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This looks easily understandable up to "At some point, such coverage must have a discontinuity, i.e. jump in the direction of the vector field." I don't know if there is an easy way to describe this to Joe on the street, but it would help. - T
T, I have made an attempt to correct the description of the hairy ball problem as it relates to the travelling wave and the e and h planes. Kgrr 13:42, 11 August 2005 (UTC)
I think that the 3rd paragraph and the 4th paragraph describe the same thing.
"An antenna emits an electromagnetic wave that has two components - the electric and magnetic fields. These are at right angles to each other and also at right angles to the direction of travel of the wave. This presents a problem for a theoretical isotropic radiator since there will be places on the unit sphere where we cannot specify a unique "polarization direction" for the direction of the electric field."
says the same as:
"This is because the electromagnetic wave is made up of two perpendicular components - the electric field E and the magnetic field H. The emitted electromagnetic wave moves perpendicular to the E-plane and H-plane. The wave cannot be lined up so that there is radiation in all directions and that neither the E or H planes cancel each other out. There must be a discontinuity."
Except the second is clearer. I think they should be only one paragraph, preferably the second. (The remark that "An antenna emits ..." is useful though. As is the reminder that perpendicular means at right angles).
I'll change this in a few weeks time if no one objects.
Some inaccuracies and omissions here (I intend to fix these at some point):
I've rewritten it - but reading it back, I see a flaw in my argument. So it still needs fixing. -- catslash 16:18, 21 July 2007 (UTC)
This is well worth a read: Scott, W.; Hoo, K.S., "A theorem on the polarization of null-free antennas", IEEE Trans. on Antennas and Propagation, vol. AP-14, no. 5, Sep 1966, pp. 587-590. It reviews the proof of Mathis, and shows that "...that elliptical polarization of all axial ratios, ranging from circular polarization of purely one sense, through linear, to circular polarization of the opposite sense, must exist in the far-field of a null-free antenna". -- catslash 14:17, 25 July 2007 (UTC)
You are correct that what I had put was wrong - and I don't have any problem with you reverting it. However, what is there at the moment is equally wrong. Let me take your points in reverse order.
I still intend to write something more accurate -- catslash 14:32, 31 August 2007 (UTC)
Come to think of it, although the pressure of a sound wave is a scalar field, the velocity (or displacement or acceleration) of the medium is a vector, and it's something like (or at least that's above). Anyway it satisfies the Helmholtz equation, and is purely radial (not transverse) and isotropic, so I reckon that demolishes the Helmholtz equation argument? -- catslash 15:37, 31 August 2007 (UTC)
That's correct. In cartesian coordinates, the Vector laplacian reduces to three scalar laplacians. However, in spherical coordinates (which is what we are dealing with here), the two operators are completely different, and should not be confused. -- Mr. PIM 23:16, 31 August 2007 (UTC)
I think where your logic breaks down is that the wave equation for vector fields and for scalar fields should be treated as different equations, even though there is a lot of similarity between the two. I think if you try to plug an isotropic radiation pattern into the Helmholtz equation, you will discover that the equation cannot be satisfied. -- Mr. PIM 05:04, 1 September 2007 (UTC)
You're taking this discussion outside of my league. I'm not an expert on sound waves. I'll just leave saying that if you can come up with additional reasons why an isotropic radiator cannot exist, go ahead and list them. I had only two bones to pick about what you wrote (or more accurately, what I understood from your writing)
Since you do not hold those positions, I have no issues. Go ahead and make whatever changes you feel are necessary, just do not write something that suggests either of those two facts. -- Mr. PIM 17:54, 1 September 2007 (UTC)
I am new to Wikepedia talk pages, and I'm not sure this is the right way to add my 2 cents worth, but here goes.
The discussion in the talk page seems to be nearly on track, but that awareness is not yet reflected in the page "Isotropic Radiator" itself.
An isotropic radiator of electromagnetic waves is certainly possible, and two different (theoretical) examples have been given in the note of Matzner and mine that is referenced at the bottom of the Wiki page.
It would be preferable if the text of the Wiki page were updated to reflect to insights contained in the references. I'm not sure how to proceed. I can edit the page if that is appropriate, but maybe it's better if a past editor make changes....
--kirkmcd@princeton.edu -- Kirktmcdonald ( talk) 20:27, 10 December 2007 (UTC)
I'm not sure if anyone is watching this page, but these points are correct: an isotropic radiator is NOT excluded if you don't insist on linear polarization, and there are antennas which do not have nulls in their total radiation pattern. In particular, the turnstile antenna (which the WP article mistakenly identifies as being directional). Though I hate to resort to it, I am looking at a RS which says "its three dimensional radiation pattern is nearly omnidirectional." I could compute just how close it is to being isotropic, but that would be OR so I'll skip it. But I'm tagging the claim that a short dipole has the lowest gain possible, since that is wrong, and so is the blanket statement that there must be a null point. EITHER you retract those claims, OR you qualify it as saying "For linearly polarized antennas...." I'll wait for someone already involved with this page to correct it, before I do that myself. Interferometrist ( talk) 22:11, 31 March 2011 (UTC)
If an Isotropic antenna cannot exist, then what is the device shown in the image? I'm guessing is as some antenna designed as a very close approximation to a isotropic antenna, but if that is the case, it really ought to be mentioned. 74.5.162.102 ( talk) 23:34, 22 October 2009 (UTC)
Is there some reason (tradition, definition, ...) why an isotropic radiator must be a point source? Is it so that the radiation can travel an unbounded distance? If not, then why can't it be either of the following?
The latter has in common with a point source that it is ideal and physically unrealizable, but the former is easily realized and is the basis for constructing excellent approximations to a black body when a small hole is drilled in it. At the center of a spherical cavity the radiation is uniform in all directions, meeting that condition, and unlike a point source there is nothing unphysical about the center of a spherical source.
In the latter, every photon travels a finite distance before being absorbed by a CO2 molecule, and the uniformity of the gas ensures uniformity of the radiation at each frequency. (There is no frequency at which the probability of absorption by a nearby CO2 molecule is exactly zero.) The gas is supercritical and pressure broadening is extreme, with photons whose wavenumber is in the vicinity of 650 cm−1 having mean free paths on the order of millimeters or less.
A spherical parcel of Venusian atmosphere of radius 1 m and altitude 1 km would be an extremely good approximation.
While the latter seems likely to be OR, the former obviously isn't, but the reason for excluding it is not obvious to me, though presumably it's a reasonable reason. -- Vaughan Pratt ( talk) 00:33, 13 November 2011 (UTC)
The last sentence of the lead says "Isotropic radiators obey Lambert's law." If the radiation is coming from a point source (like a star), what is Θ in Lambert's cosine law? This sentence would seem to be contradicted by section 7 of these notes which are in good agreement with what I learnt working and publishing in computer graphics at Sun Microsystems and later teaching computer graphics at Stanford (before we hired Marc Levoy and Pat Hanrahan and I could go back to teaching algebra and logic). -- Vaughan Pratt ( talk) 05:46, 15 November 2011 (UTC)
Meanwhile it occurs to me that more careful definitions of "point source" and "Lambertian surface" might clarify things. A point source is not literally a point in the geometric sense, but rather merely the limiting case of the distribution of radiation from a radiator as it shrinks to a point (or as the sphere centered on it grows unboundedly). In that sense of "point source" a point could be either flat, or spherical, or some other shape, counter to geometric intuition but in good agreement with optical intuition where "distribution of radiation in the limit" is a concept outside the realm of geometry.
Likewise a Lambertian surface need only be locally flat, meaning comprised of elemental flat surfaces each of which has its own normal. For a smoothly curved surface we still need to take a limit, not of distance from the radiator however but of size of the elemental surfaces.
With the concepts thus clarified (hopefully copacetically) we have the following four examples.
These examples demonstrate the logical independence of isotropic and Lambertian, neither of which need imply the other, though both can hold and neither can hold.
Absent objections I'll modify the last sentence of the lead accordingly, which certainly is problematic as it stands. -- Vaughan Pratt ( talk) 16:23, 15 November 2011 (UTC)
The editing history of this important page goes back to 2005 making this twelve years of editing yielding just one reference to back up a point... Really? Claims without "inline" references are on the chopping block. Let's see if we can't do better. I will help where I can, but come on folks, you know the Wikipedia rules. crcwiki ( talk) 18:51, 5 September 2017 (UTC)
Chetvorno you've inserted a surprising caveat: https://en.wikipedia.org/?title=Isotropic_radiator&diff=prev&oldid=798961436. Can you source it, please? Currently it seems to contradict the first sentence in the lead:
Thanks. fgnievinski ( talk) 01:14, 28 February 2024 (UTC)
This is the
talk page for discussing improvements to the
Isotropic radiator article. This is not a forum for general discussion of the article's subject. |
Article policies
|
Find sources: Google ( books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL |
This article is rated Stub-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
|
This looks easily understandable up to "At some point, such coverage must have a discontinuity, i.e. jump in the direction of the vector field." I don't know if there is an easy way to describe this to Joe on the street, but it would help. - T
T, I have made an attempt to correct the description of the hairy ball problem as it relates to the travelling wave and the e and h planes. Kgrr 13:42, 11 August 2005 (UTC)
I think that the 3rd paragraph and the 4th paragraph describe the same thing.
"An antenna emits an electromagnetic wave that has two components - the electric and magnetic fields. These are at right angles to each other and also at right angles to the direction of travel of the wave. This presents a problem for a theoretical isotropic radiator since there will be places on the unit sphere where we cannot specify a unique "polarization direction" for the direction of the electric field."
says the same as:
"This is because the electromagnetic wave is made up of two perpendicular components - the electric field E and the magnetic field H. The emitted electromagnetic wave moves perpendicular to the E-plane and H-plane. The wave cannot be lined up so that there is radiation in all directions and that neither the E or H planes cancel each other out. There must be a discontinuity."
Except the second is clearer. I think they should be only one paragraph, preferably the second. (The remark that "An antenna emits ..." is useful though. As is the reminder that perpendicular means at right angles).
I'll change this in a few weeks time if no one objects.
Some inaccuracies and omissions here (I intend to fix these at some point):
I've rewritten it - but reading it back, I see a flaw in my argument. So it still needs fixing. -- catslash 16:18, 21 July 2007 (UTC)
This is well worth a read: Scott, W.; Hoo, K.S., "A theorem on the polarization of null-free antennas", IEEE Trans. on Antennas and Propagation, vol. AP-14, no. 5, Sep 1966, pp. 587-590. It reviews the proof of Mathis, and shows that "...that elliptical polarization of all axial ratios, ranging from circular polarization of purely one sense, through linear, to circular polarization of the opposite sense, must exist in the far-field of a null-free antenna". -- catslash 14:17, 25 July 2007 (UTC)
You are correct that what I had put was wrong - and I don't have any problem with you reverting it. However, what is there at the moment is equally wrong. Let me take your points in reverse order.
I still intend to write something more accurate -- catslash 14:32, 31 August 2007 (UTC)
Come to think of it, although the pressure of a sound wave is a scalar field, the velocity (or displacement or acceleration) of the medium is a vector, and it's something like (or at least that's above). Anyway it satisfies the Helmholtz equation, and is purely radial (not transverse) and isotropic, so I reckon that demolishes the Helmholtz equation argument? -- catslash 15:37, 31 August 2007 (UTC)
That's correct. In cartesian coordinates, the Vector laplacian reduces to three scalar laplacians. However, in spherical coordinates (which is what we are dealing with here), the two operators are completely different, and should not be confused. -- Mr. PIM 23:16, 31 August 2007 (UTC)
I think where your logic breaks down is that the wave equation for vector fields and for scalar fields should be treated as different equations, even though there is a lot of similarity between the two. I think if you try to plug an isotropic radiation pattern into the Helmholtz equation, you will discover that the equation cannot be satisfied. -- Mr. PIM 05:04, 1 September 2007 (UTC)
You're taking this discussion outside of my league. I'm not an expert on sound waves. I'll just leave saying that if you can come up with additional reasons why an isotropic radiator cannot exist, go ahead and list them. I had only two bones to pick about what you wrote (or more accurately, what I understood from your writing)
Since you do not hold those positions, I have no issues. Go ahead and make whatever changes you feel are necessary, just do not write something that suggests either of those two facts. -- Mr. PIM 17:54, 1 September 2007 (UTC)
I am new to Wikepedia talk pages, and I'm not sure this is the right way to add my 2 cents worth, but here goes.
The discussion in the talk page seems to be nearly on track, but that awareness is not yet reflected in the page "Isotropic Radiator" itself.
An isotropic radiator of electromagnetic waves is certainly possible, and two different (theoretical) examples have been given in the note of Matzner and mine that is referenced at the bottom of the Wiki page.
It would be preferable if the text of the Wiki page were updated to reflect to insights contained in the references. I'm not sure how to proceed. I can edit the page if that is appropriate, but maybe it's better if a past editor make changes....
--kirkmcd@princeton.edu -- Kirktmcdonald ( talk) 20:27, 10 December 2007 (UTC)
I'm not sure if anyone is watching this page, but these points are correct: an isotropic radiator is NOT excluded if you don't insist on linear polarization, and there are antennas which do not have nulls in their total radiation pattern. In particular, the turnstile antenna (which the WP article mistakenly identifies as being directional). Though I hate to resort to it, I am looking at a RS which says "its three dimensional radiation pattern is nearly omnidirectional." I could compute just how close it is to being isotropic, but that would be OR so I'll skip it. But I'm tagging the claim that a short dipole has the lowest gain possible, since that is wrong, and so is the blanket statement that there must be a null point. EITHER you retract those claims, OR you qualify it as saying "For linearly polarized antennas...." I'll wait for someone already involved with this page to correct it, before I do that myself. Interferometrist ( talk) 22:11, 31 March 2011 (UTC)
If an Isotropic antenna cannot exist, then what is the device shown in the image? I'm guessing is as some antenna designed as a very close approximation to a isotropic antenna, but if that is the case, it really ought to be mentioned. 74.5.162.102 ( talk) 23:34, 22 October 2009 (UTC)
Is there some reason (tradition, definition, ...) why an isotropic radiator must be a point source? Is it so that the radiation can travel an unbounded distance? If not, then why can't it be either of the following?
The latter has in common with a point source that it is ideal and physically unrealizable, but the former is easily realized and is the basis for constructing excellent approximations to a black body when a small hole is drilled in it. At the center of a spherical cavity the radiation is uniform in all directions, meeting that condition, and unlike a point source there is nothing unphysical about the center of a spherical source.
In the latter, every photon travels a finite distance before being absorbed by a CO2 molecule, and the uniformity of the gas ensures uniformity of the radiation at each frequency. (There is no frequency at which the probability of absorption by a nearby CO2 molecule is exactly zero.) The gas is supercritical and pressure broadening is extreme, with photons whose wavenumber is in the vicinity of 650 cm−1 having mean free paths on the order of millimeters or less.
A spherical parcel of Venusian atmosphere of radius 1 m and altitude 1 km would be an extremely good approximation.
While the latter seems likely to be OR, the former obviously isn't, but the reason for excluding it is not obvious to me, though presumably it's a reasonable reason. -- Vaughan Pratt ( talk) 00:33, 13 November 2011 (UTC)
The last sentence of the lead says "Isotropic radiators obey Lambert's law." If the radiation is coming from a point source (like a star), what is Θ in Lambert's cosine law? This sentence would seem to be contradicted by section 7 of these notes which are in good agreement with what I learnt working and publishing in computer graphics at Sun Microsystems and later teaching computer graphics at Stanford (before we hired Marc Levoy and Pat Hanrahan and I could go back to teaching algebra and logic). -- Vaughan Pratt ( talk) 05:46, 15 November 2011 (UTC)
Meanwhile it occurs to me that more careful definitions of "point source" and "Lambertian surface" might clarify things. A point source is not literally a point in the geometric sense, but rather merely the limiting case of the distribution of radiation from a radiator as it shrinks to a point (or as the sphere centered on it grows unboundedly). In that sense of "point source" a point could be either flat, or spherical, or some other shape, counter to geometric intuition but in good agreement with optical intuition where "distribution of radiation in the limit" is a concept outside the realm of geometry.
Likewise a Lambertian surface need only be locally flat, meaning comprised of elemental flat surfaces each of which has its own normal. For a smoothly curved surface we still need to take a limit, not of distance from the radiator however but of size of the elemental surfaces.
With the concepts thus clarified (hopefully copacetically) we have the following four examples.
These examples demonstrate the logical independence of isotropic and Lambertian, neither of which need imply the other, though both can hold and neither can hold.
Absent objections I'll modify the last sentence of the lead accordingly, which certainly is problematic as it stands. -- Vaughan Pratt ( talk) 16:23, 15 November 2011 (UTC)
The editing history of this important page goes back to 2005 making this twelve years of editing yielding just one reference to back up a point... Really? Claims without "inline" references are on the chopping block. Let's see if we can't do better. I will help where I can, but come on folks, you know the Wikipedia rules. crcwiki ( talk) 18:51, 5 September 2017 (UTC)
Chetvorno you've inserted a surprising caveat: https://en.wikipedia.org/?title=Isotropic_radiator&diff=prev&oldid=798961436. Can you source it, please? Currently it seems to contradict the first sentence in the lead:
Thanks. fgnievinski ( talk) 01:14, 28 February 2024 (UTC)