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Inertial frame of reference

In classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a frame of reference in which the laws of nature take on a particularly simple form.

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. Those are the frames called inertial. Originally, some physicists like Isaac Newton thought that one of those 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.

According to the special principle of relativity, all physical laws look the same in all inertial reference frames, and no inertial frame is privileged over the other. Measurements of objects in one inertial frame can be converted to measurements in another by a simple transformation — 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 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 inertial (i.e. fictitious) forces are attributed to geodesic motion in spacetime.

Due to Earth's rotation, its surface 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, the Earth is a good approximation of an inertial reference frame, adequate in many applications.

Introduction
The motion of a body can only be described relative to something else—other bodies, observers, or 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, 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 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 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, 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.

Absolute space
Newton posited an absolute space considered well-approximated by 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 (Inertialsystem) was coined by Ludwig Lange in 1885, to replace Newton's definitions of "absolute space and time" with a more operational definition. As translated by Harald Iro, Lange proposed the following 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 Blagojević: "*The existence of absolute space contradicts the internal logic of classical mechanics since, according to the Galilean principle of relativity, none of the inertial frames can be singled out.
 * Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.
 * Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon."

The utility of operational definitions was carried much further in 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."

Newtonian mechanics
Classical theories that use the Galilean transformation postulate the equivalence of all inertial reference frames. The Galilean transformation transforms coordinates from one inertial reference frame, $$\mathbf{s}$$, to another, $$\mathbf{s}^{\prime}$$, by simple addition or subtraction of coordinates:

\mathbf{r}^{\prime} = \mathbf{r} - \mathbf{r}_{0} - \mathbf{v} t $$

t^{\prime} = t - t_{0} $$

where r0 and t0 represent shifts in the origin of space and time, and v is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time t2 − t1 between two events is the same for all reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, |r2 − r1|) is also the same. Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame, 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" 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 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 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 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 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 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 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 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.

Special relativity
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 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 the Galilean transformation as the speed of light approaches infinity or as the relative velocity between frames approaches zero.

Simple example
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 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 the cars is accelerating, we can determine their positions by the following formulas, where $$x_1(t)$$ is the position in meters of car one after time t in seconds and $$x_2(t)$$ is the position of car two after time t.

 * $$x_1(t) = d + v_1 t = 200 + 22t,\quad x_2(t) = v_2 t = 30t.$$

Notice that these formulas predict at t = 0 s the first car is 200 m down the road and the second car is right beside us, as expected. We want to find the time at which $$x_1=x_2$$. Therefore, we set $$x_1=x_2$$ and solve for $$t$$, that is:

 * $$200 + 22t = 30t,$$
 * $$8t = 200,$$
 * $$t = 25\ \mathrm{seconds}.$$

Alternatively, we could choose 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 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 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 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).

Additional example
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 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 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, 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. Assuming Candace's acceleration 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 $a′ = a − A$ 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.

Non-inertial frames
Here the relation between inertial and non-inertial observational frames of reference is considered. The basic difference between these frames is the need in non-inertial frames for fictitious forces, as described below.

General relativity
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 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 1011. 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 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 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 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 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.

Inertial frames and rotation
In an inertial frame, Newton's first law, 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:

 * $$\mathbf{F} = m \mathbf{a} \ ,$$

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.

In contrast, Newton's second law in a rotating frame of reference (a non-inertial frame of reference), rotating at angular rate Ω about an axis, takes the form:

 * $$\mathbf{F}' = m \mathbf{a} \ ,$$

which looks the same as in an inertial frame, but now the force F′ is the resultant of not only F, but also additional terms (the paragraph following this equation presents the main points without detailed mathematics):

 * $$\mathbf{F}' = \mathbf{F} - 2m \mathbf{\Omega} \times \mathbf{v}_{B} - m \mathbf{\Omega} \times (\mathbf{\Omega} \times \mathbf{x}_B ) - m \frac{d \mathbf{\Omega}}{dt} \times \mathbf{x}_B \, $$

where the angular rotation of the frame is expressed by the vector Ω pointing in the direction of the axis of rotation, and with magnitude equal to the angular rate of rotation Ω, symbol × denotes the vector cross product, vector xB locates the body and vector vB is the velocity of the body according to a rotating observer (different from the velocity seen by the inertial observer).

The extra terms in the force F′ are the "fictitious" forces for this frame, whose causes are external to the system in the frame. The first extra term is the Coriolis force, the second the centrifugal force, and the third the Euler force. These terms all have these properties: they vanish when Ω = 0; that is, they are zero for an inertial frame (which, of course, does not rotate); they take on a different magnitude and direction in every rotating frame, depending upon its particular value of Ω; they are ubiquitous in the rotating frame (affect every particle, regardless of circumstance); and they have no apparent source in identifiable physical sources, in particular, matter. Also, fictitious forces do not drop off with distance (unlike, for example, nuclear forces or electrical forces). For example, the centrifugal force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis.

All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.

In Newton's time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton's laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force. Two experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking two spheres rotating about their center of gravity, and the example of the curvature of the surface of water in a rotating bucket. In both cases, application of Newton's second law would not work for the rotating observer without invoking centrifugal and Coriolis forces to account for their observations (tension in the case of the spheres; parabolic water surface in the case of the rotating bucket).

As now known, the fixed stars are not fixed. Those that reside in the Milky Way turn with the galaxy, exhibiting proper motions. 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. For instance, the Andromeda Galaxy is on collision course with the Milky Way at a speed of 117 km/s. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based on the simplicity of the laws of physics in the frame. The laws of nature take a simpler form in inertial frames of reference because in these frames one did not have to introduce inertial forces when writing down Newton's law of motion.

In practice, using a frame of reference based upon the fixed stars as though it were an inertial frame of reference introduces little discrepancy. For example, the centrifugal acceleration of the Earth because of its rotation about the Sun is about thirty million times greater than that of the Sun about the galactic center.

To illustrate further, consider the question: "Does the Universe rotate?" An answer might explain the shape of the Milky Way galaxy using the laws of physics, although other observations might be more definitive; that is, provide larger discrepancies or less measurement uncertainty, like the anisotropy of the microwave background radiation or Big Bang nucleosynthesis. The flatness of the Milky Way depends on its rate of rotation in an inertial frame of reference. If its apparent rate of rotation is attributed entirely to rotation in an inertial frame, a different "flatness" is predicted than if it is supposed that part of this rotation is actually due to rotation of the universe and should not be included in the rotation of the galaxy itself. Based upon the laws of physics, a model is set up in which one parameter is the rate of rotation of the Universe. If the laws of physics agree more accurately with observations in a model with rotation than without it, we are inclined to select the best-fit value for rotation, subject to all other pertinent experimental observations. If no value of the rotation parameter is successful and theory is not within observational error, a modification of physical law is considered, for example, dark matter is invoked to explain the galactic rotation curve. So far, observations show any rotation of the universe is very slow, no faster than once every $6$ years (10−13 rad/yr), and debate persists over whether there is any rotation. However, if rotation were found, interpretation of observations in a frame tied to the universe would have to be corrected for the fictitious forces inherent in such rotation in classical physics and special relativity, or interpreted as the curvature of spacetime and the motion of matter along the geodesics in general relativity.

When quantum effects are important, there are additional conceptual complications that arise in quantum reference frames.

Primed frames
An accelerated frame of reference is often delineated as being the "primed" frame, and all variables that are dependent on that frame are notated with primes, e.g. x′, y′, a′.

The vector from the origin of an inertial reference frame to the origin of an accelerated reference frame is commonly notated as R. Given a point of interest that exists in both frames, the vector from the inertial origin to the point is called r, and the vector from the accelerated origin to the point is called r′.

From the geometry of the situation

 * $$\mathbf r = \mathbf R + \mathbf r'.$$

Taking the first and second derivatives of this with respect to time

 * $$\mathbf v = \mathbf V + \mathbf v',$$
 * $$\mathbf a = \mathbf A + \mathbf a'.$$

where V and A are the velocity and acceleration of the accelerated system with respect to the inertial system and v and a are the velocity and acceleration of the point of interest with respect to the inertial frame.

These equations allow transformations between the two coordinate systems; for example, Newton's second law can be written as

 * $$\mathbf F = m\mathbf a = m\mathbf A + m\mathbf a'.$$

When there is accelerated motion due to a force being exerted there is manifestation of inertia. If an electric car designed to recharge its battery system when decelerating is switched to braking, the batteries are recharged, illustrating the physical strength of manifestation of inertia. However, the manifestation of inertia does not prevent acceleration (or deceleration), for manifestation of inertia occurs in response to change in velocity due to a force. Seen from the perspective of a rotating frame of reference the manifestation of inertia appears to exert a force (either in centrifugal direction, or in a direction orthogonal to an object's motion, the Coriolis effect).

A common sort of accelerated reference frame is a frame that is both rotating and translating (an example is a frame of reference attached to a CD which is playing while the player is carried).

This arrangement leads to the equation (see Fictitious force for a derivation):

 * $$\mathbf a = \mathbf a' + \dot{\boldsymbol\omega} \times \mathbf r' + 2\boldsymbol\omega \times \mathbf v' + \boldsymbol\omega \times (\boldsymbol\omega \times \mathbf r') + \mathbf A_0,$$

or, to solve for the acceleration in the accelerated frame,

 * $$\mathbf a' = \mathbf a - \dot{\boldsymbol\omega} \times \mathbf r' - 2\boldsymbol\omega \times \mathbf v' - \boldsymbol\omega \times (\boldsymbol\omega \times \mathbf r') - \mathbf A_0.$$

Multiplying through by the mass m gives

 * $$\mathbf F' = \mathbf F_\mathrm{physical} + \mathbf F'_\mathrm{Euler} + \mathbf F'_\mathrm{Coriolis} + \mathbf F'_\mathrm{centripetal} - m\mathbf A_0,$$

where

 * $$\mathbf F'_\mathrm{Euler} = -m\dot{\boldsymbol\omega} \times \mathbf r'$$ (Euler force),
 * $$\mathbf F'_\mathrm{Coriolis} = -2m\boldsymbol\omega \times \mathbf v'$$ (Coriolis force),
 * $$\mathbf F'_\mathrm{centrifugal} = -m\boldsymbol\omega \times (\boldsymbol\omega \times \mathbf r') = m(\omega^2 \mathbf r' - (\boldsymbol\omega \cdot \mathbf r')\boldsymbol\omega)$$ (centrifugal force).

Theory
Inertial and non-inertial reference frames can be distinguished by the absence or presence of fictitious forces. "The effect of this being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations…." The presence of fictitious forces indicates the physical laws are not the simplest laws available, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame: "The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system." Bodies in non-inertial reference frames are subject to so-called fictitious forces (pseudo-forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames.

To apply the Newtonian definition of an inertial frame, the understanding of separation between "fictitious" forces and "real" forces must be made clear.

For example, consider a stationary object in an inertial frame. Being at rest, no net force is applied. But in a frame rotating about a fixed axis, the object appears to move in a circle, and is subject to centripetal force. How can it be decided that the rotating frame is a non-inertial frame? There are two approaches to this resolution: one approach is to look for the origin of the fictitious forces (the Coriolis force and the centrifugal force). It will be found there are no sources for these forces, no associated force carriers, no originating bodies. A second approach is to look at a variety of frames of reference. For any inertial frame, the Coriolis force and the centrifugal force disappear, so application of the principle of special relativity would identify these frames where the forces disappear as sharing the same and the simplest physical laws, and hence rule that the rotating frame is not an inertial frame.

Newton examined this problem himself using rotating spheres, as shown in Figure 2 and Figure 3. He pointed out that if the spheres are not rotating, the tension in the tying string is measured as zero in every frame of reference. If the spheres only appear to rotate (that is, we are watching stationary spheres from a rotating frame), the zero tension in the string is accounted for by observing that the centripetal force is supplied by the centrifugal and Coriolis forces in combination, so no tension is needed. If the spheres really are rotating, the tension observed is exactly the centripetal force required by the circular motion. Thus, measurement of the tension in the string identifies the inertial frame: it is the one where the tension in the string provides exactly the centripetal force demanded by the motion as it is observed in that frame, and not a different value. That is, the inertial frame is the one where the fictitious forces vanish.

For linear acceleration, Newton expressed the idea of undetectability of straight-line accelerations held in common: "If bodies, any how moved among themselves, are urged in the direction of parallel lines by equal accelerative forces, they will continue to move among themselves, after the same manner as if they had been urged by no such forces."

This principle generalizes the notion of an inertial frame. For example, an observer confined in a free-falling lift will assert that he himself is a valid inertial frame, even if he is accelerating under gravity, so long as he has no knowledge about anything outside the lift. So, strictly speaking, inertial frame is a relative concept. With this in mind, inertial frames can collectively be defined as a set of frames which are stationary or moving at constant velocity with respect to each other, so that a single inertial frame is defined as an element of this set.

For these ideas to apply, everything observed in the frame has to be subject to a base-line, common acceleration shared by the frame itself. That situation would apply, for example, to the elevator example, where all objects are subject to the same gravitational acceleration, and the elevator itself accelerates at the same rate.

Applications
Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it. Three orthogonal gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position. Thus, inertial navigation is a form of dead reckoning that requires no external input, and therefore cannot be jammed by any external or internal signal source.

A gyrocompass, employed for navigation of seagoing vessels, finds the geometric north. It does so, not by sensing the Earth's magnetic field, but by using inertial space as its reference. The outer casing of the gyrocompass device is held in such a way that it remains aligned with the local plumb line. When the gyroscope wheel inside the gyrocompass device is spun up, the way the gyroscope wheel is suspended causes the gyroscope wheel to gradually align its spinning axis with the Earth's axis. Alignment with the Earth's axis is the only direction for which the gyroscope's spinning axis can be stationary with respect to the Earth and not be required to change direction with respect to inertial space. After being spun up, a gyrocompass can reach the direction of alignment with the Earth's axis in as little as a quarter of an hour.

title: Inertial frame of reference


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Illuminati: New World Order

Illuminati: New World Order (INWO) is an out-of-print collectible card game (CCG) that was released in 1994 by Steve Jackson Games, based on their original boxed game Illuminati, which in turn was inspired by the 1975 book The Illuminatus! Trilogy by Robert Anton Wilson and Robert Shea. An OMNI sealed-deck league patterned after the Atlas Games model was also developed.

The 409-card set was sold in packages containing two 55-card starter decks and in 15-card booster packs. The booster packs contained cards of the types 'Group' and 'Plot', but not 'Illuminati'. The INWO Factory Set was a collector's set released in April 1995, containing one of each of the 403 cards in the base set plus blank cards and three of each Illuminati card.

Steve Jackson Games published a 144-page player's guide titled The INWO Book in April 1995 that contained rules, strategies, color prints of all cards, and also included a rare card from the Unlimited Edition.

The limited edition Assassins, the game's first expansion set, was released in mid-1995 and sold in 8-card booster packs. The 100-card expansion set SubGenius was planned for release in August 1997 and ultimately released in April 1998. The Bavarian Fire Drill set was planned for release in November 1998. Both SubGenius and Bavarian Fire Drill were sold as a single-box expansion set with all cards included.

Following the release and popularity of Magic: The Gathering in August 1993, Steve Jackson Games began the development of Illuminati: New World Order, most of which occurred in early 1994. The release of the Deluxe Edition sold out by mid-1994 and was followed by the release of the Limited Edition in December 1994, of which nearly 84,000 sets "sold out almost immediately". The Unlimited Edition was released in 1995. In an article published in the November–December 1994 issue of Pyramid magazine, Steve Jackson stated that Wizards of the Coast had loaned Steve Jackson Games money to "finance the first printing of INWO", which was the biggest project the company had undertaken by an order of magnitude.

Goal of the game
Players attempt to achieve world domination by utilizing the powers of their chosen Illuminati (the Adepts of Hermes, the Bavarian Illuminati, the Bermuda Triangle, the Discordian Society, the Gnomes of Zürich, the Network, Servants of Cthulhu, Shangri-La, the UFOs, the Society of Assassins (added in the Assassins expansion), and the Church of the SubGenius (added in the Subgenius expansion). The first player to control a predetermined number of organizations (usually twelve in a standard game) has achieved the basic goal and can claim victory.

Controllable organizations include groups such as the Men in Black, the CIA, and the Boy Sprouts; personalities such as Diana, Princess of Wales, Saddam Hussein, Ross Perot, or Björne (a parody of Barney the Dinosaur); and places like Japan, California, Canada, and the Moonbase. Many organization names are spoofs of real organizations, presumably altered to avoid lawsuits.

Other ways to achieve victory include: destroying rival Illuminati by capturing or killing the last organization in their power structure; and/or fulfilling a particular goal before your opponent(s) can.

Card types

Cards come in three main types: Illuminati cards, Plot cards, and Group cards. Illuminati and Plot cards both feature an illustration of a puppeteer's hand in a blue color scheme on the rear side, whereas Group cards feature a puppet on a string in a red color scheme.

Each Illuminati card represents a different Illuminati organization at the center of each player's Power Structure. They have Power, a Special Goal, and an appropriate Special Ability. Their power flows outward into the Groups they control via Control Arrows.

Plot cards provide the bulk of the game's narrative structure, allowing players to go beyond or even break the game's rules as described in the World Domination Handbook. Plot cards are identified by their overall blue color scheme (border and/or title color). Included among the general Plots are several particular types, including Assassinations and Disasters (for delivering insults to the various Personalities and Places in play), GOAL (special goals that can lead to surprise victories), and New World Order cards (a set of conditions that affect all players, typically overridden when replacement New World Order cards are brought into play).

Group cards represent the power elite in charge of the named organization. There are two main types of Groups: Organizations and Resources.

Organizations are identified by their red color scheme (border and/or title). There are three main types of Organizations: regular Organizations, People, and Places. They all feature Power, Resistance, Special Abilities, Alignments, Attributes, and Control Arrows (an inward arrow and 0–3 outward arrows). Like their Illuminati masters, Organizations can launch and defend against various attacks. Provided that the attacking Organization has a free, outward-pointing Control Arrow, players can increase the size of their Power Structure via successful Attacks to Control, a mathematically determined method employed whenever a player wants to capture an Organization from their hand or a rival player's Power Structure. Unless the attack is Privileged (only the target and attacker can be involved), all players can aid or undermine the attack. Attacks to Destroy follow a similar game mechanic but result in the Organization's removal from the Power Structure, after which they are immediately discarded. A dice roll determines the outcome of all Attacks. Other ways to introduce Organizations to the Power Structure involve Plots, spending Action Tokens to bring Groups into play, or using free moves at appropriate times during the play cycle.

Resources represent the custodians of a variety of objects, ranging from gadgets to artefacts (such as The Shroud of Turin, Flying Saucers, and ELIZA). They are identified by their overall purple color scheme (border and/or title). Resources are introduced into play by spending Action Tokens or by using free moves during appropriate moments in the play cycle. They go alongside the Power Structure of the player's Illuminati and bestow a valid Special Ability or something similar.

Reception
In the February 1995 edition of Shadis (issue #17.5), Matthew Lee and Jim Pinto liked the durable cards printed on thicker card stock than the original game (although the cards were easier to crease during shuffling). They also liked that one starter pack was enough for two players to get started and that the rulebook was very detailed. However, they disliked that cards were swapped between players – unusual for a CCG – which meant that the players had to figure out whose cards were whose at the end of the game. They also found that "the large rulebook can be daunting, and a large number of rules must be memorized to play".

In the June 1995 edition of Dragon (issue 218), Rick Swan warned that it was a complex game: "Owing to the unconventional mechanics, even experienced gamers may have trouble at first." But he gave the game a perfect rating of 6 out of 6, saying, "Resolute players who scrutinize the rules and grind their way through a few practice rounds will discover why Illuminati has been so durable. Not only is it an inspired concept, but it’s also an enlightening treatise on the fine art of backstabbing. What more could you ask from a deck of cards?" Ten months later, in the April 1996 edition of Dragon (Issue 229), Swan, tongue in cheek, called a set of blank cards produced for INWO "tastefully understated".

In the September 1996 edition of Arcane (issue 4), Steve Faragher rated the Assassins expansion set 9 out of 10 overall, saying, "With the introduction of Assassins, it now appears to have ... a little more game balance for tournament play. A good thing indeed."

Reviews

 * Magia i Miecz (issue 40, April 1997) (Polish)
 * Dragão Brasil (issue 6, September 1995) (Portuguese)
 * Rollespilsmagasinet Fønix (Danish) (issue 7, March/April 1995)
 * The Duelist, October 1998

Awards
At the 1995 Origins Awards, INWO won Best Card Game of 1994.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Illuminati: New World Order


text:
Integration

Integration may refer to:

Biology

 * Multisensory integration
 * Path integration
 * Pre-integration complex, viral genetic material used to insert a viral genome into a host genome
 * DNA integration, by means of site-specific recombinase technology, performed by a specific class of recombinase enzymes ("integrases")

Economics and law

 * Economic integration, trade unification between different states
 * Horizontal integration and vertical integration, in microeconomics and strategic management, styles of ownership and control
 * Regional integration, in which states cooperate through regional institutions and rules
 * Integration clause, a declaration that a contract is the final and complete understanding of the parties
 * A step in the process of money laundering
 * Integrated farming, a farm management system
 * Integration (tax), a feature of corporate and personal income tax in some countries
 * Territorial integration of independent or dependent territories into a state

Engineering

 * Data integration
 * Digital integration
 * Enterprise integration
 * Integrated architecture, in an Enterprise architecture framework approach such as DoDAF
 * Integrated circuit, an electronic circuit whose components are manufactured in one flat piece of semiconductor material
 * Integrated design, an approach to design which brings together specialisms usually considered separately
 * Integrated product team, use of a team including multiple disciplines (e.g. customer, engineer, support, testing)
 * Integrated software
 * System integration, engineering practices for assembling large and complicated systems from units, particularly subsystems

Mathematics

 * Integration, the computation of an integral
 * Indefinite integration, the computation of antiderivatives
 * Numerical integration, computing an integral with a numerical method, usually with a computer
 * Integration by parts, a method for computing the integral of a product of functions
 * Integration by substitution, a method for computing integrals, by using a change of variable
 * Symbolic integration, the computation, mostly on computers, of antiderivatives and definite integrals in term of formulas
 * Integration, the computation of a solution of a differential equation or a system of differential equations:
 * Integrability conditions for differential systems
 * Integrable system
 * Order of integration, in statistics, a summary statistic for a time series

Sociology

 * Social integration, in social science, a movement of newcomers or marginalized minorities into the mainstream of a society
 * Racial integration, including desegregation and other changes in social opportunity and culture
 * Desegregation, ending a separation of races, particularly in the context of the American civil rights movement
 * Educational integration of students with disabilities

Other uses

 * Integration (festival), an annual technology and cultural festival managed by the Indian Statistical Institute
 * Integration (album), a 2011 album by Kellee Maize
 * Integration, an album by Kultur Shock

title: Integration


text:
Interstellar travel

Interstellar travel is the hypothetical travel of spacecraft from one star system, solitary star, or planetary system to another. Interstellar travel is expected to prove much more difficult than interplanetary spaceflight due to the vast difference in the scale of the involved distances. Whereas the distance between any two planets in the Solar System is less than 55 astronomical units (AU), stars are typically separated by hundreds of thousands of AU, causing these distances to typically be expressed instead in light-years. Because of the vastness of these distances, non-generational interstellar travel based on known physics would need to occur at a high percentage of the speed of light; even so, travel times would be long, at least decades and perhaps millennia or longer.

, five uncrewed spacecraft, all launched and operated by the United States, have achieved the escape velocity required to leave the Solar System as part of missions to explore parts of the outer system. They will therefore continue to travel through interstellar space indefinitely. However, they will not approach another star for hundreds of thousands of years, long after they have ceased to operate (though in theory the Voyager Golden Record would be playable in the event that the spacecraft is retrieved by an extraterrestrial civilization).

The speeds required for interstellar travel in a human lifetime far exceed what current methods of space travel can provide. Even with a hypothetically perfectly efficient propulsion system, the kinetic energy corresponding to those speeds is enormous by today's standards of energy development. Moreover, collisions by spacecraft with cosmic dust and gas at such speeds would be very dangerous for both passengers and the spacecraft itself.

A number of strategies have been proposed to deal with these problems, ranging from giant arks that would carry entire societies and ecosystems, to microscopic space probes. Many different spacecraft propulsion systems have been proposed to give spacecraft the required speeds, including nuclear propulsion, beam-powered propulsion, and methods based on speculative physics.

Humanity would need to overcome considerable technological and economic challenges to achieve either crewed or uncrewed interstellar travel. Even the most optimistic views forecast that it will be decades before this milestone is reached. However, in spite of the challenges, a wide range of scientific benefits are expected should interstellar travel become a reality.

Most interstellar travel concepts require a developed space logistics system capable of moving millions of tonnes to a construction / operating location, and most would require gigawatt-scale power for construction or power (such as Star Wisp– or Light Sail–type concepts). Such a system could grow organically if space-based solar power became a significant component of Earth's energy mix. Consumer demand for a multi-terawatt system would create the necessary multi-million ton/year logistical system.

Interstellar distances
Distances between the planets in the Solar System are often measured in astronomical units (AU), defined as the average distance between the Sun and Earth, some 1.5E8 km. Venus, the closest planet to Earth is (at closest approach) 0.28 AU away. Neptune, the farthest planet from the Sun, is 29.8 AU away. As of January 20, 2023, Voyager 1, the farthest human-made object from Earth, is 163 AU away, exiting the Solar System at a speed of 17 km/s (0.006% of the speed of light).

The closest known star, Proxima Centauri, is approximately 4.243 ly away, or over 9,000 times farther away than Neptune.

Because of this, distances between stars are usually expressed in light-years (defined as the distance that light travels in vacuum in one Julian year) or in parsecs (one parsec is 3.26 ly, the distance at which stellar parallax is exactly one arcsecond, hence the name). Light in a vacuum travels around 300000 km per second, so 1 light-year is about 1 lye12 km or 1 ly AU. Hence, Proxima Centauri is approximately 4.243 light-years from Earth.

Another way of understanding the vastness of interstellar distances is by scaling: One of the closest stars to the Sun, Alpha Centauri A (a Sun-like star that is one of two companions of Proxima Centauri), can be pictured by scaling down the Earth–Sun distance to 1 m. On this scale, the distance to Alpha Centauri A would be 276 km.

The fastest outward-bound spacecraft yet sent, Voyager 1, has covered 1/390 of a light-year in 46 years and is currently moving at 1/17,600 the speed of light. At this rate, a journey to Proxima Centauri would take 75,000 years.

Required energy
A significant factor contributing to the difficulty is the energy that must be supplied to obtain a reasonable travel time. A lower bound for the required energy is the kinetic energy $$K = \tfrac{1}{2}mv^2$$ where $$m$$ is the final mass. If deceleration on arrival is desired and cannot be achieved by any means other than the engines of the ship, then the lower bound for the required energy is doubled to $$mv^2$$.

The velocity for a crewed round trip of a few decades to even the nearest star is several thousand times greater than those of present space vehicles. This means that due to the $$v^2$$ term in the kinetic energy formula, millions of times as much energy is required. Accelerating one ton to one-tenth of the speed of light requires at least 450 PJ (world energy consumption 2008 was 143,851 terawatt-hours), without factoring in efficiency of the propulsion mechanism. This energy has to be generated onboard from stored fuel, harvested from the interstellar medium, or projected over immense distances.

Interstellar medium
A knowledge of the properties of the interstellar gas and dust through which the vehicle must pass is essential for the design of any interstellar space mission. A major issue with traveling at extremely high speeds is that due to the requisite high relative speeds and large kinetic energies, collisions with interstellar dust could cause considerable damage to the craft. Various shielding methods to mitigate this problem have been proposed. Larger objects (such as macroscopic dust grains) are far less common, but would be much more destructive. The risks of impacting such objects and mitigation methods have been discussed in literature, but many unknowns remain. An additional consideration is that due the non-homogeneous distribution of interstellar matter around the Sun, these risks would vary between different trajectories. Although a high density interstellar medium may cause difficulties for many interstellar travel concepts, interstellar ramjets, and some proposed concepts for decelerating interstellar spacecraft, would actually benefit from a denser interstellar medium.

Hazards
The crew of an interstellar ship would face several significant hazards, including the psychological effects of long-term isolation, the physiological effects of extreme acceleration, the effects of exposure to ionising radiation, and the physiological effects of weightlessness to the muscles, joints, bones, immune system, and eyes. There also exists the risk of impact by micrometeoroids and other space debris. These risks represent challenges that have yet to be overcome.

Wait calculation
The speculative fiction writer and physicist Robert L. Forward has argued that an interstellar mission that cannot be completed within 50 years should not be started at all. Instead, assuming that a civilization is still on an increasing curve of propulsion system velocity and not yet having reached the limit, the resources should be invested in designing a better propulsion system. This is because a slow spacecraft would probably be passed by another mission sent later with more advanced propulsion (the incessant obsolescence postulate). In 2006, Andrew Kennedy calculated ideal departure dates for a trip to Barnard's Star using a more precise concept of the wait calculation where for a given destination and growth rate in propulsion capacity there is a departure point that overtakes earlier launches and will not be overtaken by later ones and concluded "an interstellar journey of 6 light years can best be made in about 635 years from now if growth continues at about 1.4% per annum", or approximately 2641 AD. It may be the most significant calculation for competing cultures occupying the galaxy.

Prime targets for interstellar travel
There are 59 known stellar systems within 40 light years of the Sun, containing 81 visible stars. The following could be considered prime targets for interstellar missions:

Existing astronomical technology is capable of finding planetary systems around these objects, increasing their potential for exploration.

Slow, uncrewed probes
"Slow" interstellar missions (still fast by other standards) based on current and near-future propulsion technologies are associated with trip times starting from about several decades to thousands of years. These missions consist of sending a robotic probe to a nearby star for exploration, similar to interplanetary probes like those used in the Voyager program. By taking along no crew, the cost and complexity of the mission is significantly reduced, as is the mass that needs to be accelerated, although technology lifetime is still a significant issue next to obtaining a reasonable speed of travel. Proposed concepts include Project Daedalus, Project Icarus, Project Dragonfly, Project Longshot, and more recently Breakthrough Starshot.

Nanoprobes
Near-lightspeed nano spacecraft might be possible within the near future built on existing microchip technology with a newly developed nanoscale thruster. Researchers at the University of Michigan are developing thrusters that use nanoparticles as propellant. Their technology is called "nanoparticle field extraction thruster", or nanoFET. These devices act like small particle accelerators shooting conductive nanoparticles out into space.

Michio Kaku, a theoretical physicist, has suggested that clouds of "smart dust" be sent to the stars, which may become possible with advances in nanotechnology. Kaku also notes that a large number of nanoprobes would need to be sent due to the vulnerability of very small probes to be easily deflected by magnetic fields, micrometeorites and other dangers to ensure the chances that at least one nanoprobe will survive the journey and reach the destination.

As a near-term solution, small, laser-propelled interstellar probes, based on current CubeSat technology were proposed in the context of Project Dragonfly.

Slow, crewed missions
In crewed missions, the duration of a slow interstellar journey presents a major obstacle and existing concepts deal with this problem in different ways. They can be distinguished by the "state" in which humans are transported on-board of the spacecraft.

Generation ships
A generation ship (or world ship) is a type of interstellar ark in which the crew that arrives at the destination is descended from those who started the journey. Generation ships are not currently feasible because of the difficulty of constructing a ship of the enormous required scale and the great biological and sociological problems that life aboard such a ship raises.

Suspended animation
Scientists and writers have postulated various techniques for suspended animation. These include human hibernation and cryonic preservation. Although neither is currently practical, they offer the possibility of sleeper ships in which the passengers lie inert for the long duration of the voyage.

Frozen embryos
A robotic interstellar mission carrying some number of frozen early stage human embryos is another theoretical possibility. This method of space colonization requires, among other things, the development of an artificial uterus, the prior detection of a habitable terrestrial planet, and advances in the field of fully autonomous mobile robots and educational robots that would replace human parents.

Island hopping through interstellar space
Interstellar space is not completely empty; it contains trillions of icy bodies ranging from small asteroids (Oort cloud) to possible rogue planets. There may be ways to take advantage of these resources for a good part of an interstellar trip, slowly hopping from body to body or setting up waystations along the way.

Fast, crewed missions
If a spaceship could average 10 percent of light speed (and decelerate at the destination, for human crewed missions), this would be enough to reach Proxima Centauri in forty years. Several propulsion concepts have been proposed that might be eventually developed to accomplish this (see § Propulsion below), but none of them are ready for near-term (few decades) developments at acceptable cost.

Time dilation
Physicists generally believe faster-than-light travel is impossible. Relativistic time dilation allows a traveler to experience time more slowly, the closer their speed is to the speed of light. This apparent slowing becomes noticeable when velocities above 80% of the speed of light are attained. Clocks aboard an interstellar ship would run slower than Earth clocks, so if a ship's engines were capable of continuously generating around 1 g of acceleration (which is comfortable for humans), the ship could reach almost anywhere in the galaxy and return to Earth within 40 years ship-time (see diagram). Upon return, there would be a difference between the time elapsed on the astronaut's ship and the time elapsed on Earth.

For example, a spaceship could travel to a star 32 light-years away, initially accelerating at a constant 1.03g (i.e. 10.1 m/s2) for 1.32 years (ship time), then stopping its engines and coasting for the next 17.3 years (ship time) at a constant speed, then decelerating again for 1.32 ship-years, and coming to a stop at the destination. After a short visit, the astronaut could return to Earth the same way. After the full round-trip, the clocks on board the ship show that 40 years have passed, but according to those on Earth, the ship comes back 76 years after launch.

From the viewpoint of the astronaut, onboard clocks seem to be running normally. The star ahead seems to be approaching at a speed of 0.87 light years per ship-year. The universe would appear contracted along the direction of travel to half the size it had when the ship was at rest; the distance between that star and the Sun would seem to be 16 light years as measured by the astronaut.

At higher speeds, the time on board will run even slower, so the astronaut could travel to the center of the Milky Way (30,000 light years from Earth) and back in 40 years ship-time. But the speed according to Earth clocks will always be less than 1 light year per Earth year, so, when back home, the astronaut will find that more than 60 thousand years will have passed on Earth.

Constant acceleration

Regardless of how it is achieved, a propulsion system that could produce acceleration continuously from departure to arrival would be the fastest method of travel. A constant acceleration journey is one where the propulsion system accelerates the ship at a constant rate for the first half of the journey, and then decelerates for the second half, so that it arrives at the destination stationary relative to where it began. If this were performed with an acceleration similar to that experienced at the Earth's surface, it would have the added advantage of producing artificial "gravity" for the crew. Supplying the energy required, however, would be prohibitively expensive with current technology.

From the perspective of a planetary observer, the ship will appear to accelerate steadily at first, but then more gradually as it approaches the speed of light (which it cannot exceed). It will undergo hyperbolic motion. The ship will be close to the speed of light after about a year of accelerating and remain at that speed until it brakes for the end of the journey.

From the perspective of an onboard observer, the crew will feel a gravitational field opposite the engine's acceleration, and the universe ahead will appear to fall in that field, undergoing hyperbolic motion. As part of this, distances between objects in the direction of the ship's motion will gradually contract until the ship begins to decelerate, at which time an onboard observer's experience of the gravitational field will be reversed.

When the ship reaches its destination, if it were to exchange a message with its origin planet, it would find that less time had elapsed on board than had elapsed for the planetary observer, due to time dilation and length contraction.

The result is an impressively fast journey for the crew.

Rocket concepts
All rocket concepts are limited by the rocket equation, which sets the characteristic velocity available as a function of exhaust velocity and mass ratio, the ratio of initial (M0, including fuel) to final (M1, fuel depleted) mass.

Very high specific power, the ratio of thrust to total vehicle mass, is required to reach interstellar targets within sub-century time-frames. Some heat transfer is inevitable, resulting in an extreme thermal load.

Thus, for interstellar rocket concepts of all technologies, a key engineering problem (seldom explicitly discussed) is limiting the heat transfer from the exhaust stream back into the vehicle.

Ion engine
A type of electric propulsion, spacecraft such as Dawn use an ion engine. In an ion engine, electric power is used to create charged particles of the propellant, usually the gas xenon, and accelerate them to extremely high velocities. The exhaust velocity of conventional rockets is limited to about 5 km/s by the chemical energy stored in the fuel's molecular bonds. They produce a high thrust (about 106 N), but they have a low specific impulse, and that limits their top speed. By contrast, ion engines have low force, but the top speed in principle is limited only by the electrical power available on the spacecraft and on the gas ions being accelerated. The exhaust speed of the charged particles range from 15 km/s to 35 km/s.

Fission-electric
Nuclear-electric or plasma engines, operating for long periods at low thrust and powered by fission reactors, have the potential to reach speeds much greater than chemically powered vehicles or nuclear-thermal rockets. Such vehicles probably have the potential to power solar system exploration with reasonable trip times within the current century. Because of their low-thrust propulsion, they would be limited to off-planet, deep-space operation. Electrically powered spacecraft propulsion powered by a portable power-source, say a nuclear reactor, producing only small accelerations, would take centuries to reach for example 15% of the velocity of light, thus unsuitable for interstellar flight during a single human lifetime.

Fission-fragment
Fission-fragment rockets use nuclear fission to create high-speed jets of fission fragments, which are ejected at speeds of up to 12,000 km/s. With fission, the energy output is approximately 0.1% of the total mass-energy of the reactor fuel and limits the effective exhaust velocity to about 5% of the velocity of light. For maximum velocity, the reaction mass should optimally consist of fission products, the "ash" of the primary energy source, so no extra reaction mass need be bookkept in the mass ratio.

Nuclear pulse
Based on work in the late 1950s to the early 1960s, it has been technically possible to build spaceships with nuclear pulse propulsion engines, i.e. driven by a series of nuclear explosions. This propulsion system contains the prospect of very high specific impulse and high specific power.

Project Orion team member Freeman Dyson proposed in 1968 an interstellar spacecraft using nuclear pulse propulsion that used pure deuterium fusion detonations with a very high fuel-burnup fraction. He computed an exhaust velocity of 15,000 km/s and a 100,000-tonne space vehicle able to achieve a 20,000 km/s delta-v allowing a flight-time to Alpha Centauri of 130 years. Later studies indicate that the top cruise velocity that can theoretically be achieved by a Teller-Ulam thermonuclear unit powered Orion starship, assuming no fuel is saved for slowing back down, is about 8% to 10% of the speed of light (0.08-0.1c). An atomic (fission) Orion can achieve perhaps 3%-5% of the speed of light. A nuclear pulse drive starship powered by fusion-antimatter catalyzed nuclear pulse propulsion units would be similarly in the 10% range and pure matter-antimatter annihilation rockets would be theoretically capable of obtaining a velocity between 50% and 80% of the speed of light. In each case saving fuel for slowing down halves the maximum speed. The concept of using a magnetic sail to decelerate the spacecraft as it approaches its destination has been discussed as an alternative to using propellant, this would allow the ship to travel near the maximum theoretical velocity. Alternative designs utilizing similar principles include Project Longshot, Project Daedalus, and Mini-Mag Orion. The principle of external nuclear pulse propulsion to maximize survivable power has remained common among serious concepts for interstellar flight without external power beaming and for very high-performance interplanetary flight.

In the 1970s the Nuclear Pulse Propulsion concept further was refined by Project Daedalus by use of externally triggered inertial confinement fusion, in this case producing fusion explosions via compressing fusion fuel pellets with high-powered electron beams. Since then, lasers, ion beams, neutral particle beams and hyper-kinetic projectiles have been suggested to produce nuclear pulses for propulsion purposes.

A current impediment to the development of any nuclear-explosion-powered spacecraft is the 1963 Partial Test Ban Treaty, which includes a prohibition on the detonation of any nuclear devices (even non-weapon based) in outer space. This treaty would, therefore, need to be renegotiated, although a project on the scale of an interstellar mission using currently foreseeable technology would probably require international cooperation on at least the scale of the International Space Station.

Another issue to be considered, would be the g-forces imparted to a rapidly accelerated spacecraft, cargo, and passengers inside (see Inertia negation).

Nuclear fusion rockets
Fusion rocket starships, powered by nuclear fusion reactions, should conceivably be able to reach speeds of the order of 10% of that of light, based on energy considerations alone. In theory, a large number of stages could push a vehicle arbitrarily close to the speed of light. These would "burn" such light element fuels as deuterium, tritium, 3He, 11B, and 7Li. Because fusion yields about 0.3–0.9% of the mass of the nuclear fuel as released energy, it is energetically more favorable than fission, which releases <0.1% of the fuel's mass-energy. The maximum exhaust velocities potentially energetically available are correspondingly higher than for fission, typically 4–10% of the speed of light. However, the most easily achievable fusion reactions release a large fraction of their energy as high-energy neutrons, which are a significant source of energy loss. Thus, although these concepts seem to offer the best (nearest-term) prospects for travel to the nearest stars within a (long) human lifetime, they still involve massive technological and engineering difficulties, which may turn out to be intractable for decades or centuries.

Early studies include Project Daedalus, performed by the British Interplanetary Society in 1973–1978, and Project Longshot, a student project sponsored by NASA and the US Naval Academy, completed in 1988. Another fairly detailed vehicle system, "Discovery II", designed and optimized for crewed Solar System exploration, based on the D3He reaction but using hydrogen as reaction mass, has been described by a team from NASA's Glenn Research Center. It achieves characteristic velocities of >300 km/s with an acceleration of ~1.7•10−3 g, with a ship initial mass of ~1700 metric tons, and payload fraction above 10%. Although these are still far short of the requirements for interstellar travel on human timescales, the study seems to represent a reasonable benchmark towards what may be approachable within several decades, which is not impossibly beyond the current state-of-the-art. Based on the concept's 2.2% burnup fraction it could achieve a pure fusion product exhaust velocity of ~3,000 km/s.

Antimatter rockets
An antimatter rocket would have a far higher energy density and specific impulse than any other proposed class of rocket. If energy resources and efficient production methods are found to make antimatter in the quantities required and store it safely, it would be theoretically possible to reach speeds of several tens of percent that of light. Whether antimatter propulsion could lead to the higher speeds (>90% that of light) at which relativistic time dilation would become more noticeable, thus making time pass at a slower rate for the travelers as perceived by an outside observer, is doubtful owing to the large quantity of antimatter that would be required.

Speculating that production and storage of antimatter should become feasible, two further issues need to be considered. First, in the annihilation of antimatter, much of the energy is lost as high-energy gamma radiation, and especially also as neutrinos, so that only about 40% of mc2 would actually be available if the antimatter were simply allowed to annihilate into radiations thermally. Even so, the energy available for propulsion would be substantially higher than the ~1% of mc2 yield of nuclear fusion, the next-best rival candidate.

Second, heat transfer from the exhaust to the vehicle seems likely to transfer enormous wasted energy into the ship (e.g. for 0.1g ship acceleration, approaching 0.3 trillion watts per ton of ship mass), considering the large fraction of the energy that goes into penetrating gamma rays. Even assuming shielding was provided to protect the payload (and passengers on a crewed vehicle), some of the energy would inevitably heat the vehicle, and may thereby prove a limiting factor if useful accelerations are to be achieved.

More recently, Friedwardt Winterberg proposed that a matter-antimatter GeV gamma ray laser photon rocket is possible by a relativistic proton-antiproton pinch discharge, where the recoil from the laser beam is transmitted by the Mössbauer effect to the spacecraft.

Rockets with an external energy source
Rockets deriving their power from external sources, such as a laser, could replace their internal energy source with an energy collector, potentially reducing the mass of the ship greatly and allowing much higher travel speeds. Geoffrey A. Landis proposed an interstellar probe propelled by an ion thruster powered by the energy beamed to it from a base station laser. Lenard and Andrews proposed using a base station laser to accelerate nuclear fuel pellets towards a Mini-Mag Orion spacecraft that ignites them for propulsion.

Non-rocket concepts
A problem with all traditional rocket propulsion methods is that the spacecraft would need to carry its fuel with it, thus making it very massive, in accordance with the rocket equation. Several concepts attempt to escape from this problem:

RF resonant cavity thruster
A radio frequency (RF) resonant cavity thruster is a device that is claimed to be a spacecraft thruster. In 2016, the Advanced Propulsion Physics Laboratory at NASA reported observing a small apparent thrust from one such test, a result not since replicated. One of the designs is called EMDrive. In December 2002, Satellite Propulsion Research Ltd described a working prototype with an alleged total thrust of about 0.02 newtons powered by an 850 W cavity magnetron. The device could operate for only a few dozen seconds before the magnetron failed, due to overheating. The latest test on the EMDrive concluded that it does not work.

Helical engine
Proposed in 2019 by NASA scientist Dr. David Burns, the helical engine concept would use a particle accelerator to accelerate particles to near the speed of light. Since particles traveling at such speeds acquire more mass, it is believed that this mass change could create acceleration. According to Burns, the spacecraft could theoretically reach 99% the speed of light.

Interstellar ramjets
In 1960, Robert W. Bussard proposed the Bussard ramjet, a fusion rocket in which a huge scoop would collect the diffuse hydrogen in interstellar space, "burn" it on the fly using a proton–proton chain reaction, and expel it out of the back. Later calculations with more accurate estimates suggest that the thrust generated would be less than the drag caused by any conceivable scoop design. Yet the idea is attractive because the fuel would be collected en route (commensurate with the concept of energy harvesting), so the craft could theoretically accelerate to near the speed of light. The limitation is due to the fact that the reaction can only accelerate the propellant to 0.12c. Thus the drag of catching interstellar dust and the thrust of accelerating that same dust to 0.12c would be the same when the speed is 0.12c, preventing further acceleration.

Beamed propulsion

A light sail or magnetic sail powered by a massive laser or particle accelerator in the home star system could potentially reach even greater speeds than rocket- or pulse propulsion methods, because it would not need to carry its own reaction mass and therefore would only need to accelerate the craft's payload. Robert L. Forward proposed a means for decelerating an interstellar craft with a light sail of 100 kilometers in the destination star system without requiring a laser array to be present in that system. In this scheme, a secondary sail of 30 kilometers is deployed to the rear of the spacecraft, while the large primary sail is detached from the craft to keep moving forward on its own. Light is reflected from the large primary sail to the secondary sail, which is used to decelerate the secondary sail and the spacecraft payload. In 2002, Geoffrey A. Landis of NASA's Glen Research center also proposed a laser-powered, propulsion, sail ship that would host a diamond sail (of a few nanometers thick) powered with the use of solar energy. With this proposal, this interstellar ship would, theoretically, be able to reach 10 percent the speed of light. It has also been proposed to use beamed-powered propulsion to accelerate a spacecraft, and electromagnetic propulsion to decelerate it; thus, eliminating the problem that the Bussard ramjet has with the drag produced during acceleration.

A magnetic sail could also decelerate at its destination without depending on carried fuel or a driving beam in the destination system, by interacting with the plasma found in the solar wind of the destination star and the interstellar medium.

The following table lists some example concepts using beamed laser propulsion as proposed by the physicist Robert L. Forward:

Interstellar travel catalog to use photogravitational assists for a full stop
The following table is based on work by Heller, Hippke and Kervella.

 * Successive assists at α Cen A and B could allow travel times to 75 yr to both stars.
 * Lightsail has a nominal mass-to-surface ratio (σnom) of 8.6×10−4 gram m−2 for a nominal graphene-class sail.
 * Area of the Lightsail, about 105 m2 = (316 m)2
 * Velocity up to 37,300 km s−1 (12.5% c)

Pre-accelerated fuel
Achieving start-stop interstellar trip times of less than a human lifetime require mass-ratios of between 1,000 and 1,000,000, even for the nearer stars. This could be achieved by multi-staged vehicles on a vast scale. Alternatively large linear accelerators could propel fuel to fission propelled space-vehicles, avoiding the limitations of the Rocket equation.

Dynamic soaring
Dynamic soaring as a way to travel across interstellar space has been proposed.

Transmission of minds with light
Uploaded human minds or AI could be transmitted with laser or radio signals at the speed of light. This requires a receiver at the destination which would first have to be set up e.g. by humans, probes, self replicating machines (potentially along with AI or uploaded humans), or an alien civilization (which might also be in a different galaxy, perhaps a Kardashev type III civilization).

Artificial black hole
A theoretical idea for enabling interstellar travel is to propel a starship by creating an artificial black hole and using a parabolic reflector to reflect its Hawking radiation. Although beyond current technological capabilities, a black hole starship offers some advantages compared to other possible methods. Getting the black hole to act as a power source and engine also requires a way to convert the Hawking radiation into energy and thrust. One potential method involves placing the hole at the focal point of a parabolic reflector attached to the ship, creating forward thrust. A slightly easier, but less efficient method would involve simply absorbing all the gamma radiation heading towards the fore of the ship to push it onwards, and let the rest shoot out the back.

Faster-than-light travel

Scientists and authors have postulated a number of ways by which it might be possible to surpass the speed of light, but even the most serious-minded of these are highly speculative.

It is also debatable whether faster-than-light travel is physically possible, in part because of causality concerns: travel faster than light may, under certain conditions, permit travel backwards in time within the context of special relativity. Proposed mechanisms for faster-than-light travel within the theory of general relativity require the existence of exotic matter and, it is not known if it could be produced in sufficient quantities, if at all.

Alcubierre drive
In physics, the Alcubierre drive is based on an argument, within the framework of general relativity and without the introduction of wormholes, that it is possible to modify spacetime in a way that allows a spaceship to travel with an arbitrarily large speed by a local expansion of spacetime behind the spaceship and an opposite contraction in front of it. Nevertheless, this concept would require the spaceship to incorporate a region of exotic matter, or the hypothetical concept of negative mass.

Wormholes
Wormholes are conjectural distortions in spacetime that theorists postulate could connect two arbitrary points in the universe, across an Einstein–Rosen Bridge. It is not known whether wormholes are possible in practice. Although there are solutions to the Einstein equation of general relativity that allow for wormholes, all of the currently known solutions involve some assumption, for example the existence of negative mass, which may be unphysical. However, Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by cosmic strings. The general theory of wormholes is discussed by Visser in the book Lorentzian Wormholes.

Project Hyperion
Project Hyperion has looked into various feasibility issues of crewed interstellar travel. Notable results of the project include an assessment of world ship system architectures and adequate population size. Its members continue to publish on crewed interstellar travel in collaboration with the Initiative for Interstellar Studies.

Enzmann starship
The Enzmann starship, as detailed by G. Harry Stine in the October 1973 issue of Analog, was a design for a future starship, based on the ideas of Robert Duncan-Enzmann. The spacecraft itself as proposed used a 12,000,000 ton ball of frozen deuterium to power 12–24 thermonuclear pulse propulsion units. Twice as long as the Empire State Building is tall and assembled in-orbit, the spacecraft was part of a larger project preceded by interstellar probes and telescopic observation of target star systems.

NASA research
NASA has been researching interstellar travel since its formation, translating important foreign language papers and conducting early studies on applying fusion propulsion, in the 1960s, and laser propulsion, in the 1970s, to interstellar travel.

In 1994, NASA and JPL cosponsored a "Workshop on Advanced Quantum/Relativity Theory Propulsion" to "establish and use new frames of reference for thinking about the faster-than-light (FTL) question".

The NASA Breakthrough Propulsion Physics Program (terminated in FY 2003 after a 6-year, $1.2-million study, because "No breakthroughs appear imminent.") identified some breakthroughs that are needed for interstellar travel to be possible.

Geoffrey A. Landis of NASA's Glenn Research Center states that a laser-powered interstellar sail ship could possibly be launched within 50 years, using new methods of space travel. "I think that ultimately we're going to do it, it's just a question of when and who," Landis said in an interview. Rockets are too slow to send humans on interstellar missions. Instead, he envisions interstellar craft with extensive sails, propelled by laser light to about one-tenth the speed of light. It would take such a ship about 43 years to reach Alpha Centauri if it passed through the system without stopping. Slowing down to stop at Alpha Centauri could increase the trip to 100 years, whereas a journey without slowing down raises the issue of making sufficiently accurate and useful observations and measurements during a fly-by.

100 Year Starship study
The 100 Year Starship (100YSS) study was the name of a one-year project to assess the attributes of and lay the groundwork for an organization that can carry forward the 100 Year Starship vision. 100YSS-related symposia were organized between 2011 and 2015.

Harold ("Sonny") White from NASA's Johnson Space Center is a member of Icarus Interstellar, the nonprofit foundation whose mission is to realize interstellar flight before the year 2100. At the 2012 meeting of 100YSS, he reported using a laser to try to warp spacetime by 1 part in 10 million with the aim of helping to make interstellar travel possible.

Other designs

 * Project Orion, human crewed interstellar ship (1958–1968).
 * Project Daedalus, uncrewed interstellar probe (1973–1978).
 * Starwisp, uncrewed interstellar probe (1985).
 * Project Longshot, uncrewed interstellar probe (1987–1988).
 * Starseed/launcher, fleet of uncrewed interstellar probes (1996).
 * Project Valkyrie, human crewed interstellar ship (2009).
 * Project Icarus, uncrewed interstellar probe (2009–2014).
 * Sun-diver, uncrewed interstellar probe.
 * Project Dragonfly, small laser-propelled interstellar probe (2013–2015).
 * Breakthrough Starshot, fleet of uncrewed interstellar probes, announced on 12 April 2016.
 * Solar One, crewed spacecraft that would combine beamed-powered propulsion, electromagnetic propulsion, and nuclear propulsion (2020).

Non-profit organizations
A few organisations dedicated to interstellar propulsion research and advocacy for the case exist worldwide. These are still in their infancy, but are already backed up by a membership of a wide variety of scientists, students and professionals.
 * Initiative for Interstellar Studies (UK)
 * Tau Zero Foundation (USA)
 * Limitless Space Institute (USA)
 * Tennessee Valley Interstellar Workshop (TVIW), business name Interstellar Research Group (IRG) (USA)

Feasibility
The energy requirements make interstellar travel very difficult. It has been reported that at the 2008 Joint Propulsion Conference, multiple experts opined that it was improbable that humans would ever explore beyond the Solar System. Brice N. Cassenti, an associate professor with the Department of Engineering and Science at Rensselaer Polytechnic Institute, stated that at least 100 times the total energy output of the entire world [in a given year] would be required to send a probe to the nearest star.

Astrophysicist Sten Odenwald stated that the basic problem is that through intensive studies of thousands of detected exoplanets, most of the closest destinations within 50 light years do not yield Earth-like planets in the star's habitable zones. Given the multitrillion-dollar expense of some of the proposed technologies, travelers will have to spend up to 200 years traveling at 20% the speed of light to reach the best known destinations. Moreover, once the travelers arrive at their destination (by any means), they will not be able to travel down to the surface of the target world and set up a colony unless the atmosphere is non-lethal. The prospect of making such a journey, only to spend the rest of the colony's life inside a sealed habitat and venturing outside in a spacesuit, may eliminate many prospective targets from the list.

Moving at a speed close to the speed of light and encountering even a tiny stationary object like a grain of sand will have fatal consequences. For example, a gram of matter moving at 90% of the speed of light contains a kinetic energy corresponding to a small nuclear bomb (around 30kt TNT).

One of the major stumbling blocks is having enough Onboard Spares & Repairs facilities for such a lengthy time journey assuming all other considerations are solved, without access to all the resources available on Earth.

Interstellar missions not for human benefit
Explorative high-speed missions to Alpha Centauri, as planned for by the Breakthrough Starshot initiative, are projected to be realizable within the 21st century. It is alternatively possible to plan for uncrewed slow-cruising missions taking millennia to arrive. These probes would not be for human benefit in the sense that one can not foresee whether there would be anybody around on Earth interested in then back-transmitted science data. An example would be the Genesis mission, which aims to bring unicellular life, in the spirit of directed panspermia, to habitable but otherwise barren planets. Comparatively slow cruising Genesis probes, with a typical speed of $$c/300$$, corresponding to about $$1000\,\mbox{km/s}$$, can be decelerated using a magnetic sail. Uncrewed missions not for human benefit would hence be feasible.

Discovery of Earth-like planets
On August 24, 2016, Earth-size exoplanet Proxima Centauri b orbiting in the habitable zone of Proxima Centauri, 4.2 light-years away, was announced. This is the nearest known potentially-habitable exoplanet outside our Solar System.

In February 2017, NASA announced that its Spitzer Space Telescope had revealed seven Earth-size planets in the TRAPPIST-1 system orbiting an ultra-cool dwarf star 40 light-years away from the Solar System. Three of these planets are firmly located in the habitable zone, the area around the parent star where a rocky planet is most likely to have liquid water. The discovery sets a new record for greatest number of habitable-zone planets found around a single star outside the Solar System. All of these seven planets could have liquid water – the key to life as we know it – under the right atmospheric conditions, but the chances are highest with the three in the habitable zone.

title: Interstellar travel


text:
Interior Gateway Routing Protocol

Interior Gateway Routing Protocol (IGRP) is a distance vector interior gateway protocol (IGP) developed by Cisco. It is used by routers to exchange routing data within an autonomous system.

IGRP is a proprietary protocol. IGRP was created in part to overcome the limitations of RIP (maximum hop count of only 15, and a single routing metric) when used within large networks. IGRP supports multiple metrics for each route, including bandwidth, delay, load, and reliability; to compare two routes these metrics are combined into a single metric, using a formula which can be adjusted through the use of pre-set constants. By default, the IGRP composite metric is a sum of the segment delays and the lowest segment bandwidth. The maximum configurable hop count of IGRP-routed packets is 255 (default 100), and routing updates are broadcast every 90 seconds (by default). IGRP uses protocol number 9 for communication.

IGRP is considered a classful routing protocol. Because the protocol has no field for a subnet mask, the router assumes that all subnetwork addresses within the same Class A, Class B, or Class C network have the same subnet mask as the subnet mask configured for the interfaces in question. This contrasts with classless routing protocols that can use variable length subnet masks. Classful protocols have become less popular as they are wasteful of IP address space.

Advancement
In order to address the issues of address space and other factors, Cisco created EIGRP (Enhanced Interior Gateway Routing Protocol). EIGRP adds support for VLSM (variable length subnet mask) and adds the Diffusing Update Algorithm (DUAL) in order to improve routing and provide a loopless environment. EIGRP has completely replaced IGRP, making IGRP an obsolete routing protocol. In Cisco IOS versions 12.3 and greater, IGRP is completely unsupported. In the new Cisco CCNA curriculum (version 4), IGRP is mentioned only briefly, as an "obsolete protocol".

title: Interior Gateway Routing Protocol


text:
IRS (disambiguation)

IRS is the United States Internal Revenue Service.

IRS may also refer to:

Arts and entertainment

 * I.R.S. Records
 * "I.R.S.", a song by Guns N' Roses on their album Chinese Democracy
 * Irwin R. Schyster, wrestler Mike Rotunda
 * IR$, Franco-Belgian comics

Economics

 * Indian Revenue Service
 * Interest rate swap
 * Internal Revenue Service (Ghana)

Organisations

 * Independence Republic of Sardinia, a political party, Italy
 * Leibniz Institute for Research on Society and Space, of the Leibniz Association

Medicine

 * Indoor residual spraying of insecticide
 * Insulin receptor substrate, a ligand
 * Intergroup Rhabdomyosarcoma Study Group

Transportation

 * Independent rear suspension, a form of car independent suspension
 * International Railway Solution, International Union of Railways leaflets
 * International Railway Systems, a Romanian company
 * IRS Airlines, Nigeria

Other uses

 * International Rules Series, Australia–Ireland football competition
 * Indian Remote Sensing satellite
 * Indian Readership Survey
 * Integrated reception system, for broadcast signals
 * Institutionalized Riot Systems

title: IRS (disambiguation)