Tachyonic field
In physics, a tachyonic field, or simply tachyon, is a quantum field with an imaginary mass.[1] Although ta
than light) are a purely hypothetical concept that violate a number of essential physical principles, at least one
believed to exist. Under no circumstances do any excitations of tachyonic fields ever propagate faster than li
(imaginary) mass has no effect on the maximum velocity of signals, and so unlike faster-than-light particles th
fields play an important role in physics[3][4][5] and are discussed in popular books.[1][6]
The term "tachyon" was coined by Gerald Feinberg in a 1967 paper[7] that studied quantum fields with im
permitted faster than light propagation, but it was soon realized that this was not the case.[2] Instead, the
configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting
This process is known as tachyon condensation. A famous example is the condensation of the Higgs boson in the
In modern physics, all fundamental particles are regarded as localized excitations of fields. Tachyons are unus
localized excitations from existing. Any localized perturbation, no matter how small, starts an exponentially g
everywhere inside the future light cone of the perturbation.[2]
Interpretation
Overview of tachyonic condensation
Although the notion of a tachyonic imaginary mass might seem troubling because there is no classical interpre
quantized. Rather, the scalar field is; even for tachyonic quantum fields, the field operators at spacelike separ
thus preserving causality. Therefore, information still does not propagate faster than light,[8] and solutions
(there is no violation of causality).
The "imaginary mass" really means that the system becomes unstable. The zero value field is at a local ma
potential energy, much like a ball at the top of a hill. A very small impulse (which will always happen due to qu
down with exponentially increasing amplitudes toward the local minimum. In this way, tachyon condensation
local limit and might naively be expected to produce physical tachyons, to an alternative stable state where no
field reaches the minimum of the potential, its quanta are not tachyons any more but rather are ordinary partic
Higgs boson.[9]
Physical interpretation of a tachyonic field and signal propagation
There is a simple mechanical analogy that illustrates that tachyonic fields do not propagate faster than light
explain the meaning of imaginary mass (the mass squared being negative).[2]
Consider a long line of pendulums, all pointing straight down. The mass on the end of each pendulum is con
springs. Wiggling one of the pendulums will create two ripples that propagate in both directions down the lin
turn oscillates a few times about the straight down position. The speed of propagation of these ripples is deter
springs and the inertial mass of the pendulum weights. Formally, these parameters can be chosen so that the p
limit of an infinite density of closely spaced pendulums, this model becomes identical to a relativistic field
particles. Displacing the pendulums from pointing straight down requires positive energy, which indicates
positive.
Now consider an initial condition where at time t=0, all the pendulums are pointing straight up. Clearly this is
can imagine that they are so carefully balanced they will remain pointing straight up indefinitely so long as
upside-down pendulums will have a very different effect from before. The speed of propagation of the effects of
since neither the spring tension nor the inertial mass have changed. However, the effects on the pendulums a
different. Those pendulums that feel the effects of the perturbation will begin to topple over, and will pick up sp
In physics, a tachyonic field, or simply tachyon, is a quantum field with an imaginary mass.[1] Although ta
than light) are a purely hypothetical concept that violate a number of essential physical principles, at least one
believed to exist. Under no circumstances do any excitations of tachyonic fields ever propagate faster than li
(imaginary) mass has no effect on the maximum velocity of signals, and so unlike faster-than-light particles th
fields play an important role in physics[3][4][5] and are discussed in popular books.[1][6]
The term "tachyon" was coined by Gerald Feinberg in a 1967 paper[7] that studied quantum fields with im
permitted faster than light propagation, but it was soon realized that this was not the case.[2] Instead, the
configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting
This process is known as tachyon condensation. A famous example is the condensation of the Higgs boson in the
In modern physics, all fundamental particles are regarded as localized excitations of fields. Tachyons are unus
localized excitations from existing. Any localized perturbation, no matter how small, starts an exponentially g
everywhere inside the future light cone of the perturbation.[2]
Interpretation
Overview of tachyonic condensation
Although the notion of a tachyonic imaginary mass might seem troubling because there is no classical interpre
quantized. Rather, the scalar field is; even for tachyonic quantum fields, the field operators at spacelike separ
thus preserving causality. Therefore, information still does not propagate faster than light,[8] and solutions
(there is no violation of causality).
The "imaginary mass" really means that the system becomes unstable. The zero value field is at a local ma
potential energy, much like a ball at the top of a hill. A very small impulse (which will always happen due to qu
down with exponentially increasing amplitudes toward the local minimum. In this way, tachyon condensation
local limit and might naively be expected to produce physical tachyons, to an alternative stable state where no
field reaches the minimum of the potential, its quanta are not tachyons any more but rather are ordinary partic
Higgs boson.[9]
Physical interpretation of a tachyonic field and signal propagation
There is a simple mechanical analogy that illustrates that tachyonic fields do not propagate faster than light
explain the meaning of imaginary mass (the mass squared being negative).[2]
Consider a long line of pendulums, all pointing straight down. The mass on the end of each pendulum is con
springs. Wiggling one of the pendulums will create two ripples that propagate in both directions down the lin
turn oscillates a few times about the straight down position. The speed of propagation of these ripples is deter
springs and the inertial mass of the pendulum weights. Formally, these parameters can be chosen so that the p
limit of an infinite density of closely spaced pendulums, this model becomes identical to a relativistic field
particles. Displacing the pendulums from pointing straight down requires positive energy, which indicates
positive.
Now consider an initial condition where at time t=0, all the pendulums are pointing straight up. Clearly this is
can imagine that they are so carefully balanced they will remain pointing straight up indefinitely so long as
upside-down pendulums will have a very different effect from before. The speed of propagation of the effects of
since neither the spring tension nor the inertial mass have changed. However, the effects on the pendulums a
different. Those pendulums that feel the effects of the perturbation will begin to topple over, and will pick up sp
