![Faster than light implies time travel diagram](https://upload.wikimedia.org/wikipedia/commons/8/88/Faster_than_light_implies_time_travel_diagram.svg)
Faster-than-light (also FTL, superluminal or supercausal)
travel
Travel is the movement of people between distant geographical locations. Travel can be done by foot, bicycle, automobile, train, boat, bus, airplane, ship or other means, with or without luggage, and can be one way or round trip. Travel c ...
and
communication
Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
are the conjectural propagation of
matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
or
information
Information is an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
faster than the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
(). The
special theory of relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
implies that only particles with zero
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
(i.e.,
photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alway ...
) may travel ''at'' the speed of light, and that nothing may travel faster.
Particles whose speed exceeds that of light (
tachyon
A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such partic ...
s) have been hypothesized, but their existence would violate
causality
Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...
and would imply
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
. The
scientific consensus
Scientific consensus is the generally held judgment, position, and opinion of the majority or the supermajority of scientists in a particular field of study at any particular time.
Consensus is achieved through scholarly communication at confe ...
is that they do not exist. "Apparent" or "effective" FTL, on the other hand, depends on the hypothesis that unusually distorted regions of
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
might permit matter to reach distant locations in less time than light could in normal ("undistorted") spacetime.
As of the 21st century, according to current scientific theories, matter is required to travel at slower-than-light (also STL or subluminal) speed with respect to the locally distorted spacetime region. Apparent FTL is not excluded by
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
; however, any apparent FTL physical plausibility is currently speculative. Examples of apparent FTL proposals are the
Alcubierre drive
The Alcubierre drive () is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable ...
,
Krasnikov tube
A Krasnikov tube is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an immobile Alcubierre drive (and like them requires exot ...
s,
traversable wormholes, and
quantum tunneling
In physics, a quantum (plural quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property can be "quantized" is referred to as "the hypothesis of quantizati ...
.
Superluminal travel of non-information
In the context of this article, FTL is the transmission of information or matter faster than ''c'', a constant equal to the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in vacuum, which is 299,792,458 m/s (by definition of the metre) or about 186,282.397 miles per second. This is not quite the same as traveling faster than light, since:
*Some processes propagate faster than ''c'', but cannot carry information (see examples in the sections immediately following).
*In some materials where light travels at speed ''c/n'' (where ''n'' is the
refractive index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
The refractive index determines how much the path of light is bent, or ...
) other particles can travel faster than ''c/n'' (but still slower than ''c''), leading to
Cherenkov radiation (see
phase velocity below).
Neither of these phenomena violates
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
or creates problems with
causality
Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...
, and thus neither qualifies as ''FTL'' as described here.
In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.
Daily sky motion
For an earth-bound observer, objects in the sky complete one revolution around the Earth in one day.
Proxima Centauri, the nearest star outside the
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
, is about four and a half
light-year
A light-year, alternatively spelled light year, is a large unit of length used to express astronomical distances and is equivalent to about 9.46 trillion kilometers (), or 5.88 trillion miles ().One trillion here is taken to be 1012 ...
s away.
[
] In this frame of reference, in which Proxima Centauri is perceived to be moving in a circular trajectory with a radius of four light years, it could be described as having a speed many times greater than ''c'' as the rim speed of an object moving in a circle is a product of the radius and angular speed.
It is also possible on a
geostatic view, for objects such as comets to vary their speed from subluminal to superluminal and vice versa simply because the distance from the Earth varies. Comets may have orbits which take them out to more than 1000
AU. The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, and therefore non-inertial, frame.
Light spots and shadows
If a laser beam is swept across a distant object, the spot of laser light can easily be made to move across the object at a speed greater than ''c''.
Similarly, a shadow projected onto a distant object can be made to move across the object faster than ''c''.
[
] In neither case does the light travel from the source to the object faster than ''c'', nor does any information travel faster than light.
Closing speeds
The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. This may approach twice the speed of light, as in the case of two particles travelling at close to the speed of light in opposite directions with respect to the reference frame.
Imagine two fast-moving particles approaching each other from opposite sides of a
particle accelerator
A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams.
Large accelerators are used for fundamental research in particle ...
of the collider type. The closing speed would be the rate at which the distance between the two particles is decreasing. From the point of view of an observer standing at rest relative to the accelerator, this rate will be slightly less than twice the speed of light.
Special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
does not prohibit this. It tells us that it is wrong to use
Galilean relativity
Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frames of reference. Galileo Galilei first described this principle in 1632 in his '' Dialogue Concerning the Two Chief World Systems'' using t ...
to compute the velocity of one of the particles, as would be measured by an observer traveling alongside the other particle. That is, special relativity gives the correct
velocity-addition formula
In relativistic physics, a velocity-addition formula is a three-dimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive Lorentz transformations, so they also relate different f ...
for computing such
relative velocity
The relative velocity \vec_ (also \vec_ or \vec_) is the velocity of an object or observer B in the rest frame of another object or observer A.
Classical mechanics
In one dimension (non-relativistic)
We begin with relative motion in the classi ...
.
It is instructive to compute the relative velocity of particles moving at ''v'' and −''v'' in accelerator frame, which corresponds to the closing speed of 2''v'' > ''c''. Expressing the speeds in units of ''c'', ''β'' = ''v''/''c'':
:
Proper speeds
If a spaceship travels to a planet one light-year (as measured in the Earth's rest frame) away from Earth at high speed, the time taken to reach that planet could be less than one year as measured by the traveller's clock (although it will always be more than one year as measured by a clock on Earth). The value obtained by dividing the distance traveled, as determined in the Earth's frame, by the time taken, measured by the traveller's clock, is known as a proper speed or a
proper velocity
In relativity, proper velocity (also known as celerity) w of an object relative to an observer is the ratio between observer-measured displacement vector \textbf and proper time elapsed on the clocks of the traveling object:
:\textbf = \frac
...
. There is no limit on the value of a proper speed as a proper speed does not represent a speed measured in a single inertial frame. A light signal that left the Earth at the same time as the traveller would always get to the destination before the traveller.
Possible distance away from Earth
Since one might not travel faster than light, one might conclude that a human can never travel further from the Earth than 40 light-years if the traveler is active between the age of 20 and 60. A traveler would then never be able to reach more than the very few star systems which exist within the limit of 20–40 light-years from the Earth. This is a mistaken conclusion: because of
time dilation
In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
, the traveler can travel thousands of light-years during their 40 active years. If the spaceship accelerates at a constant 1 g (in its own changing frame of reference), it will, after 354 days, reach speeds a little under the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
(for an observer on Earth), and time dilation will increase the traveler's lifespan to thousands of Earth years, seen from the reference system of the
Solar System
The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
— but the traveler's subjective lifespan will not thereby change. If they were then to return to Earth, the traveler would arrive on Earth thousands of years into the future. Their travel speed would not have been observed from Earth as being supraluminal — neither for that matter would it appear to be so from the traveler's perspective– but the traveler would instead have experienced a length contraction of the universe in their direction of travel. After the traveler reverses course, the Earth will seem to experience much more time passing than the traveler does. So while the traveler's (ordinary) coordinate speed cannot exceed ''c'', their
proper speed, or distance traveled from the Earth's point of reference divided by
proper time
In relativity, proper time (from Latin, meaning ''own time'') along a timelike world line is defined as the time as measured by a clock following that line. It is thus independent of coordinates, and is a Lorentz scalar. The proper time interval ...
, can be much greater than ''c''. This is seen in statistical studies of
muon
A muon ( ; from the Greek letter mu (μ) used to represent it) is an elementary particle similar to the electron, with an electric charge of −1 '' e'' and a spin of , but with a much greater mass. It is classified as a lepton. As wi ...
s traveling much further than ''c'' times their
half-life
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
(at rest), if traveling close to ''c''.
Phase velocities above ''c''
The
phase velocity of an
electromagnetic wave
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
, when traveling through a medium, can routinely exceed ''c'', the vacuum velocity of light. For example, this occurs in most glasses at
X-ray
An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30&nb ...
frequencies. However, the phase velocity of a wave corresponds to the propagation speed of a theoretical single-frequency (purely
monochromatic) component of the wave at that frequency. Such a wave component must be infinite in extent and of constant amplitude (otherwise it is not truly monochromatic), and so cannot convey any information.
Thus a phase velocity above ''c'' does not imply the propagation of
signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
with a velocity above ''c''.
[
]
Group velocities above ''c''
The
group velocity of a wave may also exceed ''c'' in some circumstances. In such cases, which typically at the same time involve rapid attenuation of the intensity, the maximum of the envelope of a pulse may travel with a velocity above ''c''. However, even this situation does not imply the propagation of
signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
with a velocity above ''c'', even though one may be tempted to associate pulse maxima with signals. The latter association has been shown to be misleading, because the information on the arrival of a pulse can be obtained before the pulse maximum arrives. For example, if some mechanism allows the full transmission of the leading part of a pulse while strongly attenuating the pulse maximum and everything behind (distortion), the pulse maximum is effectively shifted forward in time, while the information on the pulse does not come faster than ''c'' without this effect. However, group velocity
can exceed ''c'' in some parts of a
Gaussian beam
In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. Thi ...
in vacuum (without attenuation). The
diffraction
Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a s ...
causes the peak of the pulse to propagate faster, while overall power does not.
Universal expansion
![History of the Universe](https://upload.wikimedia.org/wikipedia/commons/d/db/History_of_the_Universe.svg)
The
expansion of the universe
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
causes distant galaxies to recede from us faster than the speed of light, if
proper distance and
cosmological time
Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at ...
are used to calculate the speeds of these galaxies. However, in
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, velocity is a local notion, so velocity calculated using comoving coordinates does not have any simple relation to velocity calculated locally. (See
Comoving and proper distances
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...
for a discussion of different notions of 'velocity' in cosmology.) Rules that apply to relative velocities in special relativity, such as the rule that relative velocities cannot increase past the speed of light, do not apply to relative velocities in comoving coordinates, which are often described in terms of the "expansion of space" between galaxies. This expansion rate is thought to have been at its peak during the
inflationary epoch
__NOTOC__
In physical cosmology, the inflationary epoch was the period in the evolution of the early universe when, according to inflation theory, the universe underwent an extremely rapid exponential expansion. This rapid expansion increased the ...
thought to have occurred in a tiny fraction of the second after the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
(models suggest the period would have been from around 10
−36 seconds after the Big Bang to around 10
−33 seconds), when the universe may have rapidly expanded by a factor of around 10
20 to 10
30.
There are many galaxies visible in telescopes with
red shift numbers of 1.4 or higher. All of these are currently traveling away from us at speeds greater than the speed of light. Because the
Hubble parameter
Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
is decreasing with time, there can actually be cases where a galaxy that is receding from us faster than light does manage to emit a signal which reaches us eventually.
[
]
However, because
the expansion of the universe is accelerating, it is projected that most galaxies will eventually cross a type of cosmological
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
where any light they emit past that point will never be able to reach us at any time in the infinite future, because the light never reaches a point where its "peculiar velocity" towards us exceeds the expansion velocity away from us (these two notions of velocity are also discussed in
Comoving and proper distances#Uses of the proper distance). The current distance to this cosmological event horizon is about 16 billion light-years, meaning that a signal from an event happening at present would eventually be able to reach us in the future if the event was less than 16 billion light-years away, but the signal would never reach us if the event was more than 16 billion light-years away.
Astronomical observations
Apparent
superluminal motion is observed in many
radio galaxies
A radio galaxy is a galaxy with giant regions of radio emission extending well beyond its visible structure. These energetic radio lobes are powered by jets from its active galactic nucleus. They have luminosities up to 1039 W at radio wav ...
,
blazar
A blazar is an active galactic nucleus (AGN) with a relativistic jet (a jet composed of ionized matter traveling at nearly the speed of light) directed very nearly towards an observer. Relativistic beaming of electromagnetic radiation from the ...
s,
quasars, and recently also in
microquasar
A microquasar, the smaller version of a quasar, is a compact region surrounding a stellar black hole with a mass several times that of its companion star. The matter being pulled from the companion star forms an accretion disk around the black hole ...
s. The effect was predicted before it was observed by
Martin Rees
Martin John Rees, Baron Rees of Ludlow One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 23 June 1942) is a British cosmologist and astrophysicist. He is the fifteenth Astronomer Royal, ...
and can be explained as an
optical illusion
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual perception, percept that arguably appears to differ from reality. Illusions come in a wide v ...
caused by the object partly moving in the direction of the observer, when the speed calculations assume it does not. The phenomenon does not contradict the theory of
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
. Corrected calculations show these objects have velocities close to the speed of light (relative to our reference frame). They are the first examples of large amounts of mass moving at close to the speed of light. Earth-bound laboratories have only been able to accelerate small numbers of elementary particles to such speeds.
Quantum mechanics
Certain phenomena in
quantum mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, such as
quantum entanglement
Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of ...
, might give the superficial impression of allowing communication of information faster than light. According to the
no-communication theorem
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurem ...
these phenomena do not allow true communication; they only let two observers in different locations see the same system simultaneously, without any way of controlling what either sees.
Wavefunction collapse
In quantum mechanics, wave function collapse occurs when a wave function—initially in a superposition of several eigenstates—reduces to a single eigenstate due to interaction with the external world. This interaction is called an ''observa ...
can be viewed as an
epiphenomenon
An epiphenomenon (plural: epiphenomena) is a secondary phenomenon that occurs alongside or in parallel to a primary phenomenon. The word has two senses: one that connotes known causation and one that connotes absence of causation or reservation ...
of quantum decoherence, which in turn is nothing more than an effect of the underlying local time evolution of the wavefunction of a system and ''all'' of its environment. Since the underlying behavior does not violate local causality or allow FTL communication, it follows that neither does the additional effect of wavefunction collapse, whether real ''or'' apparent.
The
uncertainty principle
In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
implies that individual photons may travel for short distances at speeds somewhat faster (or slower) than ''c'', even in vacuum; this possibility must be taken into account when enumerating
Feynman diagram
In theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduc ...
s for a particle interaction. However, it was shown in 2011 that a single photon may not travel faster than ''c''. In quantum mechanics,
virtual particle
A virtual particle is a theoretical transient particle that exhibits some of the characteristics of an ordinary particle, while having its existence limited by the uncertainty principle. The concept of virtual particles arises in the perturbat ...
s may travel faster than light, and this phenomenon is related to the fact that static field effects (which are mediated by virtual particles in quantum terms) may travel faster than light (see section on static fields above). However, macroscopically these fluctuations average out, so that photons do travel in straight lines over long (i.e., non-quantum) distances, and they do travel at the speed of light on average. Therefore, this does not imply the possibility of superluminal information transmission.
There have been various reports in the popular press of experiments on faster-than-light transmission in optics — most often in the context of a kind of
quantum tunnelling phenomenon. Usually, such reports deal with a
phase velocity or
group velocity faster than the vacuum velocity of light. However, as stated above, a superluminal phase velocity cannot be used for faster-than-light transmission of information.
Hartman effect
The Hartman effect is the tunneling effect through a barrier where the tunneling time tends to a constant for large barriers. This could, for instance, be the gap between two prisms. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted. There is a non-zero probability that the photon will tunnel across the gap rather than follow the refracted path. For large gaps between the prisms the tunnelling time approaches a constant and thus the photons appear to have crossed with a superluminal speed.
However, the Hartman effect cannot actually be used to violate relativity by transmitting signals faster than ''c'', because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate". The evanescent waves in the Hartman effect are due to virtual particles and a non-propagating static field, as mentioned in the sections above for gravity and electromagnetism.
Casimir effect
In physics, the
Casimir–Polder force
In quantum field theory, the Casimir effect is a physical force acting on the macroscopic boundaries of a confined space which arises from the quantum fluctuations of the field. It is named after the Dutch physicist Hendrik Casimir, who predi ...
is a physical force exerted between separate objects due to resonance of
vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experiment ...
in the intervening space between the objects. This is sometimes described in terms of virtual particles interacting with the objects, owing to the mathematical form of one possible way of calculating the strength of the effect. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. Because the effect is due to virtual particles mediating a static field effect, it is subject to the comments about static fields discussed above.
EPR paradox
The EPR paradox refers to a famous
thought experiment
A thought experiment is a hypothetical situation in which a hypothesis, theory, or principle is laid out for the purpose of thinking through its consequences.
History
The ancient Greek ''deiknymi'' (), or thought experiment, "was the most anc ...
of
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
,
Boris Podolsky
Boris Yakovlevich Podolsky (russian: link=no, Бори́с Я́ковлевич Подо́льский; June 29, 1896 – November 28, 1966) was a Russian-American physicist of Jewish descent, noted for his work with Albert Einstein and Nathan ...
and
Nathan Rosen
Nathan Rosen (Hebrew: נתן רוזן; March 22, 1909 – December 18, 1995) was an American-Israeli physicist noted for his study on the structure of the hydrogen atom and his work with Albert Einstein and Boris Podolsky on entangled wave functio ...
that was realized experimentally for the first time by
Alain Aspect
Alain Aspect (; born 15 June 1947) is a French physicist noted for his experimental work on quantum entanglement.
Aspect was awarded the 2022 Nobel Prize in Physics, jointly with John Clauser and Anton Zeilinger, "for experiments with entangl ...
in 1981 and 1982 in the
Aspect experiment
Aspect's experiment was the first quantum mechanics experiment to demonstrate the violation of Bell's inequalities. Its 1982 result allowed for further validation of the quantum entanglement and locality principles. It also offered an experimental ...
. In this experiment, the measurement of the state of one of the quantum systems of an
entangled pair apparently instantaneously forces the other system (which may be distant) to be measured in the complementary state. However, no information can be transmitted this way; the answer to whether or not the measurement actually affects the other quantum system comes down to which
interpretation of quantum mechanics
An interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraord ...
one subscribes to.
An experiment performed in 1997 by
Nicolas Gisin
Nicolas Gisin (born 1952) is a Swiss physicist and professor at the University of Geneva working on the foundations of quantum mechanics, and quantum information and communication. His work includes both experimental and theoretical physics. He ...
has demonstrated non-local quantum correlations between particles separated by over 10 kilometers. But as noted earlier, the non-local correlations seen in entanglement cannot actually be used to transmit classical information faster than light, so that relativistic causality is preserved. The situation is akin to sharing a synchronized coin flip, where the second person to flip their coin will always see the opposite of what the first person sees, but neither has any way of knowing whether they were the first or second flipper, without communicating classically. See
No-communication theorem
In physics, the no-communication theorem or no-signaling principle is a no-go theorem from quantum information theory which states that, during measurement of an entangled quantum state, it is not possible for one observer, by making a measurem ...
for further information. A 2008 quantum physics experiment also performed by Nicolas Gisin and his colleagues has determined that in any hypothetical
non-local hidden-variable theory, the speed of the
quantum non-local connection (what Einstein called "spooky action at a distance") is at least 10,000 times the speed of light.
Delayed choice quantum eraser
The
delayed-choice quantum eraser is a version of the EPR paradox in which the observation (or not) of interference after the passage of a photon through a
double slit experiment
In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles; moreover, it displays the fundamentally probabilistic nature of quantum mechanica ...
depends on the conditions of observation of a second photon entangled with the first. The characteristic of this experiment is that the observation of the second photon can take place at a later time than the observation of the first photon, which may give the impression that the measurement of the later photons "retroactively" determines whether the earlier photons show interference or not, although the interference pattern can only be seen by correlating the measurements of both members of every pair and so it can't be observed until both photons have been measured, ensuring that an experimenter watching only the photons going through the slit does not obtain information about the other photons in an FTL or backwards-in-time manner.
Superluminal communication
Faster-than-light communication is, according to relativity, equivalent to
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
. What we measure as the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
in vacuum (or near vacuum) is actually the fundamental physical constant ''c''. This means that all
inertial
In classical physics and special relativity, an inertial frame of reference (also called inertial reference frame, inertial frame, inertial space, or Galilean reference frame) is a frame of reference that is not undergoing any acceleration. ...
and, for the coordinate speed of light, non-inertial observers, regardless of their relative
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
, will always measure zero-mass particles such as
photon
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
s traveling at ''c'' in vacuum. This result means that measurements of time and velocity in different frames are no longer related simply by constant shifts, but are instead related by
Poincaré transformation
Poincaré is a French surname. Notable people with the surname include:
* Henri Poincaré (1854–1912), French physicist, mathematician and philosopher of science
* Henriette Poincaré (1858-1943), wife of Prime Minister Raymond Poincaré
* Luci ...
s. These transformations have important implications:
*The relativistic momentum of a
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
ive particle would increase with speed in such a way that at the speed of light an object would have infinite momentum.
*To accelerate an object of non-zero
rest mass
The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is the portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, i ...
to ''c'' would require infinite time with any finite acceleration, or infinite acceleration for a finite amount of time.
*Either way, such acceleration requires infinite energy.
*Some observers with sub-light relative motion will disagree about which occurs first of any two events that are separated by a
space-like interval. In other words, any travel that is faster-than-light will be seen as traveling backwards in time in some other, equally valid, frames of reference, or need to assume the speculative hypothesis of possible Lorentz violations at a presently unobserved scale (for instance the Planck scale). Therefore, any theory which permits "true" FTL also has to cope with
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
and all its associated paradoxes, or else to assume the
Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
to be a symmetry of thermodynamical statistical nature (hence a symmetry broken at some presently unobserved scale).
*In special relativity the coordinate speed of light is only guaranteed to be ''c'' in an
inertial frame; in a non-inertial frame the coordinate speed may be different from ''c''. In general relativity no coordinate system on a large region of curved spacetime is "inertial", so it is permissible to use a global coordinate system where objects travel faster than ''c'', but in the local neighborhood of any point in curved spacetime we can define a "local inertial frame" and the local speed of light will be ''c'' in this frame, with massive objects moving through this local neighborhood always having a speed less than ''c'' in the local inertial frame.
Justifications
Casimir vacuum and quantum tunnelling
Special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
postulates that the speed of light in vacuum is invariant in
inertial frames. That is, it will be the same from any frame of reference moving at a constant speed. The equations do not specify any particular value for the speed of light, which is an experimentally determined quantity for a fixed unit of length. Since 1983, the
SI unit of length (the
meter
The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
) has been defined using the
speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
.
The experimental determination has been made in vacuum. However, the vacuum we know is not the only possible vacuum which can exist. The vacuum has energy associated with it, called simply the
vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experiment ...
, which could perhaps be altered in certain cases. When vacuum energy is lowered, light itself has been predicted to go faster than the standard value ''c''. This is known as the
Scharnhorst effect. Such a vacuum can be produced by bringing two perfectly smooth metal plates together at near atomic diameter spacing. It is called a
Casimir vacuum. Calculations imply that light will go faster in such a vacuum by a minuscule amount: a photon traveling between two plates that are 1 micrometer apart would increase the photon's speed by only about one part in 10
36. Accordingly, there has as yet been no experimental verification of the prediction. A recent analysis
argued that the Scharnhorst effect cannot be used to send information backwards in time with a single set of plates since the plates' rest frame would define a "preferred frame" for FTL signalling. However, with multiple pairs of plates in motion relative to one another the authors noted that they had no arguments that could "guarantee the total absence of causality violations", and invoked Hawking's speculative
chronology protection conjecture
The chronology protection conjecture is a hypothesis first proposed by Stephen Hawking that laws of physics beyond those of standard general relativity prevent time travel on all but microscopic scales - even when the latter theory states that it ...
which suggests that feedback loops of virtual particles would create "uncontrollable singularities in the renormalized quantum stress-energy" on the boundary of any potential time machine, and thus would require a theory of quantum gravity to fully analyze. Other authors argue that Scharnhorst's original analysis, which seemed to show the possibility of faster-than-''c'' signals, involved approximations which may be incorrect, so that it is not clear whether this effect could actually increase signal speed at all.
The physicists
Günter Nimtz
Günter Nimtz (born 22 September 1936) is a German physicist, working at the 2nd Physics Institute at the University of Cologne in Germany. He has investigated narrow-gap semiconductors and liquid crystals. His claims show that particles may tra ...
and Alfons Stahlhofen, of the
University of Cologne
The University of Cologne (german: Universität zu Köln) is a university in Cologne, Germany. It was established in the year 1388 and is one of the most prestigious and research intensive universities in Germany. It was the sixth university to ...
, claim to have violated relativity experimentally by transmitting photons faster than the speed of light.
They say they have conducted an experiment in which microwave photons — relatively low-energy packets of light — travelled "instantaneously" between a pair of prisms that had been moved up to apart. Their experiment involved an optical phenomenon known as
"evanescent modes", and they claim that since evanescent modes have an imaginary wave number, they represent a "mathematical analogy" to
quantum tunnelling.
Nimtz has also claimed that "evanescent modes are not fully describable by the
Maxwell equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
T ...
and quantum mechanics have to be taken into consideration." Other scientists such as
Herbert G. Winful and Robert Helling have argued that in fact there is nothing quantum-mechanical about Nimtz's experiments, and that the results can be fully predicted by the equations of
classical electromagnetism
Classical electromagnetism or classical electrodynamics is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model; It is, therefore, a classical fie ...
(Maxwell's equations).
Nimtz told ''
New Scientist
''New Scientist'' is a magazine covering all aspects of science and technology. Based in London, it publishes weekly English-language editions in the United Kingdom, the United States and Australia. An editorially separate organisation publishe ...
'' magazine: "For the time being, this is the only violation of special relativity that I know of." However, other physicists say that this phenomenon does not allow information to be transmitted faster than light. Aephraim Steinberg, a quantum optics expert at the
University of Toronto
The University of Toronto (UToronto or U of T) is a public research university in Toronto, Ontario, Canada, located on the grounds that surround Queen's Park. It was founded by royal charter in 1827 as King's College, the first institution ...
, Canada, uses the analogy of a train traveling from Chicago to New York, but dropping off train cars from the tail at each station along the way, so that the center of the ever-shrinking main train moves forward at each stop; in this way, the speed of the center of the train exceeds the speed of any of the individual cars.
Winful argues that the train analogy is a variant of the "reshaping argument" for superluminal tunneling velocities, but he goes on to say that this argument is not actually supported by experiment or simulations, which actually show that the transmitted pulse has the same length and shape as the incident pulse.
Instead, Winful argues that the
group delay
In signal processing, group delay and phase delay are delay times experienced by a signal's various frequency components when the signal passes through a system that is linear time-invariant (LTI), such as a microphone, coaxial cable, amplifie ...
in tunneling is not actually the transit time for the pulse (whose spatial length must be greater than the barrier length in order for its spectrum to be narrow enough to allow tunneling), but is instead the lifetime of the energy stored in a
standing wave which forms inside the barrier. Since the stored energy in the barrier is less than the energy stored in a barrier-free region of the same length due to destructive interference, the group delay for the energy to escape the barrier region is shorter than it would be in free space, which according to Winful is the explanation for apparently superluminal tunneling.
[For a summary of Herbert G. Winful's explanation for apparently superluminal tunneling time which does not involve reshaping, see ]
A number of authors have published papers disputing Nimtz's claim that Einstein causality is violated by his experiments, and there are many other papers in the literature discussing why quantum tunneling is not thought to violate causality.
It was later claimed by Eckle ''et al.'' that particle tunneling does indeed occur in zero real time.
Their tests involved tunneling electrons, where the group argued a relativistic prediction for tunneling time should be 500–600 attoseconds (an
attosecond is one quintillionth (10
−18) of a second). All that could be measured was 24 attoseconds, which is the limit of the test accuracy. Again, though, other physicists believe that tunneling experiments in which particles appear to spend anomalously short times inside the barrier are in fact fully compatible with relativity, although there is disagreement about whether the explanation involves reshaping of the wave packet or other effects.
Give up (absolute) relativity
Because of the strong empirical support for
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
, any modifications to it must necessarily be quite subtle and difficult to measure. The best-known attempt is
doubly special relativity, which posits that the
Planck length is also the same in all reference frames, and is associated with the work of
Giovanni Amelino-Camelia and
João Magueijo.
There are speculative theories that claim inertia is produced by the combined mass of the universe (e.g.,
Mach's principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothe ...
), which implies that the rest frame of the universe might be ''preferred'' by conventional measurements of natural law. If confirmed, this would imply
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
is an approximation to a more general theory, but since the relevant comparison would (by definition) be outside the
observable universe
The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time, because the electromagnetic radiation from these obj ...
, it is difficult to imagine (much less construct) experiments to test this hypothesis. Despite this difficulty, such experiments have been proposed.
Spacetime distortion
Although the theory of
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
forbids objects to have a relative velocity greater than light speed, and
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "
recession velocity
Recessional velocity is the rate at which an extragalactic astronomical object recedes (becomes more distant) from an observer as a result of the expansion of the universe. It can be measured by observing the wavelength shifts of spectral lines ...
" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light-years from us today have a recession velocity which is faster than light.
Miguel Alcubierre
Miguel Alcubierre Moya (born March 28, 1964) is a Mexican theoretical physicist.
Alcubierre is known for the proposed Alcubierre drive, a speculative warp drive by which a spacecraft could achieve faster-than-light travel.
Personal life
Alcubie ...
theorized that it would be possible to create a
warp drive
A warp drive or a drive enabling space warp is a fictional superluminal spacecraft propulsion system in many science fiction works, most notably '' Star Trek'', and a subject of ongoing physics research. The general concept of "warp drive" wa ...
, in which a ship would be enclosed in a "warp bubble" where the space at the front of the bubble is rapidly contracting and the space at the back is rapidly expanding, with the result that the bubble can reach a distant destination much faster than a light beam moving outside the bubble, but without objects inside the bubble locally traveling faster than light. However,
several objections raised against the Alcubierre drive appear to rule out the possibility of actually using it in any practical fashion. Another possibility predicted by general relativity is the
traversable wormhole
A wormhole ( Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.
A wormhole can be visualized as a tunnel with two ends at separate p ...
, which could create a shortcut between arbitrarily distant points in space. As with the Alcubierre drive, travelers moving through the wormhole would not ''locally'' move faster than light travelling through the wormhole alongside them, but they would be able to reach their destination (and return to their starting location) faster than light traveling outside the wormhole.
Gerald Cleaver and Richard Obousy, a professor and student of
Baylor University
Baylor University is a private Baptist Christian research university in Waco, Texas. Baylor was chartered in 1845 by the last Congress of the Republic of Texas. Baylor is the oldest continuously operating university in Texas and one of the fir ...
, theorized that manipulating the extra spatial dimensions of
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
around a spaceship with an extremely large amount of energy would create a "bubble" that could cause the ship to travel faster than the speed of light. To create this bubble, the physicists believe manipulating the 10th spatial dimension would alter the
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
in three large spatial dimensions: height, width and length. Cleaver said positive dark energy is currently responsible for speeding up the expansion rate of our universe as time moves on.
Lorentz symmetry violation
The possibility that Lorentz symmetry may be violated has been seriously considered in the last two decades, particularly after the development of a realistic effective field theory that describes this possible violation, the so-called
Standard-Model Extension. This general framework has allowed experimental searches by ultra-high energy cosmic-ray experiments
and a wide variety of experiments in gravity, electrons, protons, neutrons, neutrinos, mesons, and photons.
The breaking of rotation and boost invariance causes direction dependence in the theory as well as unconventional energy dependence that introduces novel effects, including
Lorentz-violating neutrino oscillations
Lorentz-violating neutrino oscillation refers to the quantum phenomenon of neutrino oscillations described in a framework that allows the breakdown of Lorentz invariance. Today, neutrino oscillation or change of one type of neutrino into another i ...
and modifications to the dispersion relations of different particle species, which naturally could make particles move faster than light.
In some models of broken Lorentz symmetry, it is postulated that the symmetry is still built into the most fundamental laws of physics, but that
spontaneous symmetry breaking
Spontaneous symmetry breaking is a spontaneous process of symmetry breaking, by which a physical system in a symmetric state spontaneously ends up in an asymmetric state. In particular, it can describe systems where the equations of motion or ...
of Lorentz invariance shortly after the
Big Bang
The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
could have left a "relic field" throughout the universe which causes particles to behave differently depending on their velocity relative to the field; however, there are also some models where Lorentz symmetry is broken in a more fundamental way. If Lorentz symmetry can cease to be a fundamental symmetry at the Planck scale or at some other fundamental scale, it is conceivable that particles with a critical speed different from the speed of light be the ultimate constituents of matter.
In current models of Lorentz symmetry violation, the phenomenological parameters are expected to be energy-dependent. Therefore, as widely recognized,
[Overbye, Dennis]
''Interpreting the Cosmic Rays''
The New York Times, 31 December 2002 existing low-energy bounds cannot be applied to high-energy phenomena; however, many searches for Lorentz violation at high energies have been carried out using the
Standard-Model Extension.
Lorentz symmetry violation is expected to become stronger as one gets closer to the fundamental scale.
Superfluid theories of physical vacuum
In this approach the physical
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
is viewed as a quantum
superfluid
Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...
which is essentially non-relativistic whereas
Lorentz symmetry
In relativistic physics, Lorentz symmetry or Lorentz invariance, named after the Dutch physicist Hendrik Lorentz, is an equivalence of observation or observational symmetry due to special relativity implying that the laws of physics stay the same ...
is not an exact symmetry of nature but rather the approximate description valid only for the small fluctuations of the superfluid background.
Within the framework of the approach a theory was proposed in which the physical vacuum is conjectured to be a
quantum Bose liquid whose ground-state
wavefunction
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements ...
is described by the
logarithmic Schrödinger equation In theoretical physics, the logarithmic Schrödinger equation (sometimes abbreviated as LNSE or LogSE) is one of the nonlinear modifications of Schrödinger's equation. It is a classical wave equation with applications to extensions of quantum mech ...
. It was shown that the
relativistic gravitational interaction arises as the small-amplitude
collective excitation
In physics, quasiparticles and collective excitations are closely related emergent phenomena arising when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum.
For ex ...
mode whereas relativistic
elementary particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, an ...
s can be described by the
particle-like modes in the limit of low momenta. The important fact is that at very high velocities the behavior of the particle-like modes becomes distinct from the
relativistic one - they can reach the
speed of light limit at finite energy; also, faster-than-light propagation is possible without requiring moving objects to have
imaginary mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
.
FTL neutrino flight results
MINOS experiment
In 2007 the
MINOS collaboration reported results measuring the flight-time of 3
GeV GEV may refer to:
* ''G.E.V.'' (board game), a tabletop game by Steve Jackson Games
* Ashe County Airport, in North Carolina, United States
* Gällivare Lapland Airport, in Sweden
* Generalized extreme value distribution
* Gev Sella, Israeli-Sou ...
neutrinos
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass is ...
yielding a speed exceeding that of light by 1.8-sigma significance. However, those measurements were considered to be statistically consistent with neutrinos traveling at the speed of light. After the detectors for the project were upgraded in 2012, MINOS corrected their initial result and found agreement with the speed of light. Further measurements are going to be conducted.
OPERA neutrino anomaly
On September 22, 2011, a preprint from the
OPERA Collaboration indicated detection of 17 and 28 GeV muon neutrinos, sent 730 kilometers (454 miles) from
CERN
The European Organization for Nuclear Research, known as CERN (; ; ), is an intergovernmental organization that operates the largest particle physics laboratory in the world. Established in 1954, it is based in a northwestern suburb of Gene ...
near
Geneva, Switzerland
Geneva ( ; french: Genève ) frp, Genèva ; german: link=no, Genf ; it, Ginevra ; rm, Genevra is the List of cities in Switzerland, second-most populous city in Switzerland (after Zürich) and the most populous city of Romandy, the French-speaki ...
to the
Gran Sasso National Laboratory
Laboratori Nazionali del Gran Sasso (LNGS) is the largest underground research center in the world. Situated below Gran Sasso mountain in Italy, it is well known for particle physics research by the INFN. In addition to a surface portion of the ...
in Italy, traveling faster than light by a relative amount of (approximately 1 in 40,000), a statistic with 6.0-sigma significance. On 17 November 2011, a second follow-up experiment by OPERA scientists confirmed their initial results.
However, scientists were skeptical about the results of these experiments, the significance of which was disputed. In March 2012, the
ICARUS collaboration failed to reproduce the OPERA results with their equipment, detecting neutrino travel time from CERN to the Gran Sasso National Laboratory indistinguishable from the speed of light. Later the OPERA team reported two flaws in their equipment set-up that had caused errors far outside their original
confidence interval
In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as 9 ...
: a
fiber optic cable
A fiber-optic cable, also known as an optical-fiber cable, is an assembly similar to an electrical cable, but containing one or more optical fibers that are used to carry light. The optical fiber elements are typically individually coated with ...
attached improperly, which caused the apparently faster-than-light measurements, and a clock oscillator ticking too fast.
Tachyons
In special relativity, it is impossible to accelerate an object the speed of light, or for a massive object to move the speed of light. However, it might be possible for an object to exist which moves faster than light. The hypothetical
elementary particle
In particle physics, an elementary particle or fundamental particle is a subatomic particle that is not composed of other particles. Particles currently thought to be elementary include electrons, the fundamental fermions ( quarks, leptons, an ...
s with this property are called tachyons or tachyonic particles. Attempts
to quantize them failed to produce faster-than-light particles, and instead illustrated that their presence leads to an instability.
[Randall, Lisa; ''Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions'', p. 286: "People initially thought of tachyons as particles travelling faster than the speed of light...But we now know that a tachyon indicates an instability in a theory that contains it. Regrettably for ]science fiction fans
Science fiction fandom or SF fandom is a community or fandom of people interested in science fiction in contact with one another based upon that interest. SF fandom has a life of its own, but not much in the way of formal organization (although ...
, tachyons are not real physical particles that appear in nature."
Various theorists have suggested that the
neutrino
A neutrino ( ; denoted by the Greek letter ) is a fermion (an elementary particle with spin of ) that interacts only via the weak interaction and gravity. The neutrino is so named because it is electrically neutral and because its rest mass ...
might have a tachyonic nature, while others have disputed the possibility.
General relativity
General relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
was developed after
special relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
# The laws o ...
to include concepts like
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
. It maintains the principle that no object can accelerate to the speed of light in the reference frame of any coincident observer. However, it permits distortions in
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
that allow an object to move faster than light from the point of view of a distant observer. One such
distortion
In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
is the
Alcubierre drive
The Alcubierre drive () is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding space behind it, under the assumption that a configurable ...
, which can be thought of as producing a ripple in
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
that carries an object along with it. Another possible system is the
wormhole
A wormhole ( Einstein-Rosen bridge) is a hypothetical structure connecting disparate points in spacetime, and is based on a special solution of the Einstein field equations.
A wormhole can be visualized as a tunnel with two ends at separate p ...
, which connects two distant locations as though by a shortcut. Both distortions would need to create a very strong curvature in a highly localized region of space-time and their gravity fields would be immense. To counteract the unstable nature, and prevent the distortions from collapsing under their own 'weight', one would need to introduce hypothetical
exotic matter
There are several proposed types of exotic matter:
* Hypothetical particles and states of matter that have "exotic" physical properties that would violate known laws of physics, such as a particle having a negative mass.
* Hypothetical partic ...
or negative energy.
General relativity also recognizes that any means of faster-than-light
travel
Travel is the movement of people between distant geographical locations. Travel can be done by foot, bicycle, automobile, train, boat, bus, airplane, ship or other means, with or without luggage, and can be one way or round trip. Travel c ...
could also be used for
time travel
Time travel is the concept of movement between certain points in time, analogous to movement between different points in space by an object or a person, typically with the use of a hypothetical device known as a time machine. Time travel is a w ...
. This raises problems with
causality
Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...
. Many physicists believe that the above phenomena are impossible and that future theories of
gravity
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...
will prohibit them. One theory states that stable wormholes are possible, but that any attempt to use a network of wormholes to violate causality would result in their decay. In
string theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...
, Eric G. Gimon and
Petr Hořava have argued that in a
supersymmetric
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories ...
five-dimensional
Gödel universe, quantum corrections to general relativity effectively cut off regions of spacetime with causality-violating closed timelike curves. In particular, in the quantum theory a smeared supertube is present that cuts the spacetime in such a way that, although in the full spacetime a closed timelike curve passed through every point, no complete curves exist on the interior region bounded by the tube.
In fiction and popular culture
FTL travel is a common trope in
science fiction
Science fiction (sometimes shortened to Sci-Fi or SF) is a genre of speculative fiction which typically deals with imaginative and futuristic concepts such as advanced science and technology, space exploration, time travel, parallel unive ...
.
See also
*
Faster-than-light neutrino anomaly
In 2011, the OPERA experiment mistakenly observed neutrinos appearing to travel faster than light. Even before the source of the error was discovered, the result was considered anomalous because speeds higher than that of light in vacuum are g ...
*
Intergalactic travel
Intergalactic travel is the hypothetical crewed or uncrewed travel between galaxies. Due to the enormous distances between the Milky Way and even its closest neighbors—tens of thousands to millions of light-years—any such venture wo ...
*
Krasnikov tube
A Krasnikov tube is a speculative mechanism for space travel involving the warping of spacetime into permanent superluminal tunnels. The resulting structure is analogous to a wormhole or an immobile Alcubierre drive (and like them requires exot ...
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Variable speed of light
A variable speed of light (VSL) is a feature of a family of hypotheses stating that the speed of light may in some way not be constant, for example, that it varies in space or time, or depending on frequency. Accepted classical theories of physi ...
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Wheeler–Feynman absorber theory
The Wheeler–Feynman absorber theory (also called the Wheeler–Feynman time-symmetric theory), named after its originators, the physicists Richard Feynman and John Archibald Wheeler, is an interpretation of electrodynamics derived from the assu ...
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Slow light
Slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low group velocity. Slow light occurs when a propagating pulse is substantially slowed by the interaction with the medium in which the propagatio ...
Notes
References
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External links
Measurement of the neutrino velocity with the OPERA detector in the CNGS beam with more details on phase and group velocity, and on causality
*Alcubierre, Miguel;
ttp://members.shaw.ca/mike.anderton/WarpDrive.pdf ''The Warp Drive: Hyper-Fast Travel Within General Relativity'', Classical and Quantum Gravity 11 (1994), L73–L77br>
A systemized view of superluminal wave propagation*
ttp://www.theculture.org/rich/sharpblue/archives/000089.html Relativity, FTL and causality*
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Conical and paraboloidal superluminal particle acceleratorsRelativity and FTL (=Superluminal motion) Travel Homepage
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Interstellar travel
Physics in fiction
Science fiction themes
Theory of relativity
Warp drive theory
Tachyons
Velocity