Hartman effect
Encyclopedia
The delay time for a quantum tunneling particle
is independent of the thickness of the opaque barrier. This is called the Hartman effect, after Thomas Hartman who discovered it in 1962. In 2007, Nimtz and Stahlhofen demonstrated quantum tunneling of "evanescent modes"
across a gap might result in virtual particles traveling faster
than light
.
. and with infrared pulses by Longhi et al. This could, for instance, be the gap between two prism
s. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted
. There is a finite probability
that a 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. Alfons Stahlhofen and Günter Nimtz
developed a mathematical approach and interpretation of the nature of evanescent modes as virtual particles, which confirms the theory of the Hartmann effect.
However, an analysis by Herbert Winful suggests that the Hartman effect cannot actually be used to violate relativity
by transmitting signals faster than the c
, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate". Winful means by this that the photons crossing the barrier are virtual photons, only existing in the interaction
s and could not be propagated
into the outside world.
Subatomic particle
In physics or chemistry, subatomic particles are the smaller particles composing nucleons and atoms. There are two types of subatomic particles: elementary particles, which are not made of other particles, and composite particles...
is independent of the thickness of the opaque barrier. This is called the Hartman effect, after Thomas Hartman who discovered it in 1962. In 2007, Nimtz and Stahlhofen demonstrated quantum tunneling of "evanescent modes"
Evanescent wave
An evanescent wave is a nearfield standing wave with an intensity that exhibits exponential decay with distance from the boundary at which the wave was formed. Evanescent waves are a general property of wave-equations, and can in principle occur in any context to which a wave-equation applies...
across a gap might result in virtual particles traveling faster
Faster-than-light
Faster-than-light communications and travel refer to the propagation of information or matter faster than the speed of light....
than light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
.
Overview
The Hartman effect is the tunnelling effect through a barrier where the tunnelling time tends to a constant for large barriers. This was first described by James Hartley in 1962. The Hartman effect was demonstrated with evanescent microwaves by Achim Enders and Günter NimtzGünter Nimtz
Günter Nimtz 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 and was engaged in several interdisciplinary studies on the effect of non-ionizing electromagnetic radiation in...
. and with infrared pulses by Longhi et al. This could, for instance, be the gap between two prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...
s. When the prisms are in contact, the light passes straight through, but when there is a gap, the light is refracted
Refraction
Refraction is the change in direction of a wave due to a change in its speed. It is essentially a surface phenomenon . The phenomenon is mainly in governance to the law of conservation of energy. The proper explanation would be that due to change of medium, the phase velocity of the wave is changed...
. There is a finite probability
Probability amplitude
In quantum mechanics, a probability amplitude is a complex number whose modulus squared represents a probability or probability density.For example, if the probability amplitude of a quantum state is \alpha, the probability of measuring that state is |\alpha|^2...
that a photon
Photon
In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...
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. Alfons Stahlhofen and Günter Nimtz
Günter Nimtz
Günter Nimtz 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 and was engaged in several interdisciplinary studies on the effect of non-ionizing electromagnetic radiation in...
developed a mathematical approach and interpretation of the nature of evanescent modes as virtual particles, which confirms the theory of the Hartmann effect.
However, an analysis by Herbert Winful suggests that the Hartman effect cannot actually be used to violate relativity
Causality
Causality is the relationship between an event and a second event , where the second event is understood as a consequence of the first....
by transmitting signals faster than the c
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, because the tunnelling time "should not be linked to a velocity since evanescent waves do not propagate". Winful means by this that the photons crossing the barrier are virtual photons, only existing in the interaction
Feynman diagram
Feynman diagrams are a pictorial representation scheme for the mathematical expressions governing the behavior of subatomic particles, first developed by the Nobel Prize-winning American physicist Richard Feynman, and first introduced in 1948...
s and could not be propagated
Propagator
In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to travel with a certain energy and momentum. Propagators are used to represent the contribution of virtual particles on the internal...
into the outside world.