative below) act on every ounce of our being, while proper-accelerations are usually caused by an external force.

Covariant derivative

covariant differentiationcovariant differentialtensor derivative
Note that geometric accelerations (due to the connection term in the coordinate system's covariant derivative below) act on every ounce of our being, while proper-accelerations are usually caused by an external force.

Inertial frame of reference

inertial frameinertialinertial reference frame
At low speeds in the inertial coordinate systems of Newtonian physics, proper acceleration simply equals the coordinate acceleration a=d 2 x/dt 2.

Gravitational field

gravitationalgravitational fieldsgravity field
If one chooses to recognize that gravity is caused by the curvature of spacetime (see below), proper acceleration differs from coordinate acceleration in a gravitational field.

Newton's laws of motion

laws of motionNewton's second lawNewton's second law of motion
At low speeds in the inertial coordinate systems of Newtonian physics, proper acceleration simply equals the coordinate acceleration a=d 2 x/dt 2.

Coriolis force

Corioliscoriolis effectCoriolis forces
Such geometric (or improper) forces include Coriolis forces, Euler forces, g-forces, centrifugal forces and (as we see below) gravity forces as well.