Faster-than-light

Superluminal velocity is a velocity that is greater than the natural constant speed of light. This is also called superluminar.

• 4.1 Superluminares tunnels
• 4.2 EPR effect

• 6.1 superluminal velocity in the expansion of space-time
• 6.2 Cosmological theories with variable light speed
• 6.3 The Alcubierre Van den Broeck warp field
• 6.4 wormholes
• 6.5 hyperspace

General

Whether matter or information in vacuum also faster than light can move or spread ( superluminar, spacelike ), is a negated by the vast majority of physicists, but not yet finally clarified question. It is in principle not depend on whether an object faster than light moving, but whether a causal relationship between two space -time points can be made which are separated as much space or as short a time that a connection between them only could be achieved by faster than light. This includes, for example, the situation of an object that suddenly disappears in one place, at one light year to appear away after less than a year. In classical Newtonian mechanics objects can be accelerated arbitrarily. Since the theory it sets no limits, even the speed of light could be surpassed. However, Newtonian mechanics is valid only approximately, for sufficiently small velocities ( v « c). At higher speeds, however, relativistic effects occur that prevent exceeding the speed of light.

In science fiction books and movies travel are often depicted with superluminal speed than reality because otherwise interstellar travel would take from a dramaturgical point of view far too long. The same applies to the communication between two stations or spacecraft. The data transfer takes place in these stories almost always without delay instead, even if the ships are light years apart and so every piece of information according to current scientific knowledge, so at least this time for the distance from the transmitter to the receiver would need. The television images of the moon landings, however, already required 1.3 seconds on its way to Earth, a communication between Earth and Mars, for example, takes, depending on the position of the two planets to each other between three and 22 minutes.

The distinction between superluminal and lower the speed of light is absolute in the context of the theory of relativity: A process that takes place in a reference system with superluminal velocity, found in any reference system rather than light, the same also applies to sub- light speed. Mathematical background is the non-existence of a Lorentz transformation, the time-like transformed into space-like vectors. So you can not just reach superluminal against the earth, for example, by first a rocket with ¾ of the speed of light shoots from the earth, and from this a rocket relative to it again flying with ¾ of the speed of light rocket launches. Due to the relativity of simultaneity relative velocities can not simply be added, as it is still very accurate true at the low speeds of everyday life. Instead, results for the total velocity after the relativistic addition theorem for velocities:

Accordingly, the second missile moves only 0.96 c. From the principle of the constancy of the speed of light, that an acceleration of a body involving mass would require the speed of light infinite amount of energy.

There are some observations that seem to confirm at first glance superluminare movements:

However, particles of matter can, under certain conditions in a medium faster than light moving, that is faster than photons in the same medium. The so-called Tscherenkowstrahlung arises. The speed of light in vacuum is thereby not exceeded.

Tachyon

Superluminare speeds are not categorically excluded by the equations of the theory of relativity, only exceeding the speed of light is not possible. Theoretically, a superluminares particles exist, the tachyon which moves exclusively superluminar and an imaginary rest mass has. However, it has a lot of paradoxical properties, for example, it accelerates ( "Runaway Solution" ), if by radiation ( for charged tachyons accelerated ) loses energy, so it is difficult to construct a theory of interacting tachyons. The idea of ​​tachyons with formal " imaginary mass " was first expressed in the 1960s by ECG Sudarshan and others. Considering tachyons but quantum mechanically, it is found that even this can not propagate faster than light as a local disturbance.

Apparent superluminal objects in astronomy

Some jets emitted by quasars seem about to move superluminar due to an observation effect. This generally happens exactly when an object approaches an observer and has a speed of at least 70.7 % of the speed of light. For example, an observed 1977-1980 jet of the quasar 3C 273 with seemingly moved eleven times the speed of light.

The possibility of this apparent superluminal velocity was discussed in 1966 Martin Rees. In 1970, the phenomenon was observed.

Theoretical considerations

A quasar in the distance stumble at time t = 0 a jet with a bright node. The node moves to the speed at the angle to the direction to the ground.

Actual motion

After the time expires, the node is in one place at a distance from the quasar.

In Erdrichtung he has then the route

To move to the observer. He has transverse the distance

Completed.

Apparent motion

The observer sees the knot on Quasar arise after the light has passed through the distance, ie at the time

The observer sees the node at the location when the emitted light at the time there was still covered the remaining distance to the observer. Since the jet is observed only in the immediate vicinity of the quasar, the optical path of the observer is practically parallel to the direction of observation of the quasar. Thus its length is

The observer reaches the light from the node at the time after

Between the observation of the emission in the nucleus and the observation of reaching the time goes by

With.

For the apparent transverse velocity, we thus find

Or with

Example: For and results, so apparently 11 times the speed of light.

Condition for observation of Superluminalität

The movement appears superluminar if so

Changing according to results

And after forming trigonometric the right:

Ways must therefore

Apply, that is for

The case. The smallest jet velocity, at which the effect can occur, results in the maximum value of. To do it

About Fast light effects in quantum mechanics

Superluminares tunnels

In the University of Cologne under the direction of Günter Nimtz the quantum mechanical effect of tunneling Superluminaren of microwave photons, which is the tunnel effect to basically was detected first.

Experiments by Nimtz type with photons of other wavelengths, in particular with visible light have taken place with other groups and have the observations of Nimtz confirmed (among Steinberg and Raymond Chiao of the University of Berkeley ), are of the experimenters as Chiao and Steinberg but interpreted differently. In all experiments, it is found that a superluminare rate then adjusts when a barrier is located between the source and the detector, which must overcome only the photons ( through tunnel ).

Effective media was transferred there in 1994 with frequency-modulated microwave part of a Mozart symphony, where Nimtz claims to measure a 4.7 - times the speed of light for the maximum and the leading edge of the wave packet. Nimtz claims to have thus the possibility of the transmission of information shown faster than light, but this was denied. If we define the speed of information transmission over the response of a detector, there is no transfer of information faster than light: A detector on an equally long compared route without "tunnel" on which the same information ( pulse shape ) propagates at the speed of light, speaks at first, because the signal on the tunnel section is much weaker, irrespective of the sensitivity of the detector.

These experiments are generally considered to be in complete agreement with one of the axioms of the theory of relativity, according to which no information propagation takes place faster than light. So you can show, for example, that a wave when tunneling is attenuated more in the rear than in the front part, so that its intensity maximum shifted forward. If we define as the position of the wave train, so you can calculate a speed faster than light, without any part of the wave train would have proceeded faster than light. , The position of the maximum

In tunneling experiments with single photons over the speed of light tunnels already been proven, see, for example, experiments of Chiao group. It takes up the tunnels, however, a large part of the tunneling photons and therefore the information here also the possibility of superluminal information transmission is controversial, see also this bibliography.

From other physicists, for example, in the review article by Privitera et al., It is noted that the Superluminalität of events is an artifact of the definition used by speed. That, for example, the group velocity of pulses in media with strong absorption and dispersion greater than the speed of light may be, but is not a signal velocity, already Leon Brillouin and Sommerfeld was known.

EPR effect

Another phenomenon that suggests the occurrence of superluminal at first glance, the EPR effect: If you have two entangled particles in different places, so that quantum mechanics predicts that a hand before measurement of the state of each of the particles indeterminate ( the value of the measurand that is not fixed ), on the other hand according to the measurement of a particle immediately the state of the other particle is fixed. This by Einstein as "spooky action at a distance " Rejected property of quantum mechanics is confirmed experimentally. However, the EPR effect will not be useful in order to communicate faster than light, since the individual measurements are taken for each accident. Only when comparing the measurement results on both particles, the correlation can be found. For this purpose, however, is only a "classic ", under light- fast information transfer required. For example, the quantum teleportation based on this combination of EPR effect and subsequent classical information transmitted.

Nick Herbert struck the early 1980s, an experiment in which in quantum mechanics, information can be transmitted faster than light, if it would be possible to produce perfect quantum copier. How Wojciech Zurek and William Wootters shortly after 1982 but showed such copiers are basically impossible ( no- cloning theorem).

Whether such information is transmitted in the EPR effect, is controversial and depends very much on the interpretation of quantum mechanics and the concept of information. One interpretation states that the particles additional information in hidden variables, that is not measurable properties that control the correlation carry. However, one can show that the measurement results should be certain statistical rules, the Bell 's inequalities obey. Violation of these inequalities was ( though still not unequivocally ) confirmed experimentally. Other explanations also consider time-reversed causal relations for quantum mechanical systems into consideration.

Time travel

According to the special theory of relativity faster than light time travel, or at least in the form of an anti- phone would allow the sending of messages to the past. The association between speed of light and time travel can be deduced from the properties of the Lorentz transformation in Minkowski diagram. Because of the ensuing paradoxes the possibility of time travel in physical theories is usually excluded. Without additional assumptions, the equations of general relativity, time travel does not prohibit, however, as first showed Kurt Gödel.

About the speed of light in cosmology

About the speed of light in the expansion of space-time

The spectra of most galaxies have redshifts that are greater, the further away the galaxies. Hubble interpreted the measured redshifts of him and other first on the Doppler effect as a result of recession velocities of galaxies and found a linear relationship between recession velocity v and distance d ( the Hubble law with the Hubble constant ). Because of the linearity of the Hubble law, the recession velocity v seems to exceed the speed of light at a sufficiently great distance.

The correct interpretation of the cosmological redshift leads to the increase in these distances due to the expansion of the universe back, not to the Doppler effect. The Hubble law is valid in the framework of relativistic cosmology at any distance if d is interpreted as the physical distance (distance at a fixed time ) and v as the temporal change of this distance. can be greater than the speed of light, which is sometimes regarded as contradictory to the theory of relativity and cited as a counter-argument to the Big Bang theory. Conceptually, however, may the distance rate of change not to be confused with a speed. Speeds are local variables that are subject to the limitations of special relativity theories. Distance subject to change as global variables not these restrictions and may be arbitrarily large. True superluminal velocities are thus not also occur in distant galaxies.

Cosmological theories with variable light speed

On various cosmological theories with a variable speed of light (Variable Speed ​​of Light Theories, VSL) have been proposed. In particular became famous a proposal by João Magueijo and Andreas Albrecht of 1999, in which the horizon problem and the problem of the flatness of the universe, which are usually explained in the framework of the Inflationary model of cosmology today, instead by up to 60 orders of magnitude higher speed of light in early universe are explained. The speed of light is in this theory a dynamic variable, so changeable over time, but in a special way that is not too strongly modifies the shape of the field equations of general relativity. The Lorentz invariance of the theory, however, is explicitly broken, there is an excellent reference system (which is determined by the cosmological expansion). After Magueijo and Albrecht also the problem of the cosmological constant is so released. Magueijo also wrote a popular book about it. A similar idea was proposed in 1992, the Canadian physicist John Moffat, also with the intention of solving the cosmological problems.

The theory is in the tradition of time-varying fundamental ( dimensionless ) physical quantities, which have been discussed for Dirac. It is useful to discuss only the variability of dimensionless quantities, since the variability dimension afflicted sizes in the physics of the units of measurement used is dependent and has no fundamental significance. In the case of VSL theories the fine structure constant is variable, which should be observable as a function of redshift in distant objects in principle.

The Alcubierre Van den Broeck warp field

Wormholes

A related effect is thus the crossing of so-called wormholes, which is often used in science fiction novels. This results in a spaceship moving locally, not faster than the speed of light, but it takes in curved space a shortcut so that it arrives but faster than the light at the target at the end. As a two-dimensional analogy one can consider the path of a folded piece of paper. Instead of remaining on the paper, a traveler can simply drill a hole in the paper and thus reach the other side of it folded. This technique also time machines would be conceivable. Although such wormholes can be constructed theoretically in the theory of relativity, but it seems that it would be very unstable in practice, so that not even information could be passed through it.

Hyperspace

Would cause a similar effect like the idea also used in the science fiction a shortcut through hyperspace, could be embedded in our space-time. The idea is the following: In order to shorten the way from the North Pole to the South Pole, you travel across the earth rather than along the surface. The path through the earth ( about the third dimension ) is shorter than the path on the ( two-dimensional ) surface. Similarly, one could imagine that our space-time is embedded in a higher dimensional hyperspace (like the Earth's surface into space ), and one might therefore shorten through hyperspace. Again, you would ( in hyperspace ) does not have to fly faster than the speed of light to arrive faster than light in normal space at the destination.

Others

The use of the English term FTL ( faster than light for ) goes back to the 1950s. In the Breakthrough Propulsion Physics Project of NASA concepts and theories of superluminal velocity were evaluated.