Lorentz transformation

From Wikipedia, the free encyclopedia

In physics, the Lorentz transformation (or transformations) is named after the Dutch physicist Hendrik Lorentz. It was the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism. The Lorentz transformation is in accordance with special relativity, but was derived before special relativity.

The transformations describe how measurements of space and time by two observers are related. They reflect the fact that observers moving at different velocities may measure different distances, elapsed times, and even different orderings of events. They supersede the Galilean transformation of Newtonian physics, which assumes an absolute space and time (see Galilean relativity). The Galilean transformation is a good approximation only at relative speeds much smaller than the speed of light.
The Lorentz transformation is a linear transformation. It may include a rotation of space; a rotation-free Lorentz transformation is called a Lorentz boost.

In Minkowski space, the Lorentz transformations preserve the spacetime interval between any two events. They describe only the transformations in which the spacetime event at the origin is left fixed, so they can be considered as a hyperbolic rotation of Minkowski space. The more general set of transformations that also includes translations is known as the Poincaré group.

History

Many physicists, including Woldemar Voigt, George FitzGerald, Joseph Larmor, and Hendrik Lorentz himself had been discussing the physics implied by these equations since 1887.^[1]

Early in 1889, Oliver Heaviside had shown from Maxwell's equations that the electric field surrounding a spherical distribution of charge should cease to have spherical symmetry once the charge is in motion relative to the ether. FitzGerald then conjectured that Heaviside’s distortion result might be applied to a theory of intermolecular forces. Some months later, FitzGerald published the conjecture that bodies in motion are being contracted, in order to explain the baffling outcome of the 1887 ether-wind experiment of Michelson and Morley. In 1892, Lorentz independently presented the same idea in a more detailed manner, which was subsequently called FitzGerald–Lorentz contraction hypothesis.^[2] Their explanation was widely known before 1905.^[3]

Lorentz (1892–1904) and Larmor (1897–1900), who believed the luminiferous ether hypothesis, were also seeking the transformation under which Maxwell's equations are invariant when transformed from the ether to a moving frame. They extended the FitzGerald–Lorentz contraction hypothesis and found out that the time coordinate has to be modified as well ("local time"). Henri Poincaré gave a physical interpretation to local time (to first order in v/c) as the consequence of clock synchronization, under the assumption that the speed of light is constant in moving frames.^[4] Larmor is credited to have been the first to understand the crucial time dilation property inherent in his equations.^[5]

In 1905, Poincaré was the first to recognize that the transformation has the properties of a mathematical group, and named it after Lorentz.^[6] Later in the same year Albert Einstein published what is now called special relativity, by deriving the Lorentz transformation under the assumptions of the principle of relativity and the constancy of the speed of light in any inertial reference frame, and by abandoning the mechanical aether.^[7]

Lorentz transformation for frames in standard configuration

Consider two observers O and O′, each using their own Cartesian coordinate system to measure space and time intervals. O uses (t, x, y, z) and O′ uses (t′, x′, y′, z′). Assume further that the coordinate systems are oriented so that, in 3 dimensions, the x-axis and the x′-axis are collinear, the y-axis is parallel to the y′-axis, and the z-axis parallel to the z′-axis. The relative velocity between the two observers is v along the common x-axis; O measures O′ to move at velocity v along the coincident xx′ axes, while O′ measures O to move at velocity −v along the coincident xx′ axes. Also assume that the origins of both coordinate systems are the same, that is, coincident times and positions. If all these hold, then the coordinate systems are said to be in standard configuration.

The inverse of a Lorentz transformation relates the coordinates the other way round; from the coordinates O′ measures (t′, x′, y′, z′) to the coordinates O measures (t, x, y, z), so t, x, y, z are in terms of t′, x′, y′, z′. The mathematical form is nearly identical to the original transformation; the only difference is the negation of the uniform relative velocity (from v to −v), and exchange of primed and unprimed quantities, because O′ moves at velocity v relative to O, and equivalently, O moves at velocity −v relative to O′. This symmetry makes it effortless to find the inverse transformation (carrying out the exchange and negation saves a lot of rote algebra), although more fundamentally; it highlights that all physical laws should remain unchanged under a Lorentz transformation.^[8]

Below, the Lorentz transformations are called "boosts" in the stated directions.

Boost in the x-direction

The spacetime coordinates of an event, as measured by each observer in their inertial reference frame (in standard configuration) are shown in the speech bubbles.

Top: frame F′ moves at velocity v along the x-axis of frame F.
Bottom: frame F moves at velocity −v along the x′-axis of frame F′.^[9]

These are the simplest forms. The Lorentz transformation for frames in standard configuration can be shown to be (see for example ^[10] and ^[11]):

where:

• v is the relative velocity between frames in the x-direction,
• c is the speed of light,
• is the Lorentz factor (Greek lowercase gamma),
• is the velocity coefficient (Greek lowercase beta), again for the x-direction.

The use of β and γ is standard throughout the literature.^[12] For the remainder of the article – they will be also used throughout unless otherwise stated. Since the above is a linear system of equations (more technically a linear transformation), they can be written in matrix form:

According to the principle of relativity, there is no privileged frame of reference, so the inverse transformations frame F′ to frame F must be given by simply negating v:

where the value of γ remains unchanged. These equations are also obtained by algebraically solving the standard equations for the variables t, x, y, z.

Boost in the y or z directions

The above collection of equations apply only for a boost in the x-direction. The standard configuration works equally well in the y or z directions instead of x, and so the results are similar.

For the y-direction:

summarized by

where v and so β are now in the y-direction.

For the z-direction:

summarized by

where v and so β are now in the z-direction.

The Lorentz or boost matrix is usually denoted by Λ (Greek capital lambda). Above the transformations have been applied to the four-position X,

The Lorentz transform for a boost in one of the above directions can be compactly written as a single matrix equation:

Boost in any direction

Boost in an arbitrary direction.

Vector form

For a boost in an arbitrary direction with velocity v, that is, O observes O′ to move in direction v in the F coordinate frame, while O′ observes O to move in direction −v in the F′ coordinate frame, it is convenient to decompose the spatial vector r into components perpendicular and parallel to v:

so that

where • denotes the dot product (see also orthogonality for more information). Then, only time and the component r_‖ in the direction of v;

are "warped" by the Lorentz factor:

.

The parallel and perpendicular components can be eliminated, by substituting into r′:

Since r_‖ and v are parallel we have

where geometrically and algebraically:

• v/v is a dimensionless unit vector pointing in the same direction as r_‖,
• r_‖ = (r • v)/v is the projection of r into the direction of v,

substituting for r_‖ and factoring v gives

This method, of eliminating parallel and perpendicular components, can be applied to any Lorentz transformation written in parallel-perpendicular form.

Matrix forms

These equations can be expressed in block matrix form as

where I is the 3×3 identity matrix and β = v/c is the relative velocity vector (in units of c) as a column vector – in cartesian and tensor index notation it is:

β^T = v^T/c is the transpose – a row vector:

and β is the magnitude of β:

More explicitly stated:

The transformation Λ can be written in the same form as before,

which has the structure:^[13]

and the components deduced from above are:

where δ_ij is the Kronecker delta, and by convention: Latin letters for indices take the values 1, 2, 3, for spatial components of a 4-vector (Greek indices take values 0, 1, 2, 3 for time and space components).

Note that this transformation is only the "boost," i.e., a transformation between two frames whose x, y, and z axis are parallel and whose spacetime origins coincide. The most general proper Lorentz transformation also contains a rotation of the three axes, because the composition of two boosts is not a pure boost but is a boost followed by a rotation. The rotation gives rise to Thomas precession. The boost is given by a symmetric matrix, but the general Lorentz transformation matrix need not be symmetric.

Composition of two boosts

The composition of two Lorentz boosts B(u) and B(v) of velocities u and v is given by:^[14][15]

,

where

• B(v) is the 4 × 4 matrix that uses the components of v, i.e. v₁, v₂, v₃ in the entries of the matrix, or rather the components of v/c in the representation that is used above,
• is the velocity-addition,
• Gyr[u,v] (capital G) is the rotation arising from the composition. If the 3 × 3 matrix form of the rotation applied to spatial coordinates is given by gyr[u,v], then the 4 × 4 matrix rotation applied to 4-coordinates is given by:^[14]

• gyr (lower case g) is the gyrovector space abstraction of the gyroscopic Thomas precession, defined as an operator on a velocity w in terms of velocity addition:

for all w.

The composition of two Lorentz transformations L(u, U) and L(v, V) which include rotations U and V is given by:^[16]

Visualizing the transformations in Minkowski space

Lorentz transformations can be depicted on the Minkowski light cone spacetime diagram.

The momentarily co-moving inertial frames along the world line of a rapidly accelerating observer (center). The vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The small dots are specific events in spacetime. If one imagines these events to be the flashing of a light, then the events that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the momentarily co-moving inertial frame changes when the observer accelerates.

Particle travelling at constant velocity (straight worldline coincident with time t′ axis).

Accelerating particle (curved worldline).

Lorentz transformations on the Minkowski light cone spacetime diagram, for one space and one time dimension.

The yellow axes are the rest frame of an observer, the blue axes correspond to the frame of a moving observer

The red lines are world lines, a continuous sequence of events: straight for an object travelling at constant velocity, curved for an object accelerating. Worldlines of light form the boundary of the light cone.

The purple hyperbolae indicate this is a hyperbolic rotation, the hyperbolic angle ϕ is called rapidity (see below). The greater the relative speed between the reference frames, the more "warped" the axes become. The relative velocity cannot exceed c.

The black arrow is a displacement four-vector between two events (not necessarily on the same world line), showing that in a Lorentz boost; time dilation (fewer time intervals in moving frame) and length contraction (shorter lengths in moving frame) occur. The axes in the moving frame are orthogonal (even though they do not look so).

Rapidity

The Lorentz transformation can be cast into another useful form by defining a parameter ϕ called the rapidity (an instance of hyperbolic angle) such that

and thus

Equivalently:

Then the Lorentz transformation in standard configuration is:

Hyperbolic expressions

From the above expressions for e^φ and e^−φ

and therefore,

Hyperbolic rotation of coordinates

Substituting these expressions into the matrix form of the transformation, it is evident that

Thus, the Lorentz transformation can be seen as a hyperbolic rotation of coordinates in Minkowski space, where the parameter ϕ represents the hyperbolic angle of rotation, often referred to as rapidity.
This transformation is sometimes illustrated with a Minkowski diagram, as displayed above.

This 4-by-4 boost matrix can thus be written compactly as a Matrix exponential,

where the simpler Lie-algebraic hyperbolic rotation generator K_x is called a boost generator.

Transformation of other physical quantities

The transformation matrix is universal for all four-vectors, not just 4-dimensional spacetime coordinates. If Z is any four-vector, then:^[13]

or in tensor index notation:

in which the primed indices denote indices of Z in the primed frame.
More generally, the transformation of any tensor quantity T is given by:^[17]

where is the inverse matrix of

Special relativity

The crucial insight of Einstein's clock-setting method is the idea that time is relative. In essence, each observer's frame of reference is associated with a unique set of clocks, the result being that time as measured for a location passes at different rates for different observers.^[18] This was a direct result of the Lorentz transformations and is called time dilation. We can also clearly see from the Lorentz "local time" transformation that the concept of the relativity of simultaneity and of the relativity of length contraction are also consequences of that clock-setting hypothesis.^[19]

Transformation of the electromagnetic field

Lorentz transformations can also be used to prove that magnetic and electric fields are simply different aspects of the same force — the electromagnetic force, as a consequence of relative motion between electric charges and observers.^[20] The fact that the electromagnetic field shows relativistic effects becomes clear by carrying out a simple thought experiment:^[21]

• Consider an observer measuring a charge at rest in a reference frame F. The observer will detect a static electric field. As the charge is stationary in this frame, there is no electric current, so the observer will not observe any magnetic field.
• Consider another observer in frame F′ moving at relative velocity v (relative to F and the charge). This observer will see a different electric field because the charge is moving at velocity −v in their rest frame. Further, in frame F′ the moving charge constitutes an electric current, and thus the observer in frame F′ will also see a magnetic field.

This shows that the Lorentz transformation also applies to electromagnetic field quantities when changing the frame of reference, given below in vector form.

The correspondence principle

For relative speeds much less than the speed of light, the Lorentz transformations reduce to the Galilean transformation in accordance with the correspondence principle.

The correspondence limit is usually stated mathematically as: as v → 0, c → ∞. In words: as velocity approaches 0, the speed of light (seems to) approach infinity. Hence, it is sometimes said that nonrelativistic physics is a physics of "instantaneous action at a distance".^[18]

Spacetime interval

In a given coordinate system x^μ, if two events A and B are separated by

the spacetime interval between them is given by

This can be written in another form using the Minkowski metric. In this coordinate system,

Then, we can write

or, using the Einstein summation convention,

Now suppose that we make a coordinate transformation x^μ → x′ ^μ. Then, the interval in this coordinate system is given by

or

It is a result of special relativity that the interval is an invariant. That is, s² = s′ ². For this to hold, it can be shown^[22] that it is necessary (but not sufficient) for the coordinate transformation to be of the form

Here, C^μ is a constant vector and Λ^μ_ν a constant matrix, where we require that

Such a transformation is called a Poincaré transformation or an inhomogeneous Lorentz transformation.^[23] The C^a represents a spacetime translation. When C^a = 0, the transformation is called an homogeneous Lorentz transformation, or simply a Lorentz transformation.

Taking the determinant of

gives us

The cases are:

• Proper Lorentz transformations have det(Λ^μ_ν) = +1, and form a subgroup called the special orthogonal group SO(1,3).
• Improper Lorentz transformations are det(Λ^μ_ν) = −1, which do not form a subgroup, as the product of any two improper Lorentz transformations will be a proper Lorentz transformation.

From the above definition of Λ it can be shown that (Λ⁰₀)² ≥ 1, so either Λ⁰₀ ≥ 1 or Λ⁰₀ ≤ −1, called orthochronous and non-orthochronous respectively. An important subgroup of the proper Lorentz transformations are the proper orthochronous Lorentz transformations which consist purely of boosts and rotations. Any Lorentz transform can be written as a proper orthochronous, together with one or both of the two discrete transformations; space inversion P and time reversal T, whose non-zero elements are:

The set of Poincaré transformations satisfies the properties of a group and is called the Poincaré group. Under the Erlangen program, Minkowski space can be viewed as the geometry defined by the Poincaré group, which combines Lorentz transformations with translations. In a similar way, the set of all Lorentz transformations forms a group, called the Lorentz group.

A quantity invariant under Lorentz transformations is known as a Lorentz scalar.

Tachyon

From Wikipedia, the free encyclopedia

Because a tachyon would always move faster than light, it would not be possible to see it approaching. After a tachyon has passed nearby, we would be able to see two images of it, appearing and departing in opposite directions. The black line is the shock wave of Cherenkov radiation, shown only in one moment of time. This double image effect is most prominent for an observer located directly in the path of a superluminal object (in this example a sphere, shown in grey). The right hand bluish shape is the image formed by the blue-doppler shifted light arriving at the observer—who is located at the apex of the black Cherenkov lines—from the sphere as it approaches. The left-hand reddish image is formed from red-shifted light that leaves the sphere after it passes the observer. Because the object arrives before the light, the observer sees nothing until the sphere starts to pass the observer, after which the image-as-seen-by-the-observer splits into two—one of the arriving sphere (to the right) and one of the departing sphere (to the left).

A tachyon /ˈtæki.ɒn/ or tachyonic particle is a hypothetical particle that always moves faster than light. The word comes from the Greek: ταχύς or tachys, meaning "swift, quick, fast, rapid", and was coined in 1967 by Gerald Feinberg.^[1] The complementary particle types are called luxon (always moving at the speed of light) and bradyon (always moving slower than light), which both exist. The possibility of particles moving faster than light was first proposed by Bilaniuk, Deshpande, and George Sudarshan in 1962, although the term they used for it was "meta-particle".^[2]

Most physicists think that faster-than-light particles cannot exist because they are not consistent with the known laws of physics.^[3][4] If such particles did exist, they could be used to build a tachyonic antitelephone and send signals faster than light, which (according to special relativity) would lead to violations of causality.^[4] Potentially consistent theories that allow faster-than-light particles include those that break Lorentz invariance, the symmetry underlying special relativity, so that the speed of light is not a barrier.

In the 1967 paper that coined the term,^[1] Feinberg proposed that tachyonic particles could be quanta of a quantum field with negative squared mass. However, it was soon realized that excitations of such imaginary mass fields do not in fact propagate faster than light,^[5] and instead represent an instability known as tachyon condensation.^[3] Nevertheless, negative squared mass fields are commonly referred to as "tachyons",^[6] and in fact have come to play an important role in modern physics.

Despite theoretical arguments against the existence of faster-than-light particles, experiments have been conducted to search for them. No compelling evidence for their existence has been found. In September 2011, it was reported that a tau neutrino had travelled faster than the speed of light in a major release by CERN; however, later updates from CERN on the OPERA project indicate that the faster-than-light readings were resultant from "a faulty element of the experiment's fibre optic timing system".^[7]

In paper accepted for publication in Astroparticle Physics by professor Robert Ehrlich it is stated that six observations based on data and fits to data from a variety of areas are consistent with the hypothesis that the electron neutrino is a tachyon with imaginary mass.^[8]

Tachyons in relativistic theory

In special relativity, a faster-than-light particle would have space-like four-momentum,^[1] in contrast to ordinary particles that have time-like four-momentum. It would also have imaginary mass and proper time.^{[citation needed]} Being constrained to the spacelike portion of the energy–momentum graph, it could not slow down to subluminal speeds.^[1]

Mass

In a Lorentz invariant theory, the same formulas that apply to ordinary slower-than-light particles (sometimes called "bradyons" in discussions of tachyons) must also apply to tachyons. In particular the energy–momentum relation:

(where p is the relativistic momentum of the bradyon and m is its rest mass) should still apply, along with the formula for the total energy of a particle:

This equation shows that the total energy of a particle (bradyon or tachyon) contains a contribution from its rest mass (the "rest mass–energy") and a contribution from its motion, the kinetic energy.
When v is larger than c, the denominator in the equation for the energy is "imaginary", as the value under the radical is negative. Because the total energy must be real, the numerator must also be imaginary: i.e. the rest mass m must be imaginary, as a pure imaginary number divided by another pure imaginary number is a real number.

Speed

One curious effect is that, unlike ordinary particles, the speed of a tachyon increases as its energy decreases. In particular, approaches zero when approaches infinity. (For ordinary bradyonic matter, E increases with increasing speed, becoming arbitrarily large as v approaches c, the speed of light). Therefore, just as bradyons are forbidden to break the light-speed barrier, so too are tachyons forbidden from slowing down to below c, because infinite energy is required to reach the barrier from either above or below.

As noted by Einstein, Tolman, and others, special relativity implies that faster-than-light particles, if they existed, could be used to communicate backwards in time.^[9]

Neutrinos

In 1985 Chodos et al. proposed that neutrinos can have a tachyonic nature.^[10] The possibility of standard model particles moving at superluminal speeds can be modeled using Lorentz invariance violating terms, for example in the Standard-Model Extension.^[11][12][13] In this framework, neutrinos experience Lorentz-violating oscillations and can travel faster than light at high energies. This proposal was strongly criticized.^[14]

Cherenkov radiation

A tachyon with an electric charge would lose energy as Cherenkov radiation^[15]—just as ordinary charged particles do when they exceed the local speed of light in a medium. A charged tachyon traveling in a vacuum therefore undergoes a constant proper time acceleration and, by necessity, its worldline forms a hyperbola in space-time. However reducing a tachyon's energy increases its speed, so that the single hyperbola formed is of two oppositely charged tachyons with opposite momenta (same magnitude, opposite sign) which annihilate each other when they simultaneously reach infinite speed at the same place in space. (At infinite speed, the two tachyons have no energy each and finite momentum of opposite direction, so no conservation laws are violated in their mutual annihilation. The time of annihilation is frame dependent.)

Even an electrically neutral tachyon would be expected to lose energy via gravitational Cherenkov radiation, because it has a gravitational mass, and therefore increase in speed as it travels, as described above. If the tachyon interacts with any other particles, it can also radiate Cherenkov energy into those particles. Neutrinos interact with the other particles of the Standard Model, and Andrew Cohen and Sheldon Glashow recently used this to argue that the faster-than-light neutrino anomaly cannot be explained by making neutrinos propagate faster than light, and must instead be due to an error in the experiment.^[16]

Causality

Causality is a fundamental principle of physics. If tachyons can transmit information faster than light, then according to relativity they violate causality, leading to logical paradoxes of the "kill your own grandfather" type. This is often illustrated with thought experiments such as the "tachyon telephone paradox"^[9] or "logically pernicious self-inhibitor."^[17]

The problem can be understood in terms of the relativity of simultaneity in special relativity, which says that different inertial reference frames will disagree on whether two events at different locations happened "at the same time" or not, and they can also disagree on the order of the two events (technically, these disagreements occur when spacetime interval between the events is 'space-like', meaning that neither event lies in the future light cone of the other).^[18]

If one of the two events represents the sending of a signal from one location and the second event represents the reception of the same signal at another location, then as long as the signal is moving at the speed of light or slower, the mathematics of simultaneity ensures that all reference frames agree that the transmission-event happened before the reception-event.^[18] However, in the case of a hypothetical signal moving faster than light, there would always be some frames in which the signal was received before it was sent, so that the signal could be said to have moved backwards in time. Because one of the two fundamental postulates of special relativity says that the laws of physics should work the same way in every inertial frame, if it is possible for signals to move backwards in time in any one frame, it must be possible in all frames. This means that if observer A sends a signal to observer B which moves faster than light in A's frame but backwards in time in B's frame, and then B sends a reply which moves faster than light in B's frame but backwards in time in A's frame, it could work out that A receives the reply before sending the original signal, challenging causality in every frame and opening the door to severe logical paradoxes.^[19] Mathematical details can be found in the tachyonic antitelephone article, and an illustration of such a scenario using spacetime diagrams can be found in Baker, R. (2003)^[20]

Reinterpretation principle

The reinterpretation principle^[1][2][19] asserts that a tachyon sent back in time can always be reinterpreted as a tachyon traveling forward in time, because observers cannot distinguish between the emission and absorption of tachyons. The attempt to detect a tachyon from the future (and violate causality) would actually create the same tachyon and send it forward in time (which is causal).

However, this principle is not widely accepted as resolving the paradoxes.^[9][19][21] Instead, what would be required to avoid paradoxes is that unlike any known particle, tachyons do not interact in any way and can never be detected or observed, because otherwise a tachyon beam could be modulated and used to create an anti-telephone^[9] or a "logically pernicious self-inhibitor".^[17] All forms of energy are believed to interact at least gravitationally, and many authors state that superluminal propagation in Lorentz invariant theories always leads to causal paradoxes.^[22][23]

Fundamental models

In modern physics, all fundamental particles are regarded as excitations of quantum fields. There are several distinct ways in which tachyonic particles could be embedded into a field theory.

Fields with imaginary mass

In the paper that coined the term "tachyon", Gerald Feinberg studied Lorentz invariant quantum fields with imaginary mass.^[1] Because the group velocity for such a field is superluminal, naively it appears that its excitations propagate faster than light. However, it was quickly understood that the superluminal group velocity does not correspond to the speed of propagation of any localized excitation (like a particle). Instead, the negative mass represents an instability to tachyon condensation, and all excitations of the field propagate subluminally and are consistent with causality.^[5] Despite having no faster-than-light propagation, such fields are referred to simply as "tachyons" in many sources.^{[3][6][24][25][26][27]}
Tachyonic fields play an important role in modern physics. Perhaps the most famous is the Higgs boson of the Standard Model of particle physics, which—in its uncondensed phase—has an imaginary mass. In general, the phenomenon of spontaneous symmetry breaking, which is closely related to tachyon condensation, plays a very important role in many aspects of theoretical physics, including the Ginzburg–Landau and BCS theories of superconductivity. Another example of a tachyonic field is the tachyon of bosonic string theory.^[24][26][28]

Tachyons are predicted by bosonic string theory and also the NS (which is the open bosonic sector) and NS-NS (which is the closed bosonic sector) sectors of RNS Superstring theory before GSO projection. However, due to the Sen conjecture—also known as tachyon condensation—this is not possible. This resulted in the necessity for the GSO projection.

Lorentz-violating theories

In theories that do not respect Lorentz invariance the speed of light is not (necessarily) a barrier, and particles can travel faster than the speed of light without infinite energy or causal paradoxes.^[22] A class of field theories of that type are the so-called Standard Model extensions. However, the experimental evidence for Lorentz invariance is extremely good, so such theories are very tightly constrained.^[29][30]

Fields with non-canonical kinetic term

By modifying the kinetic energy of the field, it is possible to produce Lorentz invariant field theories with excitations that propagate superluminally.^[5][23] However, such theories in general do not have a well-defined Cauchy problem (for reasons related to the issues of causality discussed above), and are probably inconsistent quantum mechanically.

History

As mentioned above, the term "tachyon" was coined by Gerald Feinberg in a 1967 paper titled "Possibility of Faster-Than-Light Particles".^[1] He had been inspired by the science-fiction story "Beep" by James Blish.^[31] Feinberg studied the kinematics of such particles according to special relativity. In his paper he also introduced fields with imaginary mass (now also referred to as "tachyons") in an attempt to understand the microphysical origin such particles might have.

The first hypothesis regarding faster-than-light particles is sometimes attributed to German physicist Arnold Sommerfeld in 1904,^[32] and more recent discussions happened in 1962^[2] and 1969.^[33]

In fiction

Tachyons have appeared in many works of fiction. They have been used as a standby mechanism upon which many science fiction authors rely to establish faster-than-light communication, with or without reference to causality issues. The word tachyon has become widely recognized to such an extent that it can impart a science-fictional connotation even if the subject in question has no particular relation to superluminal travel (a form of technobabble, akin to positronic brain).
Also referenced in the movie, "K-PAX". Kevin Spacey's character claims to have traveled to Earth at Tachyon speeds. In the Watchmen comic book universe, the use of tachyons can disrupt Dr. Manhattan's ability to perceive time. Tachyons also figure prominently in the Star Trek universe, and are often associated with time travel scenarios in the Star Trek universe. Also recently mentioned in The Flash episode "the Man in the Yellow Suit".^[34]

Bill Nye

From Wikipedia, the free encyclopedia

Bill Nye
Nye at Bridgewater State College on April 10, 2007.
Born	William Sanford Nye (1955-11-27) November 27, 1955 (age 59) Washington, D.C., U.S.
Residence	Los Angeles, California, U.S.
Nationality	American
Fields	Mechanical engineering
Institutions	Boeing Cornell University Planetary Society
Alma mater	Cornell University (B.S.)
Known for	Bill Nye the Science Guy
Signature

William Sanford "Bill" Nye (born November 27, 1955), popularly known as Bill Nye the Science Guy, is an American science educator, comedian, television host, actor, writer, scientist, and former mechanical engineer, best known as the host of the Disney/PBS children's science show Bill Nye the Science Guy (1993–98) and for his many subsequent appearances in popular media as a science educator.

Early life

Nye was born on November 27, 1955,^[1][2][3] in Washington, D.C., to Jacqueline (née Jenkins; 1921–2000), a codebreaker during World War II, and Edwin Darby "Ned" Nye (1917–97), also a World War II veteran, whose experience without electricity in a Japanese prisoner of war camp led him to become a sundial enthusiast.^[4][5][6] His maternal grandmother was French, from Dancevoir.^[7]
After attending Lafayette Elementary and Alice Deal Junior High in the city, he was accepted to the private Sidwell Friends School on a partial scholarship and graduated in 1973.^[8][9] He studied mechanical engineering at Cornell University (where he took an astronomy class taught by Carl Sagan)^[10] and graduated with a bachelor of science degree in mechanical engineering in 1977.^[11] Nye occasionally returns to Cornell as a professor to guest-lecture introductory-level astronomy and human ecology classes.^[12]

Career

Nye began his career in Seattle at Boeing, where (among other things) he starred in training films and developed a hydraulic pressure resonance suppressor for the 747. Later, he worked as a consultant in the aeronautics industry. In 1999 he told the St. Petersburg Times that he applied to be a NASA astronaut every few years, but was always rejected.^[13]

The Science Guy

Nye began his professional entertainment career as a writer/actor on a local sketch comedy television show in Seattle, Washington, called Almost Live!. The host of the show, Ross Shafer, suggested he do some scientific demonstrations in a six-minute segment, and take on the nickname "The Science Guy".^[14] His other main recurring role on Almost Live! was as Speedwalker, a speedwalking Seattle superhero.
From 1991 to 1993, he appeared in the live-action educational segments of Back to the Future: The Animated Series in the nonspeaking role of assistant to Dr. Emmett Brown (played by Christopher Lloyd), in which he would demonstrate science while Lloyd explained. The segments' national popularity led to Nye's hosting an educational television program, Bill Nye the Science Guy, from 1993 to 1998. Each of the 100 episodes aimed to teach a specific topic in science to a preteen audience, yet it garnered a wide adult audience as well.^[15] With its comedic overtones, the show became popular as a teaching aid in schools. When portraying "The Science Guy", Nye wears a light blue lab coat and bow tie.

Nye has written several books as The Science Guy. In addition to hosting, he was a writer and producer for the show, which was filmed entirely in Seattle.

Nye's Science Guy persona appears alongside Ellen DeGeneres and Alex Trebek in a video at Ellen's Energy Adventure, an attraction that has played since 1996 at the Universe of Energy pavilion inside Epcot at Walt Disney World. His voice is heard in the Dinosaur attraction in Disney's Animal Kingdom park, teaching guests about the dinosaurs while they queue for the ride. He appears in video form in the "Design Lab" of CyberSpace Mountain, inside DisneyQuest at Walt Disney World, where he refers to himself as "Bill Nye the Coaster Guy."

Entertainment/edutainment

Nye and Executive Director of The Planetary Society received the Committee for Skeptical Inquiry's "In Praise of Reason" Award at CSICON 2011 in New Orleans

Nye remained interested in science education through entertainment. He played a science teacher in Disney's 1998 TV movie The Principal Takes a Holiday; he made a hovercraft to demonstrate science in an unusual classroom manner. From 2000 to 2002, Nye was the technical expert in BattleBots. In 2004 and 2005, Nye hosted 100 Greatest Discoveries, an award-winning series produced by THINKFilm for The Science Channel and in high definition on the Discovery HD Theater. He was also host of an eight-part Discovery Channel series called Greatest Inventions with Bill Nye. He created a 13-episode PBS KCTS-TV series about science, called The Eyes of Nye, aimed at an older audience than his previous show had been. Airing in 2005, it often featured episodes based on politically relevant themes such as genetically modified food, global warming, and race. Nye has guest-starred in several episodes of the crime drama Numb3rs as an engineering faculty member. A lecture Nye gave several years ago on exciting children about math was an inspiration for creating Numb3rs.^[16] He has also made guest appearances on the VH1 reality show America's Most Smartest Model.^[17]

Nye has appeared numerous times on the talk show Larry King Live, speaking about topics such as global warming and UFOs. He argued that global warming is an issue that should be addressed by governments of the world in part because it could be implicated in the record-setting 2005 Atlantic hurricane season.^[18] On UFOs, he has been skeptical of extraterrestrial explanations for sightings such as those at Roswell and Malmstrom Air Force Base in 1967.^[19]

Nye appears in segments of The Climate Code on The Weather Channel, telling his personal ways of saving energy. He still makes regular appearances on the show, often asking quiz questions. In the fall of 2008, Nye also appeared periodically on the daytime game show Who Wants to Be a Millionaire as part of the show's reintroduced "Ask the Expert" lifeline. In 2008, he also hosted Stuff Happens, a show on the then new Planet Green network. In November 2008, Nye appeared in an acting role as himself in the fifth-season episode "Brain Storm" of Stargate Atlantis alongside fellow television personality and astrophysicist Neil deGrasse Tyson.^[20]

In 2009, portions of Bill Nye's shows were used as lyrics and portions of the second Symphony of Science music education video by composer John Boswell. Nye recorded a short YouTube video (as himself, not his TV persona) advocating clean-energy climate-change legislation on behalf of Al Gore's Repower America campaign in October 2009.^[21] Bill joined the American Optometric Association in a multimedia advertising campaign to persuade parents to get their children comprehensive eye examinations.^[22] Nye made an appearance in Palmdale's 2010 video "Here Comes the Summer";^[23] the band's lead singer Kay Hanley is his neighbor. Nye (as his TV persona) also made a guest appearance on The Dr. Oz Show.

In September 2012, Nye claimed that creationist views threaten science education and innovation in the United States.^[24][25][26]

In February 2014, Nye debated creationist Ken Ham at the Creation Museum on the topic of whether creation is a viable model of origins in today's modern, scientific era.^[27][28][29]

On February 28, 2014, Nye was a celebrity guest and interviewer at the White House Student Film Festival.^[30]

Scientific work

Nye orating in October 2010.

In the early 2000s, Nye assisted in the development of a small sundial that was included in the Mars Exploration Rover missions.^[2] Known as MarsDial, it included small colored panels to provide a basis for color calibration in addition to helping keep track of time.^[31] From 2005 to 2010, Nye was the vice president of The Planetary Society, an organization that advocates space science research and the exploration of other planets, particularly Mars.^[32] He became the organization's second Executive Director in September 2010 when Louis Friedman stepped down.^[33][34]

In November 2010, Nye became the face of a new permanent exhibition at the Chabot Space & Science Center in Oakland, California. Bill Nye’s Climate Lab features Nye as commander of the Clean Energy Space Station, and invites visitors on an urgent mission to thwart climate change. Beginning with a view of Planet Earth from space, visitors explore air, water, and land galleries to discover how climate change affects Earth’s connected systems, and how to use the Sun, wind, land, and water to generate clean energy. In an interview about the exhibit, Nye said, “Everything in the exhibit is geared to showing you that the size of the problem of climate change is big. Showing you a lot about energy use ... It’s a huge opportunity ... We need young people, entrepreneurs, young inventors, young innovators to change the world.”^[35]

Nye with the Chief of Naval Research Rear. Adm. Nevin Carr following the presentation of a "Powered by Naval Research" pocket protector during the Navy Office of General Counsel Spring 2011 Conference.

Nye gave a solar noon clock atop Rhodes Hall to Cornell on Aug 27 following a public lecture that filled the 715-seat Statler Auditorium. Nye talked about his father's passion for sundials and timekeeping, his time at Cornell, his work on the sundials mounted on the Mars rovers and the story behind the Bill Nye Solar Noon Clock.^[36] Bill Nye conducted a Q&A session after the 2012 Mars Rover Landing.^[37]

Nye holds several United States patents,^[38] including one for ballet pointe shoes^[32] and another for an educational magnifying glass created by filling a clear plastic bag with water.^[39][40] From 2001 to 2006, Nye served as Frank H.T. Rhodes Class of '56 University Professor at Cornell University.^[11][41] Nye supported the 2006 reclassification of Pluto from planet to dwarf planet by the International Astronomical Union.^[42]

Nye is a fellow of the Committee for Skeptical Inquiry, a U.S. non-profit scientific and educational organization whose aim is to promote scientific inquiry, critical investigation, and the use of reason in examining controversial and extraordinary claims.^[43] Interviewed by John Rael for the Independent Investigation Group IIG, Nye stated that his "concern right now... scientific illiteracy... you [the public] don't have enough rudimentary knowledge of the universe to evaluate claims."^[44] In November 2012, Nye launched a Kickstarter project for an educational Aerodynamics game, AERO 3D. The project was not funded.^[45] His book, Undeniable: Evolution and the Science of Creation, was released on November 4, 2014.^[46]

Dancing with the Stars

Nye was a contestant in the 17th season of Dancing with the Stars in 2013, partnering newcomer Tyne Stecklein. They were eliminated early in the season after Nye sustained an injury to his quadriceps tendon on Week 3.^[47]

Dance	Score	Music	Result
Cha-cha-cha	14(5-4-5)	"Weird Science"—Oingo Boingo	No Elimination
Paso Doble	17(6-5-6)	"Symphony No. 5"—Ludwig van Beethoven	Safe
Jazz	16(6-5-5)	"Get Lucky"—Daft Punk feat. Pharrell Williams	Eliminated

Personal life

Since 2006, Nye has lived in Los Angeles, though he has also owned a house on Mercer Island.^[48] As of July 2007, Nye and environmental activist Ed Begley, Jr. are engaging in a friendly competition "to see who could have the lowest carbon footprint," according to Begley.^[49] In a 2008 interview, Nye joked that he wants to "crush Ed Begley" in their environmental competition.^[50] Nye and Begley are neighbors in Los Angeles, and sometimes dine together at a local vegetarian restaurant.^[50] Nye often appears on Begley's Planet Green reality show Living with Ed. Nye enjoys baseball and occasionally does experiments involving the physics of the game. As a longtime Seattle resident before becoming an entertainer, he is said to have been a fan of the Seattle Mariners, although recently he has voiced his preference (as a D.C. native) for the Washington Nationals.^[8] He also played Ultimate while in college and for a period of time while living in Seattle.^[51] In July 2012, Nye endorsed President Barack Obama's reelection bid.^[52]

Nye announced his engagement during an appearance on The Late Late Show with Craig Ferguson and was married to his fiancée of five months, musician Blair Tindall, on February 3, 2006. The ceremony was performed by Rick Warren at The Entertainment Gathering at the Skirball Cultural Center in Los Angeles. Yo-Yo Ma provided the music.^[53] Nye left the relationship seven weeks later when the marriage license was declared invalid.^[54] In 2007, Nye received a protective order against Tindall after an incident in which she came onto his property and used herbicide to damage his garden. Tindall admitted this, but denied being a threat to him.^[55] In 2012, Nye sued Tindall for unpaid attorney's fees he incurred while he went to court in 2009 to enforce the protective order against Tindall after she allegedly violated it. According to Nye's court filings, she was ordered to pay these fees; to date, she has not paid any of it.^[56]

Nye is an avid swing dancer.^[57] He has been spotted at local dances in the Los Angeles area as well as at nationwide events such as entompology (Rochester, NY).^[58] Nye describes himself as agnostic.^[59]

Awards and honors

In May 1999, Nye was the commencement speaker at Rensselaer Polytechnic Institute where he was awarded an honorary doctor of science degree.^[60] He was awarded an honorary doctorate by Johns Hopkins University in May 2008.^[61] In May 2011, he received an honorary doctor of science degree from Willamette University, where he was the keynote speaker for that year's commencement exercises.^[62] In addition, Bill Nye also received an honorary doctor of pedagogy degree from Lehigh University on May 20, 2013, at the commencement ceremony.^[63] Nye received the 2010 Humanist of the Year Award from the American Humanist Association.^[64]