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81-462: 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 for acceleration correction. All frames of reference with zero acceleration are in

162-632: A = F {\displaystyle \displaystyle m\,\mathbf {a} =\mathbf {F} } . Consider N {\displaystyle \displaystyle N} particles with masses m 1 , … , m N {\displaystyle \displaystyle m_{1},\,\ldots ,\,m_{N}} in the regular three-dimensional Euclidean space . Let r 1 , … , r N {\displaystyle \displaystyle \mathbf {r} _{1},\,\ldots ,\,\mathbf {r} _{N}} be their radius-vectors in some inertial coordinate system. Then

243-400: A − A in the negative y -direction—a smaller value than Alfred has measured. Similarly, if she is accelerating at rate A in the positive y -direction (speeding up), she will observe Candace's acceleration as a′ = a + A in the negative y -direction—a larger value than Alfred's measurement. Here the relation between inertial and non-inertial observational frames of reference

324-441: A circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration. There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so it is only needed that a body is far enough away from all sources to ensure that no force

405-407: A frame of reference S′ situated in the first car. In this case, the first car is stationary and the second car is approaching from behind at a speed of v 2 − v 1 = 8 m/s . To catch up to the first car, it will take a time of ⁠ d / v 2 − v 1 ⁠ = ⁠ 200 / 8 ⁠ s , that is, 25 seconds, as before. Note how much easier the problem becomes by choosing

486-465: A frame of reference stationary relative to the fixed stars . An inertial frame was then one in uniform translation relative to absolute space. However, some "relativists", even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced. The expression inertial frame of reference ( German : Inertialsystem ) was coined by Ludwig Lange in 1885, to replace Newton's definitions of "absolute space and time" with

567-434: A maintaining force is perpendicular to M {\displaystyle \displaystyle M} . It is called the normal force . The force F {\displaystyle \displaystyle \mathbf {F} } from ( 6 ) is subdivided into two components The first component in ( 13 ) is tangent to the configuration manifold M {\displaystyle \displaystyle M} . The second component

648-464: A more operational definition : A reference frame in which a mass point thrown from the same point in three different (non co-planar) directions follows rectilinear paths each time it is thrown, is called an inertial frame. The inadequacy of the notion of "absolute space" in Newtonian mechanics is spelled out by Blagojevich: The utility of operational definitions was carried much further in

729-488: A particular rate with respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity. However, the general theory reduces to the special theory over sufficiently small regions of spacetime , where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity

810-476: 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 . Newtonian inertial frames transform among each other according to the Galilean group of symmetries . If this rule is interpreted as saying that straight-line motion

891-472: A point of the phase space T M {\displaystyle \displaystyle TM} of the constrained Newtonian dynamical system. Geometrically, the vector-function ( 7 ) implements an embedding of the configuration space M {\displaystyle \displaystyle M} of the constrained Newtonian dynamical system into the 3 N {\displaystyle \displaystyle 3\,N} -dimensional flat configuration space of

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972-425: A set of spacetime coordinates. These are called frames of reference . According to the first postulate of special relativity , all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation : Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form,

1053-431: A single n = 3 N {\displaystyle \displaystyle n=3N} -dimensional velocity vector: In terms of the multidimensional vectors ( 2 ) the equations ( 1 ) are written as i.e. they take the form of Newton's second law applied to a single particle with the unit mass m = 1 {\displaystyle \displaystyle m=1} . Definition . The equations ( 3 ) are called

1134-416: 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

1215-403: A suitable frame of reference. The third possible frame of reference would be attached to the second car. That example resembles the case just discussed, except the second car is stationary and the first car moves backward towards it at 8 m/s . 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

1296-409: A system becomes larger or more massive the classical dynamics tends to emerge, with some exceptions, such as superfluidity . This is why we can usually ignore quantum mechanics when dealing with everyday objects and the classical description will suffice. However, one of the most vigorous ongoing fields of research in physics is classical-quantum correspondence . This field of research is concerned with

1377-412: A system depend therefore on the observer's frame of reference (you might say that the bus arrived at 5 past three, when in fact it arrived at three). 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. See Figure 2. A car drives past them heading south. For the person facing east, the car was moving to

1458-502: Is invariant , the transformation between inertial frames is the Lorentz transformation , not the Galilean transformation which is used in Newtonian mechanics. The invariance of the speed of light leads to counter-intuitive phenomena, such as time dilation , length contraction , and the relativity of simultaneity . The predictions of special relativity have been extensively verified experimentally. The Lorentz transformation reduces to

1539-417: Is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then being able to determine when zero net force is applied is crucial. The problem was summarized by Einstein: The weakness of the principle of inertia lies in this, that it involves an argument in

1620-416: Is called the phase space of the dynamical system ( 3 ). The configuration space and the phase space of the dynamical system ( 3 ) both are Euclidean spaces, i. e. they are equipped with a Euclidean structure. The Euclidean structure of them is defined so that the kinetic energy of the single multidimensional particle with the unit mass m = 1 {\displaystyle \displaystyle m=1}

1701-584: Is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below. General relativity is based upon the principle of equivalence: There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating. This idea was introduced in Einstein's 1907 article "Principle of Relativity and Gravitation" and later developed in 1911. Support for this principle

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1782-418: Is constant, what acceleration does Betsy measure? If Betsy's velocity v is constant, she is in an inertial frame of reference, and she will find the acceleration to be the same as Alfred in her frame of reference, a in the negative y -direction. However, if she is accelerating at rate A in the negative y -direction (in other words, slowing down), she will find Candace's acceleration to be a′ =

1863-511: Is equal to the sum of kinetic energies of the three-dimensional particles with the masses m 1 , … , m N {\displaystyle \displaystyle m_{1},\,\ldots ,\,m_{N}} : In some cases the motion of the particles with the masses m 1 , … , m N {\displaystyle \displaystyle m_{1},\,\ldots ,\,m_{N}} can be constrained. Typical constraints look like scalar equations of

1944-567: Is found in the Eötvös experiment , which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 10. For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin. Einstein's general theory modifies

2025-401: Is generally characterized by the principle of complete determinism , although deterministic interpretations of quantum mechanics do exist. From the point of view of classical physics as being non-relativistic physics, the predictions of general and special relativity are significantly different from those of classical theories, particularly concerning the passage of time, the geometry of space,

2106-462: Is not an inertial frame of reference. The Coriolis effect can deflect certain forms of motion as seen from Earth , and the centrifugal force will reduce the effective gravity at the equator . Nevertheless, for many applications the Earth is an adequate approximation of an inertial reference frame. The motion of a body can only be described relative to something else—other bodies, observers, or

2187-510: Is now sometimes described as only a "local theory". "Local" can encompass, for example, the entire Milky Way galaxy : The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the Solar System . Schwarzschild pointed out that that

2268-402: Is one in which Newton's first law of motion is valid. However, the principle of special relativity generalizes the notion of an inertial frame to include all physical laws, not simply Newton's first law. Newton viewed the first law as valid in any reference frame that is in uniform motion (neither rotating nor accelerating) relative to absolute space ; as a practical matter, "absolute space"

2349-564: Is perpendicular to M {\displaystyle \displaystyle M} . In coincides with the normal force N {\displaystyle \displaystyle \mathbf {N} } . Like the velocity vector ( 8 ), the tangent force F ∥ {\displaystyle \displaystyle \mathbf {F} _{\parallel }} has its internal presentation The quantities F 1 , … , F n {\displaystyle F^{1},\,\ldots ,\,F^{n}} in ( 14 ) are called

2430-415: Is placed on a disc rotating relative to the earth, he/she will sense a 'force' pushing him/her toward the periphery of the disc, which is not caused by any interaction with other bodies. Here, the acceleration is not the consequence of the usual force, but of the so-called inertial force. Newton's laws hold in their simplest form only in a family of reference frames, called inertial frames. This fact represents

2511-442: Is present. A possible issue with this approach is the historically long-lived view that the distant universe might affect matters ( Mach's principle ). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is the possibility of missing something, or accounting inappropriately for their influence, perhaps, again, due to Mach's principle and an incomplete understanding of

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2592-482: Is the scalar product associated with the Euclidean structure ( 4 ). Since the Euclidean structure of an unconstrained system of N {\displaystyle \displaystyle N} particles is introduced through their kinetic energy, the induced Riemannian structure on the configuration space N {\displaystyle \displaystyle N} of a constrained system preserves this relation to

2673-459: Is the study of the dynamics of a particle or a small body according to Newton's laws of motion . Typically, the Newtonian dynamics occurs in a three-dimensional Euclidean space , which is flat. However, in mathematics Newton's laws of motion can be generalized to multidimensional and curved spaces. Often the term Newtonian dynamics is narrowed to Newton's second law m

2754-466: Is the velocity of the object and c is the speed of light. For velocities much smaller than that of light, one can neglect the terms with c and higher that appear. These formulas then reduce to the standard definitions of Newtonian kinetic energy and momentum. This is as it should be, for special relativity must agree with Newtonian mechanics at low velocities. Computer modeling has to be as real as possible. Classical physics would introduce an error as in

2835-417: The Galilean transformation in Newtonian physics or the Lorentz transformation (combined with a translation) in special relativity ; these approximately match when the relative speed of the frames is low, but differ as it approaches the speed of light . By contrast, a non-inertial reference frame has non-zero acceleration. In such a frame, the interactions between physical objects vary depending on

2916-442: The Galilean transformation postulate the equivalence of all inertial reference frames. The Galilean transformation transforms coordinates from one inertial reference frame, s {\displaystyle \mathbf {s} } , to another, s ′ {\displaystyle \mathbf {s} ^{\prime }} , by simple addition or subtraction of coordinates: where r 0 and t 0 represent shifts in

2997-418: The fixed stars . However, this is not required for the definition, and it is now known that those stars are in fact moving. According to the principle of special relativity , all physical laws look the same in all inertial reference frames, and no inertial frame is privileged over another. Measurements of objects in one inertial frame can be converted to measurements in another by a simple transformation —

3078-521: The law of inertia , is satisfied: Any free motion has a constant magnitude and direction. Newton's second law for a particle takes the form: 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. The force F is the vector sum of all "real" forces on the particle, such as contact forces , electromagnetic, gravitational, and nuclear forces. Classical physics As such,

3159-473: The metric connection produced by the Riemannian metric ( 11 ). Mechanical systems with constraints are usually described by Lagrange equations : where T = T ( q 1 , … , q n , w 1 , … , w n ) {\displaystyle T=T(q^{1},\ldots ,q^{n},w^{1},\ldots ,w^{n})} is the kinetic energy

3240-469: The superfluidity case. In order to produce reliable models of the world, one can not use classical physics. It is true that quantum theories consume time and computer resources, and the equations of classical physics could be resorted to in order to provide a quick solution, but such a solution would lack reliability. Computer modeling would use only the energy criteria to determine which theory to use: relativity or quantum theory, when attempting to describe

3321-530: The Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero. Consider a situation common in everyday life. Two cars travel along a road, both moving at constant velocities. See Figure 1. At some particular moment, they are separated by 200 meters. The car in front is traveling at 22 meters per second and the car behind is traveling at 30 meters per second. If we want to find out how long it will take

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3402-463: The absence of such fictitious forces. Newton enunciated a principle of relativity himself in one of his corollaries to the laws of motion: The motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line. This principle differs from the special principle in two ways: first, it is restricted to mechanics, and second, it makes no mention of simplicity. It shares

3483-467: The acceleration of that frame with respect to an inertial frame. Viewed from the perspective of classical mechanics and special relativity , the usual physical forces caused by the interaction of objects have to be supplemented by fictitious forces caused by inertia . Viewed from the perspective of general relativity theory , the fictitious (i.e. inertial) forces are attributed to geodesic motion in spacetime . Due to Earth's rotation , its surface

3564-478: The behavior of an object. A physicist would use a classical model to provide an approximation before more exacting models are applied and those calculations proceed. In a computer model, there is no need to use the speed of the object if classical physics is excluded. Low-energy objects would be handled by quantum theory and high-energy objects by relativity theory. Newtonian dynamics In physics, Newtonian dynamics (also known as Newtonian mechanics )

3645-420: The branches of theory sometimes included in classical physics are variably: In contrast to classical physics, " modern physics " is a slightly looser term that may refer to just quantum physics or to 20th- and 21st-century physics in general. Modern physics includes quantum theory and relativity, when applicable. A physical system can be described by classical physics when it satisfies conditions such that

3726-413: The cars is accelerating, we can determine their positions by the following formulas, where x 1 ( t ) {\displaystyle x_{1}(t)} is the position in meters of car one after time t in seconds and x 2 ( t ) {\displaystyle x_{2}(t)} is the position of car two after time t . Notice that these formulas predict at t = 0 s

3807-500: The configuration space of the Newtonian dynamical system ( 3 ). This manifold M {\displaystyle \displaystyle M} is called the configuration space of the constrained system. Its tangent bundle T M {\displaystyle \displaystyle TM} is called the phase space of the constrained system. Let q 1 , … , q n {\displaystyle \displaystyle q^{1},\,\ldots ,\,q^{n}} be

3888-429: The constrained dynamical system given by the formula ( 12 ). The quantities Q 1 , … , Q n {\displaystyle Q_{1},\,\ldots ,\,Q_{n}} in ( 16 ) are the inner covariant components of the tangent force vector F ∥ {\displaystyle \mathbf {F} _{\parallel }} (see ( 13 ) and ( 14 )). They are produced from

3969-405: The constraint equations ( 6 ) in the sense that upon substituting ( 7 ) into ( 6 ) the equations ( 6 ) are fulfilled identically in q 1 , … , q n {\displaystyle \displaystyle q^{1},\,\ldots ,\,q^{n}} . The velocity vector of the constrained Newtonian dynamical system is expressed in terms of the partial derivatives of

4050-483: The context of quantum mechanics , classical theory refers to theories of physics that do not use the quantisation paradigm , which includes classical mechanics and relativity . Likewise, classical field theories , such as general relativity and classical electromagnetism , are those that do not use quantum mechanics. In the context of general and special relativity, classical theories are those that obey Galilean relativity . Depending on point of view, among

4131-427: The definition of a classical theory depends on context. Classical physical concepts are often used when modern theories are unnecessarily complex for a particular situation. Most often, classical physics refers to pre-1900 physics, while modern physics refers to post-1900 physics, which incorporates elements of quantum mechanics and relativity . Classical theory has at least two distinct meanings in physics. In

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4212-550: The differences would set up an absolute standard reference frame. According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup. In Newtonian mechanics, inertial frames of reference are related by the Galilean group of symmetries. Newton posited an absolute space considered well-approximated by

4293-399: The discoverer of that particular equation. Computer modeling is essential for quantum and relativistic physics. Classical physics is considered the limit of quantum mechanics for a large number of particles. On the other hand, classic mechanics is derived from relativistic mechanics . For example, in many formulations from special relativity, a correction factor ( v / c ) appears, where v

4374-408: The discovery of how the laws of quantum physics give rise to classical physics found at the limit of the large scales of the classical level. Today, a computer performs millions of arithmetic operations in seconds to solve a classical differential equation , while Newton (one of the fathers of the differential calculus) would take hours to solve the same equation by manual calculation, even if he were

4455-457: The distinction between nominally "inertial" and "non-inertial" effects by replacing special relativity's "flat" Minkowski Space with a metric that produces non-zero curvature. In general relativity, the principle of inertia is replaced with the principle of geodesic motion , whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at

4536-443: The equations of a Newtonian dynamical system in a flat multidimensional Euclidean space , which is called the configuration space of this system. Its points are marked by the radius-vector r {\displaystyle \displaystyle \mathbf {r} } . The space whose points are marked by the pair of vectors ( r , v ) {\displaystyle \displaystyle (\mathbf {r} ,\mathbf {v} )}

4617-472: The essence of the Galilean principle of relativity:    The laws of mechanics have the same form in all inertial frames. However, this definition of inertial frames is understood to apply in the Newtonian realm and ignores relativistic effects. In practical terms, the equivalence of inertial reference frames means that scientists within a box moving with a constant absolute velocity cannot determine this velocity by any experiment. Otherwise,

4698-427: The first car is 200m down the road and the second car is right beside us, as expected. We want to find the time at which x 1 = x 2 {\displaystyle x_{1}=x_{2}} . Therefore, we set x 1 = x 2 {\displaystyle x_{1}=x_{2}} and solve for t {\displaystyle t} , that is: Alternatively, we could choose

4779-751: The form Constraints of the form ( 5 ) are called holonomic and scleronomic . In terms of the radius-vector r {\displaystyle \displaystyle \mathbf {r} } of the Newtonian dynamical system ( 3 ) they are written as Each such constraint reduces by one the number of degrees of freedom of the Newtonian dynamical system ( 3 ). Therefore, the constrained system has n = 3 N − K {\displaystyle \displaystyle n=3\,N-K} degrees of freedom. Definition . The constraint equations ( 6 ) define an n {\displaystyle \displaystyle n} -dimensional manifold M {\displaystyle \displaystyle M} within

4860-426: The inner contravariant components F 1 , … , F n {\displaystyle F^{1},\,\ldots ,\,F^{n}} of the vector F ∥ {\displaystyle \mathbf {F} _{\parallel }} by means of the standard index lowering procedure using the metric ( 11 ): The equations ( 16 ) are equivalent to the equations ( 15 ). However,

4941-403: The internal components of the force vector. The Newtonian dynamical system ( 3 ) constrained to the configuration manifold M {\displaystyle \displaystyle M} by the constraint equations ( 6 ) is described by the differential equations where Γ i j s {\displaystyle \Gamma _{ij}^{s}} are Christoffel symbols of

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5022-539: The internal coordinates of a point of M {\displaystyle \displaystyle M} . Their usage is typical for the Lagrangian mechanics . The radius-vector r {\displaystyle \displaystyle \mathbf {r} } is expressed as some definite function of q 1 , … , q n {\displaystyle \displaystyle q^{1},\,\ldots ,\,q^{n}} : The vector-function ( 7 ) resolves

5103-472: The kinetic energy: The formula ( 12 ) is derived by substituting ( 8 ) into ( 4 ) and taking into account ( 11 ). For a constrained Newtonian dynamical system the constraints described by the equations ( 6 ) are usually implemented by some mechanical framework. This framework produces some auxiliary forces including the force that maintains the system within its configuration manifold M {\displaystyle \displaystyle M} . Such

5184-626: The laws of classical physics are approximately valid. In practice, physical objects ranging from those larger than atoms and molecules , to objects in the macroscopic and astronomical realm, can be well-described (understood) with classical mechanics. Beginning at the atomic level and lower, the laws of classical physics break down and generally do not provide a correct description of nature. Electromagnetic fields and forces can be described well by classical electrodynamics at length scales and field strengths large enough that quantum mechanical effects are negligible. Unlike quantum physics, classical physics

5265-499: The motion of bodies in free fall, and the propagation of light. Traditionally, light was reconciled with classical mechanics by assuming the existence of a stationary medium through which light propagated, the luminiferous aether , which was later shown not to exist. Mathematically, classical physics equations are those in which the Planck constant does not appear. According to the correspondence principle and Ehrenfest's theorem , as

5346-675: The motion of these particles is governed by Newton's second law applied to each of them The three-dimensional radius-vectors r 1 , … , r N {\displaystyle \displaystyle \mathbf {r} _{1},\,\ldots ,\,\mathbf {r} _{N}} can be built into a single n = 3 N {\displaystyle \displaystyle n=3N} -dimensional radius-vector. Similarly, three-dimensional velocity vectors v 1 , … , v N {\displaystyle \displaystyle \mathbf {v} _{1},\,\ldots ,\,\mathbf {v} _{N}} can be built into

5427-399: 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. Assuming Candace's acceleration

5508-460: The origin of space and time, and v is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time t 2 − t 1 between two events is the same for all reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, | r 2 − r 1 |) is also the same. Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame,

5589-411: 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

5670-449: The problem unnecessarily. It is also necessary to note that one can 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 can deduct five minutes from the time displayed on your watch to obtain the correct time. The measurements that an observer makes about

5751-416: The right. However, for the person facing west, the car was moving to 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

5832-513: The same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K. This simplicity manifests itself in that inertial frames have self-contained physics without the need for external causes, while physics in non-inertial frames has external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity: The laws of Newtonian mechanics do not always hold in their simplest form...If, for instance, an observer

5913-417: 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. We stand on the side of the road and start a stop-clock at the exact moment that the second car passes us, which happens to be when they are a distance d = 200 m apart. Since neither of

5994-425: The special principle of the invariance of the form of the description among mutually translating reference frames. The role of fictitious forces in classifying reference frames is pursued further below. Einstein's theory of special relativity , like Newtonian mechanics, postulates the equivalence of all inertial reference frames. However, because special relativity postulates that the speed of light in free space

6075-413: The special theory of relativity. Some historical background including Lange's definition is provided by DiSalle, who says in summary: The original question, "relative to what frame of reference do the laws of motion hold?" is revealed to be wrongly posed. The laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing them. Classical theories that use

6156-406: 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. Alfred's frame of reference is considered an inertial frame because he is not accelerating, ignoring effects such as Earth's rotation and gravity. Now consider Betsy,

6237-420: The unconstrained Newtonian dynamical system ( 3 ). Due to this embedding the Euclidean structure of the ambient space induces the Riemannian metric onto the manifold M {\displaystyle \displaystyle M} . The components of the metric tensor of this induced metric are given by the formula where (   ,   ) {\displaystyle \displaystyle (\ ,\ )}

6318-417: The universe. A third approach is to look at the way the forces transform when shifting reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames and have complicated rules of transformation in general cases. Based on the universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by

6399-471: The vector-function ( 7 ): The quantities q ˙ 1 , … , q ˙ n {\displaystyle \displaystyle {\dot {q}}^{1},\,\ldots ,\,{\dot {q}}^{n}} are called internal components of the velocity vector. Sometimes they are denoted with the use of a separate symbol and then treated as independent variables. The quantities are used as internal coordinates of

6480-434: Was considered to be the fixed stars In the theory of relativity the notion of absolute space or a privileged frame is abandoned, and an inertial frame in the field of classical mechanics is defined as: An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed. Hence, with respect to an inertial frame, an object or body accelerates only when

6561-552: Was invariably seen: the direction of the angular momentum of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is approximately Galilean or Minkowskian. In an inertial frame, Newton's first law ,

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