Coherent isotropic radiators evade the hairy-ball theorem because they do not form continuous tangent vector fields.
the verdict
REFUTED
the evidence says no
refutedsupported
the weight of evidence
3 sources for · 0 against
Peer-reviewed literature shows that the key obstacle against the existence of isotropic antennas is the hairy-ball theorem, meaning that isotropic radiators do not evade it.
Evidence for · 3
Isotropic Radiators
2003 · cited by 21
Can the radiation pattern of an antenna be isotropic? A simple argument suggests that this is difficult. The intensity of radiation depends on the square of the electric (or magnetic) field. To have isotropic radiation, it would seem that the magnitude of the electric field would have to be uniform over any sphere in the far zone. However, the electromagnetic fields in the far zone of an antenna are transverse, and it is well known that a vector field of constant magnitude cannot be everywhere tangent to the surface of a sphere (Brouwer’s “hairy-ball theorem” [1]). Hence, it would appear that the transverse electric field in the far zone cannot have the same magnitude in all directions, and that the radiation pattern cannot be isotropic, IF the radiation is everywhere linearly polarized [2, 3]. However, electromagnetic waves can have two independent states of polarization, described as elliptical polarization in the general case. While a transverse electric field with a single, linearly polarized component cannot be uniform over a sphere in the far zone, it may be possible that the sum of the squares of the electric fields with two polarizations is uniform.
We revisit the problem of realizing perfectly isotropic antennas based on recent developments in nonlocal antenna theory. The key obstacle against the existence of exactly isotropic antennas is traced back to the hairy ball theorem in algebraic and differential topology. A path blocking the applicability of this no-go theorem is to allow for complementary longitudinal modes to coexist with matching transverse modes in the antenna exterior region. Nonlocal antennas (radiators embedded into nonlocal metamaterial exterior domains) are possible future antenna technologies capable of dealing with both transverse and longitudinal modes. It is rigorously demonstrated that the recently proposed nonlocal Proca metamaterial (massive electromagnetism) leads to small nonlocal dipole antennas with perfectly isotropic radiation pattern. A tentative proposal for a possible experimental realization of perfectly isotropic radiators in the future is briefly outlined.
We revisit the problem of realizing perfectly isotropic antennas based on recent developments in nonlocal antenna theory. The key obstacle against the existence of exactly isotropic antennas is traced back to the hairy ball theorem in algebraic and differential topology. A path blocking the applicability of this no-go theorem is to allow for complementary longitudinal modes to coexist with matching transverse modes in the antenna exterior region. Nonlocal antennas (radiators embedded into nonlocal metamaterial exterior domains) are possible future antenna technologies capable of dealing with both transverse and longitudinal modes. It is rigorously demonstrated that the recently proposed nonlocal Proca metamaterial (massive electromagnetism) leads to small nonlocal dipole antennas with perfectly isotropic radiation pattern. A tentative proposal for a possible experimental realization of perfectly isotropic radiators in the future is briefly outlined.
Everything we examined (3) — 2 independent sources
This check searched the claim as stated. It did not run a separate search for evidence against it.