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Sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference.
In this article, the term observational frame of reference is used when emphasis is upon the state of motion rather than upon the coordinate choice or the character of the observations or observational apparatus.
In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame.
On the other hand, a coordinate system may be employed for many purposes where the state of motion is not the primary concern.
For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs generalized coordinates , normal modes or eigenvectors , which are only indirectly related to space and time.
It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below:.
The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani. Although the term "coordinate system" is often used particularly by physicists in a nontechnical sense, the term "coordinate system" does have a precise meaning in mathematics, and sometimes that is what the physicist means as well.
A coordinate system in mathematics is a facet of geometry or of algebra ,   in particular, a property of manifolds for example, in physics, configuration spaces or phase spaces.
In a general Banach space , these numbers could be for example coefficients in a functional expansion like a Fourier series.
In a physical problem, they could be spacetime coordinates or normal mode amplitudes. In a robot design , they could be angles of relative rotations, linear displacements, or deformations of joints.
Given these functions, coordinate surfaces are defined by the relations:. The intersection of these surfaces define coordinate lines. For more detail see curvilinear coordinates.
Coordinate surfaces, coordinate lines, and basis vectors are components of a coordinate system. An important aspect of a coordinate system is its metric tensor g ik , which determines the arc length ds in the coordinate system in terms of its coordinates: As is apparent from these remarks, a coordinate system is a mathematical construct , part of an axiomatic system.
There is no necessary connection between coordinate systems and physical motion or any other aspect of reality. However, coordinate systems can include time as a coordinate, and can be used to describe motion.
Thus, Lorentz transformations and Galilean transformations may be viewed as coordinate transformations. General and specific topics of coordinate systems can be pursued following the See also links below.
Here we adopt the view expressed by Kumar and Barve: In special relativity, the distinction is sometimes made between an observer and a frame.
According to this view, a frame is an observer plus a coordinate lattice constructed to be an orthonormal right-handed set of spacelike vectors perpendicular to a timelike vector.
There are two types of observational reference frame: An inertial frame of reference is defined as one in which all laws of physics take on their simplest form.
In special relativity these frames are related by Lorentz transformations , which are parametrized by rapidity. These frames are related by Galilean transformations.
In contrast to the inertial frame, a non-inertial frame of reference is one in which fictitious forces must be invoked to explain observations. This frame of reference orbits around the center of the Earth, which introduces the fictitious forces known as the Coriolis force , centrifugal force , and gravitational force.
All of these forces including gravity disappear in a truly inertial reference frame, which is one of free-fall.
A further aspect of a frame of reference is the role of the measurement apparatus for example, clocks and rods attached to the frame see Norton quote above.
This question is not addressed in this article, and is of particular interest in quantum mechanics , where the relation between observer and measurement is still under discussion see measurement problem.
In physics experiments, the frame of reference in which the laboratory measurement devices are at rest is usually referred to as the laboratory frame or simply "lab frame.
The lab frame in some experiments is an inertial frame, but it is not required to be for example the laboratory on the surface of the Earth in many physics experiments is not inertial.
In particle physics experiments, it is often useful to transform energies and momenta of particles from the lab frame where they are measured, to the center of momentum frame "COM frame" in which calculations are sometimes simplified, since potentially all kinetic energy still present in the COM frame may be used for making new particles.
In fact, Einstein felt that clocks and rods were merely expedient measuring devices and they should be replaced by more fundamental entities based upon, for example, atoms and molecules.
Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities.
At some particular moment, they are separated by metres. The car in front is travelling at 22 metres per second and the car behind is travelling at 30 metres per second.
If we want to find out how long it will take the second car to catch up with the first, there are three obvious "frames of reference" that we could choose.
First, we could observe the two cars from the side of the road. We define our "frame of reference" S as follows. Note how much easier the problem becomes by choosing a suitable frame of reference.
The third possible frame of reference would be attached to the second car. It would have been possible to choose a rotating, accelerating frame of reference, moving in a complicated manner, but this would have served to complicate the problem unnecessarily.
It is also necessary to note that one is able to convert measurements made in one coordinate system to another. For example, suppose that your watch is running five minutes fast compared to the local standard time.
If you know that this is the case, when somebody asks you what time it is, you are able to deduct five minutes from the time displayed on your watch in order to obtain the correct time.
For a simple example involving only the orientation of two observers, consider two people standing, facing each other on either side of a north-south street.
A car drives past them heading south. For the person facing east, the car was moving towards the right.
However, for the person facing west, the car was moving toward the left. This discrepancy is because the two people used two different frames of reference from which to investigate this system.
For a more complex example involving observers in relative motion, consider Alfred, who is standing on the side of a road watching a car drive past him from left to right.
In his frame of reference, Alfred defines the spot where he is standing as the origin, the road as the x -axis and the direction in front of him as the positive y -axis.
To him, the car moves along the x axis with some velocity v in the positive x -direction. Now consider Betsy, the person driving the car.
Betsy, in choosing her frame of reference, defines her location as the origin, the direction to her right as the positive x -axis, and the direction in front of her as the positive y -axis.
In this frame of reference, it is Betsy who is stationary and the world around her that is moving — for instance, as she drives past Alfred, she observes him moving with velocity v in the negative y -direction.
If she is driving north, then north is the positive y -direction; if she turns east, east becomes the positive y -direction. Finally, as an example of non-inertial observers, assume Candace is accelerating her car.
As she passes by him, Alfred measures her acceleration and finds it to be a in the negative x -direction. Frames of reference are especially important in special relativity , because when a frame of reference is moving at some significant fraction of the speed of light, then the flow of time in that frame does not necessarily apply in another frame.
The speed of light is considered to be the only true constant between moving frames of reference. It is important to note some assumptions made above about the various inertial frames of reference.
Newton, for instance, employed universal time, as explained by the following example. Suppose that you own two clocks, which both tick at exactly the same rate.
You synchronize them so that they both display exactly the same time. The two clocks are now separated and one clock is on a fast moving train, traveling at constant velocity towards the other.
According to Newton, these two clocks will still tick at the same rate and will both show the same time. Newton says that the rate of time as measured in one frame of reference should be the same as the rate of time in another.
That is, there exists a "universal" time and all other times in all other frames of reference will run at the same rate as this universal time irrespective of their position and velocity.
This concept of time and simultaneity was later generalized by Einstein in his special theory of relativity where he developed transformations between inertial frames of reference based upon the universal nature of physical laws and their economy of expression Lorentz transformations.
It is also important to note that the definition of inertial reference frame can be extended beyond three-dimensional Euclidean space.
As an example of why this is important, let us consider the geometry of an ellipsoid. In this geometry, a "free" particle is defined as one at rest or traveling at constant speed on a geodesic path.
Two free particles may begin at the same point on the surface, traveling with the same constant speed in different directions. After a length of time, the two particles collide at the opposite side of the ellipsoid.
Both "free" particles traveled with a constant speed, satisfying the definition that no forces were acting. This means that the particles were in inertial frames of reference.
Since no forces were acting, it was the geometry of the situation which caused the two particles to meet each other again.
In a similar way, it is now common to describe  that we exist in a four-dimensional geometry known as spacetime. In this picture, the curvature of this 4D space is responsible for the way in which two bodies with mass are drawn together even if no forces are acting.
This curvature of spacetime replaces the force known as gravity in Newtonian mechanics and special relativity. Here the relation between inertial and non-inertial observational frames of reference is considered.
In moving picture TV the number of frames scanned per second is known as the frame rate. The higher the frame rate, the better the sense of motion.
But again, increasing the frame rate introduces technical difficulties. To increase the sense of motion it is customary to scan the very same frame in two consecutive phases.
In each phase only half of the lines are scanned; only the lines with odd numbers in the first phase and only the lines with even numbers in the second phase.
Each scan is known as a field. So the field rate is two times the frame rate. In system B the number of lines is and the frame rate is The system is able to transmit 5 sine signals in a second.
Since the frame rate is 25, the maximum number of sine signals per frame is Dividing this number by the number of lines gives the maximum number of sine signals in a line which is So the number of maximum useful sine signals is about A still frame is a single static image taken from a film or video , which are kinetic moving images.
Freeze frames are widely used on video platforms and in video galleries, to show viewers a preview or a teaser. Many video platforms have a standard to display a frame from mid-time of the video.
Some platforms offer the option to choose a different frame individually. For criminal investigations it has become a frequent use to publish still frames from surveillance videos in order to identify suspect persons and to find more witnesses.
Some humor in animation is based on the fourth wall aspect of the film frame itself, with some animation showing characters leaving what is assumed to be the edge of the film or the film malfunctioning.
This latter one is used often in films as well. From Wikipedia, the free encyclopedia. This article needs additional citations for verification.
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